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Recently a similar idea was considered in the framework of light-front
holographic QCD (LFHQCD) {{cite:f6bf7870ec4d2e82702b736e0c1a4b932219373e}}, {{cite:ab8555cc3b965157ee4b619ee649d507565f4eff}}, {{cite:ab6015b802a553c6215ce7ecb0d1b3c2e62b9a97}}.
In particular, a function [named as {{formula:c3f2c49f-08e4-480b-9da4-f3165176268e}} ] was introduced in the integral
representation of the form factor {{cite:f6bf7870ec4d2e82702b736e0c1a4b932219373e}}, {{cite:ab8555cc3b965157ee4b619ee649d507565f4eff}}:
{{formula:90b2ff14-b17e-43a3-bdf8-6fe5d6f4d117}}
| i | 2e1b3d7dcaadc1c44148db25e5daf516 |
GNNs including the state-of-the-art methods suffer from a class imbalance problem that typically deteriorates the performance of multi-class classification. Interestingly, the simplest algorithm SGC {{cite:8879a6790d96589416229ebea979d602a998233c}} outperforms recent complicated GNN algorithms in a class imbalanced setting because the complicated algorithms tend to over-fit to major classes.
GNNs generalizing to graphs with few edges within each class (we call heterophilic graphs) provide marginal classification performance gains in a heterophily setting from a graph-agnostic classifier MLP. This indicates that such GNNs almost ignore the topology information in the setting.
| i | 6f0a6dac9f469810e4833f91ec4d00c6 |
Given the sensitivity improvement to massive BBH signals with higher harmonics, we deployed our new search to analyse the publicly available O3 data from Advanced LIGO detectors {{cite:7efc8d748d564f429c87fd05ec3674d0fdf33d11}}. To do this, we divided the data into nine independent blocks of {{formula:4f9fe519-f0a8-4fce-87d3-05f916595d7f}} -day duration and analysed it using our template banks. We report all the O3 candidates reported by our searches with an IFAR {{formula:d42560d5-11ab-42a8-b041-bae934543688}} year in Table REF , finding no new candidates beyond those reported in {{cite:9db174f2ea6afbf219ce6429edc5fa12b8712e70}}, {{cite:d9cb1b19e2960a1499220ba118f15f149adf6a79}}, {{cite:97ba4432bdbde6e86d6c03df29e873fb2fad504e}}, {{cite:0fcba8ed60d9c313b3a525fbc04e4fe1701bbee8}}, {{cite:1fd87b35b8569aeb490c0c2f25467f6c1dc2bae4}}. We note that the (expected) reduced statistical significance of the reported events with respect to those obtained by existing searches highlights that these candidates are outside our target space.
| r | 343718b423064f2f342f63bfa5deb924 |
We first make note of several useful results about the solutions to the equations (REF ) and (), which have been proved in {{cite:b584bf90ab59c9aa622140dcfabff28c4e6d1e4e}}.
Before proceeding, first recall the following mapping {{formula:f54ee7c1-4b58-44b9-a193-2340ba0c0dee}} previously introduced in ():
{{formula:a1391a54-c171-4ee5-a4be-db58803c9139}}
| r | 382e61888005ef7c87afc4f5b00a9355 |
The Gross-Pitaevskii energy functional for a Bose-Bose mixture,
including the Lee-Huang-Yang
correction accounting for quantum fluctuations beyond mean-field
reads {{cite:35c272dead23543252a486ac9a36dc9b1684f0c2}}, {{cite:f63b5d8567d0be773833fdf91e6dbc45455bcc24}}
{{formula:865ede6a-5917-4c43-bb4b-81ae4c2b7205}}
| m | 95074449158eb8563df9ae7f2f1e45d9 |
Multi-layer feedforward neural networks have strong expressive power. Theoretically, as long as the number of neurons is large enough, the feedforward neural networks can simultaneously approximate any function and their partial derivatives {{cite:38535208945c3bae06bd611b4b8bd1bf088c051a}}. TPINN {{cite:45ef25f0cc3d0370faa6152d03dcb51b2a8b1cf8}} is a class of deep learning algorithm where the PDE is satisfied through the loss function of the multi-layer neural networks. The TPINN algorithm is simple, which may not be efficient for some PDEs that exhibit solutions with steep gradients {{cite:044ca73d5bd340b00edfb5a1d1d4f5d16ed4d836}}. In order to improve the training efficiency of TPINN, the RAR-PINN method is proposed. The improved algorithm has great potential to be applied to various fields where adaptivity is needed {{cite:7395b5ff738081431625fb2f681c72d3bdf7bc7f}}.
| m | b1c1c6170eda8eb1841138379540815e |
We performed an error analysis on the first baseline's results. We first observe that, in 92% of the errors, the predicted span and the ground-truth overlap. Furthermore, in 56% of the errors, the predicted spans are a subset or superset of the ground-truth spans. This indicates that the model finds the rough answer regions but fails to locate the precise boundaries. To address this issue, we plan on exploring the Pointer-network {{cite:d4e5d43b44639886653ee2ccebebd8bc5b205f4c}}, which finds an answer span by selecting the boundary sentences. Unlike the first baseline which avoids an explicit segmentation step, the Pointer-network can explicitly model which sentences are likely to be a boundary sentence. Moreover, the search space of the spans in the Pointer-network is {{formula:710b1fa5-80a5-405a-9f8f-cfa243e502a5}} where {{formula:45891676-9520-4677-8470-8ed3c2d119f4}} is the number of sentences, because it selects only two boundary sentences. Note that the search space of the first baseline is {{formula:2ba10292-6a38-4d64-82f1-464818e4d003}} . A much smaller search space might improve the accuracy by making the model consider fewer candidates.
| d | baf1661bfafb5e882b728318343a72ce |
Observe that the expression (REF ), () is similar
to the Lax pair representation of the two-dimensional Toda hierarchy
{{cite:7d14bee0a672a10c0b7c1bc66cae02b0bfc5d33e}}, which carries a tri-Hamiltonian structure {{cite:5ae90d64c573d06ac8a411728cb3a3256e266ce4}}.
Following the idea of {{cite:5ae90d64c573d06ac8a411728cb3a3256e266ce4}}, we want to use the {{formula:fcf45663-2943-4436-a8ba-edc375490851}} -matrix
theory to construct Hamiltonian structures of the two-component BKP
hierarchy (REF ), ().
| i | cf80f25b213ddc696840c0f69b15f350 |
The direct strategy involves the utilization of one model that is capable of predicting the entire future trajectory in a one-shot manner. Most trajectory prediction methods are characterized by direct prediction. For example, early works adopted the Bayesian network method {{cite:313f2fda7e6e4df0fe090454a4e23475dc447819}}, the Gaussian process regression method {{cite:12df0a282f3b32f408487cf67bb7e151b589c3ab}}, and the kinematic method {{cite:3e342b65a192049281c861f47e1e8e9f7f44f82b}} to directly predict the future sequence. However, these method did not consider the interactions between agents, and usually failed in crowded scenarios.
| m | f1d8f456c4c56ecd5e808f6677ed1491 |
In Table REF , we provide the thermal ionization coefficients for K, Na, and H from {{cite:e4098d18cf5df93c6a400687fdaaaa9d46de015b}}, which is a theoretical work, to match the rates used in {{cite:3bf2a3a69ae73227dbf6d03f35e747af16574682}}. In the 1960s and 1970s, there were many discussions about the ionization rates of alkali metals. Flame experiments to measure those rates {{cite:4dc365a0d3cd823ded38fdbd91c854753b0e3285}}, {{cite:b69e544ecfadeee2b65ce4de262d37ecc0391882}} resulted in much larger cross sections than theoretically predicted {{cite:94da896560358771b4390f0c78bd91ba8c5bbb05}}, {{cite:68c582531be45a128468e0a569f916df25719024}}. {{cite:95c3a552c3b46b445e1f119db64b78a8228f272a}} argue that the experimental value of {{cite:b69e544ecfadeee2b65ce4de262d37ecc0391882}} should be preferred to the theoretical value of {{cite:e4098d18cf5df93c6a400687fdaaaa9d46de015b}}. This is debatable as the conditions in flames may be difficult to control and different from astrophysical plasmas (pressure, chemical composition), where Na and K ionize by colliding with H{{formula:0cbbdabb-b61f-4fdc-8455-bebcc531044f}} . The larger coefficient rates would suggest thermal ionization of K and Na at a lower temperature, typically {{formula:e8ba45f6-be04-43d4-ac9d-43e95e03f461}} K instead of {{formula:1f1f1d79-cff3-4cbd-82b8-dbe1a768152b}} K, which could be of importance in protoplanetary disks. For reference, we provide the experimental values of {{cite:b69e544ecfadeee2b65ce4de262d37ecc0391882}} for K and Na:
K=1.0 10-8 cm3 s-1 K-12,
| d | dc2b78892b0759d0d8ebca14585ba0d5 |
Since the interconnecting digraph with the adjacency matrix {{formula:c18761c6-4ae9-4fa0-84ad-2f551434df01}} has a spanning tree, the Laplacian matrix {{formula:a7f113a8-9a57-456f-ba12-41e254fa1287}} satisfies rank{{formula:f1764f63-71ea-4046-9fb9-4e4e622838c3}} {{cite:8f1de30d8e7c4c59660a7626d1626006aab10a69}}. So by Proposition REF , we get the characteristic polynomial of {{formula:35bafe95-aa86-4268-a411-8e50a68373a2}} as shown in (REF ), where {{formula:4018c1a3-f2c7-47e1-a41e-d0cbf774de9c}} , {{formula:05e55435-dbe9-41bf-b1d6-e3c0a0bd0c3d}} , {{formula:b2c6de53-8603-4fb6-a2ff-86d5002a4af2}} , {{formula:51162b66-c816-43cf-bf8c-7474132e3659}} are the eigenvalues of {{formula:03f66566-3b20-4605-937e-4cc299eb9880}} .
By Lemma REF and {{formula:787e6c4c-b671-477e-a9c1-2df0f01c21a7}} , we get the the characteristic polynomial of {{formula:5ffe74e8-ebd3-4b86-87bf-216bd875dfe8}} in (REF ) as follows:
{{formula:c8805bc2-5ac8-4914-a1de-8ff86dc375b0}}
| r | 0c51cb2f200b73184aa224fdc54f7b34 |
Deep reinforcement learning can be used to learn complex robotic manipulation tasks by using model-free deep policies. Kalashnikov et al. demonstrates this by proposing a QT-opt technique to provide a scalable approach for vision-based robotic manipulation applications {{cite:daf7472b31e14663630f8d6396481daec535eb4d}}. Riedmiller et al. introduced a SAC-X method that learns complex tasks from scratch with the help of multiple sparse rewards where only the end goal is specified {{cite:1542f2533e4fdebafadf480bb43fc39ab889b105}}. But training end-to-end manipulation policies that map directly from image pixels to joint velocities can be computationally expensive and time exhaustive due to a large volume of sample space and can be difficult to adapt on physical setups {{cite:58bb6ba64ce5d6020c0de97f2fc282b014f04340}}, {{cite:8a8f474fa0719f83a10bf6da07d579db43c39e1d}}, {{cite:32365d812c915c5bdce2d06311a3a530d722037e}}, {{cite:8c1a0f7f391ca0b67b1eca5c4b80ee22e21c9973}}. To solve this, many have tried pixel-wise parameterization of both state and action spaces, which enables the use of a neural network as a Q-function approximator {{cite:037573870c096b25e4432532f945463b672aa0fe}}, {{cite:9b4b04b537b62fd0ce630e2f7f5f4588035694c8}}, {{cite:fb955797feb1c56cf4ce7202b343424b08c2f9f1}}. However, these approaches have a low success rate, long learning time, and cannot handle intricate tasks consisting of multiple steps and long horizons.
{{figure:d282737b-5c83-4741-b491-30caffd3d6a4}} | i | eb07ec627305d96e183ced401f357795 |
It is important to note that while the dynamics of the ODE model captures the mean field dynamics of the edge states it overestimates the severity of the disease as compared to the network model. The cause for this discrepancy is at least three fold. First, the moment closure assumed that the average excess degree {{formula:6c7b7629-a61b-4812-bfbd-0c5c989c1817}} was equal to {{formula:6b0c7e27-d9c8-42f9-b480-7e82edf8af08}} . However, the random variables {{formula:f52d4b53-ee4a-41db-8d7d-3de2e7e9dc1b}} and {{formula:b0a4984b-5cb5-455f-baa0-b6312d4a7cd2}} have different distributions and the relationship between their averages is an inequality called the “friendship paradox” where {{formula:dd54ad3f-fa7b-4adb-adea-48f628c0fdf8}} {{cite:dd9d2890a87a0cdf6792a10254ad7cd67d4c659a}}. In particular, in graphs in which there is a significant variance in the degree distribution, it is not clear if a set of differential equations for the various compartments can be derived in the continuum limit {{cite:e60bae686e1faf6516e638b50532ca47f085ff9f}}. Second, in the derivation of the moment closure, higher order information about the topology of the network such as clustering and the number of triangles were ignored. Third, the truncation of the system at the level of nodes and edges excludes the dynamics of higher order links which depending on the structure of the graph could be relevant. Many of these challenges can be addressed by more carefully approximating the conditional distributions that arise in the moment closure approximation; see for instance {{cite:7f7962be0dac6feac3f43f7030b3c49b239975ff}}, {{cite:851480e84cc7037e140e477893d466d0667252bf}}. Nevertheless, since the ODE models provide overestimates for the severity of the disease, the critical deactivation rates given by Equation (REF ) are still useful in that they provide upper bounds for the critical deactivation rates in the realized network dynamics.
| d | 1db26ed1eb58d91af873cb3e5651e4bb |
Classic Byzantine fault-tolerant (BFT) state machine replication (SMR) protocols like PBFT {{cite:b14a8e4525e25e7ea4e7426a73fe59e93e98587a}} rely on a stable leader to drive the protocol until a view change occurs.
This limits their scalability and deployability in a context that involves thousands of nodes and requires highly distributed trust.
Recent work has been exploring an alternative, called chained-BFT or cBFT, combining decades of research in BFT and state-of-the-art blockchain work, which is considered to be the next generation BFT for blockchains.
| i | b56229d5bf1c246daa794b5729ae9791 |
To the best of our knowledge, there exist two popular methods for analyzing constrained bandits or MDPs. They are both based on primal-dual optimization and only differ in the analysis techniques. The first one is based on convex optimization tools as in {{cite:b0d7dc0960398aa8295a218163322db9126d1d1d}}, {{cite:5c261b97d23948d993a1b00cdd78ae44774ec04a}} and our paper. The other one is based on Lyapunov-drift arguments as in {{cite:ff04bf112e53cc032b2bafa3d4653b7fdcd55c45}}, {{cite:1980c359db9bcd5190de64c72c3b767c3aaea27e}}, {{cite:9ec2569de72516c03772ab4efd25cf0cfca8b0b4}}. For simplicity, we call the first method convex-opt method and the second one as Lyapunov-drift method. Before we provide further discussion, one thing to note is that all existing works only deal with UCB-type exploration for tabular or linear functions, while our paper is the first one that studies general functions with general exploration strategies.
| m | 5e4e6aff1473df6197ec97f7e392df88 |
Recently, {{cite:44a63f966e168780affe11cb8e4a4779148f7ec8}} proposed curl to deal with a fully ull setting with unknown cluster labels. We have developed our idea independently in parallel with curl but in a fully Bayesian framework. curl is the most related and comparable method to ours in the literature. curl focuses on learning representations and discovering new clusters using a threshold method. One major drawback of curl is that it has over-clustering issues as shown in their real data experiment. We also show this empirically and demonstrate the improvement of our method over curl in our experiment section. In contrast to curl, we provide a novel probabilistic framework with a nonparametric Bayesian prior to allow the model to expand without bound automatically instead of using an ad hoc threshold method as in curl. We develop a novel end-to-end variational inference strategy for learning deep representations and detecting novel clusters in ull simultaneously.
| m | 4d6375c075eced6fe88addb2fa22e6de |
Topological Insulators (TI) are a new class of material that exhibit
non-trivial band topology due to a strong spin-orbit coupling {{cite:02e3e11317e51cd457de0cb4882a17e0cd4458b8}}, {{cite:af2733b13c99ec25fb58990ef12be7ced01cebd3}}, {{cite:e186add78cf10eef71be10dd2ac84325abf1e293}}, {{cite:77d26fd348096aa5c837f8ca6062823a46f18975}}, {{cite:cbc1c65de20f57bf263cf7be1ed591fdb7858ec3}}, {{cite:06ac1a3dd27104a797fb806ac1d631693599b668}}, {{cite:b766f33943996f0acf909c14e53363f7bad63145}}, {{cite:5068d40c9033d20d42202f8f3a7394b32eaaf445}}. They remain insulating in bulk, but the
most intriguing characteristic of them is the presence of gapless conducting
edge states (in two dimensions) and surface states (in three dimensions). In 3D
TIs, the spin of a moving particle is helically locked to the momentum at
their surface {{cite:bc9f2f781e902a16ef2b34763abf25b4b759e336}}, {{cite:bfd46c02673afd405ecc477ee2295b0944c91b68}}, {{cite:690ff80ddf9a36fa813bda0c50313b459c3fb258}}, {{cite:203d23d1d9b40db3de3aacc229a409de4d040b8d}}, {{cite:5313eb3f66a494a5eb1c7a371abd3dbb64b2ac11}}, {{cite:5c1330eab59abca18b3dbfb466d3652160b791da}}, {{cite:c49c72651cd3a53a1636422f8bb4d0914eacc382}}. Due to
spin-momentum locking, it is possible to induce new phases when a magnetic
or superconducting element is brought in close proximity with the 3D TIs.
Previous works indicate that when a conventional s-wave superconductor is
coupled with 3D TIs then the superconducting correlation is induced at their
surface {{cite:3f73718cd4833931f8b21ea043938f7049c792c5}}, {{cite:602673b92fe00be7eca8610378de747609a57209}}, {{cite:ff048bce0b0e3b1fd526db7a153c9cd354efe604}}, {{cite:c3fc05b78de12a90ddd0ef7e9601ba8f2e1df20a}}. In contrast to the
conventional spin-singlet Cooper pairing, the induced superconductivity is an
admixture of both singlet and triplet correlations due to spin lifted
degeneracy at their surface {{cite:8f0296c6e1f0e66271078d32f171b4ceff92f625}}, {{cite:cac18fc600c8feba7c74ec748e4102794931dfff}}, {{cite:59043630d511a99a35413dbd5976f518f5e4688c}}. Moreover, the
Andreev Bound States (ABS) formed in superconductor-topological
insulator-superconductor (S{{formula:60fe2c9d-b6c5-484e-9ac1-8163ad303aa1}} TI{{formula:8c42aabe-2a98-4bee-8fa8-1c589c32c083}} S) Josephson junctions can exhibit zero
energy crossing, when the phase difference between the superconductor is
{{formula:b125b77f-2ccc-45bc-b843-aff5280b25be}} . Thus it can host Majorana quasiparticle {{cite:8f0296c6e1f0e66271078d32f171b4ceff92f625}}, {{cite:cac18fc600c8feba7c74ec748e4102794931dfff}}, {{cite:ff048bce0b0e3b1fd526db7a153c9cd354efe604}}, {{cite:c3fc05b78de12a90ddd0ef7e9601ba8f2e1df20a}}, {{cite:59043630d511a99a35413dbd5976f518f5e4688c}}, {{cite:3f73718cd4833931f8b21ea043938f7049c792c5}}, {{cite:602673b92fe00be7eca8610378de747609a57209}}, {{cite:4b8dba743eafd25771accbc3fd687523897cf6b1}}, which is a fermionic mode of its own
antiparticle. Though in conventional S{{formula:0a4efd72-0115-4fbd-a7c7-73f01f471f76}} N{{formula:94514ac1-d17d-4438-9e55-0eac0ef53625}} S junctions, a weak backscattering
can splits the spin degeneracy at {{formula:4a2ffb0f-b89b-487c-816c-dc4aed7d4ee5}} , however, due to non-trivial topology,
S{{formula:209f8240-e748-40a9-9fdb-74906d6027c7}} TI{{formula:7fbf8d2c-7628-46a4-9af5-5fffa048a23b}} S junctions can support {{formula:0500cdd9-650b-4176-826f-d72e62653027}} -periodic Josephson supercurrent.
Recently, their is a growing interest
to understand the robust phenomena like, zero-energy Majorana modes
{{cite:8f0296c6e1f0e66271078d32f171b4ceff92f625}}, {{cite:cac18fc600c8feba7c74ec748e4102794931dfff}}, {{cite:ff048bce0b0e3b1fd526db7a153c9cd354efe604}}, {{cite:c3fc05b78de12a90ddd0ef7e9601ba8f2e1df20a}}, {{cite:59043630d511a99a35413dbd5976f518f5e4688c}}, {{cite:3f73718cd4833931f8b21ea043938f7049c792c5}}, {{cite:602673b92fe00be7eca8610378de747609a57209}}, {{cite:4b8dba743eafd25771accbc3fd687523897cf6b1}} and topological
superconductivity {{cite:6b0a14c905bd596fce583390a1ed5fb79e19a362}}, {{cite:1757c8e663faf74c7dff6cce5540d291dbe9435a}}, {{cite:866d76daa317b081386b9eeae8cdaead6f94c3ca}}, {{cite:94c1086adeea1dd5f500d273f7077c672c296897}}, {{cite:d75be13f0aafcf8078b6c2bc1b4753b40f5b0fb4}}, {{cite:6985eb36556ae3b0788b6a80be77c46dcb3ee201}} on
the surface of 3D TIs. Experimentally it is very challenging to distinguish
topologically trivial and non-trivial {{formula:6048bd0f-c606-4103-a9d9-1ad55cc07ef1}} modes. It is due to the reason
that most of the TIs discovered till now are not perfectly insulating in bulk.
But recently, it is reported that the majority of helical supercurrent
is due to its surface and only a feeble contribution arises due to the bulk
{{cite:cedb6464fc28d4dceffef7c77176740e93abc9ff}}, {{cite:327ae33f5568d0df2b5d7f2cc34396fbc4b5d000}}, {{cite:8118464d757f6f1a8a8a60eb91687805c70c92eb}}. Moreover, some exotic TIs are also discovered
which display insulating bulk at low temperatures {{cite:06b365f476f7feb23cec8ec5b7668170ff981e16}}, {{cite:4f43bf8077dfbaf8516c5190546cd3899c5c50a1}}, {{cite:93a16cc1a23b63863e699b697dc9638c0e154350}}, {{cite:3509d303ee11c7146a74f443ae76ab01e1f6dab6}}.
| i | 5a623e21a70b737fe1c81e0f4b32ac75 |
Most of the works on nonequilibrium thermodynamics deal with the QE
approximations and corrections to them, or with applications of
these approximations (with or without corrections). There are two
basic formulation of the QE approximation: the thermodynamic
approach, based on entropy maximum, or the kinetic formulation,
based on selection of fast reversible reactions. The very first use
of the entropy maximization dates back to the classical work of
{{cite:a73b45c07e929e1db621440c80a56a5737398646}}, but it was first claimed for a principle of
informational statistical thermodynamics by {{cite:d90c58219146b7c370767dc9e05d60cc87de3f2e}}. A very
general discussion of the maximum entropy principle with
applications to dissipative kinetics is given in the review by
{{cite:225f1f1296d58997c05e9ee602bd0b4a01b1fc1a}}. Corrections of QE approximation with applications to
physical and chemical kinetics were developed by
{{cite:7c6eb0f82631edbf7ff73a036b5bd0173c8dfb9a}}, {{cite:e2dd36e96ed949f28afee5504f461e459af894fd}}.
| i | 18bd2ffdc9c542c0cb292ea873dc797f |
As an aside, while it is not our goal to set a task-specific state of the art, within RGM the structural embeddings yield competitive performance to other leading methods. Compared to results from the state of the art graph isomorphism networks reported in {{cite:569e51b5f6703d8a2bbf2f03e2e1efcecbf46d91}} and Weisfeiler-Lehman graph kernels {{cite:6e540f21056d2406d53692cd1ee541925ac486cd}} reported in {{cite:61a32a985b3b55b8419ca6733d07588e7f6c5637}}, the best embedding-based methods yield clearly higher numbers on IMDB-M and trail by a fraction of a percentage point on NCI1 (they trail further on PTC-MR). Note that our feature learning method is completely unsupervised (unlike the GIN neural network) and we do not tune the parameters (e.g. number of binning levels) of RGM, which could further improve performance.
{{figure:52d0ae3b-b5b0-484e-bf56-8dbeb37450d8}} | r | ffcaeaf2d527370cd5da93a4e51a42c9 |
Motor proteins (MP) are an integral part of the cytoskeleton in eukaryotic cells {{cite:85d8c5515ae1796b501adc5adde4cda00d274a08}}, {{cite:500d62cfd35a494764c86a28e8a263f942642be9}}, {{cite:fe61cc207f61809922dfdec39182885a869a7944}}. They are involved in a wide span of functions in subcellular processes, e.g., intracellular transport of cargo, cytoskeletal dynamics, stress generation, and cell locomotion. They hydrolyze ATP to undergo attachment-detachment and perform directed motion along conjugate filaments in the attached state {{cite:65d575727c071d59856317165d5120d0be352265}}, {{cite:6e99cb0c86f34ac97e2bc9450beadb8cf9521213}}, {{cite:fffdf7437f4cc0c5c7177653c81cff648185958c}}, {{cite:164979c8f426568b8c0bcbe30121a8cc8873e8c1}}, {{cite:04e6c3f7f18f661d37a2d7684b79ace1f62e4c62}}. For example, kinesin and dynein families of MPs move along microtubules, and the myosin family of MPs can move along filamentous actins. Their motion is load-dependent {{cite:d9bed324b73ef1d0530e0b0730b1f487f83bf538}}, {{cite:cea70a3343867fe672d4e921368e41abee384fe9}} and the maximum velocity they can attain is subject to the available ATP concentration {{cite:1b76cea6ae5c03761b8628f1e8308f810d72fbec}}. The local dissipation of chemical potential by ATP hydrolysis drives MPs out of equilibrium. Their direction of motion is determined by the local front-back asymmetry of conjugate filaments they can walk on. Generating non-equilibrium drive at the smallest scales, MPs constitute a class of active matter {{cite:e0ed77191d9d4f2388c4f3dc37355bfcb420960b}}, , in which time-reversal symmetry, detailed-balance condition, and equilibrium fluctuation-dissipation relation are broken.
| i | ab9bb98b711e96a7b135a1e62db6879b |
In this work, we approach the resource allocation problem through Centroidal Voronoi Tessellations (CVTs). Even though they date centuries, Voronoi tessellations (VTs) have been found to be immensely helpful in various applications ranging from health to computer graphics to natural sciences. The first documented application of Voronoi tessellations appeared in {{cite:3bb48c90925dc44ff9281be9a21b419ccf1041c6}} on the 1854 cholera epidemic in London in which it is demonstrated that proximity to a particular well was strongly correlated to deaths due to the disease {{cite:7b8065ea577a2cc09c444fe2da18f962ccdcf61b}}. In more recent decades, VTs have almost become a common basis tool for path planning algorithms by multi-robot systems in the field of coverage control {{cite:add6995c1972c12c4231418bcf3098f2994159e6}} to such an extent that the VT-based coverage control has been generalized using optimal transport-based control {{cite:05d660e4f9f7a67ac1359d9d9105368372893d45}}. An adaptive coverage controller is proposed in {{cite:444b1bcba73563b55f7bcc22827d7c169f499854}} where the leader in the leader-follower strategy therein distributes the followers within its obstacle-free sensing range, and the optimized distribution is obtained through a CVT. In their study on optimality of multi-robot coverage control, the authors in {{cite:164df52571dd5dd300d375ed9ceda4df1e9c5532}} draw a relationship between CVT configurations and the sufficient condition for optimality through the spatial derivative of the density.
| i | 298e392475258d73d29ea4e222a6c043 |
A significant difference between our results and the conclusions of the
analytical model by {{cite:8a9620ecd6610717eb7d1f8abba5f19cd9e36ab3}} are
characteristic timescales for propagation of perturbations. According to the
analytical model presented in {{cite:8a9620ecd6610717eb7d1f8abba5f19cd9e36ab3}},
characteristic propagation time of perturbations corresponds to the
thermal time scale for the entire vertical column of the disk. This
result is natural, since in frame of that analytical model, the height
of the disk is determined exclusively by the midplane temperature. In our
model, the propagation times for optically thick disks turn out to be
significantly smaller than the thermal time scale {{formula:ce1fd669-1b0f-40ad-bfd3-f1d824318122}} . This is
explained by the fact that traveling perturbations do not affect the
entire thickness of the disk, i.e. wave excitation mechanism can work in
the sub-surface layers.
| d | 5634105c645ce1e8d9dc4efcdf41111a |
The model is composed of three layers: a character-enhanced token embedding layer, a label prediction layer, and a label sequence optimization layer. The character-enhanced token embedding layer maps each token into a vector representation. The sequence of vector representations corresponding to a sequence of tokens are input to the label prediction layer, which outputs the sequence of vectors containing the probability of each label for each corresponding token. Lastly, the sequence optimization layer outputs the most likely sequence of predicted labels based on the sequence of probability vectors from the previous layer. All layers are learned jointly. For more details on the basic ANN model, see {{cite:97eaa649de4baa15055dacd7a268e2ed5b80d6b5}}.
| m | 5f952b680884bb1eeed2dc56d4b5b8ee |
In this section we discuss about the undetermined coefficient {{formula:30af8841-c748-4a1c-bef8-17e505b88876}} for both photon and gravitino cases. To determine this, we begin by studying the behaviour of actions (REF ) and (REF ) for the photon tunneling first. Apparently, one might think, for a zero rest mass field the trace of the energy-momentum tensor ({{formula:d1bda0f6-8764-4292-86c5-abdffe9c4fb3}} ) is zero. But the point is, at the quantum level it is not possible to preserve the conformal and diffeomorphism symmetries simultaneously. In fact, violation of the conformal invariance leads to a nonvanishing {{formula:faf391de-39ad-4843-bb8a-1ee1bfb3ebe2}} . For chiral theory, both of these symmetries are violated and therefore both divergence and trace of energy-momentum tensor are nonzero. This point has been rigorously studied for black hole case in {{cite:73ee6ad5c8928797b9a30b714447441d1366ca53}}. Throughout our analysis diffeomorphism symmetry is always preserved and so we connect {{formula:03f2bd2e-3ead-43a4-babe-ef5b51f68914}} only with the trace anomaly. This is done by simple scaling argument which was originally initiated by Hawking {{cite:c4a1e3f6e27b05e0bf225fabcaf7411165336f9a}}.
| d | bb08815d1535d4ff8ac4c80684349043 |
We will use the following inequality about sub-gaussian random variables. For a proof, see {{cite:1e3f17d00954986c3c1bc774cdcaa0d0771de85c}}.
| r | 1b79182542f0f81320be483c68ac832b |
We explicitly showed for the Schur index of {{formula:a757ba78-2dad-48df-82d6-bfd270746f11}}
that different choices of the expansion domains
give different functions for
single giant graviton contributions
{{formula:fa5310a5-82ee-4037-9af8-687940146663}} ({{formula:0de04143-60c7-43ad-819f-10d761b6a498}} ).
If we use {{formula:a0a1e9c6-44e8-423b-be76-3220615bdbe5}} in (REF ) both
{{formula:d8b5be54-ef01-43b2-b893-1086e958ed08}} and
{{formula:377a7577-78bc-4df7-98f4-8a52f50df2f7}} contribute to the Schur index,
while if we use {{formula:d31ad89d-cffa-48ce-8ee3-276987ba8758}} in (REF ),
{{formula:f01bcbe4-0b2d-47bf-8256-e3af75e6740a}} does not contribute.
Although we have not proved {{formula:019f52e1-d090-455e-b394-838a7381a6e7}} also vanish,
this partially explains why there are two different expansions:
the simple expansion found in {{cite:da42cba28b3a6648594f3f4ed38c4f52b86c3d55}}
and the multiple expansion in {{cite:aac539ef4eab984b3b04ddc0f31fe8e7c4963e5d}}.
It is surprising that they give the same result
even though some contributions are lost in the simple expansion.
This may be related to the fact that the set of functions
{{formula:3a175f0e-a44e-449e-8622-fc40c0853e32}} are strongly constrained.
For example, we can formally substitute negative {{formula:2673f57e-9046-43e9-828e-9d07c5a4e20b}} to expansion (REF )
or (REF ), and find that the result is vanishing.
This gives very strong constraints on the functions.
This implies that the functions share common information,
and only small subset appearing in the simple expansion
may be sufficient to give the complete answer.
It would be interesting to investigate the structure of
the constrained set of the functions.
| d | 5a875f63431cbe1064ba47e309434204 |
To illustrate the effectiveness of BRPO, we compare against six baselines: DQN {{cite:1b8ad81339f2c6a59a0142cd70f555bd83fa6568}},
discrete BCQ {{cite:8fd886b0663fe3c98fc084cea339ac974144b332}},
KL-regularized Q-learning (KL-Q) {{cite:27d33ba10f98de640464635ad6d8729e442c6f2b}},
SPIBB {{cite:d829daafd4ab6b375e0f6fd1a56cb1fbeb32db01}}, Behavior Cloning (BC) {{cite:f1a974d6a676de70c220ac898e68cf930aba21b8}}, and BRPO-C, which is a simplified version of BRPO that uses a constant (tunable) parameter as confidence weightFor algorithms designed for online settings, we modify data collection to sample only from offline / batch data..
We do not consider ensemble models, thus do not include methods like BEAR {{cite:b0f913cf38f6d2f138bb183f5c5cd045d62d2352}} among our baselines. CPI is also excluded since it is subsumed by BRPO-C with a grid search on the confidence. It is also generally inferior to BRPO-C because candidate policy learning does not optimize the performance of the final mixture policy. We evaluated on three discrete-action OpenAI Gym tasks {{cite:fd5a86e521c6811bc5b61f3507e32189c1c94816}}: Cartpole-v1, Lunarlander-v2, and Acrobot-v1.
| r | d1afa1690030f73c0f960743b0f20fbc |
Our goal is to convert an input of {{formula:e6d1c42e-4f13-4f65-8f0b-91b84c7994fb}} into an {{formula:e040250c-34fd-488c-a8d4-14d7a1f846d5}} . In a nutshell, our system fine-tunes a text-to-image and super-resolution Imagen models on pairs of {{formula:25831f3b-ef5e-4a9b-b387-5e50b3c31637}} for a very low number of iterations, and then samples from the model while conditioning on text in the form "[{{formula:c6394f7c-be65-4d93-b7b6-adb267b08b51}} ". Using Classifier Free Guidance ({{cite:8161c408be291d9eb800e0a0f6749185da825489}}) the fine-tuned model correctly takes the conditioning into account (see figure REF ). When a higher visual fidelity is needed, we also use SDEdit {{cite:48af73137dd044eda4887177affd085fd0218e41}} to maintain visual details in the original image. The user is presented with images that use combinations of the parameters mentioned (number of training steps, Classifier Free Guidance, SDEdit) allowing them to pick the most suitable version.
| m | bfce1fb42f65f236c36f8ced0bb682b1 |
and {{formula:690ceb67-f763-495c-9c88-f7aecb7cbfbf}} on {{formula:ea2dc05d-e6f8-4a60-b574-597e0d3e0c2a}} .
Parabolic regularity theory (see
e.g. {{cite:5fcdd7c24745d0f2e210610ac9bc73825ffae930}}) implies that
{{formula:e22e4c29-a27e-45e3-b0a3-f8db1cabdbe2}} and the second derivatives
of {{formula:83161732-146b-4373-998c-6645eb370e6c}} with respect to {{formula:9323a13d-0e44-4d2d-980c-7281e36034af}} are Hölder continuous.
| m | efdf7ce375eee7b83f2f68afc0d3a6b1 |
Overparameterization is a necessity for continual learning so that there can exist an infinity of potential optima for each task {{cite:dce21b06c2786a0d8867ab673fc3e27016da5b57}}. This makes it likely that there exists an optimum for some task B that is close to the solutions of some task A. We provide experimental evidence that overparameterization can provide additional benefits in combatting catastrophic forgetting for neural networks solving permutation tasks. We use a linear model with clear analogies to neural networks in order to study this behavior theoretically. In our analysis of the linear model in the overparameterized regime, non-asymptotic matrix estimates and results for orthogonal transformations provide bounds on the performance drop. Our main result shows that, under our model, catastrophic forgetting is ameliorated for sufficiently large overparameterization. For the linear setting we study, the behavior we observe can be explained geometrically: overparameterization causes the random orthogonal transformation tasks to live in approximately orthogonal subspaces, so training on subsequent tasks does not interrupt performance on learned tasks.
| d | 0d554cd512a1adadbfb79c910622cd80 |
In {{cite:e81f4d4caa439deca66b2cfacea39bff55cabd7b}}, Margulis obtained asymptotics for
the volume growth and orbit counting for balls of large radius, in the setting of manifolds with negative curvature.
Similar asymptotics were obtained in {{cite:8b253fe4c64362595597c6cb5c8aa83f3464feae}} for the Teichmüller space. To state their results,
let {{formula:af2a8989-ba33-4c2f-a0a5-b778e733d277}} be the Teichmüller space of {{formula:6ca5e9d2-f091-4a48-a0db-5ca19f1f24cc}} , a surface of genus {{formula:2423d800-7e10-46f1-9b63-a8a061a6864c}} , and denote the mapping class group of {{formula:38b100e9-d71a-469f-bc75-3799af4afb21}} by {{formula:5e50762d-67d6-4e49-9b01-fd44a93ecadc}} . Given {{formula:30a9a989-b51a-4213-923b-d339ad136511}} , let {{formula:cd97c36a-d0d4-4830-b13b-8a8991123fe6}} be the ball of radius {{formula:393cb617-0de4-477e-beb6-ac568ab7fa7b}} centered at {{formula:d9120dd5-0096-468a-b0d9-78e0a40c8e29}} , where the distance here is measured with respect to the Teichmüller metric. Denoting the orbit of {{formula:c8234d9d-a0c3-462b-bfc9-a0f9c02b509c}} under the action of {{formula:ff6cc25b-d90c-485e-ad90-ca3a17d7339d}} by {{formula:4b845baa-f74f-41aa-9de3-404c0cd21cb0}} , Theorem 1.2 of {{cite:8b253fe4c64362595597c6cb5c8aa83f3464feae}} gives
{{formula:279efed7-3a3b-49bd-aa35-4296146b8734}}
| r | c23a7e2ab19f665ff4fd4a8cde7a720a |
Our estimations indicate that the depth of field submergence for the considered population of young neutron stars is very shallow, possibly leading to the selection of these objects as rotationally powered pulsars. Smaller space velocities result with larger amount of accretion
and very long diffusion time-scales of buried magnetic fields leading to young neutron stars not appearing as rotationally powered pulsars. This hidden magnetic field scenario is recently studied by {{cite:481b4aa09ecdc2aedb03b4129da2b7c17dcafa33}}, {{cite:7c9b84ea441b88c0bead7d7dcd45a19cf2dc6dc9}}, {{cite:e1317338d6b9bda56d0f00a2896fcd8eb96905a7}}. This, as well as a more accurate numerical analysis of the field growth of pulsars, is the subject of a following work.
| d | 3d156cea64b02082767f426e5da6a519 |
To facilitate our discussion, we assume equal transmit SNRs, i.e., {{formula:4d03151f-d9c0-4ac4-915c-0b2f68183ce2}} . By identifying the asymptotic results (REF ) with {{cite:2eeb1849fe7e61f28b44801f5b7007a3c9f50365}}, {{cite:054ca9d8210a2a48538070c611c5cad447f7c54b}}, the asymptotic outage probabilities of the proposed systems with MIMO keyhole effect as {{formula:d09a7bef-81bd-46f6-9343-95903b35b051}} can be generalized as {{cite:29adad61a21da3cb36d25c00f0c82c1d5620167f}}
{{formula:77e43c22-0dfe-4617-832d-61442e5052ee}}
| r | 6baddddad22d8943d190db27e23c7906 |
The quantum anomalous Hall (QAH) insulator, which was first proposed by Haldane {{cite:3a49f3c0e1ccdb413e70a382cb98a9b24a17ebc4}}, is another key member of the family of quantum Hall insulators. A QAH insulator can have a quantized Hall conductivity even without an external magnetic field that breaks the time-reversal symmetry {{cite:3a49f3c0e1ccdb413e70a382cb98a9b24a17ebc4}}, {{cite:e3d90247ad76f37eed13132ada95f8769b196c30}}, {{cite:0cbb8553f1fab59826d994a0f5b3b834d6726964}}, {{cite:7ae46980d058b55d5f57f93e2a73ea81a908c419}}, {{cite:3f72071ad980cc687e6d6b9060197a1cacfb8b68}}, {{cite:4bedebe9345094222e3f3cc2875acd6b451fad2e}}, {{cite:1e3bd661f22a2d17030859315f4c9776dfccff7b}}. The QAH effect was first experimentally observed in Ref. {{cite:e3d90247ad76f37eed13132ada95f8769b196c30}};
in another work on finite-size effects in QAH systems {{cite:57eb27c2ab4e270add604f280c2a06dbd2beeac8}}, they adopted the magnetic doping (Mn doping) to break the time-reversal symmetry and introduce the QAH phase in the HgTe quantum well. By appropriate tuning of the doping concentration and the system size, they have obtained a variety of topological phases {{cite:57eb27c2ab4e270add604f280c2a06dbd2beeac8}}.
| i | 9f6332eeb8e4949292a4495da343b889 |
Early work conjectured the existence of a non-linear path of non-increasing loss between solutions found by SGD {{cite:674c01cec477f0266f521a569526deae6a528b70}}, {{cite:aa4b4b06aed6952e3707101c0de719599d5b5040}} and empirically showed how to find it {{cite:759ce6853b367baa3726eb869c2ae7dd6dd55de2}}, {{cite:2b4a5d9e68468d4b2a57d0c35887fad3e847d6e9}}, {{cite:ab7df5c3065ab46ab91d796dd9a4701a8086b131}}. Recently, {{cite:2ec148bf93ae5b9336c266a40e3eb6e8f80f50cd}} conjectured the existence of such a linear path between SGD solutions if the permutation invariance of neural networks' weight space is taken into account. That is, with high probability over SGD solutions, for each pair of trained networks A and B there exists a permutation of the hidden units in each layer of B such that the linear path between A and the permuted network B (B') is of non-increasing loss relative to the endpoints.
This conjecture is important from both theoretical and empirical perspectives. Theoretically, it leads to a drastic simplification of the loss landscape, reducing the complexity obstacle for analyzing deep neural networks. Empirically, linear interpolation between neural network weights has become an important tool, having recently been used to set state of the art accuracy on ImageNet {{cite:d7169cd7882e044e8560f4d36ede7f1f56baea67}}, improve robustness of finetuned models {{cite:459c66ed68a32e7847ede566ce8aa42d211d7132}}, {{cite:04b661e9bae90bb6f4c2d0f286f33901c50b3d17}}, build effective weight-space model ensembles {{cite:9d80fef1df2be53d5bb9586c9d53eb837061e808}}, {{cite:f21d1233a8b4d20b8e0437f647353357f77df74c}}, {{cite:cb6d66990bd9378d058860c844ab0199fbd2de66}}, and constructively merge models trained on separate data splits {{cite:fe024e0f74a900b8ba67f94565e4ad2963abf5f9}}, {{cite:586156c89c31e2573bf11cb21b72ed32600e8a0a}}. Therefore, any improvements toward reducing the obstacles to interpolation between trained models has the potential to lead to empirical progress in the above areas.
| i | d6a0ac6a5b871c605e7f709841a767fc |
Architecture. We use i-ResNet as the classification network {{formula:1a0a3dde-d8cc-46d2-b3fe-8bdf154cd14e}} .blueWe report additional results with another invertible network i-RevNet {{cite:535371f950640f6ceb4fe2a0649ad72ea15cc54b}} in the supplementary material.
We mostly follow the recommended configurations in {{cite:54bb9ec5f8c31001a16cdb152c41b6d06562b1b0}}, but we remove the injective padding module to improve the invertibility of off-manifold embedding vectors.
We use the Pix2Pix {{cite:b561283c90a2bda3fa28acbf12ee966fcf36fcf6}} architecture for encoding functions in our experiments for all values of {{formula:9d3f30f3-e88c-4d3b-80c4-0f264255908e}} .
To avoid linear scaling, we design our encoder architecture such that only the complexity of the first few layers depends on {{formula:4e567d5a-16ad-48dd-bb97-c32ba0376a06}} , and the rest of the architecture does not scale with {{formula:7b1a150d-5863-483e-9676-26a985c632cb}} .
See Fig. REF for the encoder architecture for {{formula:a0437756-1150-457b-999b-a461418127f2}} .
When {{formula:5f976597-cf03-4ba7-b246-2d6216684fec}} , two inputs {{formula:fc3f5cce-31b8-4ace-975c-52867de83f18}} and {{formula:846d0709-3439-4d17-a141-d952c8b276a9}} are first processed by the weight-shared network.
The two processing results are then concatenated and projected to a fixed-size hidden vector.
In general, our encoder processes {{formula:a8c3e2a1-ef72-44c6-a544-368984b6618b}} inputs in parallel, and the concatenated output is projected to the same size hidden vector.
By limiting the size of this input processing part, we control how the encoder complexity scales as {{formula:d83f98f9-ce6a-4b76-867e-dec900fa4d78}} increases.
See Sec. REF for experimental results where we demonstrate that encoding overhead can be kept nearly constant for increasing values of {{formula:6947a244-963c-4db9-8009-8de75025e3b3}} .
| m | b6b4d228cb46a4b5f92e8731500fa15f |
We also find that the “naive" identifier performs better than the “clinical only" identifier across all diseases. Its performance as a baseline draws parallels with a former study on multiclass classification problems ({{cite:4a39d75d33e19e8ac5f338898aa51473bedc95b6}}) which shows that maximum softmax output can be used directly to detect misclassified examples. The main difference is that, in our work, the CheXpert models solve a multi-label binary classification problem and cannot use sigmoid output values directly as a likelihood of misclassification. For instance, in a two-class classification task, the maximum softmax output ranges from 0.5 to 1, with 0.5 denoting high and 1 denoting low likelihood of misclassification. On the other hand, in a perfectly calibrated binary classification task, the sigmoid output ranges from 0 to 1, with both 0 and 1 denoting high confidence for the negative and positive class respectively. Therefore, in the “naive" identifier, we instead utilize the negative absolute distance from the prediction threshold to the model output. This operation transforms the sigmoid output such that it becomes analogous to the maximum softmax output of a multiclass classification task with two classes, where a higher value indicates a higher likelihood of misclassification.
| d | 6260b72364694bad1b67d50691d92be8 |
The flood images are shown in Fig. REF . ClimateGAN++ {{cite:ab0ff59dd99a88c4ca35c71ed3e248313ac838f4}} cannot reconstruct realistic reflection on the water surface, Stable Diffusion {{cite:603ab2cd883444611b2da3f33cc820583a52c64e}} synthesize realistic water appearance but also produce random objects (e.g., cars, signs) in the scene, which is not consistent across views. ClimateNeRF simulates realistic reflection and water ripples while being view-consistent. This is better demonstrated in the supp video and website
| r | d70ee80b69880c881590f0b2e42bf520 |
The quenching factor accounts for missing correlations and missing
many-body effects in the transition operators. The truncation of the
full Hilbert space to the reduced SM space has the effect of excluding
all correlations between the model-space configurations and the
configurations belonging to either the doubly-closed core or the
shells placed in energies above the SM space.
In addition, SM calculations are based on the single-nucleon paradigm
for the transition operators.
However, two-body electroweak currents {{cite:3a70feffd04a69fdf2f0d7e7f0b01703525d5f4e}}, {{cite:5ff79850c804f62f72b6dbc038e48f926a175103}}, {{cite:cb03ee48f650140a802e195a09a520c505e21d29}}, {{cite:bcfd5ae7d65e71cc0171e42e490e3f729c2149da}}, {{cite:b4c52ca2ad913fa22f98f5faeb0e03d1757fd2f0}}, {{cite:6eb72e97ca37ff0e5beb434c282972a012aebb0b}}, {{cite:c8958b2add9bb7764506372123bc27e150799954}}, {{cite:71db8fbdbf9b63bcf48477cc528bdf28277c2851}}, {{cite:03b9e1497e882f7d81260af72e0ae74e8487d896}}, {{cite:39df4453350b2ddb945b768c4fbc96cf0591926d}}, {{cite:2600395b06c938ffd100468e4cdd5f7368ddc84e}}, {{cite:b8b6362840ce520ed0a0349952081d55bc91535e}}, {{cite:2a1ae06301cb66aa75dd546fc9c4faf6797e7e1f}}, {{cite:232b1a484a28063881bc6b665e76496ec7756ef0}}, {{cite:2707113c288a3bfbcd5b1b55c0021986f11c6a3a}}, {{cite:4af1b12fd627b472205678c3419c6bc0a1a9758c}}, {{cite:1d4cfda4acff9bb52067b2b1ec9b9ffbc493eadf}}
are found to play a role in several electroweak observables.
These involve the exchange of mesons and nucleonic excitations.
| r | 8fea909a928b67f564374bba7a327292 |
Empirical evidence suggests that teams of either high or low expertise diversity may possess the potential to develop original and high-impact research.
But the level of interdisciplinarity in the approaches implemented by high-originality or high-impact teams varies substantively, which can be predicted by the team members' expertise diversity estimated using the proposed metric.
For instance, a team that applied a deep neural network method to classify skin cancer involves researchers from departments of electrical engineering, dermatology, microbiology & immunology, and computer science, spanning a wide range of research areas (Fig. REF B){{cite:ac6ca80be27e598ad8e88a76c8541d8ca1bf527e}}.
Correspondingly, they proposed a highly interdisciplinary approach by creatively adapting artificial intelligence technologies to life science problems in the paper.
In another example, a group of researchers from the same institution who focus primarily on computer vision produced a well-cited paper that trains deep residual learning networks for image recognition{{cite:43c80d3e143b67cb97af4c0faf846609d5dbdef1}}.
Their paper presents a new framework within a particular research topic of computer vision.
The distance metric accurately captures the two teams' propensity of conducting interdisciplinary research based on the prior career histories of team members.
| r | 5cb061b515c75ac8ade94a1d822e920b |
In the adaptive Metropolis (AM) algorithm by
{{cite:99076bd567c4dbf2c59a3893b61711d4eb1e56ff}}, the covariance matrix
{{formula:c7d392af-ad6a-4055-b491-61bc7ddb158c}} for the step {{formula:cfec1908-1a3f-40b7-8b23-ffb662cc3f91}} is estimated as follows:
{{formula:dc41d3e2-75ac-4f95-8bcb-afc28ffb32f8}}
| m | 5500952e44cdf3d370caccddd566e5ea |
In this paper, we have proved the conjecture of Anshu et. al. for {{formula:cb4c53fd-a629-426d-830c-07c292f6f6ac}} by proving that {{formula:39037b6f-0543-474f-a486-1ae497764dc5}} .
The conjecture remains open for {{formula:78813bf6-086d-4647-b6aa-29bf31bd781a}} .
Consider any neighborly {{formula:7e35787a-7854-4688-bfc6-02e94536b571}} -polytope whose vertices are in general position in {{formula:2330be49-c239-4e80-851b-8a263a8b988c}} .
Since the vertices are in general position, this class of neighborly polytopes are simplicial.
This class of neighborly polytopes have the same face structure ({{formula:dd18ed9c-1e4f-4ec8-bcc4-0cd883e8fb12}} -vectors) as the cyclic polytopes {{cite:c6ce9a10b0112ade9e457d1671843ffe111aaac1}}.
We conjecture that among all {{formula:5d62f0bf-a698-4d37-a771-a9b279cbdd68}} -dimensional rectilinear drawings of {{formula:90051fca-2ab3-419f-a187-c7e14745a1d2}} , the number of crossing pairs of hyperedges gets maximized if all the vertices of {{formula:a5155f14-a03c-4f36-9a10-77785dcbc231}} are placed in general position in {{formula:a91cfc70-b7a3-4ede-9855-1c07e2cd899b}} as the vertices of a neighborly {{formula:4166716c-0ca1-4ab9-a810-3d23f22c1874}} -polytope (whose vertices are in general position).
Note that a cyclic polytope (polytope whose vertices are placed on the {{formula:e5de9421-ba44-4e05-9a5a-a1dcd78a7271}} -dimensional moment curve) is also a neighborly polytope with vertices in general position.
| d | 03f89a64e2ba8eeb6fbee7e815b9472a |
By neglecting mesons' fluctuations it is easy to solve the gap equation of chiral condensate at finite temperature as well as chemical potential under rotation. As the phase diagram shown in Ref. {{cite:68c51e0b045efcf851d1d0606b9cf881318ddef8}}, {{cite:a1f8ac6e394aee396b45405d238dd31d4e390f97}}, {{cite:6006d615733b9dfe3f9ed21b4077baca33dcc563}} the vorticity serves as another kind of chemical potential which would weaken the chiral condensate at finite temperature case and complement the chemical potential at finite density case. As shown in Fig.(REF ) there is a crossover at medium temperature along the angular velocity. While at low temperature the increase of chemical potential will change the 1st order chiral restoration to a crossover in Fig.(REF ), (REF ) and (REF ). As the phase structure determines the macroscopic properties of the system it is reasonable to expect that the dependence of meson masses on the angular velocity would be smooth at medium temperature and density systems, while kinked at the 1st order point for the low density systems.
| r | e398cc959f0ae5e90539ee3ff770dc68 |
Outdoor scenes. We used KITTI odometry {{cite:8547e8c43d37c82569452a95c62b47356fd9bd90}} dataset (sequence 0-8 for train, 9-10 for eval) and sampled image pairs with a min rotation of 15{{formula:70693c52-7d11-4e07-b45b-9964c2d5f8eb}} and translation of 10m (36K train pairs, 1K test pairs, mean translation {{formula:c7e48eff-02c6-469e-9992-ce9be533b871}} m). Table REF shows generalization from MatterportA to KITTI (we cropped Matterport images to approximate the KITTI FoV). This is a hard generalization task as the distribution of relative poses in KITTI is extremely different from Matterport, yet fine-tuning with just 20% of data is on par with the local feature baselines, and strong results after retraining with 100% of the data indicates DirectionNet is also effective outdoors.
{{table:abd2f51b-6e6b-435c-8bd9-9801cd2ee143}} | r | 3b02243f53068635b708269cbd5530cf |
Estimation of equation (REF ) using the fitted values of the participation probabilities for {{formula:4abcd621-68f6-41ca-a9bd-b7635a019c29}} yields estimates of {{formula:dd758833-3d5e-48b2-8bf4-28ad0655b66b}} , {{formula:5589894b-9073-4974-a2f3-2f27820f82e4}} , and the parameters of the {{formula:6dde463d-edc3-416a-88ee-7351be290cb5}} function. The {{formula:33131f05-9570-4d9d-b874-3635ab9b3ab1}} function is estimated with conventional cubic splines, hence {{formula:b84a1dd7-1831-41cc-b9af-f2603d433e5e}} , where the {{formula:27acd211-754b-44d2-9772-a9f4a5ec1777}} are {{formula:10fc043f-626f-4ee4-836e-70bf3b8b5b66}} preset spline knots. For a given {{formula:85892c85-89b0-4b35-9cd3-41b128468566}} , the knots will are chosen to be regularly spaced within the (0.25, 0.66) range. The estimation will start with {{formula:a8be9423-b698-4987-8d7b-7e9e28baee71}} and then increase the number until a fit measure is maximized. Fit will be assessed with a generalized cross-validation statistic (GCV). Given the well-known tendency of polynomials to reach implausible values in the tails of the function and beyond the range of the data, natural splines are typically used, which constrain the function to be linear before the first knot and beyond the last knot ({{cite:abf4bcc2fb591aef2b696ba41da12ef926a59bd0}}). Imposing linearity on the function in those two intervals requires modifying the spline functions to accommodate this; the exact spline functions for a five-knot spline are shown in .Consistency of sieve methods is discussed by {{cite:2402fc107ae48bbd917819d6aa304c84ad3919d7}}.
| r | 0a63b8f310596ef766a4fd94c3f6e912 |
Overall Results: Fig. REF presents overall performance on ZSD and GZSD tasks across different comparison methods with two different seen/unseen split of MS-COCO. In addition to mAP, we also report recall (RE) to compare with {{cite:9ae6970ac0d39e75833e9c2d317129be6e6b9d5c}}. With 48/17 settings, our method (and baseline) beats {{cite:9ae6970ac0d39e75833e9c2d317129be6e6b9d5c}} (SB and DSES) in both the ZSD and GZSD by a significantly large margin. Similarly, in 65/15 split, we outperform our baseline by a margin 3.92 mAP (12.40 vs. 8.48) in ZSD task and 4.15 harmonic-mAP in GZSD task (18.18 vs. 14.03). This improvement is the result of end-to-end learning, the inclusion of the vocabulary metric to update word vectors and the proposed loss in our method. We report results on GloVe and FastText word vectors in the Table REF
{{figure:3b86e06a-e805-4e1e-a5e7-ef20fbeee967}} | r | 1acac8e392f1ba05c028e636e62dbf01 |
We compute the unsupervised explanations for the penultimate layer of our composer classification system and test multiple NTD ranks.
As in {{cite:d2cf2f11b4b429bbc907e51f4ad1320f893ee894}}, we present each concept to the user through the five piece excerpts with the highest average concept presence.
The presentation of piece excerpts is more challenging for musical data than for images.
Although symbolic performances can be visualised with piano rolls, some musical elements (e.g., harmonic elements) may be hard to understand in this format.
We opt for a mixed audio-image visualisation where each excerpt is represented both with a piano roll (with a colour scale for velocity information) and with a listenable MIDI file.
We create interactive piano roll visualisations (using Plotly {{cite:32baabdbe00f0a0d19bc436c218fbf1c849390a7}}) in which the user can zoom in and out to explore different resolution levels. The concept presence heatmap is displayed as a semi-transparent mask over the piano roll. A heatmap with a fixed threshold, as proposed in {{cite:d2cf2f11b4b429bbc907e51f4ad1320f893ee894}}, is hard to interpret for our data, so the user is presented with a slider that adapts the heatmap threshold (see Figure REF ).
We also provide “contrastive examples” for each concept, i.e., the 5 excerpts where the average concept presence is minimal.
Although our explainer could find relevant concepts starting from a dataset that includes any number of composers, we focus on the results with only two composers. According to psychological studies {{cite:25f33a5cf92e55e9041826ad94f7d098aa5af1b2}}, explanations are easier to understand when they involve only a small amount of information and when they target contrast cases {{cite:a5ed5ba530250dc27b4adc80e560991c506dd3f8}}, i.e., understanding why a composer is selected instead of another is easier than understanding why a composer is selected in general.
For this reason, we also focus on C-CAVs with opposing conceptual sensitivities, i.e., negative for one class and positive for the other.
We experimented with three different non-negative factorisation approaches: *ntd applied to the 4d matrix (as explained in Section REF ), *ntd on a 3d matrix with concatenated horizontal and vertical dimensions, and *nmf on a 2d matrix (as proposed by {{cite:d2cf2f11b4b429bbc907e51f4ad1320f893ee894}}) with concatenated horizontal, vertical, and piece dimension.
| r | f64a5568bce935e3a2811225e2e697e1 |
All these characteristics align well with the design choices of CNNs: selecting local features and combining them locally is the natural structure emerging from the image classification task—it represents the winning ticket that can be more easily trained.
While other features like weight sharing simply cannot be reproduced in this model, the presence of similar masks at different locations is a sign of translational invariance (or the closest version of it available in these mostly centered images, an experiment with complete translational invariance is presented in SM REF ).
In this sense, this procedure could suggest network structures even better aligned with the data from a real dataset, leading to more effective architectures. For instance the sparse sampling, even at this low image resolution, is reminiscent of dilated convolutions {{cite:b262640f5e63b16d82ef84c95e5a360b9371a7a9}}.
| d | 39835ba4afa63f72b16d944c7db67dca |
Kingma and Ba {{cite:a9c04d1f565ed2500eb837182944256f72a3f194}} tried to prove that their Adam optimizer zeroed the error-measure known as regret over time, in a learning task called online convex optimization {{cite:580611794a4fda0ec286700ce4c57d3415b8d262}}. Rubio {{cite:18fbdf491859e30e56c5e3626bb34b6ea1d426f9}} and Bock et al. {{cite:ede043e53c231beb5573ff21ce9575d04055b0b5}} found mistakes in the proof, and Bock et al. managed to repair most of them, but they could not verify one key statement, called Lemma 10.4 in Kingma and Ba's paper and Conjecture 4.2 in Bock's. We will show that this conjecture is in fact false, but a modified version of it is true, and can replace it in Bock's proof.
| i | 5827d3011e51d4e86f69751515308238 |
We designed experiments that helped us to comparatively evaluate the performance of 10 state-of-the-art CNNs models on three classes classification of COVID19, normal, and pneumonia classes. This list of considered CNNs architectures consisted of models as; the famous VGG and variant {{cite:b82a23c2d2b05787dabce042b1ef6804778ea229}}, Xception {{cite:cf64d5f77203c66b0c4442dd11e71b730e6d0837}}, DenseNet and variants {{cite:33bc894007461ba4b8debe6afac231001b7042c7}}, Inceptions {{cite:c00ab47af3b19026b5cc099d816553bc0e446cdf}}, Resnet50 {{cite:781f4097f9ae1cc747411c7bc228b6df79783f05}}, InceptionResNetV2 {{cite:b82a23c2d2b05787dabce042b1ef6804778ea229}}, NASNetMobile {{cite:7f6f21aa845deee16b49a2febf2e134e7e88c760}}, NASNetLarge {{cite:7f6f21aa845deee16b49a2febf2e134e7e88c760}} and EfficientNet {{cite:440d7514f0264b70155107d262a23daf5b0c70c6}}. Figure REF presents the class-wise confusion matrix of all our ten trained models that were trained under experimental setting given in Table REF .
| d | f53abe5ac37ab75c383ba804c6737296 |
More generally, we identify the novel direction and length extrapolation gSCAN tasks as a particular kind of compositional generalization task that requires generating OOD output sequences. This “decode-side” flavor of compositionality is germane to many seq2seq tasks, including visual question answering/automated captioning, code generation, and length extrapolation in seeded text generation {{cite:0247382821107487d16e5c6025ac81d9224c4357}}, {{cite:e607625143f40f318dccdb42ef0d311978164e18}}, {{cite:f14305e512f3fb03bb5cad1b6161dfe4b24e8878}}. As we show, the difficulty presented by such tasks can sometimes be ameliorated by reformulating the problem into a series of incremental sub-sequence generations which resemble what models see during training. As formulated in this paper, RD is specific to gSCAN, but in the future this general approach could be adapted to other tasks and datasets. The key challenge to such an adaptation would be finding (or constructing) an analogue to the gSCAN grid world; a supplemental object whose state can be incrementally updated on the basis of predicted outputs.
| d | 49ef4690292e806c5b082ee10f475d23 |
Considering the success that neural transformers have demonstrated across various natural language processing tasks {{cite:06a9f693411cae10d8e1012fcf1930fe0be0e9a9}}, {{cite:f1a13c388931b2929336401fda835538e9482c45}}, {{cite:9d1a596322f69ba5e3856ea6b5d488ffdf2b1540}} including offensive language identification {{cite:6aaf0cf2293aca60bd76084bc50842c0ca5e1fce}}, {{cite:7e9e18cce1b521e61c58d3e7e07159006a3f404b}}, {{cite:6eeb2d3e0f887ea768aec3bbd982fbc276b6890d}} we used transformers to tackle this task too. We explored transformer architectures in two different environments; single task learning and multi task learning.
| m | 7abd828c8ba9db268f8021c914971ff2 |
Figure REF demonstrates the relation between the effective tidal deformability {{formula:7a985eec-391a-4ccb-a72a-7756cbf1a67b}} and the radius {{formula:200ecf48-f687-4b20-be6d-5dfbfad63778}} of a {{formula:bd1365ff-b468-45cc-ad0e-1980e915bb9a}} neutron star. As a reference we used the range of the component masses of the GW170817 event {{cite:03e046a6d6584c70487246166ccbaac780b4125c}}. The shaded regions correspond to approximate relations proposed in Ref. {{cite:74b08a8e91afecd04142d54370bf30f073491c75}}. We observed that as the temperature increases, the marks are shifted to higher radii. Therefore, if we take into consideration the thermal effects, possible constraints on the radius could lead to constraints on the value of the possibly existing temperature.
{{table:0c11a35d-842d-4a25-aa70-1b75cd84bf6f}}{{figure:7df14285-fe6b-4c61-85ea-4a7e017a0f9b}} | r | 8fa4e124fd1cdaf15bf3b211254099be |
In Fig. REF , we show the measured {{formula:2a59d269-6dab-432a-b367-844eec91c6ce}} for hadron combinations with ({{formula:71425aa2-bc1e-48dc-8cbf-1da1a4bf458a}} , {{formula:e57c7ead-be0c-41bc-b802-4d6c0f64d33a}} ) {{formula:cf5a5868-6855-4eaa-9a82-1a5084a06869}} (0, 0), (4/3, 2) in 10%-40% Au+Au collisions at {{formula:86be0a0e-d231-4a68-80c0-7ded523f3123}} GeV. The {{formula:3abe453c-d075-4f5d-983c-6f14bc51f7eb}} -slope parameters of the measurements are extracted. For {{formula:7d69a6eb-709d-4d39-acb1-e7b97e907fe5}} and {{formula:c5d6d8ea-d7fa-41dd-abc9-000783fe3f8c}} (identical quark combination case), the value of the slope is a minimum compared to {{formula:c9b7df89-f99a-4726-9ebc-2b2bb5607dd5}} = 4/3 and {{formula:afd647f5-3f34-4754-bceb-944540ad4e2e}} = 2 cases. This minimum deviation from zero implies that the coalescence sum rule holds with the identical quark combination. The deviation of the slope from zero increases as we move to {{formula:4efe879c-c23f-45d1-b8a3-78cd7ab9a68e}} = 4/3 and {{formula:67d2e45c-9b7c-4667-b9a1-05e33b036279}} = 2 case. A Multi-Phase Transport (AMPT) {{cite:e8509d954d22cafb3f79282d35d17d973b303799}}, {{cite:339b17544f9c435e3410b1085b8c760c8eef8438}} model calculation can describe the measured {{formula:d4d89096-dda4-47a8-b805-c4ccbe6c0ff3}} within errors for the {{formula:0cc5da8a-0fac-4ef1-b9dc-c80ab62503ce}} , {{formula:1e0883a3-77d2-4a4d-b7f1-5f744fe41004}} case. For {{formula:01a754d4-dbb2-47b4-bcf7-a72a2c86b551}} = 4/3 and {{formula:c9e264fb-5b42-42fa-a226-0ee6689c4354}} = 2, AMPT depicts a completely opposite trend compared to the data.
{{figure:b7b132d1-3fe5-44c1-bc00-d07980750146}}{{figure:e08885ac-0b0b-49b9-96f2-645ca4f47e78}} | r | f8d4736d91179fff53a5d641ed64053b |
We describe three methods which are based on perturbation of the input. These methods are inspired by occlusion analysis {{cite:88f9d98ca80e16396969300dd801011946d85e56}} and are model-agnostic (access to the model structure, weights and gradients is not required). The input is perturbed in ways described below and the output score is observed given the perturbed input. Figure REF shows the process of Conditional Occlusion (top) and Context-Agnostic Conditional Occlusion (bottom). Figure REF shows the process of Pairwise Occlusion.
| m | a1990c438bb6c152e0a5f926d9651e3b |
between the two objective functions {{formula:cfa071d4-a432-4d3b-bb8d-255fc634ff09}} and {{formula:5e2e377e-2069-41f5-92f6-340df314c7a6}} , for different values of the parameter {{formula:0ceb2434-3666-4545-a246-b5459fa784be}} (an adaptive version of the method can be applied in cases for which the classical weighted sum method fails, e.g., when the Pareto frontier is nonconvex {{cite:c7fac40a50bf5c07936f9fd79b52962dcb87e747}}). Assuming that both {{formula:33eb38be-b042-4449-bf73-22c94f3f7710}} and {{formula:eeb657f0-b381-4692-aed2-434c3bd6fce4}} are differentiable and the optimization problem is unconstrained (i.e., {{formula:112a816f-d081-42a5-8b31-af37d2194ab8}} ) or that it can be reduced to an unconstrained optimization problem by using a suitable penalization approach, one could perform the optimization numerically by applying the classical gradient method, possibly combined with a multi-start approach. In order to reduce the computational effort needed for the exact computation of the gradient at each iteration of the gradient method, one could replace it with its approximation obtained by applying PCA to the gradient field {{formula:e1d4d92a-230d-4038-b557-9da224bb2b74}} evaluated on a subset of points {{formula:a94284f8-e85f-4ef2-a095-6eca1c33deda}} (for {{formula:6b5f59d5-191b-49e7-a04b-401d03a5ba04}} ), then projecting the exact gradient onto the subspace generated by the average of the gradients {{formula:d8938a0c-3df0-4377-b753-eed1df080e94}} , and by the first principal directions found by PCA, when this is applied to the dataset {{formula:93f96ca7-7f01-49f5-8935-f879c6c72e43}} , after a pre-processing step, which makes it centeredIt is common practice to apply PCA to centered (also called de-meaned) data matrices {{formula:dd9f4bc6-837b-4c62-9bb8-92e413c3aec8}} , i.e., having the form {{formula:5d140db5-cec6-40e2-be6c-39a3b01b2ecf}} , where {{formula:ff359d9d-e8be-4680-a096-bb4bb9ea6ed1}} denotes a column vector made of {{formula:d72e1821-8857-45c1-b2eb-52ac70eee148}} ones, and {{formula:2a68f696-6f1b-4b5d-9556-e3f7dfd32e49}} is a column vector whose elements are the averages of the corresponding columns of {{formula:aa31b161-aed3-4d0d-b6ad-5202b468c4a1}} . This does not change the quality of the results of the theoretical analysis, because, by linearity, the centered convex combination of two data matrices {{formula:59e01bcf-410b-4c67-9f33-e7e80e3bf79a}} and {{formula:a4e5e875-492f-4606-ab1e-1048d6524ee9}} is equal to the convex combination of the two respective centered data matrices {{formula:a3e8e144-25d2-419c-83dd-9b6d5dbf81f7}} and {{formula:b01e5b27-e193-4296-8f09-596a6a0d1355}} .. Due to the structure of the objective function {{formula:a9eafe7f-97b6-419d-bcce-edd38a92058f}} , such dataset (represented by a data matrix {{formula:e802336f-1e02-419f-ae32-951ce52992a7}} ) would be made of the convex combination (with coefficients {{formula:54cfded5-c110-40d4-83b0-4bf20f5f3ebc}} and {{formula:802f6a41-a621-478d-b853-100048dbd31d}} ) of the two datasets {{formula:df60af4f-a7a9-4e6c-bd78-cb97e8b01178}} and {{formula:5f0a6213-e032-47b3-ace7-cc43683064e9}} , represented respectively by the two data matrices {{formula:1305a54d-b18d-4665-9e13-c18885caf60d}} and {{formula:a5db70b4-f166-418f-bf63-b56b18f0bc56}} . In this context, the results of our theoretical analysis could be useful to restrict the application of the weighted sum method to a coarse grid of values {{formula:0f1fa682-98e6-4629-a095-3c9b93b99ea5}} for {{formula:54637fe5-1d31-4c24-95b2-da1bdf46d543}} , from which one could infer, for other values of {{formula:9d39055e-8d15-4bbf-8df5-d94945222a64}} , the empirical variances of the projections of the (de-meaned) data matrices {{formula:a24726b8-abaa-426c-86e6-d72d848ba76a}} onto the principal directions either selected or discarded by PCA, when PCA is applied to each such data matrix {{formula:9c575a5c-0b97-44e4-be05-420d728adef6}} . Moreover, in view of this application to multi-objective optimization, the theoretical analysis of this work could be extended by finding upper bounds on the Jordan canonical anglesThese, loosely speaking, represent the smallest angles between corresponding elements of the orthonormal bases of two subspaces of {{formula:3151a89f-8c06-4533-9722-4d90d63a04ad}} , being the bases chosen to minimize such angles. For rigorous definitions, see {{cite:91bde836e0b7111e02d76acecc484ae34a9519ae}}, {{cite:9908f0bfd6c614825cc6f4f7ea3baab7779bcf3d}} and the references therein.
between the subspaces found by PCA applied to the data matrices {{formula:d32bd48f-81bd-4d3f-8c40-ae1f9f4e7e4b}} generated from {{formula:9302c305-261a-4d49-884f-1d27db7fca13}} and {{formula:4672d778-682e-4532-955b-9ba5439d1253}} for two different values of {{formula:a3eaffbb-bd3a-4b27-ae1e-52347018aed2}} . Such an extension could be derived by applying a variation (proved in {{cite:91bde836e0b7111e02d76acecc484ae34a9519ae}}) of the well-known Davis-Kahan theorem in matrix perturbation theory {{cite:9e259296d90819085711805039cbb82cf1f4e544}}. A second extension of the analysis to the case of nonlinear versions of PCA, such as kernel PCA {{cite:02dcf7e1e9656b41cd48fa9f4c45dbf19eaf1302}}, seems also possible (e.g., via the kernel trick).
| d | b564873801a85dd296ed88744fb13141 |
In this paper we propose a novel TM matching and retrieval method based on the Universal Sentence Encoder {{cite:6e051e1a8bd60f0ae0e72874095cf5747b3a2445}} which has the capability to capture semantically similar segments in TMs better than methods based on edit distance. We selected the Universal Sentence Encoder as our sentence encoder since it outperforms other sentence encoders like Infersent {{cite:f98803793a4527d0c2f7069b6bfb56f901339d31}} in many Natural Language Processing tasks including Semantic Retrieval {{cite:6e051e1a8bd60f0ae0e72874095cf5747b3a2445}}. Also the recently release of Multilingual Universal Sentence Encoder https://tfhub.dev/google/universal-sentence-encoder-multilingual-large/3 is available on 16 different languages {{cite:ce626ac6421b999ba24f2afca58b0c22faeefdb3}}. Since we are planning to expand our research to other language pairs than the English - Spanish pair investigated in this paper, the multilingual aspect of the Universal Sentence Encoder can prove very useful.
| i | 9112945e0856c3b5c89238ca7e135489 |
Over the next few years, progress continued using a combination of methods. These include improving the generative model architecture with modifications like multi-scale generators {{cite:b4e5df23bbad25ef33f33101ba54d27063ddc3b9}}, {{cite:c1aa70206ba2800f9e893bc2cc4d310efd482d93}}, integrating attention and auxiliary losses {{cite:dbfea6a7581990047dc2c085f6a5c5ba474e164c}}, and leveraging additional sources of conditioning information beyond just text {{cite:43fa621d3bd74db0d0ee31b6dab74db71d397c9f}}, {{cite:d5607901a05fa53e9b89a71973d32cf06702214f}}, {{cite:842d9ace4f3c20096425224512551617283dd9d7}}.
{{figure:93f2ba2f-c8bb-46df-ab83-9fd7aded7d25}} | i | a073b03c424a82b06b9702a6afcb413c |
Following {{cite:d8bd4ce471337c1e2b30e7773dc5ea8974db67d0}}, we represent 3D shapes and 3D sketches as point clouds, and train the model via a Siamese training with a triplet loss {{cite:fe585732c264dff4edb8848f0d8ffea45c8afc3e}}, {{cite:b773f9ebbc97a5e38bc39e6c71d69174685c132d}}, {{cite:a0746cb82c23d33adb62fa62847084ff3dd61dff}}, {{cite:e1525efb66ff3321bad6fc614e204f793a23c94b}}. As a 3D sketch and shape encoder we exploit PointNet++{{cite:85ca84a3abefc9c4b645c487cd0a60561d89ea82}}, where the same set of weights is used to encode both modalities.
| m | 6d39b7eb8f0d60b79b382b1fbc4d8b40 |
The organizer baseline F1 scores for the validation and test data are 0.58 and 0.654 respectively.
The details of the baseline are given in {{cite:f86e0bd83224c11acdf376a0af76cff2f9d20e9a}}.
The obtained results with our submitted runs are given in Table REF .
For SkipGRun, we achieved 0.6913 of F1 score with 0.6952 and 0.6893 of precision and recall respectively.
The SkipGRun outperformed the CbowRun by around 0.40 in terms of F1 score.
CbowRun outperformed the organizers' baseline by a slight margin, however, SkipGRun outperformed the baseline by around 0.4 in terms of averaged F score.
| r | 40a17a3dbbecaf2d288c3617c6b196b2 |
Next, the computer vision community has recently begun using Fitzpatrick Skin Type (FST) categories to describe skin tone in images, for the purpose of evaluating algorithms across this measure. This methodology has been proposed in studies of gender classification {{cite:7df3012e5a33cddc24fca0513d79df81b76170be}}, biometric recognition {{cite:cf667bab2ddfc26b3ccf22b341314bde93d9a312}}, {{cite:f0c7a38a0cae4229501dd4afefb5137a75bc12db}}, {{cite:2ecab2c37b2905d636f0224e89d6c91576ea60f3}}, {{cite:f8c445d5c4ed0442eedc7e9d3b1c72c43ff1d88d}}, and pedestrian detection {{cite:f817a51f66cfd1afccf01cd87888f515a08af058}} algorithms. It has also been suggested as a standardized method for documenting the performance of a generic machine learning algorithm {{cite:9e510a3684076592c9a871c46916dc54bc3f67af}}. Our work shows that this novel use of FST may be problematic for at least three reasons. First, as we discuss, FST was designed to classify UV sensitivity of an individual with specific labels assigned to each category. FST is not an arbitrary ordinal scale and other ordinal scales with different category labels or a different method for arriving at these labels are not likely to produce equivalent results. FST has been shown in medical literature to be a generally unreliable estimator of skin pigmentation {{cite:e635627bc79da1291a4aa29e5db7cf1f2fc48ecd}} and a specifically unreliable estimator for people of color {{cite:77c66efefb25345c2ce61ff8a19ae73d8cb37abf}}, {{cite:aed665ea840ab173def002058bcb636bd6d99ed7}}, {{cite:4777f4ff4a91bd2bb19da0b98b22e7b43738b360}}, {{cite:081c7c5825ed1dc5d79e80a447d9cfc60ceaa8a7}}. FST assessment is subject to inter-rater reliability issues {{cite:2ecab2c37b2905d636f0224e89d6c91576ea60f3}} and known rater biases {{cite:5ef834e25cc4d67fe2f7b04bee7b3a7aab779472}}, {{cite:31e4ea69fd14205e5221e85f5e4238b7134c8657}}, {{cite:32958f184b76936fd37d727816aacfaeb28acdc3}}, most notably conflating skin tone and other features related to the race of the subject and of the rater {{cite:40226bdec5a9176e968310ba63c80072e10af9ca}}. Because of these concerns, we believe FST is a poor choice for evaluating computer vision applications.
| d | f2bd6177644b5b4ea3a1dc95702f3bd9 |
The similarities between chemical enrichment of the IGrM in lower-temperature groups and the ICM in massive objects is further supported by the shallow dependence of gas global metallicity on the system mass (or temperature).
In contrast to observational findings, where lower iron abundances were typically observed in group-size systems compared to clusters, {{cite:1ddabc022aec21e16f6685c63fd6656a50266918}} report
a shallow, mildly anti-correlating, metallicity-temperature relation, employing semi-analytic models of galaxy evolution.
Simulation results, like those presented in {{cite:a1e1d68eb066e6ea5d96b79d2598e017f81979be}} and {{cite:5438eecac216506cc365ad1891350f7e92bae62b}}, also predict a shallow anti-relation between metallicity and temperature, that extends without breaks from clusters down to groups.
More recently, {{cite:e453279f9370d0b8f47ad420dea1593ec316526f}}
compare the relation between temperature and iron abundance in the core (i.e. {{formula:14f544eb-528d-4317-b57c-9eb4926c8a7c}} ) of simulated groups and clusters with recent results from the CHEERS sample {{cite:81e21fa1415c992fe6266cefe00766872e7aa054}},
also finding a shallow anti-correlation overall, with a mass-invariance of the IGrM and ICM iron abundance in cool-core clusters, as shown in Fig. REF .
In the Figure, in particular, the simulated data (star symbols) are reported together with the best-fit relation for the whole sample, and for the CC and NCC subsamples, with the former in better agreement with the CHEERS results .
{{cite:a1e1d68eb066e6ea5d96b79d2598e017f81979be}} show that a flat relation with temperature applies as well when abundance ratios relative to iron are investigated (e.g. O/Fe, Si/Fe, S/Fe etc.).
Interestingly, this is also in line with recent observational findings .
| r | 2956cfa50cd8c183df4d7248d9ebca87 |
Going beyond biomedical applications, the generalized form of the Sticky PDP is presented in Section of Supplementary Material.
In addition to extending PDPs to discrete time series type data, the generalized formulation offers a diverse palette of parametric and nonparametric
models for capturing the distinctive features of data in various applications. The range of models
includes Dirichlet processes, PDPs, infinite HMMs, hierarchical Dirichlet process (HDP) {{cite:674f4157085115ca9b59cabc0230c86ada2c2ee0}}, {{cite:d5296219d07e62b7545cab22f4608491ad100ff4}}, finite HMMs, nested Chinese restaurant processes {{cite:f1b4003f38cf65d6a11b956176b95452a32c8a6a}}, nested Dirichlet processes {{cite:2532965a8fe4bd40de5ee8fe424c3ce0e5b3fbdf}}, and
analysis of densities models {{cite:b9e73b2ec5f83ce47d32a938652e7e185f426c8b}}.
| d | cc1d41c8113b970247668e39136f518f |
We have shown that the EMG model leads to a larger value of {{formula:b67df730-312b-4c08-9672-290e4380ef88}} compared to the {{formula:080d4130-666c-4aaa-8a7e-31b08a68a439}} CDM one. Therefore, we would like to test it against weak lensing data. Strictly speaking, this would require using data from e.g. the KiDS-VIKING galaxy shear measurements. However, it was claimed in Refs. {{cite:0d6d657eb9141c7d15364264e8a3490769e2bdff}}, {{cite:26b838286b19543b78f7a4d7d72b972a78819f9c}} that the same results can be obtained by implementing weak lensing data through a Gaussian prior on the parameter {{formula:e952b705-c44d-4a33-acdf-a04b2f2754c9}} (see also Ref. {{cite:c0c034f72450ecf4c31c105788a756f799d0a3d0}} for a thorough comparison of this method to the correct use of cosmic shear measurements). With these caveats, we follow Refs. {{cite:0d6d657eb9141c7d15364264e8a3490769e2bdff}}, {{cite:26b838286b19543b78f7a4d7d72b972a78819f9c}} and present in Fig. REF and Table REF the results for the data set P18 + BAO + FS + SN + {{formula:8e866572-f7fe-4d08-88a3-0b0889b4a4f2}} + {{formula:65198206-596d-414b-a6ba-38d735391ce8}}. Note, despite being far from a resolution to the {{formula:0028bec7-9e80-416a-b1ed-b60e58d81d5a}} tension, the EMG model shows now a much smaller {{formula:ccc2d643-934d-44f6-83d2-3eb2e3144511}} and a bestfit value of {{formula:82a9867f-b8c6-474c-8b96-cda6b386da45}} , lower than the one obtained for {{formula:9da024c7-a139-42fe-89ef-e7d807a624e0}} CDM i.e. {{formula:8c548149-4939-4d62-abc7-53885e43deff}} . This confirms the conclusion of Ref. {{cite:c0c034f72450ecf4c31c105788a756f799d0a3d0}} for EDE models that, even though it is true that the {{formula:571abb19-0348-428c-aa8f-517852005c02}} tension is not resolved within this model, the same holds for the {{formula:32833ade-90d7-4ebf-8bad-91d411f450d7}} CDM model which, however, is not able to address the {{formula:8f0bf274-b425-4a5f-a987-3fb4dadb6b88}} tension, as opposed to the EMG model, for which we obtain a mean {{formula:4ff27d2c-2a83-4feb-bba1-af56a56a4302}} and a best fit of {{formula:74016439-beef-4f53-95df-b36104e50c41}} km s{{formula:8b8b241b-659c-4147-a0de-d9a2c23bd033}} Mpc{{formula:8fc0b4a5-ea06-428e-bb5a-852933c67e6e}} .
| r | 13e40a24528c95b851184e658bf719ef |
Could Commonsense Reasoning improve CMC?
Commonsense Reasoning (CR) is based on the set of background information or world knowledge that an individual is intended to know or assume, and may be missing from context. On the other hand, Pragmatic reasoning, which the current CMC models cater to, is based on the derivation of explicit and implicit meanings within the context. The current MRC systems are nearing human performance on most datasets, however, they still perform poorly on single-turn CR based questions {{cite:756239a31c5a1d9d6c1fbae28a5cfb88924ca932}}. While there is recently increasing interest in CR in the single-turn MRC setting {{cite:a23f56f90f7ebf78396d01f89c65e615243d50ef}}, {{cite:d58d0619c355e20e50043db28d2a6995f2f6e94d}}, {{cite:d96731f211ecbabe02557c45add43b3404f2ede3}}, CMC remains relatively untouched. This may probably be due to the lack of foreknowledge requiring unanswerable questions (e.g. in SQuAD 2.0 {{cite:6967d4315fce47915f06e3f925c1db51160cdbb9}}) in current CMC datasets {{cite:bb1ef5bb1b37b3a324d9cd1d0f8b1acc90e38169}}, suggesting a need for more complex CMC datasets that incorporate CR. However, humans annotators may often apply common-sense reasoning involuntarily while answering questions or comprehending, thus leaving room for incorporating CR in models. There seems to be no recent work that invalidates, experimentally, the role of CR in CMC. QuAC, for example, is drawn from articles on personalities, and current models still lag behind the human benchmark. It may be worth experimenting if adding domain knowledge or attributes about the context, like location and gender, help improve answering these questions.
| d | 615dc50046ef3e677694c9ce9b5579a4 |
The number of passages mentioning some SWs is very small
(e.g. {{formula:8984c58b-ffdd-48cd-b430-0c2a7ae2b54a}} for {{formula:4f8c046a-7bff-4a82-a9a9-399cc2e5446a}} “Sakhmet” in Table REF ).
It is therefore necessary to explain
how can we draw reliable statistical conclusions
from the analysis of such data (FAQ REF ).
Firstly, the periods {{formula:4688c89b-8c4e-4ee0-b12f-a1460d8ab602}} and {{formula:ca254e21-848f-4a61-ade4-8ebde5097390}}
were detected from large samples of over five hundred time
points and these periodicities were extremely
significant {{cite:30174b32f75165a932510941571d1b55746bdf97}}. For example, the period {{formula:c3ee36bc-b1fe-488a-ade1-35e1c1148fe6}} reached critical
levels {{formula:c103180d-d598-46b6-9c86-e86e0a37c205}} {{cite:30174b32f75165a932510941571d1b55746bdf97}},
i.e. the probability for this period being real was {{formula:283129c5-a2a7-445b-83e0-54c295a6d675}} .
Secondly, the ephemerides of Eqs. REF and REF
are also very reliable,
because they were determined from the same large data samples
{{cite:b56a6bdcca6a3b830581ab9c453d4ba0a89d4a0f}}.
Thirdly, although the Rayleigh test significance estimates
computed by {{cite:b56a6bdcca6a3b830581ab9c453d4ba0a89d4a0f}} for some
smaller samples were not reliable, the binomial
distribution significance estimates for the very same samples
were certainly reliable (their Eq. 13: {{formula:c62ab225-6dec-407a-9cbf-aec949aea9c3}} ).
Fourthly, the order of the passages in Lists 1 and 2 is
the same (i.e. unambiguous) for any arbitrary epoch {{formula:154acfc4-4b52-4913-a8fd-9646492197b0}}
in Eqs. REF and REF .
For these four reasons,
the phase angles computed from the ephemerides
of Eqs. REF and REF
can be used just like the time given by an accurate modern clock.
For example, such a clock shows that most people go to sleep before midnight.
It is irrelevant if only a few (small {{formula:4d514a48-3abc-46fe-8711-66fedc07d0e3}} ),
or many (large {{formula:5c945956-c5b4-4bdc-9981-f78a18690e0f}} ), people go to sleep.
Rearranging the texts of CC into the increasing order of {{formula:cf6fea02-eeb9-4117-b87a-be3f0b387e8f}}
may show what the authors of CC
wrote about {{formula:4be19dac-9e2c-4404-9149-ab0754df6ffc}} “Horus”
at different phases of the cycle
(FAQ REF ).
{{figure:86000be9-c8f3-4d03-bdec-f3fd282ca093}}{{figure:9dcdef52-e4cb-4ea3-bfec-731ce4ee3252}} | m | 4050c4a5ce8a38c7cc5751973e5123c5 |
In this section, we describe in detail the framework of LimeOut that consists of two main components: LIMEGlobal and ENSEMBLEOut. It receives as input both a classifierHere we focus on binary classifiers that output the probability for each class label. and a dataset. The first component then checks whether the classifier is biased on the dataset in the sense that the predictions depend on sensitive features. To do this, we make use of LIMEGlobal {{cite:837f00ab10c4d465bcc8a8f96f46b5503507ae5a}} (see Subsection REF ). This will output the most important features (globally). If sensitive features are among the most important, then the classifier is considered unfair and the second component of LimeOut is employed. Otherwise, the classifier is considered fair and no action is taken. The second component is the core of LimeOut (see Subsection REF ). Given the most important features, ENSEMBLEOut produces a pool of classifiers using feature-drop. Each of these classifiers does not depend on the corresponding sensitive features. It then constructs an ensemble using this pool of classifiers. Following a human and context-centered approach, the choice of sensitive features is left to the user within the given context. This framework will be illustrated in Section .
| m | 95a6d0d80e8516cb6f07f7c8094a9eae |
thus we infer that {{formula:690213cf-001e-48e7-97b3-c2e9b6879cc9}} if {{formula:072c20f2-f490-44ee-9155-ede470c2b039}} . It follows from {{cite:f8437e3abd1db9722df2f3b421d70ef739e98367}} that {{formula:95066522-edf1-4db3-9d46-05bf9ff43e93}} . This contradicts to the condition {{formula:5fec3f02-7807-4dd1-bdf7-ba35c9117091}} , which means that {{formula:ffd122bb-2013-4f30-ba27-a495ee189bfe}} . Similarly, we also can get {{formula:af9f988c-7522-4bb0-80d9-65c22fe0d29b}} from {{formula:c763ac7f-00e9-447a-90a9-a08f0a8037ac}} .
| r | f32d512aab6ab771b4c56ed61a70c884 |
Multi-Cues {{cite:c4a8e7d6ed0bd07b7351d5f0bb97deccee4700d0}} calculates two similarities in separated embedding spaces and then averages them to produce a final similarity. The proposed method has higher performance compared to Multi-Cues. The similarity aggregation strategy is the main difference between the proposed method and Multi-Cues. Note that the average suffers from aligning videos and sentences due to their variations. Thus, some videos need global visual features, and some need sequential visual features. The proposed method has a flexible strategy for merging similarities. The experimental results show that the proposed strategy is more useful for measuring similarity than a naive merging approach with equal importance to each embedding space, such as average.
| r | fa6315037b5149584caf1c0ce5fe20bf |
In 1975, a so-called Randić index was proposed {{cite:06a5e0ec445856e922f09dd80e08ba740079ceb0}}, it is
defined as
| i | 8c9b321d30386db7819e274f84509a87 |
We study the co-attention module between language and vision and the interactions within this module. To study co-attention in two-stream vision-language transformer architectures, we evaluated visual attention in the model by comparing it against human attention maps. ViLBERT {{cite:42d3cbc200fde2ce44f30a996dbeb477f13e26ac}} is an extension of the BERT architecture {{cite:1aaf408148b573772f64c385016cb1cbf93f955e}} to process visual inputs. Given a question and an image, the model processes them separately in the language and visual streams, respectively. Both visual and language streams contain a stack of transformer and co-attention transformer layers. The embeddings for the word tokens and other special tokens are fed to the language stream after adding positional embeddings. The image is processed through the Faster RCNN network {{cite:6dd926ed28b3c203daa233fe4bd0879e7397144b}} to generate features for different region proposals. The feature representations of region proposals with the highest objectness score are fed to the visual stream. The model then processes these inputs through the two streams while fusing information within them using subsequent co-attention layers (Fig. REF).
| m | 753a417e4d1ec36680efbdd00efe0d91 |
The linear system of equations (REF ) can be solved using a
direct or iterative approach. If {{formula:05d688ae-ed5a-4981-8042-3e6e13b1961c}} is relatively small, a direct method
such as a Cholesky factorization ({{cite:2f04505261e20e3be332732d9cc9eab1989c1a1f}}) will work well. However, for
large {{formula:9b5924ef-7bf4-40ed-bdd7-c4c5d32017f1}} , due to well-conditioning of the matrix {{formula:25c22aec-1e87-48ca-9f07-b38362376a77}} , a CG
({{cite:2f04505261e20e3be332732d9cc9eab1989c1a1f}})
method is a better approach. Let {{formula:22129b44-56b1-4fb0-9954-fa8d5ed73fcf}} be the {{formula:3c927996-8f0a-46aa-b302-defc88ab3bc9}} conjugate
gradient estimate of {{formula:aa809e19-2f85-4cb6-a5a8-fa012845c568}} , where {{formula:ed0124c9-1503-49c1-adbf-50a7072578d8}} is the initial
guess. The main cost of the CG method is in computing the matrix vector products
{{formula:c140896f-b817-4ce9-8eed-cd4a07893b88}} . This can be done in 3 steps as:
{{formula:d766df12-e008-4204-a8ec-ff155f95805c}}
| m | 8dd70ba91eb00418bc1cee1eb6545f91 |
Maulik and Okounkov {{cite:92dc73f1738d8e302740e53f0ecaf923dae151c8}} have set up a program to realize representation theory of quantum groups of various kinds on torus equivariant (generalized) cohomology of Nakajima varieties. A central role is played by the stable envelopes, which are maps from the equivariant cohomology of the fixed point set of the torus action to the equivariant cohomology of the variety. Stable envelopes depend on the choice of a chamber (a connected component of the complement of an arrangement of real hyperplanes) and different chambers are related by {{formula:51c17cd7-c611-42ac-902e-9b9cd9fa3771}} -matrices of the corresponding quantum groups. The basic example of a Nakajima variety is the cotangent bundle of the Grassmannian {{formula:1b493c97-9363-422b-adbc-5645a538a108}} of {{formula:6960f440-614f-4362-8a1f-feae32a17b35}} -planes in {{formula:3012399a-4e5f-4979-99fa-aaa5223184fa}} . The torus is {{formula:ef8e1550-1a14-4375-a5cc-29f194b83697}} , with {{formula:7cb49582-0680-479a-94aa-5f250f9e279a}} acting by diagonal matrices on {{formula:ffdfab45-fb9b-4ef5-805b-58f9148423d1}} and {{formula:d8b8704d-d732-4283-ae3a-4d60754763f8}} acting by multiplication on the cotangent spaces. Then the Yangian {{formula:ca19274d-a5ee-4037-817a-39194995ec44}} acts on {{formula:473b7659-e303-4c64-a30c-c1b76cbacd8b}} and the action of generators is described geometrically by correspondences. It turns out that this representation is isomorphic to the tensor products of {{formula:e016b7c9-3861-40b2-b52e-d4d1ad20993d}} evaluation vector representations with the equivariant parameters of {{formula:5dbb2c5a-7f36-4c7b-98be-9f49dbaa1a94}} as evaluation points and the equivariant parameter of {{formula:b9042a54-8023-4560-bbd1-e98e3e3086bf}} as the deformation parameter of the quantum group. The choice of a chamber is the same as the choice of an ordering of the factors in the tensor product. The same holds for the affine quantum universal enveloping algebra {{formula:6476c55b-19b7-4bab-992c-f18e304020d2}} if we replace equivariant cohomology by equivariant {{formula:6741e847-37ab-4bec-b814-e7582295b1c1}} -theory. As was shown in {{cite:e09dda4b515ebe3bcf1fbd65510a1cd3997ef287}}, {{cite:86288bf616b3e148e709d8915059376dfbdd9235}}, the stable envelopes, which realize the isomorphisms, are given by the weight functions, which originally appeared in the theory of integral representations of solutions of the Knizhnik–Zamolodchikov equation, see {{cite:d027e33c957b2b6f5476d8706891335205277de9}}, {{cite:d43fe15e96e1794543c552c4fbefb74e7b881ba0}}. Their special values form transition matrices from the tensor basis to a basis of eigenvectors for the Gelfand–Zetlin commutative subalgebra.
| i | 0d063a9f31b950709f64cfca72b275e7 |
In this section, some related studies in {{cite:43e9621a43c7266c8996eb22fb8a470579c46ec7}}, {{cite:9e70c9ffc9f6618140ed4e05b955b9238601a847}}, {{cite:b3df05b74febb3dcec8fc1e9a20aca5db6e416dc}}, {{cite:038e838775a3c9b180cd9ad917e7eb6927435cb8}}, {{cite:20ad01a2eb13036effdf18ed0342800453e62989}}, {{cite:645b771809f004fc7aef4d9589cce7a4a0d42211}}, {{cite:206b3141cee2985ed3a4ec18b97cb0ecb9a174a4}} are considered and discussed.
| r | fda59ad4df55dc0a94ab6c372c477b5d |
Undoubtedly, a general problem of these task-specific semantic researches is that datasets are insufficient. Some data like driving behavior, risky scene, and even car accidents, are extremely hard to obtain. Luckily, in 2019 and 2020, an increasing amount of high-quality semantic driving dataset appeared. Some of them are common datasets, like nuScenes {{cite:3cf109280a36bc8badfc80dcbb89738e100e9ff6}}, sematic KITTI {{cite:a7554db751550b542fd4975bcdb8b42499ecaffb}} and Waymo {{cite:f13d26a25ffc7898eeeef4038ae41044d2a7272f}}. And others, although with less amount of data, are task-specific datasets, e.g. Road Hazard Stimuli dataset {{cite:7328e7d18e883dbb0afded8c7d66d93242c485ae}} for road hazard and risk annotation, Honda HDD dataset {{cite:c0f4dc79c8263eafec195ee0c501a3cc26c7a7b1}} for behavior prediction, and our Road Scene Graph Dataset {{cite:2be1c4e0c1e7b6a1737283f1d8da99f36a4903c4}}. Besides that, driving simulators like CARLA {{cite:2d9bd11375bc567fa9acc6c54ccb8a58e42c9069}} and Airsim {{cite:7164bf0cde4155541e75ad724bbd1a8c0dd0d577}} are even more important over time as for scene replay, data augmentation and reinforcement learning {{cite:e66bb2036b8e59227612e83d8b42543188f2f091}}.
| m | cbb310acdae41fd330acfaae5ca8e775 |
The maximum measured values of the volumetric VUV power were estimated as 45, 25, and 55 W/cm{{formula:10309b11-6e0f-4ab8-9b23-2197692a00ab}} (with a total input power of 100 kW) for the Lyman-alpha line, the Lyman band, and the molecular continuum, respectively. In our estimations, we have not taken into account the influence of the Werner band emission on the Lyman-alpha line because the difference in the corresponding cross-sections is about 10 times for the assumed electron temperature. It is worth noting that contrary to many other low-temperature plasma devices {{cite:ee661dee75d91dd333c67e3914e5c1193ee11f03}}, {{cite:e9fbcc5069658c5dda229a733e15eae20a477578}} where Lyman-alpha radiation was found to have the highest power we measured the molecular continuum emission to dominate. The molecular continuum emission corresponds to electronic transitions from the {{formula:9b6a7f0e-e55a-4f3b-bf89-fc043f0b87be}} triplet state to the repulsive {{formula:3f7781fa-3b42-4bf3-bd90-b7b239cb3a58}} state resulting in auto-dissociation of the molecule into ground-state hydrogen atoms. It has been found previously that up to 94% of the positive ions extracted from the SMIS 37 device are protons (as opposed to molecular ions) {{cite:21b694b820b2aa36c269ce9a04f14897eb83c4f5}}, which is commensurate with the emission power of the molecular continuum being very high. The Lyman-alpha radiation reaching the diode detector could be attenuated by absorption of the photons in the hydrogen gas containing protons. Quantifying the effect of the plasma opacity {{cite:691c2ccb4c2a8d7395d49f44ae41ba1eeae0c4a9}} would require estimating the hydrogen atom density on the line-of-sight between the discharge and the detector.
| r | 53d21c7cc75a01259d3f6e83d31e4a1d |
These 2485 quasars with {{formula:c19e6c10-e7f4-4543-bbb1-86f57ce0ff11}} (H{{formula:7eae5225-aba6-4b92-8a71-08d9f6358f3a}} ){{formula:e4ca400f-35dc-491d-9a42-491b9d94aa4c}} in Table 2 of {{cite:5c32a13219651e97755aa3fb0297e51f6d180426}} have a median of {{formula:0e666f6e-eacb-426c-af96-ecae875f8486}} (H{{formula:488cbd3f-090d-44d3-b281-4cac3e6bf37b}} ){{formula:763e5a87-72cf-4206-a2de-71a0b7a492eb}} with a typical error of 55 {{formula:a000abf4-81a0-4907-8544-17cf1b9af1f7}} , and an average and standard deviation of {{formula:cae6fc44-6cc9-4be5-851e-f3e29e89c2c5}} (H{{formula:ec8c0a2a-4cd8-4c00-bed7-8b55e28e13ee}} ){{formula:5eea6691-1d7b-4bd8-a8d6-b81222244b60}} {{formula:a0e90c1d-410a-4a32-8cd1-28c81f85c1b9}} . 1973 quasars in our sample have {{formula:c64efc8b-6f43-4487-83dd-8e36f2f71bef}} (H{{formula:7b61ed37-eb2b-45e8-a70a-ab5571bdddf5}} ){{formula:9ef423d5-7c4e-44d0-9a2c-3ed6a1c0de9e}} {{formula:73de5ccf-f4c3-4db9-a55f-863c22b1fc40}} and {{formula:64538b45-d619-4f8f-b2e9-9e39178550e1}} (H{{formula:ef26eb54-ad3b-4f2f-9a27-4d4fd79aaed0}} ){{formula:27f057ce-78e6-412a-9a5a-cc5bf24fbdb5}} {{formula:9e1e6b05-f089-4d09-8fae-970155ce7a2e}} . Considering uncertainties,
these distributions of {{formula:640aca57-4d99-4d75-8cb1-dd965b3e53df}} (H{{formula:678de559-26e1-4ede-8d12-f553b46f8721}} ) do not seem obviously different. The relevant distributions of {{formula:1814c641-a910-4d73-8307-0f255a7eccbe}} (H{{formula:6dfa12f6-431d-4d54-8151-e5e315217955}} )
are presented in Figure 7{{formula:85301ebc-0522-44b0-84f2-5192f706b0fe}} . Sources with smaller {{formula:dd3bc7f3-28b4-4de3-bfe7-7fecd8789710}} (H{{formula:35efb08f-6d69-4762-ad1c-4d30b5ca8ddb}} ) are more likely excluded by
{{formula:f3fbe3c9-849d-4505-a4a1-60495d78d809}} , which means the relative error of {{formula:efd711e2-cdf7-4780-8c9e-ac52dcd5b686}} is smaller than 1. The relative error distributions in Figure 7{{formula:26827f17-bb93-4270-abae-a09b0f2d9dee}} for the 1973 and 2485 quasar samples show that the relative error is more likely larger
for the smaller {{formula:90dcc7f0-58a2-4138-b35f-dbe6ed8732c6}} . Correlation analyses for 2485 quasars show, at the confidence level of {{formula:e81eec03-e6a1-4a23-8961-f49a23334d83}} , three positive correlations among {{formula:ad323b78-811f-4de8-b25b-28979820d3f7}} , {{formula:1962f39d-f113-478c-88c3-40a1034dfcda}} and {{formula:f34b7459-7458-4d8c-836f-2d3fb3521951}} , a positive correlation like as {{formula:ea51d271-6a75-48e0-add9-011c383fe85f}} , and a negative correlation between {{formula:83406563-8fbd-479e-bc93-636cedbe278a}} (H{{formula:42a1b744-9456-4083-8f32-d6502ac9ad72}} ) and {{formula:99cf84af-a045-4fe1-8747-64753df05287}} . These results indicate that correlations found for 1973 quasars do not originate from the selection effect, i.e., {{formula:4bf2cf32-95db-4e14-8a3b-333f039b5bfb}} will not result in illusive correlations,
though this condition will make {{formula:8f963459-fc51-4a46-8121-18e5ad31392f}} larger for the selected quasars. The fraction of blueshifted broad line H{{formula:9a4930f3-3a9b-48c5-a6a7-0acd4d9bc672}} with {{formula:e7f685a6-26d9-4ea9-b808-744673bf3083}} is about 14% for quasars in {{cite:5c32a13219651e97755aa3fb0297e51f6d180426}}, and these blueshifted quasars may be explained by additional blueshift of a kinematic origin arising from radial motion, e.g., outflows. Outflows seem exist
even if AGNs are during theirs low-flux states {{cite:fb573cd09e9fc993c76ca2119396309d78d7a735}}. Larger quasar sample, e.g., SDSS DR7 quasars in {{cite:3b936ab056572da76ed396585a53b5c8cd038142}} who gave the detailed parameters of spectra, will be used in the next work.
{{figure:b697996a-fd8a-4352-86de-f40b21108990}} | d | 7208904dc31c99bab72ce6baf74806f9 |
Bit depth refers to the color information stored in an image. More colors could be stored in an image whenever there is high bit depth in the image. In the case of black and white, it contains one bit either 0 or 1. Hence, it can only show two colors which are black and white. Furthermore, an 8 bit image can store {{formula:f70c7762-70ba-472f-9117-e00151b4889b}} which is equal to 256 possible colors, etc. It must be mentioned that, the bit depth specify image size. As the bit depth increase, image size also increases because each pixel in the image requires more information {{cite:2d96d1de65d46b6bd2cd5fdb55c4e187b86d9bb3}}.
One way to think about bit depth is to consider the difference between having the capability to make measurements with a ruler that is accurate to the nearest millimeter, compared with one that can only measure to the nearest centimeter {{cite:fabc8f389fb9932503525820b124ef24d367a884}}.
| m | 589df48430cab5896640ebf370a66f4d |
While B-tipping can be found and continued in system parameters on applying tools from theory of autonomous bifurcations {{cite:bb932d2915fc51f61f77fbe5e5e9d908819b4a43}}, {{cite:6da4c92a582db8005b16ab0e043e939b69af162b}}, {{cite:73c6da3d3b370238bdca430409e14ea9a608c9c0}} to the autonomous frozen system (REF ), this is not the case for nonautonomous R-tipping.
Furthermore, whereas Section REF
considers R-tipping for moving sinks on {{formula:c1d1f0b1-8194-4c3d-ba5c-dfcb72ba80e5}} (e.g. Figure REF (a)), some R-tipping occur from moving sinks on a semi-infinite or even finite time interval {{formula:754747db-d065-4fe3-b860-fe53a7756ac2}} (e.g. Figure REF (b)). Therefore, there is a need for
general criteria and methods to find different nonautonomous R-tipping and continue them in system parameters.
| m | b24f3bf26d9180d9688d5da346be3127 |
in {{formula:9fee89a0-2499-4bce-bcd3-8bca45f5bb79}} , where the number {{formula:5e00e32a-c10f-4774-b55e-28c97574b4bc}} of event measurements can be a random variables changing from event to event, or a deterministic quantity. For most collider events, the corresponding point patterns will not be uniformly distributed over {{formula:0e1f44f1-728c-453d-919a-b962afd6f268}} . For instance, at hadron colliders a substantial amount of the energy from the high-energy {{formula:612c9951-70e8-403c-a10f-d2ef86550f68}} -collision is emitted in the form of collimated sprays of hadrons. These hadronic sprays, known as jets, lead to clustered point patterns in the space {{formula:72e76fa3-ffa1-43e9-ab9b-302640d21906}} . For high-level observables spanning {{formula:47016d05-d879-44c9-ad4e-e816f21b97ae}} , the resulting point patterns for each event can be quite sparse, or give rise to irregularly shaped patterns when averaging over many events. For example, event point patterns in the Lund planes {{cite:08049acb3a307c78a5cbf6161012fd54f499be64}} are both sparse and irregular in shape. Building a completely general probabilistic model for event measurements {{formula:3219f07b-9485-4819-8265-749bb0fdf879}} for an arbitrary {{formula:a7946a37-a3da-41d5-8303-9b692a7f05e6}} is therefore very challenging.
| i | b23e9d300b1a268b74a09d80f2263cbc |
The intrinsic evaluation is based on semantic similarity {{cite:b12c1642a4400b20ff0b01c714585d8557678e24}} in word embeddings. The word similarity measure approach states {{cite:6a2014cd9b7037741df24aa12858cb22ac448419}} that the words are similar if they appear in the similar context. We measure word similarity of proposed Sindhi word embeddings using dot product method and WordSim353.
| m | 903bfa0e8750e6f20589eca0c0a0ab0e |
As described in Sect. REF , the OSR problem consists of two sub-tasks: (1) novelty detection for unknown classes and (2) classification for known classes.
The ViT architecture has already achieved state-of-the-art performance on many image classification benchmarks {{cite:14ca11f6b65b09b093b56cdbcee76b7cd1cc9833}}.
We keep the original ViT architecture unchanged to retain its advantage of classification task on the closed set.
In addition,
an extra detection head is attached to the feature space {{formula:35c7d87d-8e83-4ecd-bfa9-517a47bb9b35}}
in order to perform the detection task.
The overall architecture of the proposed network is illustrated in Fig. REF .
The training procedure is divided into two stages for performing the classification and detection tasks respectively.
In the following, we present each training stage and explain how to use the trained model for OSR problem.
{{figure:0b7aa493-64c5-4eea-90a2-0728208525a1}} | m | 4ecb84633bfec6eb6cbb3d2bbc2794f9 |
where
{{formula:cde21442-f01d-4c78-8541-733c33339c95}} is
a multivariate array with coefficients
{{formula:b1781dfe-b45c-4f4f-9802-fd2e22084f50}} , and {{formula:5983d440-6a4d-4490-a561-8e9d6f0a643e}}
is the finite-dimensional representation of the
nonlinear operator {{formula:aa0cf2b4-bd6a-4bc7-8549-7d6944a4bad1}} .
The number of degrees of freedom associated
with the solution to the Cauchy problem (REF )
is {{formula:b57ba496-0945-46be-a29d-e48676a3f10c}} at each
time {{formula:6556df16-76c4-4839-aa0c-d920b2724ee1}} , which can
be extremely large even for
moderately small dimension {{formula:7fa78548-b1b9-49d8-bbda-b7ac70df7b1c}} . For instance,
the solution of the Boltzmann-BGK equation
on a six-dimensional ({{formula:dec6b628-3f07-4d87-98e9-32daf7adeea7}} ) flat torus {{cite:5d839765cf0937f87187f778f09eaa46471b0432}}, {{cite:6e735863f173de92c2138a624bfb0045ba2ff63b}}
with {{formula:fcaf0c64-288e-46b9-b9ef-1cc75e33a06b}} basis functions in each position and momentum variable
yields {{formula:88686c7c-f410-40b3-b412-a4bbb0bd04ef}} degrees
of freedom at each time {{formula:0d160536-487a-49b8-b5f4-8fdba86d40f0}} .
This requires approximately {{formula:954fcc97-220c-4229-b79a-deafbf993e0a}} Terabytes
per temporal snapshot if we store the solution
tensor {{formula:adb50ade-ddcc-45a5-a3e6-bbd8f5057b9e}} in a double precision
IEEE 754 floating point format.
Several general-purpose algorithms have been developed
to mitigate such an exponential growth of degrees of freedom,
the computational cost, and the memory requirements.
These algorithms include, e.g., sparse
collocation methods {{cite:1f7f474f9658ed70ec578b81cf0e84d4a32701d6}}, {{cite:1cbd5ac7b3100cd096db7d99259a8551aa3ab490}}, {{cite:00c28fb472514afe701b56657977bd7b953b9a83}}, {{cite:e6a85aceb964e944ee63cafac55c6942c632eeab}},
high-dimensional model representation (HDMR)
{{cite:fe71514df30408aeb768cf271b9cd654a575e563}}, {{cite:96f36ad1064dc0afe71d9bcb1df1d4048e23a354}}, {{cite:b9fd43c1a4670bf67988c8faee40ef315ce3d266}}, and techniques based on
deep neural networks {{cite:32e9790be60e7ccf8e1269ab47efada136c05bda}}, {{cite:9bf762cc10d3687676b53c62ac05858ba8a482a2}}, {{cite:b16462913dde07f5c0ab0d6360e73a830ee03121}}, {{cite:f9ae03d0c91450eaaf87de40dc01be54d9d7b34a}}.
| i | cd328e842d961e9804d9216ef11f47e3 |
We performed several experiments on the proposed CoFiB algorithm. We also compared it to some of the classical denoising algorithms. For performance comparison, the widely used peak signal to noise ratio (PSNR) and the structural similarity index (SSIM) performance metrics have been used. These methods are termed objective measures. Despite these measures being widely used, visual inspection (subjective measure) of the denoised image is needed to truly ascertain the performance of an image denoising algorithm {{cite:176bf9ae45027a905031877dbbe5c24dbb7dd767}}. We will show that in almost all cases, our proposed CoFiB algorithm performs subjectively (visually) better than most of the state-of-the-art denoising algorithms such as the K-SVD {{cite:8a0590807244c0e585e535038141a41dcb7a699d}}, NLM {{cite:87b26bebfdd8e10693e9e6994d894028e3be736a}}, and BM3D {{cite:dd54f6b0a23c34e84253ade08cdd65db36c2a1ce}}. However, using the objective metrics, some of the algorithms performed better in few cases. As such, an image denoising algorithm should be evaluated both subjectively and objectively to truly ascertain the performance of such algorithm.
| r | a99ca7bb53330326e6efd7148e695790 |
The Teacher module is required to refine, process and preserve previously learnt knowledge. However, the quality of the generated knowledge by the Teacher module degenerates when learning a large number of tasks. From Theorem 2 in Section , we know that the gap on risks (evaluated by the Student module) between the target distribution and the approximate distribution, generated by the Teacher module, depends on the discrepancy distance {{formula:27bb679e-2914-430d-ab17-fedf2dc7a5a1}} , from Definition 4. While GANs have very good generalization properties, they also have physical bounds in their information learning capacity. Therefore, the Teacher is not able to generate high-quality knowledge following the training with a long sequence of tasks. This problem is related to the mode collapse {{cite:8dbe95a18db07f67cf1cb8054a8e244035314a32}}, and catastrophic forgetting {{cite:489acce17e5e419b9eae0116a8cc1c55f98fdcd7}} in GANs, where the discriminator constraints the ability to generate data corresponding to a diversity of modes in the given data. Consequently, the Student module, learning from the Teacher, is only able to capture a limited number of modes of variation across all the given tasks.
| d | 0a056afb05014934041d06edd5601912 |
In addition, the real accretion flows are generically not spherically symmetric.
The hot accretion
flow in M87* and most
other galactic nuclei consist of a geometrically thick and quasi-spherical disk. It will be more interesting to investigate the shadow with a thick disk accretion. Recently, Ref.{{cite:bb86a29e112c02f54bc74c7dbd8c32674d108ea8}} has investigated the shadow with a thin and thick accretion. They reanalyzed the orbit of photon and redefined the photon ring and lensing ring, in which the lensing ring is the light ray that intersects the
plane of the disk twice and the photon ring is that intersects the plane
three or more times. They defined a total number
of orbits as {{formula:083d5b07-c7c9-4b09-9076-ae01d0acfe71}} . In this case, {{formula:d691375c-3ebc-41de-b1df-8d920031082f}} corresponds to the light ray
crossing the equatorial plane at least twice, {{formula:01644e08-6a1c-4698-b72b-5fd825452a13}} corresponds to the light ray crossing the
equatorial plane at least three times, and {{formula:bf0cef1d-76d5-411a-95bb-703a9f11a463}} corresponds to the light ray crossing the
equatorial plane only once. For the case of {{formula:ee95c164-dc6a-4da7-8e7c-8a4530bb7bad}} , the trajectory of the light ray is shown in Figure REF . Compared it with Figure REF , we see that the photon ring is around the photon sphere, and the lensing ring is around the photon ring. It will be interesting to investigate the shadow, photon ring, and lensing ring with a thin or thick disk in the four-dimensional Gauss-Bonnet black hole. We leave it as future work.
{{figure:8744556e-5ace-4e46-b440-40ac6fb0dc3b}} | d | f8db354684f35316b0c03a3f2bf8444f |
We can apply any primal-dual algorithm from the literature {{cite:b2b05de47c7dd77af959cd074111fd890ce88c11}}, {{cite:874f407c09dabc68a6835cb1df1f8f87bff9cbde}}, {{cite:4a1baf7825a6355bcb4560d88130b74de05393ff}}, {{cite:24761ba294739737037d071713da6eff4af9d802}}, {{cite:0dab3127422655f5d00dd0d049a71fdb34dc6d64}}, {{cite:3650b94f731da0c11e7f8d65e827e71871338095}} to solve (REF ).
Here, we describe the Chambolle-Pock's primal-dual method {{cite:874f407c09dabc68a6835cb1df1f8f87bff9cbde}} to solve (REF ).
| m | ed0344a8141a75461e26cc148f50732e |
Characterising the Adaptive Adversarial Robustness.
In more strict adversarial security setting {{cite:fd150c4ea70648ff5998ba26cd1a05ac388f2096}}, an attacker could observe the input {{formula:00e13f16-30b7-46f1-bdff-c6b207b6f5ce}} and output {{formula:87879bee-89a2-479d-84d4-f23d2b813ed8}} of both speech enhancement and ASR systemIn our case, the system is equal to pre-processing U-Net{{formula:20a4fd21-0428-48ab-9ed9-ac924063e82b}} model and Deep Speech ASR for adaptive adversarial attack as {{cite:fd150c4ea70648ff5998ba26cd1a05ac388f2096}}, to craft a two-step adversarial examples in an existence of defense model. When this theoretical adaptive attack exist, we aim to enlarge the cost of attack in terms of additive noise (dB) injected into the clean speech example to access a targeted attack successful rate (TASR.) In Fig. 3, the results show that an attacker need to give additive noise from 7.63 dB (w/o enhancement) to -2.23 dB (w/ U-Net{{formula:c2ea1ef0-0005-4dd5-a071-d1bc91513a24}} ) for the Grad{{formula:39a76dcc-a01f-415c-9114-9ff1034d810f}} and 7.82 dB (w/o enhancement) -3.21 dB (w/ U-Net{{formula:c56d9b46-2e84-42bf-99de-fababc78916e}} ) on the Evo{{formula:c2b253d0-4113-44dc-a967-31b434462761}} on the Deep Speech-based ASR system to attain 100% TASR, which increase the empirical difficulty for attackers to manipulate an attack without notice in the real world and improve the adversarial robustness of ASR system.
| d | 0d8d63e0903b6c49d526363f27f60cc5 |
VAP calculations can be performed by changing the {{formula:0257bf15-01e8-44d1-a7a9-d2b0d57e4ab4}} matrix in Eq.(REF ). Here, we impose the following restrictions for the {{formula:bfcf1fad-f955-4877-b9a0-89e8cd397d97}} matrix: (1) {{formula:c2fc4dff-2c00-4406-a6f9-1210acbcf91b}} is real, (2) keeping the time reversal symmetry, and (3) no mixing between neutron and proton in the HFB transformation. Therefore the total number of free VAP parameters for {{formula:912b71a5-ff22-46f0-85b9-2ecbae3f8f86}} -shell is reduced to {{formula:f9ec60c3-8f47-4c2c-93ac-7e035fe6a7fc}} . In practice we start with {{formula:51c9b96f-12bf-4db9-a1dc-b4ef88ef453e}} and with Nilsson+BCS vacuum states
{{formula:80ef4aa3-87be-4c55-849c-00e3d97d0fd1}} obtained with randomly chosen quadrupole parameters {{cite:4d322e56c05a9ffca40eab16ef22e18f6199db80}}.
| m | 8f40c640a2774421a5e888132021e724 |
Among several consequences of Theorem REF to broad fields of mathematics, we only mention the discrete restriction for paraboloid or the Strichartz estimate on torus which was initiated by Bourgain {{cite:53d59307c13b7377637db33346441b83ecfce291}}, see also works by Burq–Gérard–Tzvetkov {{cite:0710c2924818426ea3d92bd0e6941687d32c27d0}}, Guo–Oh–Wang {{cite:b2c1a0faa954d55e1a2a94baff805c95ed2f00f4}} and Vega {{cite:68c0f216346250cf3a4f85c96db502fd9277ce26}}.
We refer the reader to the survey paper {{cite:7c41cddfe94da19cdbfd4a410178129b81a57a9e}} for other consequences to analytic number theory and comprehensive introduction to the theory, see also {{cite:98cac0d0511f5678787c4de29a707800feae0582}}, {{cite:1f9711e42fcfd195b15b13a757f4891896ba8680}}, {{cite:c0415668951598779563322387a15d5e4a3086f5}}.
| i | 16cbefa0d3abfbbae5923982cea7422a |
Once relevant attributes are identified, to explain a query {{formula:fdeb28b4-c5d0-44db-8f7d-55a7a2c1af60}} with latent {{formula:ce0d6659-95f8-43ce-91cf-ed2af7194b26}} such that {{formula:f55f3d7d-27d6-414a-83f5-82740b1353e4}} along attribute {{formula:a0e17589-05cd-4b2b-83f4-273c1df14f66}} , a set of {{formula:2d89e59b-dce0-4dba-8b30-e8ff2a5b47bd}} local images {{formula:ccd82921-7b3b-46bf-9958-fd9430888f8b}} is created, {{formula:a655974f-716b-4350-b0f7-b2d90cafdfc6}} from latents {{formula:d8ebc177-541d-463e-9ac6-f3153cf3d573}} where {{formula:86596254-6c7d-4da0-b38a-e02a06e02c6b}} and {{formula:88cd34da-63dc-4ba1-b46f-97b182868c35}} varies linearly in [A, B] and {{formula:093e52ad-c64b-4d34-b598-cb0093c7d786}} is the aforementioned attribute vector. In Figure.REF , attribute {{formula:f3a3a096-d6b1-4f08-b46a-09bd76f2106d}} corresponds to (reddish) inflammatory regions and set {{formula:249288f6-8bcf-4c15-8625-09f46044e7e4}} can be understood as images with decrease in severity of such inflammation as {{formula:397d8437-f10b-49e8-be5a-a26c982a8585}} progresses from {{formula:82abfdea-8373-47f7-b6b8-dd701c706540}} to {{formula:18f600ea-2465-4a2f-8a78-b209f77a5060}} . {{formula:8e239b33-3242-46af-9859-bbbc28cd8443}} in {{formula:38660725-63cf-4eb4-8418-a38a9ab4ede6}} are retrieved based on the classifier output for {{formula:7e5876c5-b950-43f7-b577-453173825b2d}} such that {{formula:afd2a406-a04f-4f7f-a639-41ae1e9890f7}} and {{formula:cd8a4c90-c168-4ecf-921d-fc767727c825}} where {{formula:5232cab5-ec34-456a-95f0-a80d88a91ec1}} is the softmax function. For the saliency map, to avoid the spuriousness observed in previous literature, we use the latent space to curate a neighborhood such that every image in the neighborhood of a query varies only along the chosen attribute. In other words, the pixel changes that occur in this neighborhood are neither uniform nor content blind {{cite:a0206cee55fdac9604c04fbacdb8ab3c5d0347b5}}, {{cite:1f8a6567659340d7af2d700ef3321ba4f5a1196a}}, but targeted towards those pixels that most strongly affect the attribute/biomarker. We use directional derivatives in {{formula:45e1908d-9589-4b70-9cdd-570b54c70b13}} along attribute {{formula:179e7908-d75e-4042-ad26-85d5a01bfe7c}} for identifying these regions and weight them based on semantic similarity with {{formula:08742f60-c4b2-49cc-9d69-b5f7d211e446}} to generate the saliency map. The directional derivative {{formula:9476348a-8c9f-40a1-bb49-90cd61f96670}} between the query and {{formula:b3b9a569-ebb6-4891-afe0-a71d2cd35ba5}} is given by:
{{formula:d94610a2-9ce6-4bf3-972b-1974a38f0b25}}
| m | fe0dce63494bdba261d855f3d09c0abe |
Recall that def:discrparamellipticproblem is a Ritz-Galerkin approach with the particular case of a FE space {{formula:bef1a8e9-9e6c-4963-ac0a-9be2401e97c9}} (which then makes it a finite element method).
In other words, Equation (REF ) is a Ritz-Galerkin projection of the infinite-dimensional formulation of Equation (REF ), meaning that the test space for test functions {{formula:e1de5d20-ac02-4d9c-a6a3-6a6f1886b211}} is given by {{formula:5cb42f31-28e4-4db4-8db7-e27e254a2060}} and the ansatz space for the solutions {{formula:ef58b059-536e-4e37-a3e7-ce56ea604922}} is the same.
Choices where test- and ansatz spaces are not equal are called Petrov–Galerkin approaches and can have advantages in terms of storage consumptions and approximability; cf. sec:TRRBpgapproach and sec:PG–LOD.
Petrov–Galerkin formulations are also often used for stabilizing purposes, e.g., for transport-dominated problems {{cite:06411e2aa82f7b774fd4bb05e471a194a97ebfa9}}.
We also refer to {{cite:611c1c3fdd8e8861b5b3fc3ac139db2d18c6b8be}}, {{cite:e66a2ca8f4823b07e741ff654364a9c8a945329e}} and the references therein.
Apart from these works, we note that Petrov–Galerkin formulations have become very helpful in various applications, two of which will further be discussed in sec:TRRBpgapproach and sec:LOD.
| m | a8945647d041dcb5e9fa2ee37c354c14 |
The question we want to answer in this paper is whether the introduction of additional vector-like lepton EW doublets, discussed in Refs. {{cite:74cadd0d36794f1eadf78f86f97c05f59f5c1229}}, {{cite:70d2c80caf08df4d81d9c692f9d97c92082030ad}}, {{cite:de460f9bc3487494c111e3c5249780a3fab6d643}}, {{cite:047f6c3a61ae7d42c1c365ec4e1a340e75c2090b}}, {{cite:20e80c8ee73a6645af09bed282dcd1a25ac98e98}}, in the Low-Scale SS setups may consistently explain the light active neutrino masses, the CDF II tension in {{formula:c7ec978f-8a51-4817-aee8-2302750f44f4}} , and the {{formula:b054b053-2afe-4f4f-a7c8-5676a9761e02}} anomaly. This construction would then represent a minimal setup where all the additional fields with respect to the SM spectrum are strictly necessary.
| i | dc9abb9efaf26c4b16e8f3263becc395 |
In our model, we also do not take into account dust sedimentation,
migration, growth and destruction, which play a critical role in
protoplanetary disks. Taking this processes into account can
significantly modify or even completely suppress the instability of the
disk associated with the effects of self-shadowing. We also note that the
mere presence of dust leads to its own instabilities, such as streaming
instability {{cite:ef15df9f360ecad7993b748ab6a83a2dc675fe56}}. Streaming instability now
becomes very popular for explaining turbulence and formation of planetary
embryos. The study of these processes is a separate direction for which
complex dynamical models are developed. In this work, we do not consider
all these processes, postponing the study of their interaction with the
irradiation instability for the future.
| d | 402f15f5dd4e0326b6b256a2f4f9fdb0 |
The proposed method achieves the best overall segmentation performance among the listed methods. In terms of DSC, {{cite:6c8d6b82beab8301d56d2fbd549d412e4ffc48b9}}'s method outperform the other methods with a value of {{formula:fadfac21-716a-4037-920d-033640c868fd}} . And {{cite:75d663aadd054776d419abc89f9412e094fcce5e}} achieves the best ASD results with a value of {{formula:c0682d89-01ae-4dc4-b086-ad350a74afcb}} . Compared with these method, our method obtains more than {{formula:0ea49541-7096-404d-a5c0-1fa228e6f6fc}} improvement in DSC, from {{formula:7c5ce07c-69f5-4801-8bf0-2b81d33e5d18}} to {{formula:42a70c94-56c4-4877-8e73-c7b9c9f99ae6}} ; and {{formula:c6d50161-bbe3-4908-95aa-96fca062a1a0}} improvement in ASD, from {{formula:8b32cb29-5e82-4e7e-95fd-b48fd9f3391d}} to {{formula:f641cbeb-47bd-47bd-9211-eac5e6ae8cb0}} , which is a {{formula:0a700f62-89a4-4a67-a233-1a7c773f9c43}} decreasing on the ASD value. The significant improvement on ASD indicates the effectiveness of the proposed method in delineating the organ contours, which is more valuable in clinical condition. Moreover, the proposed MetricUNet-HCP achieves {{formula:280a8847-f789-402f-9ce8-bb26dbe1b825}} and {{formula:863d273a-9f62-4fd3-8a54-d3e8941e15b9}} in mean SEN and PPV, respectively, which is better than the deformable model-based method in {{cite:97df9eac152e3b8d322fd34f5709883634727b22}} and the deep learning-based method in {{cite:6c8d6b82beab8301d56d2fbd549d412e4ffc48b9}}, {{cite:75d663aadd054776d419abc89f9412e094fcce5e}}.
By performing pair-wise t-test on the proposed method and the method in {{cite:75d663aadd054776d419abc89f9412e094fcce5e}}, the p-value indicates that the proposed method is significantly better than {{cite:75d663aadd054776d419abc89f9412e094fcce5e}}'s method in most metrics, i.e., DSC, SEN, ASD, and HD95. The tiny difference of the SEN and PPV value of the proposed method means that our proposed network is very robust at generating high quality segmentation, compared with the other methods. The robustness is also a key characteristic in clinical applications, where poor segmentation of the organ will lead to side effects. The conventional deep learning-based method in the second set of rows is not as good as the deformable models in the first set of rows. For example, VNet {{cite:c08e14abf9bde198e30c06e42a6ebf05c9f477b5}} achieves {{formula:1c6c1960-1276-435c-9bc2-b09c01b0cbea}} in DSC and {{formula:562d9a27-1d8e-4d54-86ce-3fe9b122bb42}} in ASD, which is lower than the method in {{cite:97df9eac152e3b8d322fd34f5709883634727b22}}. This is because they were not specifically designed for the segmentation of prostate in CT images, which reveals the importance of incorporating domain knowledge and preserving the neighborhood information in the final segmentation map.
| m | 48e02ab5e0d3fe6cfa440311c528bf0d |
ML research is often perceived as value-neutral, and emphasis is placed on positive applications or potential. This fits into a historical strain of thinking which has tended to frame technology as "neutral", based on the notion that new technologies can be unpredictably applied for both beneficial and harmful purposes {{cite:186d7f133dc15ceea18c9bd05f8b3d1d188efb01}}. Ironically, this claim of neutrality frequently serves as an insulation from critiques of AI and as a permission to emphasize the benefits of AI {{cite:ed79b5fc2357a12ed695f432b134f7728fa6a42f}}, {{cite:562c2f5b626f301c375020fc83ee6c4cfc34c493}}. Although it is rare to see anyone explicitly argue in print that ML is neutral, related ideas are part of contemporary conversation, including these canonical claims: long term impacts are too difficult to predict; sociological impacts are outside the expertise or purview of ML researchers {{cite:8fa29e71227b9e0be5b006ee067c592ffcee5a47}}; critiques of AI are really misdirected critiques of those deploying AI with bad data ("garbage in, garbage out"), again outside the purview of many AI researchers; and proposals such as broader impact statements represent merely a "bureaucratic constraint" {{cite:a05f2056d83baabf64420ee423a2d7d946b2cc74}}. A recent qualitative analysis of required broader impact statements from NeurIPS 2020 similarly observed that these statements leaned towards positive consequences (often mentioning negative consequences only briefly and in some cases not at all), emphasized uncertainty about how a technology might be used, or simply omitted any discussion of societal consequences altogether {{cite:64f21d242a89f5e71988d62fd60b746973b495ba}}.
| d | 7a8fda22c1404a698cf45a3053ec435b |
Most methods simply seek to reconstruct SR images with high PSNR and SSIM. However, the improvement in reconstruction accuracy is not always accompanied by an improvement in visual quality. Blau et al. {{cite:5dc7b7c6ac90360819d0114de6d64ca2612071ad}} pointed out that there was a perception-distortion trade-off. It is only possible to improve either perceptual quality or distortion, while improving one must be at the expense of the other. Hence, in this section, we provide methods to ease this trade-off problem, hoping to provide less distortion while maintaining good perceptual quality of the image.
| m | 97ae6376382a30bba9c2d2a14ca5e1a7 |
In this section, we first introduce the experiment setup and introduce how we form novel benchmarks by adapting conventional CL datasets for the CLPU problem. Then we introduce the evaluation metrics designed for measuring the agent's performance in terms of both continual learning and private unlearning. In the end, we present the evaluation results by comparing CLPU-DER++ against the following baseline methods: sequential learning (Seq), indepdent learning (Ind), Elastic Weight Consolidation (EWC) {{cite:063cd68c781afd682910073156ca622dcb74f51e}}, Learning without Forgetting (LwF) {{cite:4d35d718b2effd98bd5d2b8921862e88a20881d2}} , Experience Replay (ER) {{cite:bb8fce6c7054150856b28c33e7d82a6a8b879106}}, Dark Experience Replay++ (DER++) {{cite:7fd091b556b7b20edcf4866225fb3f0d8ad85f34}}, and Learning with Selective Forgetting (LSF) {{cite:010b75cf89435ffa1b40c38af6172bd940ea770f}}. All the above baselines except LSF are state-of-the-art CL methods, but we adapt some of them for the CLPU setting. In particular, for sequential learning, the agent performs SGD directly over the sequence of tasks. For independent learning, the agent creates a new model for each new task, and removes a model if the user requests to unlearn the corresponding task. For ER and DER++, for an unlearning task, we remove the corresponding episodic memory and let the agent perform normal ER and DER++ updates on the remaining episodic memories to accelerate forgetting.
| r | bd2ca167c04a1d128e2754a6576e50f6 |
Since all variables are real, we make use of the following integral{{cite:4838d941c661f98626e6699c5c0457753616100a}}
{{formula:f9d8f882-8fb2-4303-8973-58ce7001770f}}
| m | 7699364c295fba5cbcdbcae4e45d7ecd |
Bregman divergences and Pythagorean theorems for them are studied in information geometry {{cite:afa80b284b491a69d9dac6dc10ed245cdf9e09d7}}, {{cite:48e87548062cc849fb36cd22746eb77fc14d63ca}}, although the term is broadly used for inequalities arising from projections onto convex bodies. That a stronger guarantee than omniprediction holds true for the squared loss was observed in the work of {{cite:ab9c64b6d05face3af55de73f1aed471a84c3be9}}. This guarantee was subsequently shown to hold even with degree-2 multicalibration {{cite:fb260156a864de7cb1e2e2d7aa1e2c7b324a982b}}. Our results generalize this to all GLM losses, and only assumes calibrated multiaccuracy, while also showing that for such losses, Pythagorean theorems are equivalent to loss OI.
| d | 4b5f3999d5c632a05e0b595985196416 |
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