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(3)
The relative phase {{formula:24266009-72f8-4b97-bc33-e3b192b777af}} is very small.
This is consistent with prediction of the QCD factorization
approach {{cite:b2510f2b86bf73e5938942b21c04aa7fcc9ad1e3}}, {{cite:58a3af597412c1bf9be7cd88e9aa83586c7c9084}}, where the strong phase arising
from nonfactorizable contributions is suppressed by color
and {{formula:79cfb7c2-8427-4d7a-8b69-a3d9278cc21d}} for the {{formula:4d9cbae8-a552-4fe0-a70b-1a23e42a77d7}} -dominated processes.
The relative phases, if they could be determined experimentally,
will improve our understanding on nonfactorizable contributions,
factorization mechanism, and the strong dynamics at different
energy scales.
{{figure:b7c82bd1-ec6c-4477-a6e2-7bab629925a2}} | r | 9e825ab1b9ead4cc6ed1ef8283759a2f |
First, our algorithm alternates between computing decision rules that are compatible with a tree in Step REF , and updating the value function accordingly in Step REF . Given the value function {{formula:78568c41-7a50-43f1-9dc6-b27fce2b57d6}} , (REF ) is equivalent to an Optimal Tree Policy instance with {{formula:ab7be9d1-93d6-420b-9493-12baa348d514}} . From the equivalence of (REF ) and (REF ) (Proposition REF ), (REF ) can be solved with either exact methods {{cite:13c9fb595216493eddc28f542f09b9e1ea7b2dc1}} or heuristics {{cite:40f87004f7fa345b228ad18a15c7fd9c68ea81d0}}.
| d | 68d6b31214b7709c4c2fa8c02b7123e8 |
In all these and related considerations, a possible first-order chiral phase transition, and the quest for a corresponding critical end point in the QCD phase diagram, have always been themes of prime interest {{cite:91770ba72e5fcb3b90c66d03570193a28a41b956}}, {{cite:8f059f6c3a1ff5ac3b17e5ae2e190c684d75b683}}, {{cite:461873a91a8c6443b2a4c3150173e5175e2b1776}}, {{cite:9d6b4bf08dc96e6610dcb71539f473f3dc093bfa}}. As mentioned, lattice QCD with its limitation to small chemical potentials cannot fundamentally clarify these issues, and there is so far no empirical evidence for a critical end point. Earlier hypotheses for the existence of such a first-order phase transition were primarily based on mean-field (MF) calculations using Nambu & Jona-Lasinio (NJL) type models {{cite:ad55870473e2dfc7b9b826c4fdd002102fe757f1}}, {{cite:7d9728b6bf0d71bcd9aa004425c63e2b8a29d156}}, {{cite:dd2d985316290a05037cd75afba2838d1aecb824}}, often extended by adding some confinement aspects through the Polyakov loop (PNJL) {{cite:50f03570ced660d2edaa6b90819980a71dc5a0d5}}, {{cite:2cca910b2f99d02437dfcca7290b71049612784a}}, {{cite:4a43b1ef149a18ef6c26510424623a1632c8ce04}}. NJL and PNJL model studies {{cite:fbf55d71ec24711197be9e6e8f107232d63a6881}}, {{cite:288b7d0d33b1a46b5fc12a0753eec09141da1bc5}}, {{cite:f7b0fa3a7318b1cbbac29579447ef9ae64d7e050}}, {{cite:57131f6167217fc412926128af5d99e2f1f7476b}} already indicated that the existence and properties of the chiral phase transition are highly sensitive to variations in the strengths of vector couplings and of the axial {{formula:daf248be-a603-4a2e-8988-4eb3b0d98fda}} breaking interaction. Furthermore, results of alternative chiral models {{cite:ab606926ffaf95bbd098103486a3ac0b54a3931b}}, {{cite:f8761c9924a646876fe62122b83050c7f0abba0b}}, {{cite:34b7e6a1ae99cf6a921f00f6e6ed8b617e616006}}, {{cite:cea249ff248a543d018e6d013206569cdf52d4bd}}, {{cite:cbfc915190a293c49c188ffb1945de5075e754d4}}, {{cite:a815bcb677852a8c655f6b6b64d1650fa092d413}} pointed out that the chiral phase transition and thermodynamics at low temperature are strongly influenced by the treatment of fluctuations beyond MF.
| i | 9696a2161261a8a9994730881f2ba644 |
The proposed model is a scalable auto-encoder that uses vision transformers in its encoder and decoder parts, as illustrated in Fig REF . The degraded image is first divided into patches before entering to the encoder part. During encoding, the patches are mapped to a latent representation of tokens, where each token is associated with a degraded patch. Then, the tokens are passed to the decoder that outputs the enhanced version of patches. Unlike the CNN based auto-encoders, which were usually employed for the document image enhancement tasks, the transformer auto-encoder is profiting from the self attention mechanism which gives a global information during every patch enhancement. Both decoder and especially encoder are inspired from the vision transformer (ViT) {{cite:33751e7b0642e72681c4f916d0c7a01aaec64820}} architecture. We present more details of the model's architecture in what follows.
| m | ef25a2e950602325ad61bb3e29a3e2fc |
Then, following the classical text of Federer {{cite:b5f71dfe6cf80504050053ca7b6adc693c6feff3}}, the {{formula:858c6af5-2025-4997-b024-2d9b2db17d0e}} -dimensional upper and lower Minkowski content of {{formula:c7753f31-3230-4bf7-a49e-e35770e23b21}} are defined, respectively as
{{formula:bcad26ad-ae2f-4ef7-a5ac-8edb9590fc49}}
| r | 70e4fc5da6c69d56334bb8d759e9c2cb |
The presence of Dark Matter (DM) and its role in the formation of large scale structures of the universe {{cite:f31224bcf47b99a984960b49241e036988876898}} altogether with the observation of neutrino oscillations {{cite:a64067771e966f6a80b13ec95f3ff483469d9fd6}}, {{cite:2f3d867920fa399f232d33396c02b48469ac0476}}, {{cite:376ace21b443f99b92aefac82e2aab69f59bfbd1}}, {{cite:ec2a16b5075939c115d1e15477f76be5962679a2}}, {{cite:33dce481e2e20bd8fe01affbbc0abc46b5af821f}}, {{cite:9f2eb2429a4f36b1a713a10b609249867a2ab10b}} are some of the strongest indications that the Standard Model (SM) of particle physics lacks essential ingredients. Indeed, the SM provides a successful description of the microscopic interactions with a remarkable accuracy. However, neutrinos, which are precisely massless within the SM, should possess non-vanishing masses in order to explain successfully the observed oscillation patterns. In addition, the SM do not include a viable dark matter candidate among its large particle content. Both topics have became the ground base motivation for a large variety of the Beyond-the-Standard-Model (BSM) constructions.
| i | e4d74aadf7be50c7df5e90cae7f78382 |
Most of the research efforts in the space of detecting hateful content focus on designing and training machine learning models that are specifically tailored towards detecting specific instances of hateful content (e.g., hate speech on text or particular cases of hateful imagery).
Some examples of such efforts include Google's Perspective API {{cite:3d02f5cdd7003924b913df3b4f8d961a33b61787}} and the HateSonar classifier {{cite:161705d0a9787bf675ca844606c77306eb314b92}} that aim to detect toxic and offensive text.
Other methods aim to detect instances of hateful imagery like Antisemitic images {{cite:83f9b3f2d890e2fafb186464a08970ee8be2c763}} or hateful memes {{cite:f5e189e578cf89924aed5b8aa992bbb09672be9a}}, {{cite:a94929d07c57be5dda05193d1d0590cc15a08904}}. These efforts and tools are essential and valuable, however, they rely on human-annotated datasets that are expensive to create, and therefore they are also small.
At the same time, these datasets focus on specific modalities (i.e., text or images in isolation).
All these drawbacks limit their broad applicability.
| i | 8aeddb2fb67fe1163d9b8f78f01cc19d |
Turning now into the issues in kinetics, the {{formula:7789ca1f-d88d-44a4-8ebb-8ae40f0b8e3a}} phase transformation in zirconium base alloys comprise the process of nucleation and growth. For instance, on heating from {{formula:4e0a1287-4514-4dcc-aee5-4e731e9949b2}} phase, the transformation involves {{formula:9ab0fb2d-c38f-47e2-ac69-985112f815ba}} -nucleation, {{formula:2c86e609-1ebf-4400-babd-bf8897b14692}} -growth and {{formula:583b6b51-a55c-45ab-af94-b5755ac530f9}} -completion and vice versa; i.e. {{formula:e54ca3a9-d70b-406d-aca1-1d3208c173d6}} -nucleation, {{formula:0e8536e2-4049-4a2a-ab1d-0e314215a4e3}} -growth and {{formula:ad189c7e-fb9a-4be3-a8e3-dc99d492fbdf}} -completion. A commonly used macroscopic model for this process is the Kolmogorov-Johnson-Mehl-Avrami {{cite:2fe3c1fdb372688b67ad923252e40e159b2dec24}}, {{cite:85026df3f5021c11218f407fe2c38d41541d0417}}, {{cite:d9b73ea43da4daa1eb607cbf364f331ef313cf0f}}, {{cite:b7586a79ff65109ae48767d39f523a4786645db2}} or KJMA description {{cite:d7575af5bafeff6b603acdc4a908e7f5e5e72c3a}}, {{cite:f7e4852e9a469d5425ba8fd2e4fbbfeb8082b7a7}}. The KJMA model assumes that tiny spherical grains nucleate at a constant rate per unit volume in the metastable phase and grow isotropically at constant velocity once formed. As first formulated by Kolmogorov {{cite:2fe3c1fdb372688b67ad923252e40e159b2dec24}}, the volume fraction of the favored phase at time {{formula:7082bbf7-bbc6-4cfd-beb2-e1cf12e2f61b}} can be expressed as
{{formula:273e1210-ae07-45f3-b7cc-87f858ba12c2}}
| d | 76e80736853920b610a8c29072461f75 |
At relatively low Reynolds numbers, {{formula:4ceee466-73aa-4e32-8a58-75791e964fad}} to {{formula:2a1b4bff-4863-4c07-a5a8-59214acb1b95}} , near-wall streaks are the statistically dominant turbulent structures close to the wall and follow inner scaling {{cite:5f365dba1a2b61224af229c9614e4d794c98171d}}, {{cite:c98091a7a8727f85cf60233644bb0532595d7a09}}. That is, their features scale with velocity {{formula:d5237a47-c12e-44b4-86fb-293fd7e5fe37}} and length {{formula:618b02fd-5691-4595-93b3-892ec229cf2b}} . The predominant time-scale of the near-wall streaks is found to be {{formula:b34d8cf2-3a23-452b-8349-445fc567d88c}} and their characteristic streamwise and spanwise lengths are {{formula:276972cb-9e0e-4e4a-9ced-b3bb85d3117c}} and {{formula:08d9dfa0-5217-426e-871f-81abc33d8b7e}} , respectively. Flow control schemes that are implemented at the wall often prescribe a forcing of similar time and/or length scales to couple with these features and achieve the best result {{cite:57dfdacfe791b090416f7ae1dc83bdbde497a6af}}, {{cite:810dd20d9e06753ba362f9808a171c765ba521bf}}, {{cite:bc410b8f83408161fe7cc7a317545f8b2d93de70}}, {{cite:a6a90ddbb0e87e7e84f98704968ddff6b83e3eb5}}, {{cite:b4d0197332759d855b89de89d96ef39a53b86872}}, {{cite:5f40a3bcc6a67002afefea9a426d0ada58f2f0dd}}, {{cite:8554abb2f9935f9c4c00bfc7b2146065a7a6ed58}}.
| i | b015f236f6c33fbf131c13aab0eab7c1 |
This differential equation is well-known as the confluent Heun equation {{cite:412958927714e90e4c9e37438fb784494b858a68}}.
The relation between the master equation (REF ) and the confluent Heun equation was discussed in great detail in {{cite:1f3fe9e5fbd1871cbc2bd12a4d07ba2051d47932}}.
We construct formal series solutions at {{formula:a3094379-5032-4795-983f-45fbed1af91e}} (event horizon) and {{formula:7bad9203-1aa7-42c4-a5a8-6068fffc207b}} (spacial infinity).
The local solutions at {{formula:4ec5d974-7a64-4332-a6a7-60c4b4de28b1}} can be expressed by the local confluent Heun solution in {{cite:412958927714e90e4c9e37438fb784494b858a68}}, but we rather construct the series solutions directly for extensions to other cases.
| m | 2d0ad10dc513bc3d3e30f1e60860b093 |
Bayesian Optimization is a state-of-the-art framework that had successful implementations in machine-learning, engineering, and science {{cite:dd40c78549f93f365cd24f4575fd266d26c22b62}}. In short, the BO algorithm contains two different functionalities. The first functionality is a function approximator that tries to model the fitness as a function of the search space parameters (in our case the weights of the CPG network). In theory, this approximator can be any type of function, but in BO Gaussian Processes ({{formula:306ec413-46ba-42da-b646-e82fe5f473fd}} ) are used for their sample efficiency. The second functionality is an acquisition function that selects the next sample in the search space. The acquisition function chooses between samples that show high potential in fitness by the {{formula:54aa9391-a984-4057-b241-259fa6518257}} (exploitation), or that show a high degree of uncertainty by the {{formula:6738083e-08ad-40ec-9790-1e58b3f6f832}} (exploration).
| m | a02f2cfff90fb70667fb7a9b05dcc10c |
We propose the taxonomy depicted in Fig. (REF ).
The first distinguishing property is that
the models can be divided into two types: the ones based on processes or interactions within a city and the ones based on processes between cities.
In the former, intra-city type, most models consider that urban scaling emerges from human interactions, i.e. intentionally or accidentally meeting people, in the considered city.
E.g. the model proposed by Bettencourt {{cite:41ac8597244f474e81bcc8c4de7c03c6687d9125}} employs an analogy to the cross-section as known from physics.
Other authors propose other mechanisms based on required human interactions within cities, and we identify a set of models employing gravity ideas.
To the other branch, the intra-city type, we count three papers that elaborate on very different ideas.
E.g. the work by Ribeiro et al. {{cite:8de5a20c67713794255147fd8d0e19537eb03afb}} argues in favour of a link between urban scaling and city size distribution.
| d | 239664411fca829cbc5c2a9851ab3665 |
To end, we give a comment on the correlation length of {{formula:08d166b7-daf9-4167-83d8-7e8382d31319}} in the original Affleck-Dine baryogenesis scenario, where the Affleck-Dine field gets a negative mass from the inflationary field {{cite:b3b128fe58a652875be79a6a72a15f057bbe3e63}}. In this case, {{formula:2cddcf63-e1ca-4500-a7d4-b9cbfac2471c}} is trapped at a much larger value {{formula:7f86d1c3-18cf-481c-b4b7-bfe2a653a6e0}} . Thus, the quantum jump is just {{formula:d4608021-2cb4-444f-8ddf-57b78bb2d296}} which is much smaller than the {{formula:33faef5f-2c3a-4d8a-9994-5bcfda96e2b2}} . In this case, the correlation length of {{formula:0829406e-f3d0-4848-9b57-d56a55155592}} indeed could be much larger than our current horizon size.
| d | c37f403c4b3f6c71322be0d15e711eec |
Camera calibration is the estimation of a camera's mapping function between a set of known world points and their measured image coordinates. The parameters that define this mapping are usually divided into two categories: intrinsic and extrinsic parameters. The intrinsic parameters represent the internal characteristics of the image lens and sensors, while the extrinsic parameters model the relative position and orientation of the camera to the 3D world {{cite:70027b80bc4eccb8d8fe32439266ebf6b368186f}}.
| i | 01efea6165d2e5e7bc7cca40d1b0b7b9 |
{{formula:8d4ad816-835e-4b75-ad59-4f3adab98bb3}} By Proposition REF , since GCD-domains are integrally closed ({{cite:75c6b8a212bac578ce0eb1c7576221682b77478c}}, Theorem 50, p. 33), {{formula:f22915d0-2ec3-4974-b9ef-15e5c6cc2669}} is the quotient field of {{formula:5e190306-d299-4559-a29f-762c5eff29c4}} and {{formula:4f8fe7b8-7eba-4e2e-944a-df75a7b346fb}} is a valuation domain.
Moreover, {{formula:0815abc9-d8a6-490b-9dc2-be20fbef3a8d}} , being a localization of {{formula:453c82b4-7a79-4e1a-8dcd-b1c6b26efd1b}} , is a GCD-domain, and {{formula:24b7fe90-2a81-47cb-bfab-bddfb17da287}} , being a retract of
{{formula:a7ad15c2-7fbb-4ebe-9643-c251256c7173}} , is also a GCD-domain.
| r | e2de4859bff7b17820b65b3bacb9f5c5 |
To reduce the annotation burden on doctors, many methods have been proposed for medical image segmentation applications. Considering that unlabeled data is usually abundant and easily available, many researchers focused on implementing segmentation tasks in a semi-supervised learning fashion. The main idea of semi-supervised segmentation is to learn from a limited amount of labeled data and a large amount of unlabeled data to improve the accuracy of segmentation. According to the training manner, common semi-supervised segmentation methods can be divided into self-training {{cite:bf7580846e6b066073b128d59de04d2c2ddb1bce}}, consistency regularization {{cite:a3f28bfa72037fcefed3e3096d00423ba2852d91}}, co-training {{cite:6cf0be2882fd773f53fe1da256cd8b815547f045}} and adversarial training {{cite:6f9976e50dab5b120afe083a040f6abcc764acd0}}.
| i | da74be1eefcb97ddb1975037651adbc5 |
To solve the optimization problem (REF ) with the inequality constraint (REF ), we employ a quadratic penalty method {{cite:d01bd7012239650bf7d2c42eca0514a3f3b4775e}} by first defining
the exterior penalty function
{{formula:e2e988df-9aff-4f97-9653-7f9f28778918}}
| m | 7a4d23847cb3290a0c42933ae7d2abe7 |
Proof:
Since {{formula:27d051d2-80ec-4ddb-8cd1-4782eb4511a0}} , and {{formula:9ee3d25f-259d-4a6f-9b6a-ead24c9c321c}} is {{formula:58daff35-fdef-4419-9d7c-60098918a5ee}} -Lipschitz continuous, by {{cite:af71780380b6ded23af5793de0224d54187fa26e}}[Lemma 3.2], {{cite:f3ee84ab6aaa61d596af6172c8b22ba43ad9040f}}[Proposition 4.25] and Assumption REF , we have {{formula:a0ed3549-6906-449c-9934-84833d407d9e}} satisfies Assumption REF (1) when setting {{formula:7664c2a3-07b2-48ca-af43-7ca7f14d0c9e}} as {{formula:7a56694d-db53-4dc3-a301-617176636174}} for any {{formula:56175f89-bb0d-4103-9835-c1e7a550be7a}} , with {{formula:d0306e98-0a8d-4fd8-9411-b7902eab08bc}} . The closedness of {{formula:259ff354-44ed-4ea6-8a69-1212b53c2ead}} follows from the outer-semicontinuity of {{formula:50437ec0-2a25-48bd-90e8-d021d830333b}} and continuity of {{formula:d33a9fda-40a7-40a4-9a21-58c99b65eb42}} , and then the proof is completed.
{{formula:92d1f0dd-420b-4195-8ef6-b3ba62f1cd2d}}
| m | 73b63181a1e2efd4f6a4477165c95f81 |
Other works bring in the model compression methods into sparse adversarial training. {{cite:f8365e6afa4daba2a80584dec367b6092aba69cf}} integrates pruning, low-rank factorization and quantization into a unified flexible structural constraint. {{cite:127c6ddba921de29373bb1f5e07595bf146b6df4}} proposes concurrent weight pruning to reach robustness. Both works introduce certain sparse constraints and solve the optimization problem under alternating direction method of multipliers (ADMM) framework.
| m | 22840ed04c0b7325a0e6f8612fd6db26 |
The second methodology, pair-wise based, considers the relationship
among documents related to the same query {{cite:7946633eecdc37d4326f953ae5b6a4e4c68f72ae}}, {{cite:bb3bf8c3ba4e499f735be6e216ede5acfb157767}}, {{cite:7b079c06aff36ad857495f61ff21040cb4c42f8a}}, {{cite:04d26363da972c30590f634fc5214e88f00dada8}}, {{cite:2ab44eaf5416557d4bd2a59bcbadc7d71d131dfb}}, {{cite:509b1b31206dbc329c2802751468a8a974b23cc8}}, {{cite:8b9dd5af71412f902b06bb5109c9e7e4d72ceb98}}, {{cite:d58e96aca34b13f6944281441f44150ef01eff4f}}, {{cite:1a8d5b1ad795e93317695143588b81ca47ebe214}},
then adopts mature classification techniques to minimize the inversion
number of documents by considering document pairs. For example, RankBoost
{{cite:bb3bf8c3ba4e499f735be6e216ede5acfb157767}} plugs the exponential loss of document
pairs into a framework of Adaboost ; RankSVM {{cite:04d26363da972c30590f634fc5214e88f00dada8}}, {{cite:2ab44eaf5416557d4bd2a59bcbadc7d71d131dfb}}
uses SVM to perform a binary classification on the document pairs ;
LambdaRank {{cite:509b1b31206dbc329c2802751468a8a974b23cc8}} and LambdaMART {{cite:1a8d5b1ad795e93317695143588b81ca47ebe214}}
take into account the influence of a correctly classified document
pair to the objective measures, and achieve a big success.
| i | 2f0dd52f01e37cf984ac08a5f9906383 |
This should be compared to the usual derivation of hydrodynamics from kinetic theory, where the (linearised) collisional Boltzmann equation in the strongly collisional limit {{formula:f697e1d3-2eb8-4b40-849e-920f6dafc0a9}} is considered instead of collisionless Boltzmann equation. Using a multiple-scales expansion known as the Chapman–Enskog expansion, one finds the compressible Euler equations at the zeroth order and the Navier–Stokes–Fourier equations at the first order {{cite:3ee0047dd3c52886ad9eb777a44829f1b934556d}}, {{cite:a45add0820c87f05014311b927c95478706e9d49}}. The Chapman–Enskog expansion offers a formal derivation of hydrodynamics as an approximation to kinetic theory in the strongly collisional limit, but it does not explain why the compressible Euler equations are Hamiltonian. Conversely, Proposition REF addresses the Hamiltonian structure of the compressible Euler equations, but has no bearing on their validity as an asymptotic limit of kinetic theory.
Similarly, we can obtain a naive fluid model for an electrostatic plasma by ignoring {{formula:bcaef176-6168-473e-9609-5042868bd571}} in {{formula:af6dead7-2a91-4064-b353-cc233e210caf}} , and likewise for a self-gravitating system. Corollary REF suggests that the naive fluid models obtained this way inherit the Hamiltonian structure of 1-particle kinetic theory through the Poisson map {{formula:e7dfcf35-982a-43fd-b717-e2409cff7b07}} , but it has no bearing on the physical validity of such models.
| d | baae881ede0f5913fbbf47688bb31fa9 |
Within the cellular structure, self organisation and dynamical instabilities causes mechanical oscillations{{cite:f7b8fb506afe1433268cc2ddb099a8d328280fb5}}. These periodic jostling forces might profoundly influence the conformations of the biopolymer, mediated via the cellular fluid. Further, dielectrophoresis (DEP) experiments{{cite:c8fcd23e7569655388f0d04d917b3b4e3d466059}}, {{cite:f51c9f9f3be1c4fa92c18fd2e986581ccebd2b02}}, {{cite:7677fb343fad4d6d88ff6428876fa32e25ccb1c0}} generally involves high fields of alternating nature, where this oscillatory field is leveraged for more controlled manipulation and efficient separation schemes for DNA and other polymers.
| d | 96d66a7517e8cde1ee4ee58b9cfa20db |
+ Shake-Shake + PBA {{cite:2354de1c84473cb3784fbd98c6629a81cbf273a3}} {{formula:e815748a-52de-4731-9d03-dcee23793f5a}} {{formula:5d3f2db9-675f-4989-9f18-c78ea8b489c3}} {{formula:a9cc1513-0bc0-42a9-8e64-bec05e015f20}} -
| r | 7e7fd3503d953b4e8cf7c4933f5b702e |
The structure and characteristics of the accretion disk were calculated using our MHD model of the accretion disks {{cite:0bfd7cb292fa18a10a340f11277dadf1f1a3fdf1}}, which is based on the model of {{cite:d2fd708a91814e3a1a52d4d2b8415c4f30ac3d8f}}. The vertical structure of the disk at each radial distance {{formula:9d395909-decf-4973-8d11-10c80bfc2582}} is calculated from the solution of the hydrostatic equilibrium equation for the case of polytropic gas. It is considered that the turbulent friction is the main heating mechanism inside the disk. There is optically thin corona above the optically thick disk. The temperature of the corona is determined by the heating of the gas with incident stellar radiation. We adopted that the fraction of the radiation flux intercepted by the disk's surface is constant, {{formula:8b49a6b4-8b48-4394-bfd0-90fc4da88723}} , at every {{formula:dfe148f9-9905-4a51-8a05-4b2d3040acaa}} . Transition from the disk to its corona is treated as hydrostatic region with exponential growth of gas temperature over the local scale height of the disk.
| d | 7f2016e0b796775969f70daaa1b9d46e |
Cosmic voids are vast holes in the distribution of galaxies, which appear devoid of matter {{cite:a2f6aad85bdb3b40ccd21e897ee01e1694437e17}}, {{cite:c8ec6c19910509f38d1a9a4c8c8563a19f29fbae}}, {{cite:537934af9abb72243a57ed3b13f69a4677eda1fc}}, {{cite:af6272350e0e6085a3d8c5ff64bf8b31215925c1}}, {{cite:232f0fb1c938aba2b85d1354827e131ab8eff697}}, {{cite:e774d1e3ecafe9caf7b438fd79757606b8dfa72e}}, {{cite:8c1041c40bd814f2a840729911c5906884309545}}, {{cite:ccb8ca40b22c79d8a9eccb1fe25fddb304313a55}}. Being underdense regions, voids experience gravity effectively pulling outward and are relatively more dominated by dark energy. Hence, void properties are intimately tied to the nature of gravity and dark energy. In addition, voids are less affected by non-linear processes {{cite:46a8bee7cd045e2c0d54bbe66a126ce79f934d88}} and less contaminated by baryon physics compared to overdense regions. Thanks to these characteristics, voids have become a promising probe for testing cosmological models {{cite:82ba8abab9be7a2e89a80eda4837008d5cf1e4a6}}. For example, direct comparisons of void properties between observations and simulations have been conducted to test the {{formula:dfd00685-d26f-4380-b54f-7480b7f1ddd4}} CDM cosmology {{cite:abb67aeacfa6b8ffac120ea11ba6a24d046b300f}}, {{cite:f47c68dc920160d1f61d2be2c45ae386bc62181a}}. In particular, the void statistics including abundance, shape, and density profile have been utilized to constrain dark energy {{cite:09f08c5ed0a6dde7adcbd9285735de1e5d1b522c}}, {{cite:df985907c6ae8427915765991c3f35f69f2dd6e2}}, {{cite:084270f23f6238e0f1d2a002ed9cebfd0ce1bd1e}}, {{cite:86b80d99a5f56689bb2a900ca0922602a4efaeef}}, {{cite:f541c5ac5b2620f13378d4ce599c2f7bf953714d}}, the interaction between dark sectors {{cite:3b251b15ff587f0b9a53015b93a909a3da13848c}}, {{cite:694a24a53d35130338406d0bd076e0f8e343d754}}, gravity theories {{cite:3c99b55a19ed60e4c3c7ca7f1d180f8a77a07f86}}, {{cite:392d78738b4a22891d122b821209918a42acc7f7}}, {{cite:673b842b8ee47b683722e3f49a914ef7d67973d0}}, {{cite:c4d360de338b31f5cd971f6e8e6b6d113e12c91d}}, and initial conditions {{cite:3838ac6c1d2fa22cc5c3e609380374748cc5ebae}}, {{cite:5cb58653c7acedc1cf4d764384ca3428fe8e1e85}}, {{cite:5955414e79c64373b121b12dd24ed08f4099b94a}}.
| i | fcc12432a8c91fe6b24292569180270e |
Following the proof of Theorem REF it is fairly easy to show that the set of candidate changepoints stored by the offline pDPA algorithm {{cite:3ac553310a89f06a7b5af0b7ce016c26c4a540e1}} run for one change is included in the set of changepoints stored by {{formula:f2b74097-43e0-485b-85a1-cc75304ed0cb}} . This provides a bound on the expected complexity of the pDPA for one change. Future work may consider extending the proof of Theorem REF to get the expected complexity of pDPA for more than one change or of other functional pruning algorithms such as FPOP {{cite:010520d679bbd303b44b3f8ab03d699842467013}} or GFPOP {{cite:32466f4ddabf4b855c0104d282b0c4a96020e561}}.
| d | 98b2b79cb4a9cdfb98ad431f9243b05f |
We have shown that the lightest axion of {{formula:c3b2e7a9-b6bb-469d-8c76-ee75d02c0695}} eV implied by both the Fornax Galaxy {{cite:aa535bf3f6342a930991eaafa0021a000fa00ec6}}, {{cite:c172d5f294ebad17178f1461fea990fc15844244}}, {{cite:4668ba0e57cbb43aa80d48bb0ae441b4786a9c57}} and the central Milky Way {{cite:62bc5719dbb697dfb988083890cf6b2632cfc382}}, can also help interpret the massive compact lens of {{formula:b74e2131-4b52-48f7-a301-15f72952a7a2}} uncovered recently near the center of a massive galaxy cluster {{cite:9fea0d617783e6e10fc951adcbf17d2e73efa4ab}}.
| d | 63fabb88c389ce3082f7609a8c9bf354 |
In both cases, following {{cite:42fbde23b12a8d061e5626cb3380073024f25ad1}} consider the formal power series
{{formula:54c44557-6c87-43f5-a23a-b031f3943f1f}}
| i | 904048e1fb27632d759033766bd4174d |
For the hierarchical structure construction, we utilize the average linkage clustering approach (also known as UPGMA). The algorithm starts with nodes in a network treated as a separate cluster each. The closest pair is identified based on the lowest distance in the distance matrix {{formula:ff78d8d1-58de-4277-9ecd-efb95096157e}} (except for the diagonal elements). This closest pair forms a new cluster and it is substituted into the distance matrix instead of the original two elements. The new cluster is assigned the average of the distances of all elements of the newly formed cluster. This is repeated until we have a single cluster {{cite:753397f9084cce094fc750fd3f587d4d6f00439e}}, {{cite:29fb33d2457c9a522f0b23f354b58c9c236624aa}}, {{cite:fa26228d64c1d9b1fb52026a02c415c375aaf77d}}. Such construction can be seen as a cautious one as it uses the average distance for the new cluster instead of minima or maxima of the alternative approachesIn the Results section, we also provide two alternative clustering linkage methods – complete {{cite:753397f9084cce094fc750fd3f587d4d6f00439e}} and Ward's {{cite:de4843a668f94fcf53bb5b8830ad06de91cfa9e6}} algorithms..
| m | a3d67219e98f15ea2f3f2e5c50f3c957 |
Domain adaptation is thus proposed to transfer the knowledge learned from a source domain (e.g. synthetic images) to another target domain (e.g. real images). One common approach is to learn a domain-invariant feature space across domains by matching their feature distributions, where different matching criteria have been explored, e.g. minimizing the second order statistics {{cite:03a2017cf2deaa069dc6d976af0b98aed43e51de}} and domain adversarial training {{cite:200fd68822b9ffb69d7b3aba88723eac17f99bd3}}, {{cite:78ec722589d5190c7b74d56de01f216f6aa0c5e8}}, {{cite:5884bb9e260aab09e27a98bf91bddadadc9604f3}}
. There is also a recent research work {{cite:9fc4fe1af97f6d0863c9a05eeaa7e9904fd584d6}} which introduces distribution alignment directly in the structural output space for the task of semantic segmentation.
However, these approaches are all driven by a strong assumption that the entire feature or output space of two domains can be well aligned (see Figure REF (a)) to yield a domain-invariant representation that is also discriminative for the tasks in question.
| i | 1882b5786d87dbc707e8176bf7cdb9c7 |
One well-studied class of combinatorial operations is that of sorting operations, where for the base set {{formula:217d9527-2243-4b05-a0d9-358b1cc64225}} we take the symmetric group {{formula:cd8e7d1d-783d-4ed8-b001-85774a01e924}} – the set of all permutations of {{formula:566ec11a-8f1b-448f-9b76-59e38efd1f31}} . There are many well-known sorting procedures in the literature (see for instance {{cite:3e39e2d39b19ec151b13f6205cbc7ef8da632862}}, {{cite:86ca3a6816433e948f188ef36bb2df2e15d63ee0}}, {{cite:ba3db43d6b337cb40e91fef1db50f7245768165e}}, {{cite:1ab01d14cd292f90f601816ea6476110766da7ba}}, {{cite:1b60aa4107d28f36a59305cb2b499a8840e47658}} and the many references therein). Of most relevance to us is the pop-stack sorting operator {{formula:b6aa150d-c503-4302-95d8-ff62eb39a7d4}} , which reverses all of the descending runs of a permutation while keeping different descending runs in the same relative order. Ungar {{cite:533573a2fe10772d77a0d9f736ff777d814da802}} proved that {{formula:defa096e-3c2f-430f-88d2-e59814ca00db}} . The properties of the pop-stack sorting operator have recently been of interest to enumerative combinatorialists, yielding more modern proofs of the maximum length of forward orbits and other properties of {{formula:b18a0d16-5076-4352-8410-6ccef0100a2d}} {{cite:3e39e2d39b19ec151b13f6205cbc7ef8da632862}}, {{cite:86ca3a6816433e948f188ef36bb2df2e15d63ee0}}, {{cite:5d37f49614af2bd9ee4b123304fb39eb0bcc0334}}, {{cite:7bbe1595ae4b0fc2cd4fd9fe159435e9fb20e757}}.
| i | 7924e08dfe4e4960db44f200b4e036b7 |
For example {{cite:16b03e383d30e07bc0789870edf2b41d9cefbd5c}} and {{cite:1a4a32bdd996afc4964eb1355940f03c0b3d7fab}} determined the electron density for their sample of BCGs based on the {{formula:30a9b037-b4fe-4320-90a0-5cc9e164a736}} 6731/6716 emission line ratio and their inferred values in order of a few hundred {{formula:e469c6a0-f3ab-4fad-8546-18d88846feef}} are in very good agreement to the value {{formula:43b86b54-b987-40a5-a849-972a33e4d689}} that we determine for the M1931 BCG.
| d | d46c5180ae70bada4614a3c7ad400436 |
Semi-supervised learning (SSL) plays an important role in many real world machine learning applications, such as image classification {{cite:d8c09ef499770136bde95dc196e4c1443c66c367}}, speech recognition {{cite:cb1b0d6e8faa4994234ae6360ccfb8e9815ebd1d}}, and text categorization {{cite:418b2886bbe4f5c9823f95f76713c5714962d0d6}}, {{cite:7289eaed8b6b5efae00e77419f33c5aaafed5878}}, where the cost of annotating unlabeled data is generally considered too high to afford. SSL tries to make use of additional unlabeled data together with a limited amount of labeled data to enhance model learning accuracy {{cite:3303d525a4c4104945eac2b72daf180ef2fb21a1}}, and thus has gained a lot of researchers' attention {{cite:40322558b84954f46b80f5c28b268387f7cbb10e}}, {{cite:12401eb6ddfd8b388402d2cc4218d2421050211f}}.
| i | c758402620e089c6759cb6bdad122733 |
Bayesian Network. In this paper, we focus on Bayesian Networks due to their better interpretability compared to other machine learning algorithms. A Bayesian network is a directed acyclic graph representing causal relationship between variables using the Bayes rule {{cite:60365f4765afe60ed94960a192b97dca76961648}}. Bayesian networks were first defined by {{cite:d3d0b03f5aa0c61132c603bdd4ba78b48ca32df4}}, {{cite:d9c24bc7f3cd6e1b84dd2c163310058f72c4a497}} and used for inference in tree networks. {{cite:bc7101a3484694bd3de205780a33773722c85854}} extended the approach by including continuous random variables, {{cite:695d2e756dc438e1c3d4849826e8496afec11341}} combined statistical data and encoded knowledge. Bayesian Networks have been used in industry domains since the 1980s for diagnosing systems {{cite:d9c24bc7f3cd6e1b84dd2c163310058f72c4a497}}, {{cite:32c32083803d9147e21736a3894bb1ce3880e447}}, {{cite:4ba9525552e1507a1f3b0570d233f3c60939c1c8}}. The advantages of Bayesian networks are that built models and the connections of its elements can be visualised as easy understandable graphs. Additionally, the approach offers to incorporate uncertainty and compare different solutions. However, Bayesian Networks face some challenges. They have high computational costs when updating variables, as a variable's whole branch including all other dependent variables have to be updated as well. This update can extend up to the whole net, if the network has no separation.
| d | a7e2a1e8c25f625205a10b99f5ceb9e6 |
Pseudo-labeling is another technique to address UDA and also achieves substantial performance on multiple tasks. Pseudo-labeling typically generates pseudo labels for the target domain based on the predicted class probability {{cite:a2410d66e39987756e953f7b58e3348526e61ba7}}, {{cite:12439441ed1eb15938823f3dd93cbeb2e36c61d7}}, {{cite:987d4eb41c7bb650e29182a5db7616ae6f9df8e9}}, {{cite:f7c71a0b34f217f24ad5914d25780306593fe6f3}}, {{cite:2cf10abd0ce9eb8325205dadbc43cf551a53ee0c}}. Under such a regime, some target domain label information can be considered during training. In deep networks, the source classifier is usually treated as an initial pseudo labeler to generate the pseudo labels (and use them as if they were real labels). Different algorithms are proposed to obtain additional pseudo labels and promote distribution alignment between the two domains.
{{figure:b6426178-4b8f-4976-bb20-11ade8e4c6a4}} | m | a0467f17bdcbe31abe57aa510639aacf |
For open lossless dielectric waveguides, a regular guided mode at a
given real frequency is a proper eigenmode with a field confined
around the waveguide core {{cite:b2dbbf8e1bba14b55cf58ba4dee32a2e4921b126}}, {{cite:e253ae746068ff78d5c646b04770431e0d048467}}. It has a real
propagation constant, carries a finite power, and propagates along the
waveguide axis without attenuation.
If the waveguide is lossy, any guided mode must have a complex
propagation constant due to absorption loss, and it propagates forward
with an exponentially decaying amplitude. A leaky mode
{{cite:b2dbbf8e1bba14b55cf58ba4dee32a2e4921b126}}, {{cite:e253ae746068ff78d5c646b04770431e0d048467}}, {{cite:aba4bf76a84fea10e6b8a9f286edd27e71206ce9}}, on the other
hand, is an improper mode with a divergent field in the transverse
plane. It radiates out power in lateral directions, has a complex
propagation constant due to radiation loss, and also decays
exponentially as it propagates forward. The so-called complex modes
also have a complex propagation constant, but not because of
absorption and radiation losses {{cite:19d78aa2ae03e4c448c281dc2cbf5d030d72e09b}}.
Instead, the appearance of complex propagation
constant is related to the non-self-adjoint linear operators
in full-vector waveguide eigenvalue formulations for a given real
frequency.
Complex modes were first discovered in closed waveguides
supporting backward waves {{cite:6a0ff881da8652b8862933f71b679dd1d6c76ae3}}, {{cite:6cb15f34261bd076171c06750fcc80df24b3e3fe}}, {{cite:06a244df17b6a50236c22f15d75e05fc02e1f858}}.
The existence of complex modes in open lossless dielectric
waveguides was first demonstrated by Jabloński for a high
index-contrast optical fiber {{cite:6db2dda43f5382837a5fadeb74c2485f202dfa8e}}. It has been shown that complex modes also exist in silicon
waveguides and they are related to the numerical instability of the full vectorial
paraxial beam propagation method {{cite:fabff6f70c284fa6c954c8cdf98a334b0cb7ac50}}. In addition, complex modes also
exist in periodic waveguides {{cite:e6dfb990ea9991b754d220072c7c74e0361689b9}} and in waveguides with anisotropic media or
metamaterials {{cite:22daa4c4a8cafa39a40f9161a3daa7d335b3c899}}, {{cite:efa5bd157aa6266debc1266dd0e8636b92600de2}}.
Guided modes with complex propagation constants also appear
in {{formula:607862e1-e0de-4707-aa0e-c47f281829d4}} -symmetric waveguides where the real and imaginary parts
of the complex refractive index
profile are even and odd (in a transverse variable)
respectively {{cite:f15710cbd4c100f98ef85a4b7600ab6627403b4d}}, {{cite:76cbf25d33825502ddae07d23e143096acc624fa}}, but
they are different from the complex modes in lossless waveguides.
Unlike the leaky modes, a complex mode in an open waveguide is a proper
eigenmode with a field confined around the core. A unique property
of complex modes is that they do not transport power along the waveguide axis.
For waveguides with discontinuities or a local defects,
complex modes can be excited and must be included in
eigenmode expansions.
| i | 72d979e6561b9c7194305981eb75b6df |
Eq. (10) is analogous to the definition of total mass in the NGT. This analogy is termed as rather `deceptive' in the literature {{cite:3319a8be92bb65c9c2d1f46d588c1d8b55c46803}}, because the energy-density {{formula:936eed17-f2ea-439b-bccd-9b4e16659941}} is measured locally whereas the integral over the volume element {{formula:98f2ed98-2140-4e4e-9305-8988ea8ecb36}} is non local. The external observer measures the total mass-energy which also includes the (negative) gravitational potential energy. The possibility of the removal of this `deception' is discussed below in the discussion.
| m | c4b9cf009aae18ccb22856eead0cf693 |
We discuss now how temperature dependent {{formula:1a906d89-0141-4439-9e20-789326f56920}} and {{formula:dd290a5b-9567-4651-b1e7-cc0680bd8dac}} may affect the best fit value of the exponent {{formula:f963945d-2050-47c8-a749-74c15d6a5235}} . In the normal state, {{formula:5c412bff-a679-4821-b229-14bc56ac4833}} by virtue of the {{formula:79b2571f-8142-4cc3-8324-db51b88034ac}} dependence. In the superconducting state, {{formula:8cb33abe-c0d9-43af-a1d6-9ef641fe7254}} decreases much quicker. Down to the relative temperature {{formula:3a238490-a128-4a0a-adf0-ad4f27a72df4}} , with a good accuracy, it can be approximated as {{formula:940b6940-2602-44d8-bce1-ea11b02aa0e2}} {{cite:ca2a23992c6f20c255e4e883930c0a6b748925e0}}. Solving Eqs. (REF ) numerically for {{formula:e9f35e7b-9804-458e-84c3-311c47fff32b}} with temperature dependent {{formula:299a98e1-5a36-40cd-89e7-65f6b9638d99}} 's and with {{formula:8f7ca0cf-24d4-4ab9-8563-617c211c3437}} , we found that introduction of the temperature dependent conductivities cause a change of the temperature in the center of the normal domain {{formula:f66b904f-c3b4-417d-bfab-3833ea02d2dc}} but do not affect additional BCs (iv) and (v). We therefore used Eq. (REF ) to evaluate the effect of different but temperature independent {{formula:13805633-b9a0-4831-b5a7-c7cbb94fe947}} and {{formula:580708a5-c1b1-4049-b605-7d2e0a3c23c2}} for {{formula:3926cc1d-04d5-436d-9c4c-876d5910a0b9}} . Setting the ratio {{formula:92fc56e1-a774-474d-8d86-2c44cdc2d95f}} , we found a 15{{formula:1190070e-55e7-4231-b4fa-f024e0696aa0}} decrease in the best-fit value of the exponent {{formula:316d901c-cccf-471a-9c42-ea3646bf2b94}} . Note that {{formula:7d0d3d46-325d-4f6a-946e-6429bebf16a4}} and {{formula:7be835e0-49c2-458a-a41a-22dcd4dd2937}} enter Eq. (REF ) via the boundary condition at {{formula:ef8c5ce0-4513-42af-a3db-03bd6ead5bc2}} where they are equal. Physically, the heat flow through this N/S interface can be affected by the temperature distribution in the layer with a thickness of the order of the electron-phonon thermal length {{formula:b9a469d2-e2d5-47b5-8042-c2da1de56885}} which is about an order of magnitude less than the effective thermal length {{formula:93e92e19-bd56-4729-bbe3-1f4b9e2f6bfd}} . Since the temperature change around the domain edge is {{formula:3162a570-bab4-4e87-b0e4-3fa011d5be49}} , the temperature difference in the layer with the thickness {{formula:dde3bb02-55e8-4c7c-8d1b-66e307bdefcb}} is {{formula:4e9f51e1-e166-4fc0-966f-4c2044757b2e}} K. Corresponding change in {{formula:c69ab8d1-f30f-4646-b73b-fae5375219b8}} is less than {{formula:13eed9c5-0fee-4375-affc-3a5f4d56baa7}} which would cause a correction to the best-fit value of the exponent {{formula:c888cfc2-6fcc-480e-8f0b-2ee3f9edeca4}} remaining beyond our experimental accuracy. We, therefore, neglected the temperature variations in the electron thermal conductivity and used {{formula:7d38b0bd-a648-4c7a-b539-ee458635b843}} for the description of our experimental data.
| d | a84f50b1db19407698e538d14cc67198 |
We evaluate the performance of Magic Layouts and contrast state-of-the-art baselines such as (Faster-RCNN {{cite:2badc28463523d873f74404ec968afbf70324224}} and popular variants {{cite:adbc0ddb18112fa3f2cd0480c2b3740881d52187}}, and RetinaNet {{cite:6b58b81f97f11342391698e71c29ae631c7940ad}}) as well as the recent spatial-aware graph network (SGRN) {{cite:cc4ae86d707026657958e6f5ae21492de920a768}}.
| d | bcfad139f0d9fb0573e8079be8f270ef |
In order to leverage strong supervision, one could try self-supervised methods.
It has recently been shown that these methods, e.g. {{cite:7734d8c3c6c44d4945b0d7a4e3b4591c82aa2a4d}}, {{cite:f09010bb5da167644edab5510faeca20941e4828}} can learn generic representations that generalize for many
visual tasks, in particular in low-data regime. It would be
interesting to investigate further these methods for few-shot object detection,
this is planned as future work. In addition, we plan to try methods based on
attention mechanism instead of representation learning as our experiments
highlight some weaknesses of the latter. Attention mechanisms, have recently
shown great performance for plenty of tasks including few-shot object detection.
Finally, a change of the underlying detection architecture is required as
modifications in Faster R-CNN can be cumbersome (due to its two stages and the
generation of anchors boxes). Instead, FCOS, which is a one-stage and
anchor-less detector, is probably better suited.
| d | e441524f7faf9e24c03a8d75b1bb7290 |
The position angle of the primary jet, as determined from jet model {{cite:0263fe25a8a4bc1ace15efff08990631cdc058df}} as well as from VLBI observations {{cite:aa7f784847cab39c0a4d27d63c22e5336d66881a}}, agrees with the polarisation position angle observed in this work. The models give {{formula:f71f2178-c67d-48ea-a48e-07d203109831}} {{cite:31d9e95b3936c1dd35b2b85668e1a3210ae642a8}}. The values should be measured at a quiescent state, before or after a flare. We find that at these times {{formula:a09aceb7-88fe-4d36-82b9-dda745df3fde}} . These data will appear in more detail in a later publication (C.M., H.J., A.B.). For the secondary jet, the position angle should be {{formula:0bb43a98-e0e3-436f-9434-284e49bd2a9c}} {{cite:0263fe25a8a4bc1ace15efff08990631cdc058df}}, {{cite:31d9e95b3936c1dd35b2b85668e1a3210ae642a8}} which is quite different.
| d | aa038b2612637d6f34560ed579d7fb17 |
Finally let us comment on the cosmological constraint.
In the {{formula:1d1cb4b8-7264-4a01-9731-bbdba879c346}} model, the SM gauge bosons have only even KK modes.
In particular, the fist KK photon is projected away and cannot be a dark matter, unlike the minimal 5D UED model.
Therefore the most phenomenologically natural mass spectrum would be that the first {{formula:48754dd9-77b5-462a-b255-e0d65300574d}} gauge boson is the LKP and the first KK neutrino is the Next Lightest KK Particle (NLKP) or vice versa.The loop corrections to the {{formula:0b6d4de1-a376-4205-a1ee-0fb35243b9b2}} KK masses should be suppressed by the factor {{formula:b9c080d7-2e3a-4c15-84ed-d050761e28df}} in our model. We also note that there is no orbifold fixed point in our model, which is the source to the positive mass shift to the fermion KK modes in the 5D orbifold UED model {{cite:da4d9829bb31dfa0323912329865480e2bb1486e}}. Detailed study for the loop corrections is being performed. In worst case, we can still arrange the small tree-level mass splitting at the UV cutoff scale on phenomenological basis, as in Ref. {{cite:bd643634f27311ea27df804059c2951ae4762092}}.
Since we expect that the tree level mass splitting at the UV cutoff scale would be small compared to the KK scale {{cite:bd643634f27311ea27df804059c2951ae4762092}}, the supposed NLKP decays into the LKP with lifetime relevant to the bound coming from neutrino injection {{cite:d221930e3c5899f054863e6e908a9c3b1dfce8b6}}, if the above mass splitting is realized.
Detailed study of this issue will be presented in a separate publication.
| d | 7922cbd36e06e2d70906399755983112 |
Large changes in head pose. The reenactment results we presented are mainly frontal. This is attributed to the training data, which consist mostly of frontal poses. Actually, both 2D and 3D-based methods are limited by the head pose variation that exists in the training video. We observed that all systems struggle to synthesise poses out of the training data span. In Fig. REF , we illustrate the training frame with the most extreme head pose, in terms of yaw angle. Next to it, we show the most extreme pose synthesised by NerFACE {{cite:fdfaeb457e936ad1a8fbd3d788a12c8850b32a53}} and our method, without a substantial drop in quality. Our approach achieves higher photo-realism.
| d | a5914978b6a6196865cefe17d02181aa |
In this paper, we examine two different types of layered structures where the layers are rotated with respect to one another as sketched in Fig. REF . The geometries of the individual layers are called square (Fig. REF a){{cite:3c27e657993106a690fc696ca9a3ba3732a7e391}} and pinwheel (Fig. REF b){{cite:df0ebb10d340f1279aeb01448f6c011be8c1f380}}{{cite:fede9e1efb28b07234d958557973f9743a96a7c0}}. Regardless of the geometry, the lattice for each layer has element spacing {{formula:d9ca426b-33d9-4a76-b6a3-ff97b8827906}} and the layers are separated by a distance {{formula:01d3198e-728b-4345-bec0-cc46b1192ac5}} . The angle {{formula:ae2a8213-0f04-4e90-afd7-f55a54551c79}} defines the relative orientation of the two layers.
{{figure:74339a61-bee1-4f8e-8ba7-567667c0fb64}} | i | 85828b62d348827d8c2fa56bdc0af4ed |
With the LVD method several arm structures have been suggested.
The densest and most coherent LV ridge is called the Galactic Center (GC) Arm I, the second is Arm II, and further Arms (III and IV) have been proposed {{cite:1c725be9a34dfeba41269a1729727e7cdf920023}}.
More recent analyses have shown a larger number of arms with projected lengths {{formula:91227ea1-e461-443d-b90c-7eea8d2843a8}} pc {{cite:cb89adb5e2c06985d422e09b513f8ebd8f6e5d10}}, {{cite:e67d345d8fe2d5c69ab57aea4daa47e0b7c809ad}}.
| i | 7394f7522817d514d01811161ed0dbaa |
ItemPop recommends the most popular items (i.e., the item with the highest average rating) from currently available items to the user at each timestep. This method is non-personalized and is often used as a benchmark for recommendation tasks.
LinearUCB {{cite:c94846347af5d3f0a71db33c2ff2c6bd591e47d9}} is a contextual-bandit recommendation approach that adopts a linear model to estimate the upper confidence bound for each arm.
DMF {{cite:4cdfa0f93851042608226186de683deb46de3cfc}} is a state-of-the-art matrix factorization model using deep neural networks. Specifically, it utilizes two distinct MLPs to map the users and items into a common low-dimensional space with non-linear projections.
ANR {{cite:da8e6941db89fda1f93dfcf3769e5fe593f280b9}} uses an attention mechanism to focus on the relevant parts of reviews and estimates aspect-level user and item importance in a joint manner.
Caser {{cite:b18f5c65fab05276387b46e929bc8d8448abcbde}} embeds a sequence of recent items into an image and learn sequential patterns as local features of the image by using convolutional filters.
SASRec {{cite:5c505f72f452638ed37eff65200a0afefcdd3bf2}} is a self-attention based sequential model for next item recommendation. It models the entire user sequence and adaptively considers consumed items for prediction.
DDPG-{{formula:1f8a4a78-1331-4527-855f-d1cbaca01c0d}} NN {{cite:9a39d542183a3b175fdedfa0014f255239e8391e}} addresses the large discrete action space problem by combining DDPG with an approximate {{formula:ff744380-ee41-4797-b12a-e5043cda800a}} NN method.
TPGR {{cite:c8a34c2b550d20e760d42af2ec30fa442f0fa27e}} builds a balanced hierarchical clustering tree and formulates picking an item as seeking a path from the root to a certain leaf of the tree.
TDQN-Rec is a method that replaces DDPG in TDDPG-Rec with DQN, while retains other components the same as that in TDDPG-Rec.
MDDPG-Rec is a method that uses the same framework as TDDPG-Rec, but with vectors being derived by matrix factorization {{cite:49f846de091eb95dd34268982f0edf136503a7a8}}, rather than leveraging textual information.
| m | 7c1433fb76148e4469c2042208da4baf |
Bi-based materials are known for the presence of TSSs {{cite:9d74f6f47a1bc5b42682499c1b996ff71a36dd43}}, {{cite:10d5c7b49b9ef350f31e52d2243db89ca9613a8d}}, {{cite:d207bdac0421808537fb1b2f457d6bf89e51ecb0}}, {{cite:d4f1efa681c26df74eb058a941742835428b7b97}}, {{cite:268202eca265e524e8b9a9d06c6ef25d7c1ef67a}}, {{cite:9828aa3f88d285ef8a6538c4833b7633f1f875d0}}, {{cite:71fcc9d56df2ca2fa45897a8f88fa272db4c47b0}}, {{cite:dabfc52bde57767afd90f192d0c2eded9ecf3e3d}}. The Bi-based binary systems {{formula:f9c55401-ef2c-4fc9-a59e-ba44c9885942}} -PdBi, {{formula:c80b32f5-a192-46d3-b578-3708cd78910d}} -PdBi{{formula:7f9d100a-2958-4b0e-8ceb-abe671abd46e}} , and {{formula:4bc88fcf-e46f-496f-84ee-1903d42cf384}} -PdBi{{formula:5f9e3eb8-846a-42b1-8b75-36c5dbc0a152}} are among the promising bulk topological superconductivity candidates. Notably, in {{formula:f1c3bc15-ee8d-4ef8-9bea-a8a672c8a644}} -PdBi{{formula:5f6471fa-3ddc-44e8-bd0f-124436158fcc}} and non-centrosymmetric {{formula:1e0fd458-a05c-42f3-8e45-dbbe5cafc126}} -PdBi, Rashba surface states near the Fermi level, {{formula:1009f307-34f9-4ed3-a154-7871a9a928d9}} were theoretically predicted and experimentally verified via angle-resolved photoemission spectroscopy (ARPES) with intrinsic superconductivity {{cite:3826c494165f28e6b004a8982a09b0f3b5185b33}}, {{cite:6a8c1f90b88a285628ed4bda2e993f303f56649f}}, {{cite:66ff57c55b6d37e1252de02550d1adfabc1a0d0c}}, {{cite:bbfe56e4bd3593b62ecb838ec9c99a770aeebbba}}, {{cite:c83988597f25d63eb676d4d8d2954f5184614c00}}, {{cite:831c559381d78a2a7c9ef2afa4512ff0c639266e}}. Moreover, the observed non-helical spin texture near {{formula:10403494-dd3e-44fc-aaca-d967577f6e3c}} for {{formula:64a8ee1b-a588-4615-bd3c-f439b7d280b6}} -PdBi{{formula:b4863e4b-a85a-4568-9d34-e417eb2b0570}} combined with the various reports of fully gapped multiband superconductivity in bulk, suggests the realization of Majorana fermions at the surface states {{cite:284cefdcc3ce3a64240292c04c9acdf314429ab0}}, {{cite:19a856994fc649fae752a549810739c672abdb7a}}, {{cite:666b3b4dd67ca3ee6038c9557766fa1fe21ff5f5}}, {{cite:07666f25b3482fadcf72b18551e3160e4b72250c}}, {{cite:970e07caecd6729590ad84accb0b77048e75b973}}.
| i | 6161cf57034d408938c934b1d5914df8 |
A more challenging direction is to retrieve relevant commonsense or passages from open source and incorporate them as evidence for answer prediction.
Previous work {{cite:9e8ad24e8f08311fdb8dd45653972217f6445f63}}, {{cite:3c9464fb98f87a23ab94f3bdbfddadb6ac47461e}} can only achieve poor performance on this topic due to intrinsic noise in retrieved passages. Further research can focus on improving evidence retrieval and predicting answers from noised evidence.
| d | 7ff0d60520c7cafe21c1ed9de012bac6 |
In this section, we evaluate our proposed multi-level SMDP through numerical and simulation results. The results are compared with the staggered threshold and bulk setup policies with parameters given in {{cite:d33a09009a890dda132e395b0e9a14f60676e309}}, and the uniform state-aggregation method in {{cite:215e7d4a0cbe22d4732825c9e975d9c42df4e96b}}. The SMDPs are solved using linear programming approaches for solving multi-chain SMDPs {{cite:70627cb09004d8819d3d22fa2632990f4f6a458d}} and Gurobi java plugin {{cite:5c99bbff3d1692d9c0c80649d99a123879f57dab}}. Hereafter, we assume {{formula:45381542-bbb9-44a7-81fc-20c54c516f61}} , implying that each Setup server consumes twice the power of an Idle server.
{{figure:66cb2578-0be6-432b-aca6-837b2aa3dec2}} | r | a4a773f7942eb3cc467a6b9f085a8478 |
The performance of deep learning-based classification should be further improved. Although the published papers showed the advantages of deep learning in EEG classification and demonstrated that deep learning is superior to conventional methods, the performance is much lower compared to the performance achieved by deep learning in image or speech classification {{cite:472236636521a49cdd9b64982a56ce2ec3488edf}}, {{cite:c83f1b7f0e760c3d61edd398495dab03242274fa}}. The reasons for the lower performance are mainly from two aspects, EEG data itself and models. On the one hand, the EEG signal is non-stationary and much variable over time, which makes the extraction of robust features difficult. An effective solution for this problem is to partition time series into short segments, which can be seen as a stationary signal. However, this is only an approximation but not a final solution. When performing cross-participant classification or cross-session classification, EEG over participants or sessions is largely variable, making the above problem more dominant. Besides, available data size in EEG studies is significantly smaller than the data size used in image or speech studies {{cite:472236636521a49cdd9b64982a56ce2ec3488edf}}, {{cite:c83f1b7f0e760c3d61edd398495dab03242274fa}}. As we know, the deep learning model requires extensive training and a large data size can benefits the model training to a great extent. Compared to those domains with millions of training data, EEG signals are collected from tens, hundreds, at most thousands of participants. These limitations of existing models and the characteristics of EEG lead to overall relatively low performance. On the other hand, most deep models are originally proposed to process other signals (e.g., images) rather than EEG. Though modifications can be utilized to these models, it is still difficult to reach its maximum performance because of the nature of unfitness.
| d | 6beaf8c88d958f0bfdbbf0d76b09a3f7 |
The lattice structure of qHPC{{formula:9cc962a7-5145-4310-92cc-e6d70f6586af}} is available from reference {{cite:c82ffb743e1648297c917d77da890c28ae71a0da}}. Its square unit cell consists of 120 carbon atoms, (see Figure REF ). We fully optimized these structures and calculated their electronic, optical, and mechanical properties through DFT calculations, as implemented in the SIESTA code {{cite:c66da5a5fd33b3fd5f3ab2eb91d5383cecca503b}}, {{cite:45ac8a8cdcd5da73e61a03e47337c402509e3770}}, {{cite:b124a3ad2f43a440d1704b55cb15530a8707fa92}}. The van der Waals corrections were adopted to describe the exchange-correlation term {{cite:03ae2d356974be1f32b198c688bc0471bf85c325}}, {{cite:7bb0ab27f6c05dfa3b5533dc6e0047cf74952329}}. The calculations were carried out within the framework of the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional {{cite:31f2d488d1bcd5d86bc1015593ddce68321beda7}}, {{cite:cd7ed7200636a039794ce8111382cab64fde39cb}} for the exchange-correlation term. We chose the norm-conserving Troullier-Martins pseudopotential to describe the core electrons {{cite:9ec3bdda37006e7384839eb87d2f8ff79dd9426b}}. The wave functions are based on localized atomic orbitals and a double-zeta plus polarization (DZP) basis set.
{{figure:ec1974bb-aaf7-4e14-9c01-4bb4f19046ac}} | m | 754cd9e67adc7e28e786c08e54ea3227 |
The main advantage of the ETDM implementation presented here, based on a general preconditioner, L-BFGS algorithm and inexact line search is robustness. For small molecules
the computational effort is similar to the standard SCF approach when the latter converges, but the ETDM is found to converge for all the molecules in the G2 set with the same set of parameter values, a set that also works for extended liquid configurations and
insulating solids.
This demonstrates the transferability of the ETDM algorithm as implemented here.
For the large systems considered here, liquid water configurations with 200 and up to 576 molecules,
the ETDM outperforms the direct SCF method up to by a factor of two
when special parametrization of skew-Hermitian matrix is used
and by around 20% when the more general scaling and squaring method is used.
The latter is more general and can be applied to any type of orbital
dependent energy functional
such as self-interaction corrected functionals {{cite:b864d4372a37482946c687e865d498c7fb4e1231}}.
| d | b0319290a8e925fc600946cd59125413 |
Linear optics has inherent probability characteristics for the implementation of controlled quantum gates. With the help of an additional entangled photon pair {{cite:6f2af1bd347d25f32073eea5e866b6ccbe3d9de2}}, {{cite:287c869508a464c9d05c7a0018e0fb7a5a518235}} or a single photon {{cite:954e7d08ea7bb720df9b26096986eedbcd78d1d1}}, optical CNOT gate with a success probability of 1/4 or 1/8 can be realistically implemented. Without auxiliary photons, CNOT gate with a success probability of 1/9 has been experimentally demonstrated in linear optics {{cite:0181cd18a1f6c10bf28f09b2285e56191c86be5e}}, {{cite:d0512c9b528b14b175b1c0205350c87ac149762c}}, {{cite:94858a9b5e2ab69f739fd18e3588f03d38400ec3}}. Remarkably, the success probability of our P-SWAP-based CNOT gate is enhanced to 1/8 without additional photons. Moreover, the success probability of our P-SWAP-based Toffoli gate (1/64) is higher than the CNOT-based protocols (1/72) {{cite:6cbefe39369f3dc8482a617af4e5c78e4f56bb79}}, {{cite:823175d0d023fca0c87335fd11208ed3c22b12f9}} and it is also higher than the no-decomposition-based one (1/133) {{cite:ca51fdc185440fd0a62ec34dff3a9addbde1f8b5}}.
| d | 6bef868504047aa8bf802960a149abde |
In addition to {{formula:3161b3b0-3f5f-4f53-8861-f30dee312207}} , the estimation and inference for noise level {{formula:75bd95be-1ebb-490a-a009-44dbbd6fc4d0}} is another importance task in high-dimensional double sparse regression. Motivated by the recent development of scaled Lasso {{cite:46d023f9330941978fabf19567dd63cee7525c53}}, one may consider the following scaled sparse group Lasso estimator:
{{formula:6748f2d9-d465-469a-9a5b-fc5a4d0f671d}}
| d | 8373adaebe649c44b1807611a7908cce |
which are the same as those used in Ref.{{cite:dd5690e56f4d4a592a1f092d3f071be24d7b53ce}}. The factorization and the renormalization scales are taken as the “transverse mass" of {{formula:0a7ccd7b-da37-40a3-97f3-4fb66bf4735e}} , i.e. {{formula:891718f3-7144-42b5-bec1-d3ca41de4af1}} . For the extrinsic PDFs, we adopt the CT14LO PDF {{cite:f83730864331b7203518724c8bc6bac902eed00d}} version extracted by the CTEQ group. For the probability ({{formula:5f394778-40c4-4f1a-b423-2ef5d91a11e9}} ) of the intrinsic charm quark in the proton, we take several values, i.e., {{formula:6fe043ca-d43f-4c68-b7c9-94c1e7df913c}} , and {{formula:7f36f6dc-9407-418e-95bd-b9bfde8ed3ac}} to see the effects of the intrinsic heavy-quarks, where {{formula:a9ee9348-7121-437d-ae61-1ec29757bfdb}} corresponds to the case that only the extrinsic mechanism is considered for the heavy quarks in the proton. We implicitly take a small transverse momentum cut for the {{formula:7668bd4a-7ae1-44b3-8064-65f1f98c0cbe}} events, i.e. {{formula:28d6fccd-5849-46a7-a900-919cb13c149e}} GeV, which was used in the SELEX experiment {{cite:702808559e78b987235917c30220f1ea31441b50}} and could be adopted by the fixed-target experiment at After@LHC.
| r | 0d87b412280dc0d9b4d9aab92168a6e6 |
Optionally, we apply a PCA (Principal Component Analysis) transformation to reduce further the number of features to the range of 30-50 features. This speeds up the computation of pairwise distances between the data-points in the next stage and suppresses some noise without severely distorting the inter-point distances {{cite:2b2137a3ef6634bceacf0cae7b4f56fb3b5fa22d}}. t-SNE then embeds these features in 2 dimensions. The malware instances are depicted as scatter plots. t-SNE outperforms other data embedding techniques such as PCA, Sammon mapping, Isomap and LLE.
| m | b6abaa1d77e1d30451b87597449c50cf |
Complicating matters is that even when regularity conditions hold
at parameters near singularities and boundaries,
convergence of the expected AIC may be slowed, and
a generalized form may converge faster to its target. In this sense, the AICg
can be thought of as a finite sample size correction to the
standard AIC. While the AICc {{cite:bd3e9a7d1d7799bfe777c35f73178b409e5558b9}}, {{cite:538019e6cd1642d602f4a83a5e8d16b4616868b7}} also has this interpretation, our generalized
form is more generally applicable.
| i | 8ba1959dd916e25c6d6b4bd2387355ff |
This small-scale quantitative study of model evaluations provides clues as to the values and goals of the ML research communities. Test data was often old (e.g., the CONLL 2003 English NER dataset {{cite:cd9a4c04da80ccdac617d56456fcfcfaf97208ca}} used in two papers); optimizing for these static test sets fails to account for societal and linguistic change {{cite:3e6e97938b445fbae32aea582a8f884e8648c215}}. Disaggregation of metrics was rare, and fairness analyses were absent despite our sample being from 2017 onward, concurrent with mainstream awareness of ML fairness concerns. Despite being acknowledged by influential thought-leaders in ML to be unrealistic for applications {{cite:305a8156475447f3769913296f7a745ba085bcbd}}, using I.I.D. test data is the norm. These are in alignment with the learner-centric goals of evaluations (Section 2). Similarly, with a few exceptions in our sample, there was general paucity of discussions of tradeoffs such as accuracy vs resource-efficiency that are typical of engineering disciplines {{cite:9f30e9d7a22cd5bb8d7f89d10c7b19eb7eb55da0}}, suggesting that the ML research disciplines generally aspire to scientific goals concerning understanding and explaining the learner. With this lens, the disciplinary paradigm of measuring accuracy on I.I.D. test data is not surprising: the goal is to assess a model's ability to generalize. This assessment would then give us good guarantees on the application's behavior, if the practical challenges of ascertaining the data distributions in an application ecosystem can be overcome. In practice, however, these challenges can be severe, and the research papers we surveyed do not generally tackle questions of uncertainty regarding data distributions.
| d | 07aff70402400f500521017c97a310c6 |
Since blind deblurring methods cannot be implemented in real-time, we next use three non blind deblurring methods (as explained in section ) with a known PSF. Since the blind method {{cite:172c2900ebcf863c9d7423cec96b6518c121eff6}} gives good results, it stands to reason that it is able to fairly model the underlying blur kernel associated with the blurred images. Hence, we use the PSFs returned from {{cite:172c2900ebcf863c9d7423cec96b6518c121eff6}} and perform non-blind deblurring using Wiener filter, RL {{cite:7bdf19e9d1a72b55dfda13c093db306a8380a28a}}{{cite:f79e342a18a18544e2cfb4e148e8b50674c40d09}} and {{cite:63753dc2c2a0d86ebe94a7195291258125ebb052}}.
| r | 0752f4c09ac55a2d9907f498ff01032a |
The initial discovery of the anti-D3-NS5 metastable state was performed from probe computations in {{cite:1f2bcd1f36959356c85d96d346177f0d564816a4}} in two complementary ways: {{formula:134c9cc4-2045-4bd8-80af-e795567ebe0a}} using the worldvolume theory of the anti-D3 branes and {{formula:20399ffd-63ad-4e61-9b42-25b67be7b35f}} using a worldvolume theory for the NS5 branes. In the D3 perspective {{formula:1eeb9a45-2356-4da9-8860-ef442aef0f82}} , the non-abelian DBI action is best understood in the super-Yang-Mills limit, which, effectively, restricts the description close to the north pole of the {{formula:b83cb819-ceea-4c19-b563-56509cd14163}} {{formula:6993b7c5-4b5d-4428-b1b4-e45d5770bc3c}} . The NS5 brane perspective {{formula:7d9cbc5d-4e0c-450a-ac1d-f21d4448f9e0}} does not have this restriction but the formulation of an effective worldvolume theory for NS5 branes is more challenging. KPV employed an abelian DBI action that arises by S-duality from the DBI action of the D5 brane. This step is dubious (see e.g. {{cite:3ddf333cf9f8a7fb343a97e18bfdcd0493bd5677}}), because it is in conflict with the regime of validity of the probe approximation that requires {{formula:57f29a58-26ec-41b4-9f8b-8dc86b29c6f5}} .
| d | 7f2afd596f6bb0d95312c133be1db45e |
For appropriate transition densities, {{cite:2c8912567600efb88476369533da3653eb4d9f5a}} showed that the
forward and reverse-time Markov chains may be viewed as discretized
diffusions. We derive the continuous-time limit of the procedure
presented in sec:discr-sett-mark and establish convergence results. The
Markov chain with kernel (REF ) corresponds to an
Euler–Maruyama discretization of {{formula:ec3d6794-a3d7-44bc-b598-baf9b5f712a1}} , solving
the following SDE
{{formula:4487973a-8d15-478d-a1b8-56cc9da44a22}}
| r | 410f4236c0690595107b9e8a52e10947 |
We calculate the excitonic spectra by solving the Bethe-Salpeter equation (BSE) in the Tamm-Dancoff approximation
{{cite:bc71d6607f2d24ad80f1817c88096f37a7bb2e0c}}, {{cite:4956096e6251787eb31bf9fed0806634b0845ce0}}:
{{formula:fbfc0e3b-27b6-4b68-8906-2cadb578817b}}
| m | 6ba203023577e469a5da82d50f2822e9 |
We show more visualizations and quantitative results to show the efficacy of our method. Namely, Section shows qualitative comparisons between our method and existing state-of-the-art methods, StyleGAN2-ADA {{cite:8429e3eb250e188d721b0c1d123ac6a0ea10632b}} and DiffAugment {{cite:6387e4ea4d115a4761e7be633341cf8cf08f8aa4}}. In Section , we show more evaluation of our model on other metrics. Section details our training hyperparameters, discriminator architectures, and selected models in each experiment. In Section , we discuss the societal impact of our work.
| d | 93a6fe6eb1b467778b997d5a2439a428 |
Episodic Rehearsal: store a subset of the datasets used to later "rehearse" them in subsequent training of newer tasks. While this method might be the easiest to implement out of the 2 sub-types, the model can easily overfit to the subsets due to the limited number of samples, and does not scale well in terms of memory cost.
Generative Rehearsal: store the previous tasks' distributions instead of the raw samples, which can later be used to project and generate auxiliary data for replay purposes. Although this method has not been used frequently in recent studies on CL, the recent emergence of generative networks opens a potential for new Generative Rehearsal models {{cite:e92f17c16db3aca582a7b8f76a7da7973f46edc2}}.
{{figure:024e7b03-459a-4277-9e09-e2f9e70ffcec}} | m | 9f17ab2a4cc0546c3025752597543578 |
We then report the WER performance of MSRL in various conditions, as well as comparing it with other competitive methods. Four recent published methods are selected as strong baselines, which are RNN-T {{cite:5d7d6ec2789b9eddfd3b9b3d4d2ce549f71612f9}}, TM-seq2seq {{cite:c82bbdd8671eb630215e3ea06ea332be87796a02}}, AE-MSR {{cite:98f32b8b050e645672d921f5a40ec641b06bb746}}, and AV-HuBERT {{cite:14b03ab114f1d1c48393b16658a34fb71d7c641b}}. Since RNN-T and TM-seq2seq methods focus on clean conditions, and the AE-MSR is only evaluated on babble noise, we only report the available results from their respective papers. For AV-HuBERT, the “babble", “speech", and “clean" columns present the WER results from original paper. The “natural" and “music" columns were reproduced using the official code as they are not available in original paper. The comparison of WER results is shown in Table REF .
| m | 94fb38ac4dce3222434d5d9d4b052c9e |
We compare the proposed network LS-MBD-LCISTA (fig:ls-mbd-lista) against the optimization-based method of fixed and structured MBD (FS-MBD) {{cite:6d475d0cfce7ae6c95e72fc660396b3859ff3832}}; FS-MBD uses source information in the Fourier domain to design a compression matrix {{formula:756562f8-4bb9-4571-a040-42ab35a05a44}} , uses a blind-dictionary calibration for structured source estimation, and solve the sparse coding step using FISTA {{cite:c7ef68ceb157e1098ed989c1f11df53c3c18c24b}}{{cite:5235cfa915dcb7f411858e45cfffdff90e69b63b}}. For a fair comparison, we assume both nof the methods know the source shape; hence, the problem reduces to designing/learning the compression.
| m | 9424c153f451334e32cc90e70965d770 |
Path-following (PF) is one of the most fundamental tasks to be executed by autonomous vehicles. It consists of driving a vehicle to and maintaining it on a pre-defined path while tracking a path-dependent speed profile. Unlike trajectory tracking, the path is not parameterized by time but rather by any other useful parameter that in some cases may be the path length. Thus, there is more flexibility in making the vehicle first converge to the path smoothly then move along it while tracking a given speed assignment. Path following is useful in many applications where the main objective is to accurately traverse the path, while maintaining a certain speed is a secondary task. Stated in simple terms, it is not required for the vehicle to be at specific positions at specific instants of time, a strong requirement in trajectory tracking. All that is required is for the vehicle to go through specific points in space while trying to meet speed assignments, but absolute time is not of overriding importance. From a technical standpoint, when compared with trajectory tracking, path following has the potential to exhibit smoother convergence properties and reduced actuator activity {{cite:2b612a0297f8167826749feb008f958f22805990}}.
For these reasons, in a vast number of applications path-following is performed by a variety of heterogeneous vehicles, of which marine vehicles {{cite:28ba3fb3423c5682559c5011109195dc92df9a3b}}, {{cite:738dbf6d49b28fd944668952ebcd661297bdb98b}}, {{cite:ff7f96377d44196f175d1ae2b9f6792684faab78}}, ground vehicles such as Mars rovers {{cite:23083ee18c50ca4688ec9a410f77953cae8c396e}}, {{cite:ef34c42d35ff9af9b84cab44de9e9593cdbdd680}}, {{cite:b802af101bfb3182e83a6282d793059f6dd98c93}}, fixed wing aerial vehicles {{cite:c09e454d25b81460d290abb9100c4443bbd7d5ae}}, {{cite:c83afc85ed5075c60e9c78b73adca1df08823438}}, {{cite:dc71d3530460ef388471826f365be5dae49fa84b}}, autonomous cars {{cite:de7e6175e673d907e2a7c8d2011885d7f9735e15}}, {{cite:e2cd8b20092a20f88a3cc127f5eaad388d7ef345}}, {{cite:8193de9e4df1a2f43d673548f0fa3aec151d01bc}}, {{cite:876755e9d44f3a0f22d346cf94780d2d7d53d7b0}}, and quad-rotors {{cite:57d359b40101ff7d1b71c711061a906dc756bea3}} are representative examples.
| i | ad5af7a7425d74ec674b2b79ebbf11d4 |
In this work, we investigate a set of leptophilic models, {{formula:2d8a592c-958e-44e0-9621-85acee0c3a16}} , {{formula:2848be7b-383d-4434-ad81-393428cad228}} and {{formula:1ff14e49-a8ce-4bae-b1f0-2726845335ad}} , where neutrino quark couplings arise only at one loop level and, due to this suppression, are therefore expected to modify the neutrino-nucleus recoil rate and the neutrino floor minimally. Still, a provision of a very light {{formula:7eee6493-2870-4a0b-bf86-7d454c9ec87a}} is still there in these models, as this suppression can lead to relaxed constraints from proton beam dump and hadronic colliders. Further, due to absence of {{formula:f10f4eda-604b-4487-b963-4359cf4de678}} boson couplings to the {{formula:8d796bd2-fb32-439f-9239-17241217080c}} in the case of {{formula:3bd60296-5ab6-40a8-8cf2-8cd39d27c762}} case, electron beam dump experiments put no constraints on low {{formula:a6d768a8-a6cb-4d33-a00a-4af41746e9cc}} mass region of the parameter space, where that is ruled out for other {{formula:02985575-3d65-4d12-99e6-b26e49d0f1c0}} models listed above. {{formula:01726604-37d3-4ad9-b4cd-85e016b10e02}} model can explain the anomalous magnetic moment of muon, i.e. {{formula:6616b0bc-d03f-4f08-b883-17f017e4e04d}} {{cite:e66a3b268f92fa14c7bd50f4c1d1b94f85717953}} in the sub-GeV {{formula:9613ed9d-3e06-4fe3-8e78-a3da95def1b1}} parameter space, which is also central to presence of a light DM with observed relic density. These {{formula:c6cf1a32-0f91-453e-9fe9-f12ed795abcd}} models are also well motivated by results from DM indirect detection experiments (i.g. DAMPE {{cite:b3aac3fd61e34e8e3b282c7cc24282342f4f83b9}} and AMS02 {{cite:2a5d8f2e6eb70cad6151d628812ed5f5711ccd52}} etc ), along with the possible explanation of {{formula:f76ac52d-e78b-4865-aa2c-c091b2c12f70}} excess observed in cosmic rays through DM annihilation to leptons via {{formula:a10638fe-76f2-47ba-9bd2-43459a9fe500}} .
In this parameter region of {{formula:48959cb5-e5a9-4055-8099-e7ccdcaaaf64}} , there is an extra contribution through {{formula:6877342f-e508-42b7-8918-5039f954a8fe}} in the CE{{formula:0d788d80-4961-4d99-8b9a-70bd6aa6a0a9}} NS process, paving way to its significant enhancement compared to the SM value, aided by the lightness of the {{formula:cef0b14c-13cb-4700-a34a-1812d0c2af69}} boson. This can potentially lead to excess amount of neutrino recoils, preferably in the low recoil energy domain. This increment can essentially lead to an enhancement in the neutrino events background present in DM direct detection experiments, which translates to more DM-nucleon cross section region not being viable to distinguish DM events from neutrino events, therefore, resulting in an upliftment of the neutrino floor.
| i | a9ca80bee1cd6110cbbaccd851bc26b0 |
Datasets and Settings: We use widely popular datasets {{cite:0954b4b9a73157ec13768414b2ba2251ddd03c7a}}, {{cite:0358f7a3b6a1672b506395cd4cc465e58a38272f}}: MUTAG, NCI1, and the OGB-MolHIV for graph classification; PATTERN and CLUSTER for node classification; and ZINC for graph regression task (details in REF ). We borrow experiment settings and baseline values from {{cite:07f7d4d4104d6be11dde8ecc340151d495b28bbd}}, {{cite:0954b4b9a73157ec13768414b2ba2251ddd03c7a}}, {{cite:33991a4e5bcb8a74ab4e9551193bbf77b86430f1}}, and the number of parameters are same with corresponding baseline in RQs.
| r | 57c981da1b0cf8310f75d30d65a336b5 |
All the improvements over {{cite:ba4807111adefa8caaca8ad758aa591b6f2be138}} mentioned above (excluding the generalization by King) maintain {{formula:0dd78e2b-3be5-4743-bd8f-020300390c02}} -approximate distances rather than exact distances. A result by Roditty and Zwick {{cite:175d5d058fce07ce8e76e8cf75b7195989e93905}} suggests that this is necessary since breaking the {{formula:4a002246-b951-4a4c-b0ea-3850fd7d8f3d}} bound while maintaining exact distances would lead to major breakthroughs for, e.g., Boolean matrix multiplication. Henzinger et al. {{cite:f3e64caf9f6538db0610f3a2e241a1f2dba30a2f}} later showed that such a result would give a truly subcubic time algorithm for online Boolean matrix-vector multiplication which again would be a major breakthrough. This suggests that, in order to break the {{formula:a054a5a9-434b-4d74-8d83-f3e303ab9511}} bound, approximation is necessary.
| i | 7361cb003a4a3cbdf9bda652f0c3c2aa |
Other approaches. To address the challenge, we also have tried two other approaches: transformer-based behavior cloning {{cite:4b6d7e50736623cc49d4975320c29003b029df2e}} and offline reinforcement learning {{cite:2a44f528a30e45ee3c8fb5641cc290bb24bf1d6c}}. However, the hundreds of demonstrations we collected for the human study are far from enough to train a transformer model. For OpenD, we set the physics update frequency to be 60 Hz. Planning and behavior cloning last at least 5 seconds on average to open the cabinet. Therefore, the algorithm for long-horizon planning and high-dimensional control for hands does not converge during reinforcement learning.
| d | ce69ea994f27b21fdc748c75a845f97f |
where {{formula:a13d89dd-f50b-4531-beeb-4062bf5c8b6d}} is the magnitude of the electron charge, and {{formula:06748d45-76b2-46bd-90be-a32d81c55d4b}} [with {{formula:27d3b4fa-2dbf-4706-8aec-c147a6616b13}} and {{formula:d0aa39ef-176f-4ea0-8414-29cac7763dbe}} ] are the normalized (by {{formula:8b8a1bd4-4ccf-4794-bfa1-8fe90be4daa6}} ) invariant electric and magnetic field strengths, i.e. the magnitudes of the electric and magnetic field strengths in a reference frame where they are locally either zero or parallel.
Eq. (REF ) is valid in a locally constant field approximation based on an assumption that the characteristic length and time scales of the {{formula:83389c17-57d5-44c4-9f8d-4ea761c74435}} pair production process (the Compton length {{formula:0ee187ca-3b5e-467c-9400-502d65db7e0c}} and time {{formula:b0e76120-e7f6-425b-b638-76abb779e1dd}} scales) are much smaller than the carrier wavelength ({{formula:1220bbde-c0fb-4710-8621-f80976638dae}} ) and the period ({{formula:83f3319d-5366-43fb-a8cf-1a0b036a5880}} ) of the laser field, respectively {{cite:710279672c4a01e9314ccbe77ae2ce9c9a99c360}}.
In particular, pair production is negligible if {{formula:6f4d9471-52b2-4248-be98-ebc8b37c90af}} is small or vanishing in a focal region, while in the opposite case of nearly vanishing {{formula:b64cc7ee-e137-493c-8435-05e3d1945fdb}} Eq. (REF ) reduces to
{{formula:c512d9e3-5ed2-4e12-b2f3-9aeafa4893cf}}
| m | 1b9ea9f21562d9f95332e3765c0ceac8 |
The scoring function used here is found by automated machine learning techniques (AutoML) {{cite:e2c40a35102ef2831b3bc18cd742740941a938d0}}, {{cite:59ad583cf6d5f10bd02dbb6097a3ed98fece8906}}.
We first describe the search space where we find the scoring function (SF) in Section REF .
And our search algorithm is introduced in Section REF .
| m | 836609773601470b5bda00bd7b75a11e |
Young star-forming regions often host massive stars ({{formula:789695d5-bc0a-494b-b8ee-c3fcc2daf4da}} M{{formula:1294ab8f-6d17-4bd9-ab1e-8552291f57bb}} ), whose rapid internal evolution produces intense far ultra violet (FUV) and extreme ultra violet (EUV) radiation fields. Several authors {{cite:eec4702f8870eb3491fcbdb517e4f99f8c3b983e}}, {{cite:58b96c0177d07cfe76d0bba033f3c7831a7770bd}}, {{cite:4dab9ee46cc3a1b18b77d40da285996335824262}}, {{cite:b49e60a765b4609b118738378723da808041f585}}, {{cite:0fd7cd1b61c7ba055dc29c7585d5a02cfcac0995}}, {{cite:8c9e390a1df8fa00a6ce06d7a18a446275f7508c}}, {{cite:1f62c7c81799d8b84cfe5ad9bd2bdc0b7e0cf4be}}, {{cite:1285cfc6cf14fd345116ac8d8c73051d9dbbe91a}}, {{cite:1202b8f77a5b65be012cc711635c72a7ccf58cf7}}, {{cite:ee5c3ae4300a7e4565badd38aee5ff9eca33672a}} have shown that these radiation fields can destroy or reduce the masses of protoplanetary discs by photoevaporating the gas {{cite:8c9e390a1df8fa00a6ce06d7a18a446275f7508c}}. Massive stars are inherently rare, but for example in a region containing 1000 low-mass stars one or two stars {{formula:cdb1dcc1-a3cd-427f-be54-31893777b8f4}} 20 M{{formula:8107ec8c-52c6-4893-883c-8880310a4133}} are expected from randomly sampling the stellar Initial Mass Function (IMF). Several authors {{cite:0e664f9c7b9319d862e542a5c6755f8821ad4994}}, {{cite:91f67b404cbcc6860fbe4ea512dd70206cc51268}} have argued that the only limit on the mass of a star that can form is the molecular cloud mass, so occasionally a low-mass star-forming region containing only tens to hundreds of stars could produce high-mass stars (and observational examples of this appear to exist).
| i | c22de04a45bab6368ed4749eba1fdf5f |
Another useful direction is a hierarchical multivariate dynamic model (HMDM) setup where the observed data vector {{formula:1cf38420-17c2-4b53-9d90-ece27c646d62}} follows a multivariate Gamma distribution.
Several multivariate extensions of the univariate gamma distributions exist in the literature (see {{cite:e45c4d51c9c6ad364602c565fa09767bebdb5c55}}, {{cite:d0f33823335034032e96951e9038ad2501d8e82e}}, {{cite:385e4fa141cd968586d39eb1f77ab15a090d7ed8}}, and {{cite:8bce00e00ed7b8aa6026814e55552faf22550951}} and references therein).
Here we define multivariate gamma distribution as defined in {{cite:64e82ef40ddc503bc55643a2fd528155b392ca2d}} which is in the same spirit as in {{cite:385e4fa141cd968586d39eb1f77ab15a090d7ed8}}.
Following {{cite:385e4fa141cd968586d39eb1f77ab15a090d7ed8}} and {{cite:64e82ef40ddc503bc55643a2fd528155b392ca2d}} to define the probability distribution function (p.d.f.) of an {{formula:8e4a3766-ba60-4d66-8f1f-9129655c3dc6}} -variate gamma distribution, we assume that
{{formula:96c63c33-7daa-4bd9-aaa9-44808126d378}}
| d | 45a1a8ecb60f5c14f745a76c19ac7bca |
The AOUP describes the motion of colloids in a bath
of active particles {{cite:b3420932898829f5366ac98bcc372963eab9d41b}}, {{cite:cbb2f56c7476d048f1abc567f0e81d3e8c3176e5}}, {{cite:d13e17d728a6141044012a7c621b55e2482158a6}} and, in the case of a bacterial
bath, Wu and Libchaber {{cite:a0af752999aa515843163f996d05e38c247a34a4}} showed that the activity of the bacteria enhanced the diffusion of passive tracer particles by two to three orders of magnitude relative to the thermal case. Finally, while the AOUP model provides
accurate predictions for a range of complex phenomena {{cite:1ae5d8ebd55dafbcc2c50101cf228b64df91df34}}, {{cite:6365fa05e5128c635dcb8a54966e913328d9b4d4}}, {{cite:1bff6587bd8fca12153ff55f44c8b750799267db}}, {{cite:f27191be8aaceb4cf8d2f2c5e5edc2f6ffe4064d}}, in contrast to the so-called Active Brownian Particle (ABP) and Run-and-Tumble models, a theoretical advantage of the AOUP is its Gaussian nature {{cite:552331a0969bf465e1c347534619879aa927ca2d}}. Moreover, similar to the ABP,
the long term behavior of the AOUP is also diffusive {{cite:1bff6587bd8fca12153ff55f44c8b750799267db}}. These issues motivate our use of the AOUP model framework to describe the motion of active particles in ice under an external temperature gradient. We analyze these particles in three dimensions using a multiple scale expansion to derive the associated Fokker-Planck equation. Similar approaches have been used in the case of a passive Brownian particle {{cite:29fa6b22c45c31e3a60ee9a0e54c246399b9d1b8}}, {{cite:879bea67da8f22e97727d1df6d25c579064fa93e}}, {{cite:e17b4fb422afdc733e320f9f59b2c77f1e7aa08f}} and for an active Brownian particle in a channel {{cite:740658df6bdd364bc6c35d80f632fe96ed7eafc2}}.
| i | c61d04717be5fe7d48985606e0ff0eb5 |
Our electronic structure calculations are performed within
density functional theory (DFT){{cite:2879d540edae7940fbf8aaa9288f933b68586306}} using
the full-potential linearized augmented plane-wave
method as implemented in the WIEN2k package{{cite:ed06a60185b2d7b39245898e217e20dec5490169}}.
We employ the generalized gradient approximation (GGA){{cite:e569fb8b128c98915ea821d596d47e7fa4f12e58}}
for the exchange-correlation potential.
For all our {{formula:829ae50e-57e2-4218-9317-ee28257388fb}} systems,
a simplified cubic {{formula:fcb4fba8-6021-478f-9cb7-aa0c24e4289a}} crystal structure is assumed,
with both the tilting and breathing distortions neglected,
and the volume is fully relaxed within GGA.
The basis set size is fixed by setting {{formula:918d398d-8c88-4e99-bf44-dfd418c3f199}} ,
where {{formula:df26b631-b8e2-45f3-9b89-34e5ea714920}} is the smallest muffin-tin sphere radius and {{formula:b7aa503e-7d9e-426d-8223-31743e8a2322}}
is the cut-off wave vector. A {{formula:ec8b2aba-1c7e-4b25-a850-f1f9dd328556}}
grid of {{formula:b7eed809-3902-4228-b54e-0078ca6e4dd8}} -points is used for integrating
over the first Brillouin zone.
Atomic and molecular orbital projections are done within muffin-tin spheres.
Projections onto molecular orbitals are done with a modified
version of WIEN2k, as discussed in Ref. Foyevtsova2.
Tight-binding (TB) parameters are obtained by using
the maximally localized Wannier functions (MLWF) method
as implemented in the wannier90 code{{cite:20d32827d9739a9ce19704ee9aa86cd86b11e08b}}.
{{figure:90e34f6e-2b3f-4b2c-8729-e0a2f4bc1ed3}}{{figure:75c765ee-7a31-4a7f-8825-9a7b29b5999d}}{{figure:1e4f2f93-4e2a-42e8-b24e-5ac60299b56a}}{{table:64f4ba3f-c268-4945-afa3-661fede18477}} | m | 879dbd455dbb06e09580760204f8f68e |
Low-data regime.
On the VTAB benchmark, we use a similar setup and hyperparameter budget as {{cite:ae7afe55e38718b89ed44feed89af3bc4da0bb0d}}
(but fine-tune with half the schedule length). tab:vtab shows that, while performance is similar for V-MoE-H/14, experts
provide significant gains at the ViT-L/16 level,
indicating that despite the large size of these models, they can still be fine-tuned with small amounts of data and no further tricks.
{{table:132295d6-53fe-4176-8cdb-00990b4aab97}} | r | 34bfadca6f72206bfa25f4d6b966c273 |
In this paper, we have presented an efficient method for sparse identification of dynamical systems described by ordinary differential equations. We have shown that the Levenberg-Marquardt algorithm, on which our method is based, can be rewritten in a form that enables parallel computation to a large extent. Therefore, the wall time required to solve the identification problem can be greatly decreased. In addition, we have presented a sparsification approach based on backward elimination that utilizes the same time-efficient computation strategy to estimate the relevance of any given network edge, so that only those network edges that have a small effect on the quality of the model fit are removed. We have illustrated with two examples that our method is not affected by many of the limitations, such as fixed sampling rates, full state measurements, and linearity of the model, that plague other methods (e.g., in {{cite:87ee5578008aa66382c25a8fe6b5bb2cc2e683a4}} and {{cite:9e02a8adab6c45030733a0433fddcb051a925212}}). This flexibility is essential for the applicability of the method in many industrial settings. The main drawback of our approach is the relatively large computational demand. However, utilizing the time-efficient algorithm presented in this paper, the wide applicability of our method is likely to outweigh the larger computational cost in many practical scenarios.
| d | a3aece9264c3791d6af20e43701b72b8 |
It should be noted that a recent trend in incorporating machine learning, especially deep learning, into modeling molecular potentials emerged {{cite:a14b88b757913ffe6df95f23e08c4b61571b65dd}}, {{cite:4bad91bba5826d39976434060119df3815f6438b}}, {{cite:08170f820f501d8f9d275b0f33a40a430f0f3853}}. Another related field of HamNet is neural physics engines {{cite:c01473b9b1225a55e4c496a75b36133b74758c89}}, {{cite:69de69a55397967459ffec04fbffd388e9f3b82a}}, {{cite:b2bd3f177c4eb331eca157d0202499fc2f928c88}}, which learn to conduct simulations that conform to physical laws. The design of the Hamiltonian Engine in our paper is highly motivated by these works, while the ultimate goal of HamNet is to derive well-designed molecular representations, instead of to accurately model the molecular dynamics. Also, instead of using the structural optimization to derive stablized conformations after a force-field (potentials in HamNet) is established, HamNet uses the Hamiltonian Engine to make the whole process differentiable.
| d | 1747b61958e3a86dcdba782e3225dc12 |
ACNN: A CNN-based model {{cite:a1a9687eeba1028b296c98f2e0d9e7d231dbd11c}} coreference resolution model that can also produce the mention and mention-cluster embeddings at the same time.
C2F: The end-to-end coarse-to-fine coreference model {{cite:c2770e22fc5035dcaa32e1be79013bd73296a1b4}} with BERT {{cite:a391574c1f773366add49167bb14c043061aaa83}} or SpanBERT {{cite:42328a44dcdbbeeaf41383eb6d1d7e0eb826c8d6}} as the encoder.
CorefQA: An approach that reformulates the coreference resolution problem as a question answering problem {{cite:7eeca9985f0717bbda95a367d7a74a508862f040}} and being able to be benefited from fine-tuned question-answer text encoders.
| m | a67e153fc11f0f650d39edc9d8e90460 |
Still, the fact that we can train an SVM that matches (and even outperforms) its corresponding deep GLN indicates that our theory allows us to successfully disentangle the particular optimization procedure used from the inductive bias it implements.
This means that we can consider alternative learning algorithms that find the same stationary points, but have other benefits, for example faster convergence, more efficient computations, or higher biological plausibility.
To this end, comparing the inductive bias of gradient descent to that of the local learning rule conventionally applied to GLNs (for instance using the results by {{cite:69cd431572ed4bd03ce38ad182995acf1580997e}}) may help us design new local learning rules that generalize better.
Finally, our framework connects networks trained with gradient descent to SVMs, which have formal adversarial protections {{cite:690163f23469214e39b5fead7d6626daf6ec18dd}}, {{cite:d2aa1a81e3d92083de31950f3d5915411b368176}}.
This perspective may therefore allow us to learn more robust networks, either by imposing the results of infinite-time training or by changing the inductive bias.
| d | c218dcb2cf99fc07b60a87bc89c7129c |
In Figs. REF and REF we report
results for {{formula:4ee9c25d-6f42-4182-ad58-d1c1c609f6f1}} . In this case, the order parameter {{formula:f76c8db8-dfe0-4cf9-b78c-c7881a1b7e4d}}
defined Eq. (REF ) is critical, signalling the breaking of the
SU(2) symmetry and therefore the presence of a transition that belongs
to the CP{{formula:89babde7-8eb3-419a-ae4a-0f2a2d23ad74}} or O(3) universality class. In
Fig. REF we report a scaling plot of {{formula:0c35abe2-6652-4473-b8a7-31748ccc62a4}} using
{{cite:55489513033f30dc4114d9d78ae78d774326c343}} the O(3) estimate {{formula:8c012e39-7cd9-4385-8115-b62dd424699c}} (accurate
estimates of the O(3) exponents can be found in
Refs. {{cite:55489513033f30dc4114d9d78ae78d774326c343}}, {{cite:3cc011317e3b7cb26e90655e44b335be26676e55}}, {{cite:664ed02cb92d4ae0f259d06cddbb8707da7cf76f}}, {{cite:a8ccff1547dbf2a2fc26981807fdcccbedc6bab0}}, {{cite:ae2077e04b5798f142d010647e8d56414a1765e4}}, {{cite:4fddf0b98753c574f75a92ff0e068e71876a6b5f}}, {{cite:7fd7da748b99a799f2e83600027a724dcf19beb8}}) and the
estimate of the critical temperature {{formula:685fbf0b-eb9e-4a9a-aabc-9dfae2f7e1c1}} , obtained by
performing biased fits of the data, in which {{formula:e16d6b4d-3bbd-457d-9343-7b861f276781}} was fixed to the
O(3) value. The agreement is excellent. As before, we also considered
{{formula:f55887fc-ee05-4e1b-9cc9-d0604de7c80f}} versus {{formula:9155074c-08d0-4ae8-80fd-0c198d424cfe}} . Data fall on top of the O(3) curve (it is reported
in the appendix of Ref. {{cite:223ae13bf3044eab641f70f2a7ca4b006a7b8444}}) with small corrections
that are consistent with Eq. (REF ) and the O(3) value of the
scaling-correction exponent, {{cite:55489513033f30dc4114d9d78ae78d774326c343}} {{formula:64d037e4-1997-4822-851c-a194a1722447}} .
We also mention that correlations of the operator {{formula:ad338eba-d276-4ed1-bd56-c8baae417a5b}} are not
critical, as expected.
{{figure:78aa6100-e4a7-4f96-b9b4-07217dbf9836}} | r | fd466534a968e7b1799f2aaa59321433 |
Therefore, {{cite:47a1d1ddfe82e02f6eaff469b2862651704d20a5}} propose to replace the buffer with a generative model in the form of the Generative Adversarial Network (GAN) {{cite:7e8699ae6711e4d487a0d4da423b2edbdc0fa702}}. Any structure used to regenerate past data may also suffer from catastrophic forgetting. To avoid it, the authors propose a self-rehearsal procedure to train the generative model with both new data and regenerations of previous examples. {{cite:f16d9f519f9a645fc948d44afcb51a8cbb03f17d}} extend this idea to Variational Autoencoder (VAE) by {{cite:4856bee20c243b9d232afe610077b1209a2920e6}}. Additionally, the authors combine the generative model with the base classifier, which reduces the cost of model retraining.
| m | f404da8647e71f72297fc62bef7b7557 |
We further compare the performance of MirrorNet with state-of-the-arts reported in {{cite:75a1bca4025459b3fc16ce29eb0817a619a1c3b9}}. Table REF shows the performance of different methods in terms of E-measure ({{formula:ec1a2308-0fa4-4859-978f-8e9471e5425e}} ) {{cite:ac07384520a6ea479fa28333e87c9646eaa79c4d}}, S-measure ({{formula:3b27bbe3-65c3-49dc-a006-b41cc42909f2}} ) {{cite:37e879a29783e0c4b48f7e943e9ddfc77cefc9c1}}, weighted F-measure ({{formula:cb3c8a86-bd36-4f64-9810-5ee39b37f5f8}} ) {{cite:488fd4894ccadd53ec417110555084a1a179cb85}}, and MAE {{cite:c4f57f55899eea8d19017913727df7e78b49269e}}. Note that these metrics were proposed in {{cite:75a1bca4025459b3fc16ce29eb0817a619a1c3b9}}. As can be seen, the recently proposed methods tend to achieve better results. Our proposed method, MirrorNet, achieves the best performance in terms of {{formula:345c8e59-fb42-4f24-8b95-f38d8f82378f}} , {{formula:1adfa127-ae8f-4f77-a069-d1e23545aacf}} , {{formula:565d5160-012d-4f90-82b1-039295b7e8a5}} , and MAE. MirrorNet with ResNeXt-152 backbone surpasses the state-of-the-art methods by a remarkable margin in all metrics.
| m | a3bcff0f6b35c33dc031ba39de0ce55b |
Unconventional computing frameworks, such as reservoir computing (RC) {{cite:455155eeb1987279a8f03f411f3d7fae82e568ed}}, {{cite:78be43bc2304db7cfa4676d6b68c7d6394a1ee6c}}, aim to take advantage of the dynamic traits of a given substrate to perform computational tasks.
RC was originally developed as a method to avoid the difficult task of training recurrent neural networks but has since been expanded: by training a single linear readout layer, the nonlinear dynamics of any high-dimensional driven system, even a physical reservoir, can be tapped into to solve complex tasks {{cite:97e13bc6616088422fbc6fd68a01925e04284af4}}, {{cite:638c37638816a90fbb4a24bf65d007413f9c34e6}}, {{cite:79d0aa87c084bf3944a8880cc13dce04f9c1ac57}}.
It is generally understood that computational substrates used in such frameworks must be constructed within a certain dynamic regime to show the desired behavior allowing them to perform as “good” computational substrates; however, for many complex substrates, both theoretical and physical, designing the substrate within this regime poses a challenge.
| i | 69043affb04314a9a9b4e0f4f2078517 |
We rewrite Theorem 8.2 of {{cite:4e7052764bfad7abc2f4a5c456b196b6ec764cef}} for our convenience.
| r | 644c26c865461f2ae5a224838a4b21f3 |
All code was developed in Python language.
The machine learning techniques presented for the activity recognition and the CNN-based decoder were implemented with the Tensorflow/Keras framework.
The computational models were implemented using the NetPyNE platform {{cite:235b3d2398048c8cd804a9efafbb6e561600cf31}}.
The robot simulation was implemented in the Gazebo simulator {{cite:d5460555c099b540d9613aae85ea3db691d10c0b}} with the Robot Operating System (ROS) {{cite:8e34e1324696f11d9911e1a8f6cc73db53729068}} as a middleware.
The next subsections will provide the implementation details of this work.
| m | 55722585d23ef58ba7dd937aa596fd93 |
Density functional theory (DFT) based calculations are performed to study the structural, electronic, and magnetic properties of Fe{{formula:525e0b38-a4cd-406e-adc0-ee0cb7197743}} GeTe{{formula:013f2d50-baa0-41dc-8152-13c59b2bc578}} (FGT family) systems. Structural optimizations are performed using Vienna Ab initio Simulation Package (VASP){{cite:5f77c63543b91469d08966c36f354a30ef5ac6e6}}, {{cite:5a5097cae569f80f673b0d665203da3697ae54d4}}, where the exchange-correlation potential has been treated with the generalized gradient approximation (GGA), with the Perdew-Burke-Ernzerhof (PBE) functional{{cite:cfe2b715b229c10e1218c099408947b14a09f896}}. We use 18{{formula:c51af4c4-836a-4de3-b6da-a15afd85eb88}} 18{{formula:3e04490b-36fc-4123-b0f7-747f791be256}} 1 Monkhorst-Pack {{formula:86041c65-3d0b-4b8b-9d43-b17656e30ac8}} -point mesh in our calculations for Brillouin zone (BZ) integration.{{cite:8e6ae8d3f9a0ec36b86b7aad5cbf71106d387bd4}} To model isolated 2D monolayers, the interaction between periodic images of the supercell along the {{formula:5100599a-3c9b-45bc-b0a2-097be01bfbda}} -axis was reduced by adding a 20 Å vacuum region perpendicular to the surface of monolayers. The lattice constants and atomic coordinates were optimized by minimizing energy based on the conjugate gradient method with a force component tolerance of 0.01 eV/Å on each atom. The energy cutoff for the plane-wave basis set was set to 500 eV.
| m | 7490190e90d54422e8bee9d93e6dd34b |
Wireless technologies have been anticipated to move from the conventional orthogonal to non-orthogonal solutions to meet requirements of future wireless networks, such as, ubiquitous coverage, high data rate, low latency, high transmission reliability and scalability {{cite:82e407f5c7a32123a8dc8cc5f394769524f8381f}}, {{cite:5072c7f40fa950bd39565c6517304e26b5fa2098}}. In particular, using non-orthogonal multiple access (NOMA) techniques, different users can simultaneously share the same wireless resources for supporting a massive number of devices. Moreover, in NOMA, multiple users can transmit data at different power levels over the same radio resources, which facilitates successive interference cancellation (SIC) to be effective for detecting the desired signal. Thus, NOMA is a potential solution to improve spectrum efficiency, reduce latency and provide high reliability, and facilitate massive connection compared to the conventional orthogonal multiple access (OMA) {{cite:6a565875e249096bd7ca4927f2f7757144863c9d}}.
| i | 0ef25b25eb9f21e263c203659167ded9 |
The current rise in popularity of colloidal active matter is due in large part to the recent advances in colloidal synthesis. Through the pioneering work of synthetic chemists and material scientists, there is now a number of experimental realizations of synthetic microswimmers and active colloids. These active particles can be thought of as synthetic analogs of swimming bacteria. However, a major benefit of these synthetic variants is that, unlike bacteria, it is possible to systematically tailor inter-particle interactions and modulate their swimming velocity. For details about the growing library of synthetic microswimmers and their associated propulsion mechanisms, we direct the readers to several recent reviews on the subject {{cite:4abae3474076b75a97b9d7089207125890a19c64}}, {{cite:409c6a73437df268662ef33f7c71bd1b886b206a}}, {{cite:133171e645d6e6b31f366d8aa02bfd1fef036217}}, {{cite:8cd36a70c945c5923a6f7d8c7463b039eefe4266}}.
| i | aed3594a5ff0efaa0a61c4ff8f47f8ad |
We discussed in Section and Section that various methods to calculate sparse loadings exist. For the examples in Section we used the method of {{cite:1865069f80df0fb444997c9f3bb79210614a081b}}, and the loadings for the example in Section were obtained by the technique of {{cite:c127671756f66d6f6253aaf24ae53ca838ccdea8}} respectively.
| r | fe904335cf82e19436a5025d24df0545 |
For the case of LRHRC we find a rich phase diagram, where the power-law distributed unitary interactions are leading actors in determining the properties of the stationary phase. For {{formula:cf5b5bd8-418b-4c47-b7f2-1473da1604b0}} the system persists in a volume-law phase for any measurement rate {{formula:e81d1376-ae5b-4179-a824-ac295b278ed4}} . In this regime, each unitary layer act as a global random gate on the full Hilbert space, hence at each time step the state points toward a fully random stabilizer state. Instead for {{formula:7a11d998-3436-45ba-bf96-ccd996fd435b}} we identify a line of non-conformal critical points separating a volume-law phase from a phase with subextensive system size scaling of the entanglement entropy.
The subextensive phase exhibits algebraic growth of the entanglement entropy with {{formula:5afa29be-cb0e-4cd8-800f-533c7176c0e9}} for {{formula:1062b51d-65e9-462e-86ca-141a3855bf48}} and a constant value for {{formula:ed5c31ea-551c-40cf-88fb-edc0ad9de71b}} (area law). This separation is neat in the antipodal negativity, which increases algebraically for {{formula:7d72d24b-e791-4353-9041-4ad94ecc9df6}} and decreases algebraically for {{formula:f7a2aebc-b8a1-4280-8691-876f24339de9}} .
We locate the crossover point {{formula:f2be6489-b41e-4b99-8a2b-e334594207e5}} using a counting argument in the limit {{formula:423028ff-ad5c-4615-9686-a27660954d6d}} . The numerics for {{formula:36321530-772d-4380-af73-1dd073cfe882}} suggests the qualitative properties of the phase are captured with the limit {{formula:ee20dd93-664d-4425-aedc-b8a613f95f74}} . In particular, the algebraic exponent characterizing the system size scaling of the negativity ({{formula:60f3d6e8-1938-4ee3-8d3d-184ed47b9179}} ) matches the value obtained from the counting argument {{formula:4567b3da-4572-45b0-b4f8-d46f09b6d39b}} .
Finally, for {{formula:f95ff9c4-d885-4a62-8756-ffca4d2de8c5}} our findings conclude the phase transition is between a volume-law and an area-law phase, with the universality class compatible with that of short range clifford circuits {{cite:aae88ada72fc7adeb6e170df8d7f6e05b4cc4bad}}.
Overall, parts of our analysis are compatible with the results obtained in Ref. {{cite:9949ec430638e663c1a4237d58fc8789b1d0d13a}}, where a similar but different long-range protocol is considered, suggesting these models critical point belong to the same {{formula:1d061a16-0e74-4202-8d81-f33e168b63e4}} -dependent universality classes.
| d | 49cd0e7fc082e1a8d8063c562ecff3f1 |
In Table REF , we provide our ablation table by also adding the results with the content variable. As explained in the main paper, content variable does not improve the performance of our models in contrast to the state of the art video prediction {{cite:0daa2ca83ff0f3ef5ec7947da0e1c419da5020df}}, therefore omitted in our formulation.
{{table:8221010f-74d0-4a93-91d4-fb0a8de9074f}} | r | 736926ac5dc689bc8956af0f84ecb04f |
where {{formula:a7594b92-de34-482a-b7ca-19e7b906148e}} , {{formula:28f9ab57-9844-4dbc-802b-9402282430f1}} and {{formula:3dae172b-3212-43fe-bf53-96f24631f423}} denote, respectively, the number of free neutrons, protons, and total nucleons with local densities less than {{formula:13a26b19-ca31-4616-949b-33054f58875d}} at rapidities {{formula:b2c55538-d370-48c3-b4f9-4a50be2d5762}} , and {{formula:d053fe48-4b03-4ba9-ac96-3bc180fc3988}} is 1 for neutrons and {{formula:78982244-4a72-443d-8d47-15fcc75ca187}} for protons. From this formula, we can see that the isospin fractionation effects are incorporated into the collective flow {{cite:dc2b50d874b998b95c5ca01547249968c5de3aea}} of both neutrons and protons through {{formula:4b6649b4-30cd-4c6c-b516-df5f9b44729c}} and {{formula:12ccede0-459d-4171-91a1-bb8dad3cdb72}} . To understand this effect, we show first in Fig. REF the collective flow of free neutrons and protons as a function of the center-of-mass rapidity. First, it is seen that, consistent with the previous result in Ref. {{cite:48893d50f893a379ec34dbe7cf5e5325335c7d51}}, the proton flow is less sensitive to {{formula:26451f53-9e11-4b11-93c1-516863728435}} but higher than the neutron flow due to the Coulomb repulsive effects. Second, with a certain {{formula:15ecf5dc-b4c8-40ec-9304-2c6fee1c1e02}} , we can observe that the transverse flows either for neutrons or protons are not changed essentially in the left and righ panels of Fig. REF . This means that the transverse flow is relatively insensitive to the actual value for {{formula:c2e46aa1-de58-443f-9b8f-e462c8bb4268}} at any given density, but is mainly sensitive to the slope of {{formula:83b8e501-814b-425e-b101-aab505a06f90}} , which governs the pressure that the symmetry energy provides in a neutron-rich system as well dense astrophysical environments such as neutron stars. It should be mentioned that this finding is similar to that observed in the ratios/differences of neutron vs proton elliptic flows in Refs. {{cite:891ad0f3241e3a1dd1426e970afed20438dc346b}}, {{cite:cd7e09c7ee88907b3e0ad2e2980861c225954df4}} as well that observed much earlier in Ref. {{cite:1b6344a00158ea3099e3210d081a39bb9aeaae42}}.
Nevertheless, the sensitivities of transverse flows to {{formula:906288ed-a16a-4978-97b7-a1e591933289}} are not obvious either for neutrons or protons. Shown in Fig. REF are {{formula:1bdfdad2-7a3d-402f-a7ae-4ee6d91deece}} and {{formula:b0d3da71-e43a-4a17-a218-7dd9c2117be3}} as a function of the center-of-mass rapidity, respectively. First, since the mass between the target and projectile has a little difference, we thus observe that the shapes of both {{formula:6ca6d6d4-7767-4955-9864-d69b93feb40a}} and {{formula:d5d23153-ebb1-4bfc-8a27-7445b0461d54}} are a little asymmetric between the target and projectile rapidities. Second, it is seen that
varying {{formula:a0444260-96dd-4504-88e0-6cdd28ab9858}} from {{formula:ed0eb985-16c1-4d22-a46b-98d6560feea3}} to {{formula:5732d1f7-189a-4346-92df-cae4c3783b8e}} MeV causes more (less) free neutrons (protons) on the whole for both Case I and Case II. Certainly, we can also find that effects of {{formula:a14325bc-c165-4232-83d6-1ad29ba6415f}} on either {{formula:d5630e59-1d9b-442c-a569-ed458d0f76e4}} or {{formula:947b8a39-0636-4b56-b385-5012acfa17e8}} are reduced somewhat in mid-rapidities for Case II compared to those for Case I. Also, the effects even reverse at the target and/or projectile rapidities. To understand these observations, we show in Fig. REF the isovector potential of Case I and Case II at both {{formula:85689043-ec22-42b2-a7b1-637852c747b2}} and {{formula:64cf4045-75fc-40f3-8461-6709c9f3db93}} . First, it is seen that {{formula:810d526f-c4fa-40ff-b9a5-9ffda6562ce9}} affects the isovector potentials mainly at high densities, and thus the high-density behavior of {{formula:c66e0d61-2e79-4e2c-8e78-e83e51b00f9e}} dominates {{formula:4b49f208-3be1-4d5a-b93d-57bb3330e9ca}} and {{formula:eac0ec72-5511-441e-a1e9-d1f4fe121848}} . Moreover, varying {{formula:21704aa8-98e9-438b-ab50-637626db3262}} from {{formula:c9eb3162-ff7c-4cb0-a120-1959448171f4}} to {{formula:a7d0431b-0d63-4e35-b2a5-56853aa632ae}} MeV, the neutrons feel stronger repulisve effects while the protons feel stronger attractive effects on the whole for both Case I and Case II. Naturally, we can observe more free neutrons but less free protons with larger values for {{formula:67e523ba-4100-4f66-af47-507b6c736f64}} . Second, we observe that the differences of isovector potentials at {{formula:44a7ff0c-ebda-4278-8556-99af8ca16271}} between Case I and Case II are negligible, while the differences of isovector potentials at {{formula:eef4fb67-a975-4541-ae8d-8738caf0dc3a}} with different {{formula:24a3a5ce-6235-40dc-ac54-ea9a48b4c059}} are smaller in Case I than those in Case II. This is exactly due to the more accurate criterion, i.e., {{formula:e5f13cfa-6e9f-4b93-82db-53ea802481f9}} MeV, used in Case I that reduces the effects of {{formula:f5ee6245-b3d4-4d31-b73d-c7a844348ac2}} on the isovector potentials and {{formula:15a7f9ca-b4c5-467a-b4af-8a4251108920}} at subsaturation densities. Moreover, since the effects of {{formula:c92eef6f-2713-44f5-b37c-dabe98fd76fc}} on the isovector potentials at low densities are opposite to those at high densities, the effects of high-density symmetry energy/potential on observables at compress stages are likely to be smeared out by low density symmetry energy/potential at the expansion stages. In particular, nucleons with target and/or projectile rapidities experience longer time in the expansion stages and emit later compared to those at midrapidities, the effects of low density symmetry energy/potential on observables are naturally considerable. This is the reason we observe in Case II that the isospin fractionation effects are reduced slightly at midrapidities but reversed at target and/or projectile rapidities.
{{figure:4dc76bdc-9fdb-4c7b-be82-762371931501}}{{figure:3ffcf9d6-f39d-40ec-82ef-bf64354f8456}}{{figure:f33df698-d89b-4760-9d13-fd88a48aed38}}{{figure:7bad965e-55b1-468b-8029-80bf14df3e78}} | r | 46d5f035e66e5cd7885e822036fc00b2 |
(ii) According to numerical simulations with some analytical analysis
{{cite:45502f9e4932d6775f6d23ed365d21e60dfbb288}}, {{cite:3691b34a54ba14e6629d8eddf4e7dc567964fef1}}, {{cite:7431be3ad68a0b8d85dc68e8b4a02a8f51d2c342}}, {{cite:b115cfb94e3f772bf93dd808a56738c7d0bfe11b}},
{{formula:714828ca-caa5-469d-b309-86662b3d0adb}} is usually a function of per-site energy, i.e.
{{formula:ed508faa-4100-43af-95e0-2de4c21fbfc2}}
| d | 1ad444259f61a63480022d38b2049b77 |
Emotion-dependent models may require more training data than emotion-independent models because the number of units/models is increased by multiple times (n times where n is the number of emotions). However, with the recent advancement of pretrained acoustic models, the amount of data needed for training speech recognition models is greatly reduced. For example, Wav2vec 2.0 {{cite:08a6b28cbd0656f8c694f8a813d8bceb9da36fd9}} outperforms the previous state of the art on the Librispeech {{cite:9f72ff84e88d85c78db3c3d8e4becff6e4ab4263}} test set in terms of word error rate while using 100 times less labeled data. By fine-tuning Wav2vec 2.0, we can train well-performing emotion-dependent models even with a small amount of data.
| i | b2dcf0447079afb2e9e4d56a9034f84a |
We train MoE models based on the Transformer-big architecture {{cite:9efc7b64af64bf1362cc490cd7feaeb289a1ff35}} with 10 billion parameters on the Web-50 dataset for up to 20k steps, it is very time consuming to train such large models for too many steps.
In Table REF , we report the throughput of different methods measure in two different clusters: the cluster of V100 GPUs with a 100Gb/s InfiniBand fabric and the cluster of A100 GPUs with a {{formula:55760a2c-24f2-43e5-8e8f-0f787f6e9a48}} Tb/s InfiniBand fabric.
We observe that both Gate-Drop and Gate-Expert-Drop get higher throughput than the baseline in either cluster.
It is noted that the relative throughput improvement of our methods in the V100 cluster is more significant because the hardware (GPU for computation and InfiniBand for communication) is much slower than the A100 cluster.
Higher improvement is expected with slower hardware where communication is the bottleneck.
| r | fef9b068c2a3bd2904dd9746ad1ea336 |
Next, we will introduce a new property of dynamical systems which give a sufficient condition for that {{formula:bfa9861a-4b7d-41be-895d-29a573158093}} is a nonempty open and dense set in {{formula:baa6a99f-5b32-4f09-914f-9739dc2c6e2e}}
Before that, we recall specification-like properties.
The specification property ({{formula:925970a4-0329-4484-8484-233ecdeb537e}} ) introduced by Bowen {{cite:ef84d7e94619070f9783df214c62a65aa1487baa}} plays an important role in hyperbolic dynamics and thermodynamical formalism. Based on this property, a number of classical results have been established, including growth rate of periodic orbits {{cite:ef84d7e94619070f9783df214c62a65aa1487baa}}, uniqueness of equilibrium states {{cite:e963da9111d71498c8991fea0f86061e694e950d}} and so on.
In recent years this notion served as a basis for many developments in the theory of dynamical systems, especially in multifractal analysis {{cite:612558811dfc84ac3673a51db7adafc2d99662c9}}, {{cite:e1c1bfab78a9c5b551fed968b201f71b9ea2c9b7}}, {{cite:f94160d8679075a65bd012d482cee4be823d194c}}, {{cite:201a171c64f65c97184de7ed1fefd4e4a2955521}}, {{cite:8c238c4ff14c8656ba637c237bc18dae9b996d2f}}. For systems with specification property, Li and Wu showed in {{cite:8c238c4ff14c8656ba637c237bc18dae9b996d2f}} that {{formula:b4f3d914-62d8-48fb-9ee7-907a068b35c3}} is either empty or residual for any {{formula:3ff585f3-4083-426e-ab2b-8924ee410f26}} . Dong, Tian and Yuan proved in {{cite:201a171c64f65c97184de7ed1fefd4e4a2955521}} that for systems with asymptotic average shadowing property and measure center coinciding with {{formula:9ee3f6c7-3b79-4f54-a9e6-042e9ec3a99f}} , {{formula:b19cee93-8a5a-460b-a4d0-80cde62b0c0d}} is either empty or residual for any {{formula:17c43918-c14b-45d9-8009-58d8e40e670b}} and {{formula:8d9d880c-ac87-4e93-b9e8-62679eb5d69d}} is residual in {{formula:13a65388-b665-4413-a6bb-be9a106dbbe3}} .
| r | 99cb420e574e7c9921df6b82b2cb834e |
Another major set of algorithms, known as empowerment, have also proposed using intrinsic rewards as the sole goal of behavior {{cite:953a9fc683a42b249404387c0b4ee7480def4ab3}}, {{cite:9182b7cc58e8f8f0b6b0fb654c00a3f2687b6ec2}}, {{cite:a5976134cf66aa7f495b35c7a8e5d769858469cc}}. In this approach, the mutual information between a sequence of actions and the final state is maximized.
This approach differs from ours in several fundamental ways. First, action-state path occupancy is maximized when both action and state entropy increase, while empowerment increases when action entropy increases and state entropy decreases given the performed actions. This makes empowerment agents to prefer states where actions leads to large and predictable changes, such as unstable fixed points {{cite:9182b7cc58e8f8f0b6b0fb654c00a3f2687b6ec2}}.
One drawback is that empowered agents tend to remain close to those states without producing diverse behavioral repertoires, as it also happens in causal entropy approaches {{cite:bf980f2900f80f4d21e3ee1894baf2a0da0c1398}}. For instance, in the cartpole setting, both empowered and a causal entropy agents balance the pole upwards and cease behavior when that state is reached {{cite:9182b7cc58e8f8f0b6b0fb654c00a3f2687b6ec2}}, {{cite:bf980f2900f80f4d21e3ee1894baf2a0da0c1398}}.
In contrast, entropy seeking agents generate rich behavioral repertoires while avoiding states with little action-state entropy.
Another crucial difference is that empowerment cannot be formalized as a cumulative per-step objective (see Sec. REF for a proof; {{cite:9182b7cc58e8f8f0b6b0fb654c00a3f2687b6ec2}}, {{cite:b0957148c5ed8fa26c078897ca35d590eee318f3}}, {{cite:a5976134cf66aa7f495b35c7a8e5d769858469cc}}), in contrast to action-state path entropy. The fact that mutual information and channel capacity are not additive over Markov chains makes it difficult to formalize them as a cumulative objective that could benefit from the tools of dynamic programming {{cite:83b15fb3790ccdeecb6d23c48b37025e27091773}}, {{cite:b0957148c5ed8fa26c078897ca35d590eee318f3}}. We note, however, that an approximation to empowerment having the desired additive property could be readily obtained from our framework by putting {{formula:3744cc45-fa08-4243-8472-337b92a07ed5}} in the expected return in Eq. (REF ), such that predictable state transitions would be preferred over more stochastic ones.
| d | caee5f86439bf3f1a554db1d8591d058 |
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