text stringlengths 54 548k | label stringclasses 4
values | id_ stringlengths 32 32 |
|---|---|---|
Wang et al. tackled multi-label classification by employing ranking and thresholding heuristics to refine the set of predictions {{cite:f72e629fe2521bcc091ad13a39a0d227592418b8}}. In this work a joint image-label embedding is produced to capture semantic label dependency as well as image-label relevance {{cite:f72e629fe2521bcc091ad13a39a0d227592418b8}}. RethinkNet {{cite:d39fbda01fd1fefda1a10524968d3a37a4cb80dc}} reformulates the sequence prediction problem in the multi-label classification paradigm by adopting a recurrent neural network (RNN) to gradually refine predictions and to store the label correlation information together with a subsequent class-level analysis. Ge et al. propose a weakly supervised curriculum learning pipeline for multi-label object recognition, detection, and semantic segmentation {{cite:a734a22151e4087938414962874242b33a9906bc}}. It employs an algorithm for filtering, fusing, and multi-label classifying object instances using class occurrences collected from multiple mechanisms {{cite:a734a22151e4087938414962874242b33a9906bc}}.
| m | 76e525fc2411d3b5c5e3cca942f57dca |
If the ring is large, the problem can be well approximated by
the straight-line infinite crystal lattice {{cite:b1ca0d0969bfad7b262634699f10a5661f6cfbe4}}
with the period {{formula:c30c8819-2269-4708-9fad-eb40efe1b4db}} . Then, {{formula:2408117c-7099-4010-b623-e02434460e13}} and
expressing the Bloch functions via the Wannier ones
allows to take the {{formula:b1cb5158-be75-4fb0-b39b-d2e3bded9b3c}} -derivative inside Eq. (REF ),
{{formula:6c5e1d04-8b06-4918-84b0-9907f5ed9e5d}}
| d | c13ba72285f944eb6a64241fce838076 |
We have applied the model to the observations of the Milky Way disk and empirically determined the metallicity yield {{formula:e21d030f-ce68-4e8d-8227-931643403c78}} . We obtained {{formula:1fa1dd22-9da1-479e-882a-746953bfcc5f}} , where {{formula:ba41ed6b-b33a-4e18-ab92-f1b28f7e5f01}} is the metallicity mass fraction of young B-stars in the solar neighbourhood {{cite:004f32d1d98964b52cc986b45ffcadfd52bf9040}}. {{formula:2673e8de-dbd5-4237-829c-799dd7fe9a03}} is the fraction of stellar mass returned to the ISM and has been adopted as R = 0.4 in our model calculation (other values of {{formula:15027b2b-1aba-42ce-bb5a-58a3d8b2b6ed}} were also tested but the influence of varying {{formula:8d0ff416-0e4f-40ef-99d3-8cb46177a8e8}} was found to be small). Using a B-star mass fraction of oxygen to total metallicy {{formula:f7e916f9-2fb1-4443-84a3-4e120bf57ea9}} , we determined an oxygen yield of {{formula:c9a5062e-c0c9-48b9-a9c9-c3573d2d54fd}} = 0.00313. With a galactic wind mass-loading factor
{{formula:12df963b-36ed-4462-b384-0bb41ca07309}} and a very low accretion gain {{formula:11dc4bc3-a5c7-47b9-b7ff-0c649d3ae9ad}} , the model reproduces the observed metallicity gradient very accurately. We conclude that based on our model fit the Milky Way disk is characterised by a low accretion rate and a moderate galactic wind mass loading factor. We note, however, that this result is in disagreement with the estimate of the Milky Way infall rate from ultraviolet absorption line studies of halo high velocity clouds in the sightline of halo stars from which {{cite:dd55ac5cbf72d0354500a623fae1f450602c2dff}} estimate an infall rate of 0.8 to 1.4 {{formula:b4fcb7d3-1c92-46b0-bef7-31dc31e906f4}} yr{{formula:86c357a9-8cf9-499b-b059-168247c8f4aa}} . With a Milky way star formation rate of {{formula:14d41fcb-7422-470c-a65e-b4433de5e951}} {{formula:b4b014c1-8b79-409a-9efe-dd5d739f0d22}} yr{{formula:8126e68d-0b25-4c4b-b348-87f6114b0631}} {{cite:2605ffc375356d1391abd2d80699fefa002807d6}}, {{cite:d43358628e8b4294512f44c58765df4db823d50c}}, this would lead to a value of {{formula:6086a8a3-a52c-448b-b67d-00f58cb8020f}} between 0.35 to 0.93 much larger than our very good fit indicates. However, we also note that {{cite:2605ffc375356d1391abd2d80699fefa002807d6}} do not rule out star formation rates a factor of two higher for alternative choices of the initial mass function and that the determination of the infall rate depends on a variety of parameters which are not well constrained as discussed by {{cite:dd55ac5cbf72d0354500a623fae1f450602c2dff}}.
| d | fcdc5af55f8a56fac459f840d7c70346 |
To further understand the magnetic interactions in BMTO, DFT calculations have been performed using the plane-wave-pseudopotential approach as implemented in Quantum ESPRESSO {{cite:a0673a23166b1fab9e9ea2e7e86364e6f33bb5e7}}. The experimentally obtained structure has been considered for the calculations. The ultra-soft pseudopotentials are used to describe the electron-ion interactions {{cite:0100c725a15f7d45bc47beb41b647b86ccd7c432}}, in which the valence states of Mn include 15 electrons from 3s, 3p, 4s and 3d; Ba includes 10 electrons in 5s, 5p, and 6s; Te includes 10 electrons in 5s and 5p orbitals; and O includes 6 electrons from 2s and 2p shells. The exchange-correlation functional is approximated through PBE-GGA functional {{cite:e8453a7f513e821699ab8221bf75f9ec0c2c52d5}}. The convergence criterion for self-consistent energy is taken to be 10{{formula:eb27d21b-5a3b-4588-88c9-1e058cdb40d4}} Ry. A k-mesh of 4 {{formula:ba175ea2-52e9-4bd3-b0c9-44f539c27c1a}} 4 {{formula:ef9210c9-1509-4928-9d34-3d311f9c654a}} 2 is used for the Brillouin zone integration of the supercell of size 2 {{formula:dff74a4c-0a00-4c67-8b03-2bfa98910e49}} 2 {{formula:0c24f797-4aa4-4e47-9e20-b219a510fe56}} 2. The kinetic energy cut-off for the electron wave functions is set at 30 Ry and the augmented charge density cut-off is set to be 300 Ry. We have also performed test calculations with a higher energy cut-off of 40 Ry and charge density cutoff at 400 Ry as well as with a higher k-mesh of 8 {{formula:eca4d718-6275-4b1e-87b9-872a31604291}} 8 {{formula:277563cf-0c30-4783-8c44-b626ada24c74}} 4. As the results remain the same below the tolerance level, we have used the lower cut-off and lower k-mesh to reduce the computational time. The strong correlation effect is examined through Hubbard U formalism {{cite:684ff5a8bb9d08c520f98a201990a2c9ca13fb2b}}. The magnetic coupling strengths are evaluated as a function of U in this strongly correlated system.
| m | 198943782c5ba4f4f409875d30e88b1e |
This work proposes a generative model for macroscale communication in the brain that we show predicts directed, instantaneous, and task-specific communication dynamics. We compare our model on a synthetic task that tests the requirements we set out for our model and find that our model can accurately uncover the communication dynamics we incorporate into the synthetic data. Then, we train our two models on three fMRI tasks and find that reconstruction error decreases with higher sparsity parameters, indicating that the sparse prior on brain communication dynamics fits our data. The sparsity of macroscale brain communication needs to be studied further but aligns with findings in computational neuroscience {{cite:67a1dbf4667aed5ecbfcf4a7ba2ba9fb1023f5d0}} and the design principles of the brain {{cite:1a645a6c1e7410985868a9324b590d3b35ecbdfe}}. We use a model with the lowest reconstruction error to predict what task small time windows are from in a test set and compare the classification accuracy with a commonly used metric, dynamic functional connectivity (dFNC). Our model performs much better with smaller window sizes, supporting our claim that our model predicts instantaneous communication. Then, to understand the added benefit of directed models, we look at the absolute sum of the communication for each task and find that almost all, especially strong, connections are directed. The directions and the strength of the communication also align with neuroscientific priors we have about how regions affect each other. Thus, our results confirm what we set out to incorporate into our model from the beginning.
| d | 25cede75751ef8df6c6398fa033302b4 |
Coulomb and Riesz gases are a classical field with applications in spherical packing {{cite:9b6bb4ee42a22918e24f67ea8ca3eecad27cdd01}}, {{cite:bbc9f8a329f74611fd6d25b38e100b3e1e33033f}}, {{cite:cad98bbedba45943aae0b292cda9195072bc6bf7}}, {{cite:637b731f7868db3fbc3ff0c21c45a028edbb1725}}, {{cite:0a9f89e72d3d66b379412f8452dfcb13811717d7}}, statistical mechanics {{cite:e47beae74d2a70fbea09910e9b256e707b093c00}}, {{cite:11c95a395fe16159fd3f9ff0301629cb5c8b6485}}, {{cite:2b3530bdcae9fd3eab0eceba3979a1583e06dbbf}}, {{cite:f98c73f2b8192427a6f9afddb8a9c528703de5de}}, {{cite:ea009eafe5316d03d5d255b659cfe0168ed4c93f}}, random matrix theory {{cite:d7b84a20379ccb2d98bfdceaa65dd3a996385b74}}, {{cite:bb509901901bbe8b985152d51d2831db687492a8}}, {{cite:3272c7662166f82a1c081f829878036123e42b5e}}, {{cite:85b891c154279e8d64d550461d3a3a1ae1798524}}, {{cite:5fc5f876495e682c2b6014ff13c7fe958f5a109e}}, {{cite:0ef85c41865bef4dde89d98b1878789ffb7b6bf9}}, {{cite:fe6696fa86181831dae6bf84a8067235dab7fa52}},and mathematical physics {{cite:649be50047685e712c7e962827dc61ba8e7428eb}}, {{cite:edc8699f82bacc43fee6a9084f7413947449ee46}}, among other fields.
| i | a463d2330e04ac0b161dea863478e180 |
In either case, inflation could play an important role as part of a more comprehensive picture.
While inflation does not make universes like ours more
numerous in the space of all possible universes, it might provide a more
reasonable target for a true theory of initial conditions, from quantum cosmology or
elsewhere. (This is a possible reading of {{cite:5afb8ca71f7a59af51720cd74b63e3963dd8bbbc}}, {{cite:e13719dc100af5c368fea2075bcd18a954c7d292}}, although
those authors seem to exclude non-smooth initial conditions a priori, rather than
relying on some well-defined theory of initial conditions.)
| d | 6b3efd949559bf37a1fae844dad27976 |
In {{cite:408375308d27cca23a90f41540083f0b1bb38448}}, the traditional detection based methods are replaced by the density estimation based crowd counting methods, which can detect the density of crowd with high performance
and high precision. However, the encoder and decoder of traditional CNN based
density estimation methods have low correlation, which is difficult to remain the spatial information
of the image. The Trellis Encoder-Decoder networks including multi-path decoder and encoder, is
proposed to improve the accuracy of counting. The structure of network is shown in Fig. REF . Only two pooling layers are applied to reduce the loss of spatial pixel accuracy. In addition, a multi-scale encoder is designed to improve the adaptability of network to the large variation of the object size.
{{figure:e5f9ff14-bbaf-44ab-8421-f5de9e12d4a2}} | m | 0eb51ed8be0600e92756ac1bed9d80bc |
Here, few aspects need to be clarified. First, the field redefinition derived here is purely dissipative correction taken care by the medium interaction and should
not be confused with that due to thermodynamic frame choice mentioned in {{cite:ec071adc613a5347a18cc8748d882814acdabf1e}}, {{cite:c6b4c12135713c677916afba9956cd8568874e69}}, {{cite:ad5c39c06a1086724dcb4c2987ae1d42cbb238fb}}, {{cite:3243367dcd6741602ba32d19aa0f35440e942394}}. The corrections
are expressed in terms of the dissipative forces which is why only the spatial gradients over fields are appearing in the corrections and not
the time derivatives as for the other case. Second, the conservation of energy momentum and particle number shown here is purely
macroscopic. Eq.(REF ) and () do not hold for any arbitrary {{formula:639ce4df-89cb-4949-af22-03039c2cf551}} . If only the field corrections are properly implemented in
thermodynamic identities, the {{formula:63ab481c-ddda-49fa-8b76-5f3e54cb1921}} obtained from transport equation for next order satisfies those equations such that it can be said that the dissipative
field correction and conservation laws are compatible with each other. The only case where conservation holds at microscopic level (form of {{formula:e567a94d-3d7b-4c8e-81ec-a1d87b9e1ead}} does not matter)
known to author is the new collision term proposed in {{cite:fea0c49e5374b787f6876cb5e2a94d6a86eef455}} where the mentioned integrals are identically zero without the need of
extracting {{formula:cceafa94-9d48-4836-ad38-57592792f07e}} from order by order gradient expansion.
| d | 1b326951266cae337f7fbf1011880dfd |
Automatic Threshold Detection. In certain scenarios there may not be a good setting for the tolerance parameter. In this case automated methods like {{cite:77f4cacc83d97bb781400ccd1b523ded81f02add}}, {{cite:76b3c4412bcbb65f2100b2392eb79817433ff913}} can be used to perform an iterative optimization of the fairness hyperparameter before the actual model training is started.
| d | 7a6713b7bebc099f63a6f966fc27650f |
A final consideration to be mentioned here is that the stochastic
nature of the turbulent spectrum of the velocity field was not taken into
account, namely, in this paper, the seed to generate the random numbers was
the same for all simulations and it was fixed from the beginning. However, it has
been shown elsewhere that simulations with different realizations of the random seeds can have
significant differences in their outcomes; see for instance {{cite:fb6214de697eaff37e9a09d4e1146698165f52c9}}, {{cite:cf6ca61b3ccf5a2f6ad6a07257330ac3099e8537}}, {{cite:8cba6ca1cc78c41b9b2bcc7ffd5e442e4326cf1f}}, who used
different random seeds to make a suite of turbulent simulations.
| d | 4a411497196001139dde33ba1cb05af3 |
There are many natural examples where Condition G is met. E.g. if
{{formula:499d289d-fa36-4891-a19a-e9cbca10c360}} is the ideal ring of an algebraic number field {{formula:0d8bd02e-679f-4ced-8ee7-e7eeab2972a3}} , then a
well-known result, see e.g. Lemma 4.9. on p. 143 of {{cite:bdd3ad2891322902712885ba617d2d64ac9bc280}},
provides the estimate {{formula:a3afe910-1b1f-461f-993d-ce5da635d13e}} for
all {{formula:e3da0225-e3e3-4d18-b58f-e7117e2d6f25}} (where {{formula:97463d8d-04a4-40ac-93ef-e2d8d46de652}} is the classical {{formula:fcd92c47-c072-4412-b2a1-e5d58feba7b2}} -term divisor
function and {{formula:d8efe9be-0ae8-4130-a383-21329bb4c967}} is the degree of the algebraic number field {{formula:902364e1-8e3d-4b16-8754-2fcc6c327927}}
in question). It is clear that in case {{formula:0c280216-b8a7-4a08-afcc-4fae7cf18148}} also
Condition G must hold. Actually, {{formula:b9ca0a1f-b8e7-41e7-afae-18a8554c487e}} and by
well-known number theory we also have
{{formula:32a3a50d-c520-47d4-98b4-d147a6140d74}}
| d | 8f2370922254f6c3dbfbc3f837fe3ce5 |
We train MoE models based on the Transformer-base architecture {{cite:9efc7b64af64bf1362cc490cd7feaeb289a1ff35}} on the WMT-10 dataset for more than 100k steps using different methods. The results are shown in Table REF .
We see that both Gate-Drop and Gate-Expert-Drop have higher throughput than the baseline method with
relative improvement {{formula:e68605b3-f793-4d4f-8d9e-431d3b6a95d3}} and {{formula:3fc0bf39-343a-407e-a4a2-64d2ce0af37d}} respectively.
Gate-Expert-Drop has higher throughput than Gate-Drop because computational cost is further reduced by skipping experts.
| r | f740a6ca4d03c22ad49e3e542dc98f2a |
As an additional refinement, the aggregate robustness scores can be replaced with more precise plots of model robustness across the perturbation parameter space (e.g., {{cite:a67b508596cdfc0899f8d2ba32b5a14d69841955}}, {{cite:d0c67cbb61bcd05718b0e4c58514bf58044a7057}}). This can provide detailed insights into the specific regions where models may fail, which is especially beneficial in safety- and security-critical applications.
Beyond that, a careful, fine-grained inspection of the robustness results can help pinpoint failure modes, i.e. specific conditions where model robustness is lower than in others (e.g., direct sunlight or very low brightness, as shown in Figure REF ).
Improving the training data sets based on the results obtained in the robustness tests, e.g. by using specially selected, augmented or synthesised data, seems a promising direction for alleviating their shortcomings.
{{figure:521a5d5e-02fa-4f34-bc70-4b034a69be68}} | d | bc8f800b955f8a9cafeae37a715c9193 |
An interesting question is whether the framework introduced above holds for loop amplitudes. There are a couple of ambitwistor formulas for loop amplitudes {{cite:a2ebc65514ef43c93c490ff601c3f58610f57187}}, {{cite:12e460695a2dc8f76617869a3eda04ed6456b85b}}, the most successful being the ones based on nodal surfaces {{cite:35b9d6ec39ada02693cc820066a7c1c202ebe064}}, {{cite:8f2f46656e7a95010d693d6861e0cc7a7c5b3199}}, {{cite:ad5219e39695b943ee63721a1bdd537ecec6d7e9}}, {{cite:e70458ea413abc4e121f703ef8d452d84bf48df7}}. The latter can be generalized to the celestial case making use of our replacement rule (REF ) to extract numerators in front of the Mellin transform of a scalar quantity. The outstanding issue is that the loop-level scattering equations and the numerators can depend on the loop momentum which we'd rather not have in a purely celestial description. If one goes back to position space Feynman diagrams this problem is absent since we can leave all the internal propagators in their position space representation. Numerators that don't depend on loop momentum can still be pulled out in front as operators acting on a scalar loop diagram, but now there is a proliferation of different topologies coming from the loop diagrams. It would be interesting to see if there is a way to encode the effect of loop momentum in the numerators in terms of operators acting on the external variables. Perhaps, some insight could be gained from explicit Mellin transforms giving loop-level celestial amplitudes {{cite:cbe8c9efbfd71cb079bb7c1325be09cb10b61ba0}}, {{cite:41201603c804e48c7857d05e7bd97dba004dd4b3}}, {{cite:920b488ad9cbbebda3f66a38b66d727bbc52ab33}}.
| d | a9a52884dae423074af25a3cbb10dc3a |
We show a more experimentally realizable setup to construct a characteristic system satisfying the criteria (i)-(iii).
To this end we hereafter focus on the uniform hopping case, {{formula:4086b7ec-49c9-4136-b70d-bdb006d191b4}} . Then, all CLS many-body states {{formula:70f2a635-b1ad-4216-b631-f069586adae6}} are degenerate with zero-energy.
Hence, a linear superposition of CLS many-body states {{formula:0b9e8f24-e79c-4035-a781-567b7da8840a}} is also a certain eigenstate for {{formula:977507c4-ae04-49dc-bf16-3f99a977b668}} . Such a state can have a large EE, at least not having area-law EE. The property of the EE for such a state are discussed in Appendix A.
Hence, in order to construct explicit multiple QMBSs in this system, it is better that such degeneracy is lifted as much as possible.
To this end, we employ the finite linear potential {{formula:f587fbae-b14a-4fb3-93fa-888082eb7968}} , where {{formula:65cefe13-d070-4f10-b0b3-d164e0fcbb69}} , that is,
the linear potential {{formula:14a96fd4-e6b7-480b-9e41-54fd2b79e137}} is perturbative {{cite:5b9f86f11a1f3208e8ccee386322d4f06b78477b}}.
Practically, the introduction of the linear potential {{formula:01276a1d-ad7c-4ec9-984d-c8f03b8ccc1f}} is more realistic than setting the fine-tuning of the unit-cell dependent hoppings {{formula:4f715c79-5216-464b-bba7-668896cba57e}} .
With finite {{formula:e31f4038-c040-48fc-8ada-996775e654ff}} , the CLS of Eq. (REF ) is not the single particle eigenstate for {{formula:47207789-1994-494c-a021-8e0a5b893385}} ,
hence neither is the many-body state of Eq. (REF ).
If {{formula:2bac79b6-ce4f-4e6c-9bc1-784c51fa9a05}} is large,
the system can turn into the Wannier-Stark localization {{cite:7c40f2e3da6a6312947adf075f069991840544d4}}, {{cite:f3e3ff121adde03198cc6c7f0a4ecb9ac5571c59}}, {{cite:4ffe6fcadce43d0124b2cb565361cd0480eff1b7}}, {{cite:d9fa6130c3657dfa8631e739d2319283295450ee}}, {{cite:b9315fec330e727547627fc8eed68f760b84f6ce}}, {{cite:4feeee2adede92140da222b5c71161657d05b446}}, but we do not focus on such a regime.
For later purposes, we denote the total Hamiltonian by {{formula:8f1b2f78-6081-47ee-af3b-6ca610108654}} .
| m | 8700ade3ccbbbff3b785d649321f61f7 |
We have made use of the generalized method{{cite:3e6952646eed320ebbced686ac88e58a5b13f31a}}, {{cite:5363b70683f343d72855f2de6d7e7c77db6deb3d}} of handling such quark triangle diagrams in the framework of {{formula:c62021b2-81ad-46fd-aa4e-9dcd9e87ae03}} BSE under Covariant Instantaneous Ansatz, which is a Lorentz-invariant generalization of Instantaneous Approximation. In this approach, we have been able to express {{formula:22b6f5e6-c6c5-4ed3-926a-c3473f524538}} as a linear superposition of terms (similar to {{cite:3e6952646eed320ebbced686ac88e58a5b13f31a}}, {{cite:5363b70683f343d72855f2de6d7e7c77db6deb3d}}) involving combinations of {{formula:9f2af65d-eff8-4943-b19c-cc95392f109e}} , and {{formula:d54cf918-7b45-48d3-8631-1c7a05d6e3d2}} components of Salpeter wave functions of final hadron, with the terms involving {{formula:6863218f-0a7e-4404-a259-e3c672a16eac}} being associated with coefficients, {{formula:37c6c87a-bc6f-49a1-86e8-76577b662c28}} and {{formula:efb2acb8-1010-4397-a1dd-b41bf1702a20}} , while the {{formula:a547436d-b34c-4412-913c-9bc69b58e3d1}} being associated with {{formula:4b4cb83c-bb90-45db-a344-15495db32db2}} and {{formula:bdc5a53e-b3a5-48ce-be81-fe5498a7d4d2}} , which are the results of pole integration in the complex {{formula:d166fd5a-dea1-4580-84d5-add1e7b567dc}} -plane ({{formula:e69812bf-13c0-4412-9451-6df67b884173}} being the component of internal momentum {{formula:4f934c23-4a73-4439-89fa-52f571f93559}} of initial hadron that is longitudinal to external momentum, {{formula:4efdf665-1769-4438-b454-6830783bb69d}} ). This superposition of all possible terms is a feature of relativistic frameworks. Due to this after the integration over the fourth (longitudinal) component ({{formula:cc438f9e-7281-49a2-b273-caf5ddb2b221}} )of internal hadron momentum, {{formula:14b05071-611b-4f63-a521-c1888169a17c}} is carried out using Covariant Instantaneous Ansatz, the 3D form of {{formula:f965929b-7264-4f38-84bd-0b5ca27e8ca1}} is still relativistically covariant. At leading order in QED and QCD, we obtain the results, {{formula:134c7a81-0256-4102-ad0d-c722d022b97a}} , {{formula:59f82021-504a-479e-ab43-cf560bc8d046}} , {{formula:d8c43f06-e98c-4e11-83c2-07de840a48e7}} , and {{formula:2d77fb47-25f3-4e9a-a7f5-69cb990a0f5a}} , and provide a sizable contribution to cross section, which might be mainly due to the BSE being a fully relativistic approach that incorporates the relativistic effect of quark spins and can also describe internal motion of constituent quarks within the hadron in a relativistically covariant manner. Our results of {{formula:8c03b196-cbe0-49b3-a888-c0894be791e2}} , and {{formula:11274239-00e1-40ae-8ca2-fd1302f677c5}} are in reasonable agreement with results of {{cite:cfe20d70ced6524d923648502b94f3d9f9b1e780}}, {{cite:35a3b082cbde0aee76796dcfaf9f5554284d07da}}, {{cite:9aee523db687561c321259f3bf122cbc3c30cf3c}}, as shown in Tables 1-2.
We wish to point out that this is further validated by a recent calculation {{cite:7d7ff9770ac18dbfeda6c1b38b6280b8c31f9501}} on {{formula:445c143e-3f31-4811-83aa-7ebf3749177b}} using Light cone expansion, where the authors had shown that by taking intrinsic motion of quarks inside the hadrons, one can significantly increase the value of cross section. Further calculations will be done on incorporation of NLO QCD corrections to these processes.
| d | 76492437080e87a4bb7e829a7a8491ed |
The following geometric lemma can be obtained by directly replacing
the energy density associated to the harmonic map with {{formula:24173437-133d-4001-bcd1-909eb090a62d}} in
{{cite:17b14d852fcbf1ef2d697c450ae6886277220171}} or the Yang-Mills case in {{cite:6454c0dfd32a8e3e666f58a541bc5b076234832a}}
| r | 3c8e7349745f0d79b69606f3bf4fd501 |
Taking a look at the first table, it can be appreciated that a mild dynamics of the vacuum is very much welcome, specially in the case where the time evolution of {{formula:5093e7aa-2179-4247-a691-843fb04ab500}} is activated close to the moment when the contribution of this quantity becomes relevant, namely at {{formula:c7123de5-1912-4938-bb73-a9248db04a53}} . It is in this particular scenario where the impact on the description of the cosmological data string SNIa+BAO+{{formula:eedf94b1-a9ff-4a2e-9fd3-48f364cabe9c}} +LSS+CMB becomes extraordinary significant on statistical terms, since {{formula:30034bde-9a33-4563-834f-bf6cb35ec3cf}} which means that a very strong evidence, in favor of this model, is found, when it is compared with the {{formula:9202c975-fd7b-423c-9ad1-39efc3cce964}} CDM model. At very high redshift the physics of the type I RRVM with a threshold remain basically unaltered with respect to the {{formula:1ddfd4bd-7666-45be-988b-b384f0f202cb}} CDM, however, the activation of the dynamics of the vacuum at {{formula:1ab9ed00-9017-423b-91e4-0deec891ecf0}} allows to suppress an exceedingly amount of structure in the universe, thus leading to a better description of the {{formula:9e7b8bb8-dd1c-4251-a386-54a9195a4e5e}} data set. On the contrary, non of the other models beyond the standard one is preferred by the cosmological data, and the DIC indicates moderate evidence against them ({{formula:211b38d3-b027-46de-9b94-41af70a3b3e1}} ). We would like to remark that even if the RRVM's under study are not favoured by the data, in all cases the values of {{formula:f6487f7b-445b-4d19-a631-855bce670f6c}} (or the analogous observable {{formula:ce4cd9c3-00d3-466b-86d9-749d584e87d7}} for the type II RRVM and the BD-{{formula:94aa930c-4c71-4f89-b3c3-06dc7d7b1163}} CDM models) remain compatible with recent weak lensing and galaxy clustering measurements {{cite:1ee76ca615a3f48dd07c1bac22c2f1624da1cee0}}, hence smoothing out the {{formula:864df9e2-6dbd-48df-a811-a044009c33f6}} -tension. Just by including the {{formula:d09ac2dc-9fcd-4932-9df7-2d8f7348f417}} prior in the data set the results change in a very significant way as it can be observed from Table 2. The {{formula:41ed2ca7-5507-45df-b68c-d2bd99b3ab46}} CDM model, as well as, the two versions of the type I RRVM model are not able to accommodate high values of the {{formula:df39e2e3-0379-4a8a-8c37-dc91d6dee852}} parameter, hence, all of them show their inability to alleviate the {{formula:8a79a9de-a471-4969-ae56-7331c7642863}} -tension. However, the DIC still decides very strongly in the case of the type I RRVM with threshold. On the other hand, the type II RRVM and the BD-{{formula:c5bb6baf-a636-4b24-83b9-d81beca2e004}} CDM model seem to have no problem to fit the {{formula:cc2d9b2b-2e16-4411-9402-d34e4c044d72}} prior since in both cases the fitting value for this parameter is {{formula:e21ce231-ce01-4e0d-abf3-497c07e70bda}} km/s/Mpc. To fully appreciate how the cosmological models deal with the {{formula:65201e7e-1e62-4fbf-b349-402b332393df}} and the {{formula:bb6a44a7-8ef0-4960-9ed8-6456c91e6f64}} tensions simultaneously, we have included Figure 1, where we have depicted the contour plots for the different models in the {{formula:e8cebe2e-1b14-48ca-970e-c5f50dea7097}} -{{formula:a3abe0d8-7ced-44eb-af24-c6b51b32cc8e}} planes of the parameter space. As mentioned before, the RRVM's are able to keep the values of the different parameters related with the structure formation ({{formula:2dc102c8-83ec-40d4-91cb-8d3dbe7bb866}} ) at an intermediate value between Planck measurements {{cite:e645d303c4630911e72c7c0906dc13c3e5d57383}} and cosmic shear data {{cite:1ee76ca615a3f48dd07c1bac22c2f1624da1cee0}}. Remarkably enough, in the case of the type II RRVM and the BD-{{formula:9d74ae65-7fa4-4a9b-b14d-96a116eb8396}} CDM models, the contour lines in Figure 1 show a preference for relatively high values of {{formula:d713cf70-1eae-44ca-9333-180a043c67ce}} (the tension is lowered at {{formula:aa2f1c27-7e3d-4227-9fab-1c62cd7861f9}} ) while keeping {{formula:5f4472cc-a1ae-48de-9711-fc9816ca7571}} in the low value range (the tension remains at {{formula:93e5ef24-eded-4e95-a298-319a53b99176}} ), thus smoothing out both tensions at a time. We conclude that the models studied in this paper provide very interesting alternatives, either considering a time-evolving vacuum energy density or by extending the paradigm of General Relativity, to alleviate the {{formula:65cc2534-37a8-43c0-877f-c39901f57701}} and the {{formula:885290b9-a6c3-4ce5-b8b6-6ab1ad98dc2c}} tensions. The better performance of the aforementioned models is reconfirmed by the Deviance Information Criterion, which points out that in some cases a very strong evidence in favor of a nonstandard model is found.
| d | 75b0dfb07a27afe4d2949d73a02bac8c |
Persistent homologyThis article is intended for readers with and without a background in persistent homology and TDA. Therefore we include an Appendix defining common terms all highlighted in italics first time they are mentioned refers to a TDA technique wherein combinatorial structures are successively built from a data set, and their homology is used to define descriptors of the shape of the data. These novel techniques have been used to analyze the arterial networks in the brain {{cite:4435f63b3a4561530750e92e3a8f9624e469d2a8}} and bronchial networks {{cite:d41119c55cb82ffc80f8e0f0b1417416faa2e42b}}, but to our knowledge, this study is the first to use persistent homology to characterize pulmonary arterial networks. Bendich et al. {{cite:4435f63b3a4561530750e92e3a8f9624e469d2a8}} analyze human brain arterial trees generated from a tube-tracking segmentation algorithm on magnetic resonance images (MRI). Using these trees, they compute degree-0 persistent homology and find it strongly correlated with age, while degree-1 persistent homology correlates strongly with sex. In {{cite:d41119c55cb82ffc80f8e0f0b1417416faa2e42b}}, persistent homology compares airway CT images from healthy and chronic obstructive pulmonary disease (COPD) patients. This study found that degree-0 persistent homology can distinguish the patient groups, while degree-2 persistent homology only can distinguish inspiration and expiration.
| i | d0599f0315dd8a93435a0b8d79b3409d |
where {{formula:000000e3-f56c-4d75-93b5-cd2e64b06123}}{{formula:38043e3f-2e87-4e45-b271-a964565928ff}} is the curvature at the saddle point of the barrier.
The curvatures {{formula:49860255-911b-407c-b52b-eac2f27a4391}}{{formula:243cb307-611f-484d-8517-72f186f0e1ca}} and {{formula:f9355a2b-36fe-426d-81be-7a9d95572f97}}{{formula:f735c535-b731-4aff-9435-92742933aeda}} can be easily calculated with the
microscopic temperature dependent fission barriers and the mass parameters, as discussed in Ref.{{cite:1d319404db1124073897fbb79f88f6352196073a}}.
There is a narrow transition in ImF formulas from low to high temperatures, which is dependent on the critical temperature {{formula:c15608df-2a08-4738-b55b-854784a4e11e}} {{cite:2ef63a1d93c99e5673ea381d779d35d3455083ef}}.
The ImF method has been widely applied in chemistry reactions in a thermal bath. For nuclear fission studies, ImF shows that the fission lifetime
decreases very rapidly at low excitations and decrease slowly at high excitations {{cite:1d319404db1124073897fbb79f88f6352196073a}}. With temperature dependent fission barriers, it is a success for ImF
to reveal that the compound nucleus {{formula:282d0e2f-0dd7-4610-a1d8-1cc1daadfa18}} Cn in cold fusion can not survive at high excitations while {{formula:c843790c-c3ec-46d4-83a8-a885b24da2ba}} Fl in hot fusion still has a considerable survival probability at high excitations {{cite:1d319404db1124073897fbb79f88f6352196073a}}.
| m | a6be38cc9f43a688b1d0e59de02c24a4 |
Fast R-CNN*: We compare with Fast R-CNN {{cite:36c7843dd9a13d9b1feb3134eb21ec33fd30649b}} to quantify the importance of contextual representations in CoVA. We use the DOM tree instead of selective search {{cite:1ed79cc4cc00abdf170b9dc4cc726e7965b3ea28}} for bounding box proposals. Since the proposals are exactly localized on the webpage, there is no need for bounding box regression. We also use positional features as described when discussing the representation network (Sec. REF ) for a fair comparison with CoVA. We will refer to this baseline as `Fast R-CNN*.'
| m | 7ccd327a84d8c2b14f93ae9b3b7fde51 |
Add basis.
From the term {{formula:77af083a-8f9b-4a0a-ad83-5110f8c45d78}} .
We first focus on the Vlasov equation and consider the discretization of {{formula:27c461e0-cadf-4777-a121-11aaf25b1666}} . The treatment of {{formula:c4252c83-c78e-4d99-8080-0e6c07370e97}} is the same.
Similar to the 1D1V case, to account for upwinding, we split {{formula:49883edc-db36-4c9f-a4fa-0493e1209eb4}} into {{formula:baa149a8-2e65-472d-ad41-e04455490974}} and {{formula:3a0e3d9f-3909-4e93-a570-c8e4268c7649}} and denote by {{formula:1b47269c-be48-4ed7-9e3b-8b7357d6aca6}} and {{formula:d7bcd5c9-f7d2-488d-b51e-6adaad25957a}} the biased upwind high order finite difference operators. Then {{formula:54f507ad-b8a4-45b0-b1ac-d3b4032a518b}} is approximated by the sum of two fourth-order tensors in the HT format denoted by {{formula:8af93b10-5d90-4b53-88d5-33c7a913c8c9}} and {{formula:b8d73b92-c453-46d7-8e2c-59eb385529dd}} . Both tensors have the same dimension tree, frames and transfer tensors as {{formula:8f37e875-63c9-4b87-87d3-0711ab0b0140}} , except that {{formula:a7fdac56-17c6-4381-aac3-6204c0350425}} has frame {{formula:379d0398-b988-4ebd-93e2-bd5193756370}} in direction {{formula:46ea6dbe-2a24-4d28-bad7-27b5ede9ba2c}} and frame {{formula:4c2944d8-6438-42d9-99e3-9e22de40699c}} in direction {{formula:94b0968e-30d0-4755-81a9-3084705f24ee}} , and {{formula:e95b684d-b47b-4ae5-b2bc-a40c965814bd}} has frame {{formula:b0caecd1-3999-4d42-82a4-08332f20eb6b}} in direction {{formula:78f62740-ca5a-4953-b904-ed5204795c91}} and frame {{formula:7e5c3219-a273-4aff-b8f2-17e1f9668dd2}} in direction {{formula:c403cd0a-be79-4406-b196-836915c7143d}} , see Figure REF (a).
From the term {{formula:2a4603c7-894e-49da-9f44-cba08081d824}} .
We start from discussing the discretization of {{formula:4340f261-17cd-4688-a8ee-d6d7f991658c}} . Since {{formula:ec4ee23f-8e70-4f8a-8367-54e54c52af2f}} is expressed in the HT format, we propose the following splitting strategy:
{{formula:c6aa14a3-ffa1-45c1-a910-29e3cabd22c2}}
where {{formula:9ba0a63b-a058-47ea-92c9-9f1ca61529a9}} is the maximum absolute value of {{formula:5a88c28b-efe6-4beb-9e85-0bc97da2d320}} over the physical domain. The entries of {{formula:636005e5-7645-48d7-bf85-75983f015530}} and {{formula:41ead276-dcd2-4b55-bf9f-a5e6eab36ef1}} are nonnegative and nonpositive respectively. Furthermore, {{formula:6e34df51-3cbf-4160-83a5-2aed9b1ea3da}} and {{formula:c6bc88ec-3f12-4b8d-9f47-02601480a43a}} are still in the HT format. Then, {{formula:cac228b7-7470-4c21-a4ad-1e8908610c59}} is approximated by the sum of two tensors {{formula:491fccb3-ee27-4456-80fd-84d514fe77cc}} and {{formula:587be855-f616-46ca-b00b-0a3b0fca084c}} . In particular, assume {{formula:8b67c002-fe6c-4b81-98f1-c2183f1bdeec}} has frames {{formula:f4c7ecd6-9459-4cae-905d-00ce15f11686}} and {{formula:9504c5bf-498f-4074-8805-21e1eebd3673}} in direction {{formula:b7ea3939-65b1-4d55-a0c4-130c08b25050}} and {{formula:b530b85c-f19e-4a04-aef4-3878709aa3d1}} and transfer tensor {{formula:b19f42be-db66-418a-9226-f1d4db44d10f}} ,
{{formula:adbda486-6534-40ee-a823-c20cfc68b8da}}
Then, {{formula:2cd60ae0-a1e0-419c-b472-2cad45130a8b}} has a similar tree structure as {{formula:dcab602b-d12b-43bb-9f61-d1cf1e8d8e74}} with new frames {{formula:6a21a771-3f0f-4d45-a510-b5182928d927}} , {{formula:5a833401-3e38-4e36-b615-35ca069f2391}} . From (REF ) and (REF ), {{formula:116b875a-a229-48e2-8314-cde06f9de151}} has {{formula:02c17734-7652-4a83-95b6-04861a6d6b13}} frames with entry-wise multiplication
{{formula:60151fa5-a940-4b48-841e-4ed61a9ea80d}}
Correspondingly, the transfer tensor becomes {{formula:12afcee1-eea1-46d9-a9a7-1ccfe2283f64}} with size {{formula:c396ec02-1f4b-4e54-a0c4-65d90cd33e26}} , where {{formula:f6915774-fce9-41dc-be37-c79832e138b2}} denotes the generalized Kronecker product {{cite:51bf492102de51334374b9ead11a1a0930981682}}.
In addition, the frames in the {{formula:7bc28c84-820e-4d84-8a29-667d7e60d37c}} direction are replaced with {{formula:a007a107-2e4a-4dc3-bdc6-091eff996fbd}} . See Figure REF (b) for illustration of the added tensor due to {{formula:9cc56f2d-0879-467b-9294-b681a4956578}} . A similar extension can be done for the tensor from {{formula:b877da77-32a7-4074-b4aa-799a60e71680}} .
When a second order SSP time integration method is used, then {{formula:65c757a8-077b-42d8-8b85-cc82025e7620}} is approximated by {{formula:590e22c3-85cb-4d4b-b268-d4ddfd9b8cd1}} , together with about ten additional tensors in the adding basis step. We hence need to remove redundant basis to avoid exponential rank increase, meanwhile not compromising much accuracy.
Remove basis.
We employ the standard hierarchical HOSVD for removing basis, which is implemented in the Matlab toolbox htucker {{cite:a91bd5e57a3783d7726e7a5eda09d97b9f4ada5a}}, {{cite:8a723fa69a6d23134f96e46e90cf146b5f61f0f0}}. The procedure is similar to the case of {{formula:48875c2f-df97-464b-97f9-37d3bbc0d3e7}} , which consists of orthogonalizing the frames and transfer tensors, computing the reduced Gramians and the associated eigen-decompostion with truncation (depending on the truncation threshold and the maximal rank allowed) at all nodes in the dimension tree, and then obtaining the truncated HT tensor {{formula:5715e0b5-008f-47fa-9700-1ac008c84119}} with updated frames and transfer tensors. Such a truncation procedure costs {{formula:d50ad592-480a-4ac6-9a80-3b1713a5967a}} , without exponential dependence on {{formula:61676a50-bf6b-4a43-bf06-2302ec0bf621}} , and ensures quasi-optimal truncation accuracy ({{cite:c82f9d0839d81443c845c6c8036680f900cc00b3}})
{{formula:292360c2-2c7f-4d1a-aa4e-4170fbab9fb9}}
where {{formula:160a38c7-cc86-498b-8097-3c42c76e0ca5}} is the best approximation to {{formula:1eb34e09-25e4-45fe-ac9e-095589297f00}} with the hierarchical ranks bounded by those of {{formula:d42de247-d074-441a-9af4-ec9c5460fa34}} . We can further combine the addition and truncation procedures for improved efficiency and stability, which is proposed in {{cite:8a723fa69a6d23134f96e46e90cf146b5f61f0f0}}.
{{figure:947d5d85-4db5-456e-8306-be37fab53415}} | m | 970a3947c434727dc2dd42a03321ea88 |
Unlike RISE {{cite:e158f009635edce5771202dcb7b4d816a858d96e}}, which generates masks randomly (it is worth noting that that at large number of masks the effect of this is minimal, though we imagine that this is not the case when the number of masks is small) and methods which learn secondary models through gradient descent such as {{cite:767077f9d12b02ba94e0bac212699ea22a2cf140}}, {{cite:a63bdb96721efcc136d931d071637c5b6e74e790}}, {{cite:e04394bdf043e8655a4f4bc835e5d3c17544369f}}, HiPe contains no random elements. However, HiPe is not able to capture instances where the salience of two spatially distinct features in combination is greater than the sum of each feature individually (i.e. if perturbing the microwave and oven at the same time changes the prediction more than the difference when perturbing the oven plus the difference when perturbing the microwave), since we perturb only one locality at a time – this unlike RISE, which with a high enough number of random masks will presumably capture this phenomenon (although with an uncertain degree of precision), and unlike Extremal Perturbation, which by design will capture any combination of features if trained for long enough (albeit at significant time cost, as our experiments show).
| d | bbde575dc986768389fa1b3b8f4eb6e3 |
To investigate the characteristics of the gamma-ray emission, we used Fermi-LAT (P8R3, {{cite:8ac9c3314c41106e542ce3a8c5f7cb39f2aefcd0}}, {{cite:35900214d0f7ee3452528bd3dcab2f34420798d0}}) data spanning from 2008 August 4 to 2019 April 24 (or 239557417 - 577782027 seconds in Fermi Mission Elapsed Time), in the energy range from 200 MeV to 500 GeV. We retrieved the data from a region of interest (ROI) defined by a radius of 20{{formula:004a605f-352b-4c95-913f-428cb601eb23}} around the position of PSR J1023–5746 (RA= 155.76{{formula:4a0aeb51-4229-41e6-8a6d-82e2e07d5849}} , DEC = -57.77{{formula:588a02f1-c198-4a20-be2b-028c82cb60a0}} , {{cite:09d45109ed9e5c5c55b2ef36714b364de5935739}}). The events were selected with a minimum energy of 200 MeV, to avoid events poorly reconstructed due to the large angular resolution and the large crowding of sources in the region. The analysis of the LAT data described above was performed by means of the fermipy python package (version 0.18.0), based on the Fermi Science Tools {{cite:73741ddfeec000201190364173ec654fcc37c2b6}}. More details on the analysis are described in {{cite:fb50989cf0b0c4ab3d86a2b91ff400f2ba0c08a9}}.
{{figure:87850acc-e45d-4615-9dd3-165742a5e62f}} | r | 2d5e04c86e54fe5dd46dc3b581793545 |
Recently there has been much interesting progress in application of resurgence theory and exact WKB analysis to quantum mechanics (e.g.{{cite:5c8c91375f7ecb009fb53d97c269ef8d74025709}}, {{cite:32aeec46d92239d09bfeefe1c9d6f627af36f628}}, {{cite:7588efc918a35a1de9c8984e99784add3da987a4}}, {{cite:edfa1ded2d82f8d95033c2d8ae25f9d8e71314b2}}, {{cite:310bd12c011247019ee77faabadc71ee4cf1d672}}, {{cite:bc70dc3c553ffd7279900ccc96b98e651de6fc00}}, {{cite:c04abda57e568f276262d5e922226843568870bf}}, {{cite:8bc662d2e5f7dff2f31874c43af82855f50a1985}}, {{cite:79fde749b78fa88763827cfb97c9a7f2dd90bec3}}, {{cite:cbbca76f25f06549ed05b6196be012178e474f3d}}, {{cite:4b9cde4b369a149f2fdb94f72f92d89aed3f1950}}, {{cite:b6e314db64f4cc8af3dd6a29df7d04d71da6af25}}, {{cite:7b8c19c6582221df7877f338be23c01405211762}}, {{cite:1c75ec83f67721459089abc0f843ee11266ec82e}}, {{cite:30f792f13693b4070a784bc8050ee74af0a432b4}}). At the same time many interesting relations have been discovered between quantum mechanical systems and supersymmetric gauge theories (e.g.{{cite:b3f66097d2a9239b3618405b439002ce951f2a06}}, {{cite:44f48408cdec4f15794004146425ede27a7506a0}}, {{cite:095862f86d7975c125ae36a1557ce53bb3144dbd}}, {{cite:fe05bd05d67c3deb870727cce9d7cfbf3c461bfe}}, {{cite:94fcd5023179effccff73a2ca53faaaffca85ea1}}, {{cite:0812f99022615c18f4bdc1123e2080eb1cb9a6cb}}, {{cite:1f273c4b967d438f67a14dd441ff6e4e026812db}}, {{cite:f0eab4e278c40f00c1667ef7d5bd8986fed93741}}, {{cite:0bda43b7f0bf502239384c37a164ffa8e56db0b3}}, {{cite:d54aeb4f207b250e0be8703e425bdff24f62d7e6}}, {{cite:a38eb4ae0f5b82b21a55c13cc90fe6feca94dc53}}, {{cite:7234de5048120922ed6c7ab28f1df509047b12aa}}, {{cite:85f4dadd024a25cbdcf669675baff3538f5455a3}}, {{cite:b8fe7e613d61c1ddea58ce7246e058a2a2e2437c}}, {{cite:affb64a13195e88830029929c76f6c28b3c6a0a3}}, {{cite:a55e7db0a86efc586335c71e61215e4ebd776758}}, {{cite:307d1917bfce60bda0542c47024c48783819a6f6}}, {{cite:cc24c5d072508e41655c8d47f0965b783e03144f}}, {{cite:a0125b6711b234bcbd631a95974f89944b7867a7}}, {{cite:c4f00826097e8edcee9aab1c530b622f81c7411c}}, {{cite:b05b5eb92bb7e28008fe7b872a1bbcf66a514c8c}}, {{cite:de6e21db40906647c53ca217fa8a1585e90671e5}}, {{cite:70116c930ed3434c4ddf34dce8e9c8e4db306f87}}, {{cite:db70909e2854e0288b4dbdbcbde3473a02341a74}}). These relations benefit both the study of supersymmetric gauge theories and quantum mechanical systems. In particular, they provide various tools to study the quantum mechanical problems in the context of quantization of Seiberg-Witten curves {{cite:3013e836de5ea96fcc998c926fcce6b326217326}}, {{cite:249abf582e0a5e1c93f1965a971d1b3bc994542d}} in certain 4d {{formula:84ec238b-8d7a-4f74-ad02-d2a6c1ca87ad}} theories. Such tools are also very useful purely from the purpose to study differential equations, which could have broad applications, as an example see the recent developments in applying Seiberg-Witten techniques to black hole perturbation theory {{cite:e5935d8865acc64b407514ba315cf47f2387924a}}, {{cite:06b0fc8f06655c31ba70369b308eb98fba01947c}}, {{cite:e8bf3d7cea0fb64397587f73abe42533d24c03a9}}, {{cite:e51af7a58ecbadf47d6bfff049a4126c1e5bc8eb}}.
| i | 47ba2df428e0e2cd10f9d7656403882a |
Although in previous section we have explored both the plane wave and Gaussian basis, there are two characteristics we have maintained constant over all the previous methods: all simulations were done in the Schrödinger picture and in second quantization. This changes in later articles {{cite:2fd60f257d212f3caa50237a2decd689e565db14}}, {{cite:e3c78cbc7d6d44f20ba0505927f2ad35d67cac94}}, {{cite:dc4bc809f5727e01a4ac50f8c0c17b4a4aad652e}}, and in this appendix we present how the interaction picture can help make more efficient Hamiltonian Simulation algorithms {{cite:2fd60f257d212f3caa50237a2decd689e565db14}}.
| m | cd0a23e819b3c55d711bf38ae120c856 |
The second statement in Theorem REF indicates that {{formula:e583d109-c127-44f2-b7c4-4add05d1a273}} is analytically stable, not only with respect to the Poisson metric,
but also the background metric {{formula:a48cfcc6-74f0-42cd-9cbb-83514c2e402a}} . It may be mentioned that it is facilitated by the feature of the stability of vector bundles, while the
issue is more complicated in the setting of holomorphic bundles. We will use Mochizuki's exhaustion method in {{cite:f7afb2c0be249464baaba41414ed8d20d0afa0ff}}, where he proved
the existence of exhaustion function {{formula:87403821-7fac-495b-b6a0-cace903dc51f}} . Denote by {{formula:5c46b203-8d6c-4a1f-9849-0ff1c9e4cb46}} the set where {{formula:ad66232b-6fcb-4ac4-ad95-a62996f0a3a7}} and we firstly consider the parabolic heat flow
{{formula:a370b254-ff96-4450-b17f-faf7d3ec33d2}} on {{formula:40d28a0f-708b-49a6-a7e1-b8493a116798}} , which can be regard as the vector bundle analogy of Eells-Sampson's flow for harmonic maps or Donaldson's heat flow {{cite:a097030bf1bedd32d110662c81e5453028dae280}}, {{cite:41c0818911e6e6f1c40407e71f534ecae7e924c0}}. For arbitrary {{formula:dff84bb5-cfbd-4b16-89c0-c3e3375a8c6c}} , we show the existence and uniqueness of the long-time solution to {{formula:cfa41b0a-81f7-44f5-adab-570a78459f57}} , also the Dirichlet boundary problems for harmonic metric and Poisson metric are uniquely solvable, see Proposition REF and Proposition REF .
Next we observe in Proposition REF that the crucial identity {{formula:a63977da-f95b-4203-875f-e15c8c146399}} , based on which serval core a prior estimates are established. Once the zeroth estimate of a sequence of the solutions to the Dirichlet boundary problem is obtained,
the evolved metrics are completely controlled and will converge to a Poisson metric. Finally, we prove the uniqueness and the second statement by comparing the analytically stabilities with respect to different reference fiber metrics.
| r | 4abb09d732099302ff4d89d97b8f38c8 |
The third attack we considered is a backdoor attack from {{cite:282add41b9ad94b2ce6a19580adf5588c2bbb276}}.
The attack aims to insert a backdoor functionality while preserving high accuracy on the validation set.
Similarly, the search for the attack gradient is formalized as an optimization
problem and the authors tweak the objective function with some stealth metrics
to make the attack gradient hard to detect.
We refer to the attack as Model Poisoning Attack (MPA).
| m | 1a48186bc121482705104f09533c68e8 |
We present the developed framework that leverages recent advances in Implicit Neural Representations (INR) {{cite:5d8d232a62652b3ee7f3e1949cf4d063664473f7}}, {{cite:ad9c461b35bc915b36a48211339f907f2e4ec711}}, {{cite:470f28675c2a356113d4713e99df7e8ab5f6f6a5}}, {{cite:7361d24d7e10b9cd3f6832a04160e576bb646763}} and draws inspiration from mesh-free methods for PDE solving. We first start by giving a mathematical definition of a PDE. Next, we showcase the proposed "MAgNet" and derive two variants: A grid-based architecture and a graph-based one.
| m | c25006e19f4d115f665458b8341ac889 |
There are several possible formulations on {{formula:0d33471c-93a8-41a2-a0ff-f3da416b06cd}} in the literature, and the one we present {{formula:b94022d8-80f1-4e00-9e95-6dc331b3b3f5}} is known as the Fletcher-Reeves formula {{cite:e43b6c86ebb079aac7925b99e9ecc4ff90135a22}}; see {{cite:3280219d4e9dac8e5121a4813d1351e329a79e92}}, {{cite:f7b7b26f237d8f64fb46e66b9ea940ef72d6c286}}, {{cite:78d4164fecec0454575ab6e9cd131477be0b1e96}}, {{cite:686af919680f8fc4ec4ff3c15d3cd7b26dc5528b}}, {{cite:db6c2d9430332c2e1987ca79e597780ebc5847f5}} for other formulations and related theoretical properties.
The NCG has been empirically found to have some similar convergence properties as the classical linear CG method. There have been several analyses to show a descent property and convergence of NCG for a general function under some forms of the Wolf conditions for inexact line search of {{formula:e8adbf5c-d1e9-4a02-ae1a-c2ab427473cd}} ; see {{cite:e09664c0139ea841c63db37dbca81fdfd745559c}}, {{cite:a3b4d87b80fb5b6c947ddba6a4a092ef97a5a76d}}, {{cite:f7b7b26f237d8f64fb46e66b9ea940ef72d6c286}}, {{cite:db6c2d9430332c2e1987ca79e597780ebc5847f5}}, {{cite:8376363f6337ccc46bb42e1298a0966387d54419}}, {{cite:f9b750991bdf19a532bdcd4d30a5e39e5f1927e0}}. However, there appears to be no result characterizing its CG-like accelerated convergence rate.
| m | b19f8ca4978a2043918f73d21a4a1876 |
In Figs. REF , REF and REF we show the
the fits of (REF ) (solid lines) and (REF ) (dashed lines)
to the data on multiplicity
distributions from the LHC. For each figure we adjusted three numbers
{{formula:25c70448-7996-4107-b0fa-10fb95c69064}} , {{formula:cf0074c1-dfd9-4c92-aac2-9d25225dea13}} and {{formula:7a551a90-ca0c-44f5-ac0e-ba2cddefb20c}} . They are listed in Table REF .
As it can be seen both models overshoot the
data at large {{formula:220cf39c-536d-402d-a379-0db538e950c8}} in all data sets. The model GL, as expected, overshoots
the data at small {{formula:5005d11f-55f3-4cd4-8ac8-e4142fefa3c7}} . In Figs. REF and REF the theoretical
curves have essentially the correct shape. In contrast, in Fig. REF ,
in some cases, the data show a curvature which is absent in the theoretical
curves. A careful comparison between set I and set II was done in
{{cite:d6a806dc991bdb1dfe1f81b590e93df1edfe7ed0}}. The conclusion then was that set I is compatible with KNO
scaling while it is violated in set II. There seemed to be something different
happening in set II. Now set II has been enlarged with new data points from
higher energies and the agreement with models KL and GL is better. From the
perspective of low x physics, set III is the most interesting data sample
because the cut {{formula:c3f5563c-2100-4dec-9328-f821dd9886e9}} MeV removes a (significant ?) part of the
non-perturbative events. These events are not related to parton branching
or to the evolution equations. As can be seen in Table REF , the
value of {{formula:4b9093dd-6b74-40ff-906f-1ff2b151d900}} is larger, indicating a stronger dependence on the
energy {{formula:7279a9ba-0cc3-4056-9a04-79148b1ba58a}} , typical of perturbative physics. Finally, the overall
agreement between theory and data is better.
| r | 7f301a1bfaa3d99c1714323c13352172 |
There are two works that are most relevant to our paper. {{cite:a596bbb21a7029c582674414af63aeb5547021a1}} extracts adversarial examples to watermark neural networks. Their experiment was conducted on MNIST dataset {{cite:29076913a85715898dbe2792ff4ea7955e6ac846}} which only contains binary images of handwritten digits.
Although, the method in {{cite:a596bbb21a7029c582674414af63aeb5547021a1}} is similar to our vanilla C-examples, we highlight that we use random initialization instead of true data and therefore our method is data-free.
In our experiments, we report the performance of the vanilla C-examples as a baseline rather than the watermarking method {{cite:a596bbb21a7029c582674414af63aeb5547021a1}} due to their similarity.
Another work proposes sensitive examples {{cite:7a35f175ee668db573f7141117c570b15378e85d}} from a DNN as its fingerprints.
Similar to {{cite:a596bbb21a7029c582674414af63aeb5547021a1}}, its fingerprinting also relies on adversarial examples.
This paper regards all the pruned models as compression attack and reject the pruned models even the test accuracy degradation after pruning is minor (e.g., 0.65%).
Different from {{cite:7a35f175ee668db573f7141117c570b15378e85d}}, we believe that an effective fingerprinting method should be robust to pruned models and recognize pruned models as non-attack. To demonstrate the robustness problem of {{cite:7a35f175ee668db573f7141117c570b15378e85d}}, we use pruned models to evaluate the robustness of sensitive examples.
With 8 sensitive samples, the Robustness (i.e., accuracy on pruned models) is only 0.04%, demonstrating that pruning is treated as illegitimate by sensitive samples, which is unreasonable due to the wide application of DNN pruning for size reduction and inference acceleration especially on edge devices with limited resources.
| m | e1492a919d7bd1a5f576d0f5a0e6b406 |
It is far easier to verify a proof than to find one. This intuitively clear
fact has been given precise meanings in several settings, leading to such landmark results as the IP {{formula:6018de6f-5e0a-45d2-b0b6-3ab4fb356c5b}}
PSPACE {{cite:0f56f48f7389ee66a3b780ad96329fe230a14619}} and PCP Theorems {{cite:7166c1ad95640e8de346e4dacf00377931bbccb0}}, {{cite:3d254119e19c1c47c6536b91044b6a4da4bdf7be}}. There is
a growing body of work on results of this flavor for space-efficient
computations on large data streams {{cite:98c32728babc0b95aa9cf73ea6d237564ef21e40}}. In this setting, a
space-bounded client (henceforth named Verifier) that can only process inputs
in the restrictive data streaming setting has access to a
computationally powerful entity (henceforth named Prover), such as cloud
computing service, that has no such space limitations. As past work has shown,
many fundamental problems that are intractable in the plain data-streaming
model—in the sense that they cannot be solved using sublinear space—do
admit nontrivial solutions in this Verifier/Prover model, without
Verifier having to trust Prover blindly.
| i | bf6b1686206592356f2d9b3e485976f2 |
In this paper we have used a combination of phenomenological and microscopic theoretical reasoning to build a coherent picture of the superconductivity and related phenomena in TTG. We argued that the superconducting state is a superposition of spin singlet and spin triplet pairings. We showed how this explains the contrasting effects of small displacement and {{formula:3b20712d-db5e-4792-9013-021da99a8f92}} fields, even though both break mirror symmetry. We also showed that the mirror symmetry explains the striking difference between the stability of TTG and TBG superconductors to in-plane fields despite their close microscopic relationship. We proposed that the re-entrant superconductivity recently observed in twisted trilayer graphene {{cite:0d553ad2cdd9048d20a4e0c7212dc2609a87273f}} can be explained by a spin-valley locked superconductor which undergoes a quantum Lifshitz transition into a finite-momentum pairing state in the presence of an in-plane magnetic field. The close relationship between TBG and TTG when the displacement field and magnetic field are turned off enables insights from the bilayer system to contribute to the study of the trilayer case, and vice versa. One consequence of this is our conclusion that the normal state near {{formula:a0f2e296-9dc7-46db-abdc-14e97c5d8c54}} in twisted bilayer graphene may be a {{formula:b9da8308-b3b5-4e88-a1b3-8d5011d7c80c}} TI.
| d | 7b3b5d941a6ae94c218173c525af8511 |
Each combination of model and dataset prompted a group of experiments, in which we varied the maximum learning rate {{formula:ab31437b-743e-49fa-964a-b9b32e53ed28}} , reached after 50 linear warming-up steps ({{formula:3b859a15-69e7-4100-8215-748df91f1426}} , {{formula:382cfacd-e92f-4be4-bef7-6495038c795d}} , {{formula:90d52aaa-0da1-44cb-9077-e83cd0c7fe2f}} , {{formula:2a2896c9-a383-45bf-9ff7-ec2650fbda4f}} , {{formula:d57c4216-7fab-41c7-9c39-1eb9a9175793}} , {{formula:d0857f9a-4dd4-4cf5-98d5-2ac55850d1f7}} , {{formula:7eca240a-4184-4dd9-a96f-e29f7495d12b}} , and {{formula:660128c2-e717-4901-8d99-249e6b0a437a}} )We used learning rate values based on the ones used in {{cite:b9d55545294cde2752367a177b623406b9d1770a}} and {{cite:bea9cb877cd9fcd2201c6e229117f55ae92c2e90}}, and included larger values to get a more general picture of the performance evolution., the maximum input sentence size {{formula:5453b02c-deb0-425f-9e70-3276df0efaa5}} (52, 68, 131, and 200 tokens) and the categorization threshold probability {{formula:8c4e596f-bee3-40e7-a040-4d551deeac04}} , above which a category is assigned to a document by the model ({{formula:923c070b-e065-4b8a-a340-d837cca9482a}} , {{formula:8c384ad6-aec8-4374-93d1-ac6ba4689316}} and {{formula:270892fc-e53e-4a07-a040-35f5dcc8e5b5}} ).
| r | 4c68c85280b2c5b24f5332adee4b9a2e |
Example 2.5 (Training of two-layer neural networks)
Here we present a particular example related to the training of two-layer neural networks. The universal representation theorem, see e.g. {{cite:053d5088cdcf6afd5b76c305c30d869ade47fb47}}, states that any given continuous function {{formula:518cbd4e-da97-4339-b099-5c22e620154d}} on compact support can be approximated by the parametrization of the two-layer neural networks, namely,
{{formula:c8eaeb8b-7ea3-4cbf-8880-9656fc32ea2f}}
| r | 9a53ad494f700ea46693a1b2d2b1da09 |
The HUMBI dataset {{cite:7fd8013ee7e870ddd55af92bf5b4768a879ce3be}} has a high diversity of human subjects in terms of body shape, age, ethnicity, clothing and accessories. We train on this data in order to evaluate the robustness and generalization capabilities of our method.
Figures REF and REF show some results on test subjects unseen during training. In the latter, we show the benefits of using neural rendering by comparing with surface renderings of the inpainted SMPL mesh. Despite the accuracy of the SMPL annotations on this dataset, we can clearly see the inherent limits of texture based approaches. They typically fail in regions where the true surface largely differs from the template shape which is often the case with hair or wide cloths. In contrast, even though our approach makes use of the SMPL vertices, we exhibit good robustness to these cases.
{{figure:0edda26e-edbf-439f-89f4-c42a69d6b0f9}} | r | 424d52b522dcbba0405fa65bbf075d09 |
Fig. REF illustrates the critical scales for suppression of superconductivity with DC current {{formula:6a262cdf-e1be-4ebb-bdd9-b775d3c6f2c6}} and magnetic field {{formula:3ae5d156-903d-4ac6-9092-bc614f5501f4}} .
Fig. REF a shows a strong non-linearity in 4-terminal DC measurements. {{formula:c8933381-84f0-4c23-b8cb-e15699643528}} is the DC current excitation sourced through the large source and drain contacts, and {{formula:751ee9ac-2fa3-45a4-9bdd-386351ac5cae}} the DC bias measured by adjacent voltage probes on the channel. This non-linearity follows a power law {{formula:bb4d1246-79f8-49b4-aef4-aff6134d8931}} with a temperature-dependent exponent {{formula:e3f906e2-ee8e-4862-a974-91ad7a383f67}} shown in Fig. REF b. This is reminiscent of the BKT Berezinskii–Kosterlitz–Thouless (BKT) transition framework, based on breaking of vortex-antivortex pairs by DC current in a 2D superconductor. The BKT transition point signaled by {{formula:c5bcf495-a18b-4cfc-aee5-415ca74670a6}} is at 365 mK, only slightly below {{formula:e8407cb2-fd5e-4459-a24c-d6f260439b59}} 380 mK. Very similar transitions have been reported in LaAlO{{formula:c7c026d9-a484-4d1e-9b40-67bde3ca1815}} /SrTiO{{formula:c68463a2-1a38-49a4-9047-09fa5cbbb51c}} 2DEGs {{cite:a3c0e72557449750c31aebbf566a8fd7f4f445c7}}, {{cite:2df9d68310f87552c440050c28c1018f54e8c00e}}, {{cite:c80ad3b065031c31c0ec296c0c9d1238fc12f755}}, {{cite:f2b6a0ac567eb04438e7fd979c31585ca4f27751}}. As pointed out in {{cite:c80ad3b065031c31c0ec296c0c9d1238fc12f755}}, {{cite:f2b6a0ac567eb04438e7fd979c31585ca4f27751}} a failure point of the BKT description is that it entails a discontinuous jump in {{formula:4ba94431-7543-48cf-8741-47328d412c4a}} , rather than a gradual transition. The rate of increase in {{formula:1caf50f3-35cf-4f8b-b667-c598a0ee1c7b}} with {{formula:5b7c22f1-3fa5-419c-97a3-14c809860ec6}} in Fig. REF b is similar to that in {{cite:c80ad3b065031c31c0ec296c0c9d1238fc12f755}}, {{cite:f2b6a0ac567eb04438e7fd979c31585ca4f27751}}.
| r | 5905a6cf5c6620c9df39e43881e77fe2 |
Although discourse relations have been the subject of growing attention in corpus linguistic studies as well as in NLP and computational linguistics research, the gap between linguistic and computational approaches remains wide. In recent years, we have seen the emergence of “Transformers” which are deep neural networks based on self-attentional mechanisms, which have been shown to be able to better deal with long-range correlations in text processing {{cite:a5bd716b3b330eee87335fefad3cc6a05bf44c63}}. Prominent state-of-the-art models like “GPT” {{cite:2d51a2a414fab16472131f7a4a4d40a9620ae584}} and “XLNet” {{cite:2024dc7ddbb4199618f3d186eb75d408537995d7}} are pre-trained using autoregressive language models, while “BERT” {{cite:6534da31d07ced7debe15a358d503eaad7f2f79f}} uses a denoising approach. The usefulness of these models to discover latent relations between text units or as text analysis tools has been demonstrated in countless contributions for solving complex tasks, such as sentiment analysis {{cite:0f7dfd52bbfb8eabc0ec6f052f1405cedd632c8d}}, semantic textual matching {{cite:b496e51d82db5abdde7d81980b1f8242e776bb68}}, and semantic role labelling {{cite:cfd90b09e6c57446e4b4672b1f8d98ddce4741c0}} among many others.
| d | 87c4a3bf28083412395cf1037d9512b1 |
Finally, the FLAME module derived two sets of masses ({{formula:f7dde472-6912-4d4d-8c68-32e51c36d6fc}} ), ages ({{formula:d6e16c68-c00f-4387-ab5f-5ba95f99849e}} ) and evolutionary phases for most Gaia sources, based on either GSP-Phot or GSP-Spec results. These evolutionnary parameters were obtained by first computing a bolometric correction for each target (based on the stars' effective temperature, surface gravity and metallicity), then deriving the bolometric luminosity {{formula:9faa7330-4cdc-4190-809a-8d5d85fd1351}} (via the relation linking {{formula:ec572fe9-62e8-4030-9cac-d9570e6a2707}} with the absolute magnitude of the star), and finally getting the stellar radius {{formula:01c139c4-6ffe-4cc2-b4c1-4492e9632b6f}} via the Stefan-Boltzmann relation linking {{formula:6ff63167-329c-4c30-ac26-55852b9319ee}} with {{formula:b35f3f65-8d0e-46d2-bdc3-f40d82e0ff1a}} . The luminosities and radii are then projected on BASTI {{cite:a3cbd491e36319f969b77f21bcd8f5644a5f2ba0}} isochrones of solar metallicity to obtain {{formula:4f2b8dd1-6b2b-4906-8450-18b0f142d3be}} and {{formula:3745c0ab-0aae-4f90-bad7-fd7b19ab2498}} .
| i | 4765f658b7a0faa06b6ede0de8a332c1 |
Related to this issue is the choice of invariants used. A relatively simple polynomial invariant based on quandles was used in this paper, but is certainly not the only choice. There are many enhancements of such quandle invariants for knots, and applying them to knotted graphs would be relatively straightfoward. A sampling of these include quandle cohomology {{cite:9091fc07537fd00e96aa34f9b2e1c2d5b458421e}}, using quiver structures {{cite:28c2b428d6435629dee18b0e90ae6f0a1b70490c}}, and the fundamental quandle of a knotted graph {{cite:9cfef02641dc07f33667b0fdf40d270c369f46da}}. In particular, quandle cohomology may be an interesting method, especially due to the importance of the Pachner moves in studying states in quantum geometry (such as spin foams). Recall that the Pachner moves on a manifold triangulation are those moves that preserve topological information, so there may be interesting links between cohomology theory on piecewise-linear manifolds and their dual graphs. Examining quantum invariants for graphs – as mentioned at the end of Section – may lead to similar insights from topological quantum field theory.
| d | 02d1f36a18d2fe727565a0f0c6a1c265 |
According to {{cite:b590fc5069d124484f30022c30969c291d58237a}}, the GE2E loss {{formula:faa3981c-c020-4d3c-82b2-2523f9109472}} is the sum of all losses over the similarity matrix ({{formula:1cc87e62-f9a1-47db-b3ec-3590aaf4a174}} , and {{formula:759efb54-64de-4a96-8f08-2e4d4ccb6bf5}} ),
{{formula:2b2821e1-51b3-4ad6-978f-2e7627aeb139}}
the GE2E loss {{formula:eb95f644-e41a-46ac-b9ec-19b6971dc67d}} is the mean of all losses over the similarity matrix ({{formula:7a045735-f07b-4597-92ec-1e2e724c52b7}} , and {{formula:0c0dee52-5d7d-4bf7-a591-700483a90b33}} ),
{{formula:949cd248-fb47-4d56-8436-75c005f4d97c}}
| m | 716d3b73813b920797a3f1a08cba744f |
Integrating MixMIM to other backbones. While previous works {{cite:779908c5b31ac485add34dcc49a0e8699e8bda5d}}, {{cite:36c5a6a838de0e257f8c45a3f0a3d1bc3ccc17dc}} may be restricted to a specific architecture, our proposed MixMIM can generalize to various visual backbones, including plain ViT {{cite:a748eeaab5073c911208d11c2b678c3719ff1b2a}}, Swin Transformer {{cite:7e60662692ef06e4f5f32039cfb38316cb5b7560}}, and PVT {{cite:446179983fbd009306d420cda7e6a3518b413dd9}}.
We conduct a thorough comparison with other MIM approaches with fixed encoders. As shown in Table REF , MixMIM consumes the same or fewer epochs for pretraining but obtains consistently better performance. In particular, our MixMIM achieves 84.4% top-1 accuracy with Swin-B, +0.4% better than SimMIM {{cite:78e314dfa32fddb40661ca04d66243e4f84e8e91}} while requiring 200 fewer epochs for pretraining. With Swin-L, our MixMIM obtains 85.7% top-1 accuracy with 600 epochs of pretraining and 50 epochs of finetuning, showing higher efficiency than SimMIM. Besides, our MixMIM achieves 83.2% top-1 accuracy with PVT-L {{cite:446179983fbd009306d420cda7e6a3518b413dd9}}, improving the supervised baseline by a non-trivial margin.
| r | 7c68cdf8c7da7b8a2c74e3ff4b4f8266 |
As computing resources are limited at the edge, researchers have been actively investigating the computation offloading problem, optimizing the allocation of MEC resources to different users. {{cite:e8640aa221cfa321f0a923076b892acd89b2c5f5}}, {{cite:5eb95abc905b12abfb84d0fbfb20a93b2b8816c5}}, {{cite:ed17768a2faed37b5acfe14ee45c1ad8314f40a7}}, {{cite:09b47d60ed47a586ddbe305b93ef7740a3abdeb3}}, {{cite:9c9819f35488cab965817b586b37fc408fd710d4}}. Besides dealing with the technical challenges of computation offloading, along the road towards implementation of MEC, resource pricing and procurement solutions to optimize revenue {{cite:9b0bec3e7245bcb468bf8a2593b3da291ead4f4b}}, {{cite:0f446e17eacc0cc289479f2fa412182588597d47}}, {{cite:7ae4d2fcb17d2f0b8e6f84427720fdf62107933e}}, {{cite:1cd25560f1b1588fffe3b11050965bf24c7d5b8d}}, {{cite:bb432492c1c43c7b5caf615a45a2d3968abfc80b}}, {{cite:bc918ef22bc5aa31ecfb6c4e871d91e684c09768}}, {{cite:5ab93fb2436a636adc867bdce86981b823c2719a}} can serve as complementary mechanisms to control user demands for MEC resources and ensure good quality-of-service despite limited available resources. In cloud computing platforms (e.g. AWS and Azure), the commonly used pricing and procurement models are the On-Demand pricing model (OPM) and the Resource Reservation model (RRM). {{cite:304e996fca8baab32fc18af3a18f4b77dbaff1c3}}, {{cite:52c92386e3fc0b9d3c82b05d7ac0bb647636ba2e}}, {{cite:66ce714ee348cb236286758b0d48d030baf880a9}}, as they each cater to the different
needs of different types of users.
Specifically, in the On-Demand pricing model, users pay to use computing resources, as and when they need it,
and they are not required to make any long term commitment {{cite:bfeaca2143f24606ed745fc8ee2c083d6c4850df}}. The On-Demand model has also been used in edge computing (e.g., in AWS Local Zones {{cite:9a3dff37df04ac32989a766280e25a608db689e3}} and Juniper {{cite:9bf0e9a878f2ad72cdfacccd59a80e0e18068b90}}). In MEC, it would be suitable for individual mobile users using, for example, virtual reality or mobile gaming applications in a one-off manner; for firms when they have special one-off events in which they put up augmented reality displays or machine learning platforms; or even content providers in regions where they have fewer users and thus more variable demands.
In contrast, for the Resource reservation model,
users reserve computing resource instances in advance, across multiple timeslots, (e.g. for a year), for a discounted price {{cite:7ef3a942f3fa98b8aa441589bb32e9311b089e12}}. This model also has been used in edge computing (e.g., AWS Local Zones {{cite:9a3dff37df04ac32989a766280e25a608db689e3}}) and caters to users (e.g., corporations) who use computing resources in bulk, at periodic and pre-determined timings, and more frequently in general. In MEC, these may include firms behind public augmented reality setups, with a constant need of computing capabilities, or IoT vendors with periodic sensing and data analytical requirements for their IoT networks.
| i | 21f0ea181e33c8b9f525ef0cd4476fba |
In the targeted case case, black-box attacks were unsuccessful. the predicted heart segmentations did not resemble heart symbol shape and had low overlap with the target adversarial segmentation (Table REF and Figure REF ).
We believe using higher noise level {{formula:a24085b8-6437-4bb1-a6a9-7bb6363a58a3}} is unlikely to improve performance, since using the highest {{formula:d50b020b-f9fd-4062-a7df-51e58d9044f9}} resulted in deterioration of predicted segmentation for all structures both with respect to the ground truth and targeted segmentations (Tables REF and REF ).
This is not an unsurprising result, since targeted black-box attacks were already reported to be challenging for image classification {{cite:1ccefff95ad432b2ffc16809dd8e60499e1f2b0e}}. For example, in the study of Xie et al. {{cite:1ccefff95ad432b2ffc16809dd8e60499e1f2b0e}}, regular targeted PGD achieved only 10-20% success rate in attacking networks trained to classify ImageNet (see Table 1 from the study). Black-box attacks on segmentation networks had until now not been thoroughly studied.
Using more advanced algorithms, such as data-augmentation-based attacks {{cite:1ccefff95ad432b2ffc16809dd8e60499e1f2b0e}}, could potentially increase the success of black-box segmentation-shaping attacks.
| d | efbad7847c3b7be333da1bf23a3de577 |
To the contrary, we find that conservatives were far more likely to comment on left-leaning videos than liberals were to comment on right-leaning videos. More conservatives made at least one cross-partisan comment (82.3% vs. 62.2%) and the median fraction of cross-partisan comments among conservatives was 22.2%, while the median for liberals was only 4.8%. One possible interpretation is that some of the left-leaning channels that conservatives comment on are what are often considered as “mainstream” media, where people go to get news regardless of ideology. However, there is some evidence from other platforms that conservatives may, on average, seek out more counter-attitudinal information and interactions. On Facebook, {{cite:1d69fb82e47ee39240749ba2620cf0109bb294e5}} found that conservatives clicked on more cross-partisan content than liberal did. On Twitter, {{cite:c1d318f14d6c91625d14df7ba248272c1f7406f7}} (see Figure 4) found that conservatives were more likely to retweet URLs from left-leaning (non-fake) news sources than liberals were to retweet URLs from right-leaning (non-fake) news sources. Also on Twitter, {{cite:2a28d0b08a62d17cf7e9c9574b3e422168044df7}} found that conservatives were more likely to follow media and political accounts classified as left-leaning than liberals were to follow right-leaning accounts.
| d | ffd214edb1c066c0faa9e682a4ce8b8a |
Table REF reports the average SSIM and PSNR scores with respect to different datasets under 2{{formula:88d1cea4-8695-4c62-af5e-db5ec3a150a1}} and 4{{formula:bb288755-dfcd-4420-8ca4-9a83a5e655fe}} enlargement. As can be seen, our approach yields the best results on all datasets. This demonstrates that our model can effectively fuse the two contrasts, which is beneficial to the restoration of the target contrast. Notably, the single-contrast SR methods, e.g.,EDSR {{cite:29fd3667ef02c72cb331d224a966336db3661fe5}} and SMORE {{cite:4bfc4c517630a78c4079d60eb31daa30d03a2111}}, are far less effective than the multi-contrast models. More importantly, however, the multi-contrast SR models, i.e., Zeng et al. {{cite:3b6544c27ab70cc9b13a47a920c0f5ec427de4df}} and Lyu et al. {{cite:89201469d4c0b066f84a8500214e50201d06b0ef}}, are also less effective than our model, since they do not mine fused features of different contrast or the interaction between different modes at each stage. In particular, when the scaling factor is 2{{formula:3da058e0-bd43-4a93-a1ce-92feb5ba8cec}} on {{formula:2b790fb5-dbfc-492c-971a-e2e2c43cf7ac}} , we improve the PSNR from 29.484 dB to 31.769 dB, and SSIM from 0.682 to 0.709, as compared to the current best approach, i.e., Lyu et al. {{cite:89201469d4c0b066f84a8500214e50201d06b0ef}}. Although it is more difficult to restore images under 4{{formula:cc38c3f2-48d2-4e16-a922-c1345bc1cbd6}} enlargement than 2{{formula:19608d76-ab69-4cb1-9d31-4025c505f9ac}} , our model still outperforms previous methods in extremely challenging settings, which can be attributed to its strong capability in multi-contrast image restoration.
{{table:c25e8940-f61a-46f5-996b-9483fa25dc06}} | r | bb0e94adb2c81f9c2697dc061bdc6dbb |
This formulation is not feasible for posthoc explanation methods {{cite:06b54620b47de945e4e875f2334647b7962bd94b}}. Hence, we define explanation continuity as the Levenshtein distance between two sequences of feature attributions obtained from the explanation method. Levenshtein distance between two sequences measures the minimum number of edits (insertions, deletions or substitutions) required to change one sequence into the other {{cite:e77696522b239bdc660bd62f03223da556b0bac8}}. We use Levenshtein distance as the edit distance between the two sequence since the order of relevant features matters in explanation result. The larger the Levenshtein distance between explanations obtained for two close samples, the less continuity the method possess. The Levenshtein distance between two sequences {{formula:d87c2118-cab1-4291-8651-5c0d969a18ca}} and {{formula:fbcd7387-d9df-4bf3-b689-86f96c9f2426}} with length {{formula:ffe3de8a-e21f-429e-9210-2939549a58b6}} and {{formula:9f947ba2-0aac-4130-866c-3afa3fd97a9c}} respectively is given by {{formula:e8468fb1-9198-4220-931a-210d0d7538d0}} :
{{formula:7f06eb7a-01bd-4276-9f2a-dcd87344bfb9}}
| m | 0657f59c0507c1736eb07b01038471d6 |
The mechanism is not difficult to find, though. For example, a light spectator field will transfer the isocurvature perturbations to adiabatic ones, which is called the curvaton mechanism {{cite:b5ade9f9d87189a4c0c52856e5c439fb9fd6a4af}}, {{cite:d21ac52d1cd2d702bc235bb74ae97c3aae6d2bfd}}. Since the curvaton field is much lighter than the inflaton field, it can hardly affect the background trajectory, meanwhile can generate most of the perturbations which is then isocurvature. At the end of inflation, the curvaton field decays into radiation or matter, by which the transfer to adiabatic perturbations is performed. Moreover, we can realize the curvaton mechanism from the inflaton decay that can be dubbed as one field inflationary theory {{cite:a9d05a73f00dc28c043c7fa95fe97675a5ca5a74}}.
In this paper, we consider the curvaton mechanism under the framework of multi-field inflation, where one of the two fields in mimetic gravity acting as a curvaton, so that one can still get adiabatic perturbations after the inflation period {{cite:1121fd50583584f7c5831c485f477305a064d5bd}}. Inspired by this framework, the adiabatic perturbation is sourced by the isocurvature one which is propagating, therefore the homogeneity problem demonstrated above can be avoided.
| i | 0f2fa927be54b68c54f5e3f63e27794d |
What design notes did we learn from applying pruning to neural ODEs? Our framework suggested that to obtain a generalizable sparse neural ODE representation, the choice of activation function is important. In particular activations that are Lipschitz continuous, monotonous, and bounded are better design choices for density estimation tasks {{cite:e8f29e6b477b16c2c1f38687f9e40c5fab954fff}}, {{cite:d1583740defd418b92731c26753b85c37e1ac50b}}, {{cite:4b44687ca9a58e7120b7a689af22570e443dad6c}}. Moreover, we find that the generalizability of sparse neural ODEs is more influenced by their neural network's width than their depth (number of layers). Furthermore, pruning neural ODEs allows us to obtain better hyperparameters for the optimization problem by setting a trade-off between the value of the learning rate and weight decay.
| d | d6ea17c045a63bcf208cdcda962c3014 |
The overall framework of the proposed DeepWORD is shown in Figure REF , which consists of two parts, the detection network and the relationship prediction network. The detection network is CenterNet {{cite:d345ca22752ba42f29244e6502842980aad80d56}}, whose main task is to detect the vehicle vehicle and tires from the images, and input the detection results into the relationship prediction network. The final model will output the owner-membership relationship between the wheels and the vehicle obtained by prediction.
| m | f85f34390e26a941220057583b5a38e5 |
We will compare the results based on the overall accuracy obtained. We will also see how the methods compare in terms of inference latency. In a real system, the network that can classify with reliable accuracy faster does not need to look at the entire duration of the input, therefore, can result in a power efficient inference system. We compare the network's classification accuracy versus the time-length of the input sequence to evaluate the network's latency for classification. Lower classification latency means that we do not need to process the rest of the inputs which saves the energy consumption of the end system. In addition, we will compare the networks in terms of average spike count. Since we are not implementing the system in a hardware, spike count is a good measure of the relative inference energy of the network {{cite:2c491d00f2e71f585e92308e91f401fe45746a5a}}. More spike activity usually means more energy is consumed by the neuromorphic hardware during inference. Ideally, one would want higher accuracy, earlier inference and low spike count.
{{table:8b7fd3ee-e41c-4e1b-87c8-4c6c1c2c0389}} | r | 3747c23b88bdf2eb6db5c6bbccce3e07 |
The well-established tube model of entangled polymer melts is a mean-field model in which polymer molecules diffuse within an effective tube arising from confining constraints from the surrounding chains.{{cite:45880605eadc7883934b38dbdf1f0141abb10d04}} This snake-like motion is termed reptation. The GLaMM model,{{cite:2f70f21788a44ab04a3965a7c0821529520c687a}} a detailed refinement of the tube concept, accounts for convective constraint release (CCR),{{cite:5ff085829ef344369f78fa15afa59a188f49f2c0}}, {{cite:e11f9fed77d47ea5ac275e8cf01300ad0f7d46c1}} contour-length fluctuations, and tube stretch. However, tube models do not explicitly track the dynamics of entanglements. A kink dynamics algorithm develop by {{cite:69f7cc81a46291dbfb9165a1f07199e8fd943bd2}} explicitly models entanglements. However, this model predicts complete disentanglement of the melt under flow, in contradiction with simulations.{{cite:5b33bd1569eb5306ba7817477f3bf4f4adda2587}}, {{cite:3469c39b585d37a567c10395dd0f8ff2ec8091f2}}, {{cite:f4f255107c1656be1e780c60a8f7c41500a161f1}}, {{cite:1bf1301ab85e3820495627d7735ed79ebcacacff}}, {{cite:312f5288bc0dd81e5dcb76191aecd405d50dea48}}, {{cite:1a1bf440d55e359dfdc4e5dee8bc2fe18f5d1923}} The slip-link model overcomes these limitations by explicitly modeling the creation, destruction, and motion of entanglements.{{cite:84926b680a278e14c37a92c854bd51f6f96fcd8f}}, {{cite:89b5cd4e1921a07b82f163b4dfe3566526f26f20}}, {{cite:90fd466f62af3ec2ac5e47022f01c5b5882e9906}}, {{cite:2b1220cd0021e5b7959ab6271884c52eeb5a0605}} In this model, entanglements on a test chain arise from equilibration with a chemical potential bath, and may lost via CCR. The discrete slip-link model is equivalent to a continuous tube model in highly-entangled melts.{{cite:63cbd3be9751b1ff597880a722744babcd902938}}
| i | a005d908da702d6b2070d216d9325d70 |
The data used in this paper are the Joint Light-curve Analysis (JLA) sample{{cite:039557bd477638671bb4d916d15417ea69e8b154}},
which contains 740 spectroscopically confirmed SN Ia in a redshift range of {{formula:c977ed28-4c75-4be4-8c3b-c40257ed4eb7}}
from the Sloan Digital Sky Survey II (SDSS-II), the Supernova Legacy
Survey (SNLS), the Hubble Space Telescope (HST), and low-redshift samples.
| m | b881078599f0a095f5ec630e488e881c |
Offline Q-learning performs well across dataset compositions in a variety of
simulated {{cite:1c6dfe18f8c9a74bec4390eebc08ac402b2d70cd}}, {{cite:2e1a5c2dc6c618d533273eed8cac7330a0d56a96}} and real-world domains {{cite:427cdeaa65a4edb91095eb25fd0b11b689da245e}}, {{cite:eba0c6dd1eede0be8ac677aea038cd0a39cf8958}},
however, these are largely centered around small-scale, single-task problems where broad generalization and learning general-purpose representations is not expected. Scaling these methods up to high-capcity models on large, diverse datasets is the critical challenge.
Prior works hint at the difficulties: on small-scale, single-task deep RL benchmarks, scaling model capacity can lead to instabilities or degrade performance {{cite:7a209a10682d341ad80b406912e252b6a1ecb71b}}, {{cite:236e12672d57318afefb49d20d0a56e751d9e1c1}}, {{cite:fefff3a9256b6fcf05782cb8f200fbc59d7005a4}} explaining why decade-old tiny 3-layer CNN architectures {{cite:f8c2de070c72ac802660cd914db39fc437b82131}} are still prevalent. Moreover, works that have scaled architectures to millions of parameters {{cite:2cd361dd6bafba6f9a3da0cae94da7f4a1b4266b}}, {{cite:a3d1d1af132e9d50f6b7ff8d2b161b9de03190f9}}, {{cite:9ccebac501cd86f1c937f9c9fc24cc9600313d02}}, {{cite:17597bda57c9ecb0ada0457423435c32593490a2}} typically focus on online learning and employ many sophisticated techniques to stabilize learning, such as supervised auxiliary losses, distillation, and pre-training.
Thus, it is unclear whether offline Q-learning can be scaled to high-capacity models trained on a large, diverse dataset.
| i | 8501ffb69c318b4a85fa12c93f286ebb |
We first introduce the standard sequential RANSAC pipeline for geometric model fitting (homography or plane structure in this work), with semantic cues as input with image sequences. However, we would like to cope with possible misclassification from the instance segmentation network, and therefore we do not simply use a standard RANSAC-like plane fitting algorithm for each detected planar segment. Instead, we propose a more robust sequential pipeline using a locally optimized RANSAC alternating graph-cut and model re-fitting in the inner local optimization step (Algo. REF ) to adapt automatically to inaccurate instance segmentation and noise. Finally, we discuss how it is integrated into a feature-based SLAM framework (as shown in Fig. REF ) as a robust geometric multi-model fitting strategy in this work. The mathematical notation used in this section is adopted from {{cite:7b36aee51085fb3039f7c8377683083070834ad9}}, {{cite:638791a56eb32b04fceba9ff5920ec7cadcfd553}}.
| m | d56bbc4c1ce873b27a38de214da61346 |
We present the results obtained
without
the combined SHOES-Holicow determination of {{formula:bafb139b-d5fc-4214-97ac-56ae440ec495}} in Fig. REF and Table REF for the data set P18 + BAO + FS + SNWe have checked that the addition of a prior on {{formula:3a76298e-3e13-46bc-ac5e-f00448c10135}} to this data set does not change appreciably the results.. The results show that the mean value for {{formula:73feb7ae-4db6-4482-8939-e2c73580de7d}} in the EMG model (and in the EDE one) is only slightly larger then the one in {{formula:d62ed99a-dc13-4291-98a9-1ad91e69b9e4}} CDM, as also found in previous studies of effectively massless models of scalar-tensor theories {{cite:979fd915d4c15520091ae03799ea24d758139601}}, {{cite:b5973e5fce717c784577134cbc28081f6675c15b}} .
This can be appreciated by looking at the larger posterior distributions of {{formula:dccaf29b-0115-4b46-a389-b40ed7d0b3b3}} and {{formula:f04b8077-b88f-4aab-af77-3cc871c90cf4}} for the EMG and EDE models in Figs. REF . The incapability of EDE to solve the {{formula:b0e202ab-e195-4024-ae1c-22e90df1b668}} tension when prior information on {{formula:a25c18d0-59ca-40c0-adaf-de7640533835}} is not included, has been recently discussed in the literature {{cite:0d6d657eb9141c7d15364264e8a3490769e2bdff}}.
A similar result holds for EMG. However, it has also been proposed in Refs. {{cite:c0c034f72450ecf4c31c105788a756f799d0a3d0}}, {{cite:316936224e656ebb8adce77026537d0dc7eaf1b9}} (see also next Section), that a distinction should be made between looking at the posterior distributions and the fact that there are some parameters that fit the data in a way that is statistically indistinguishable from {{formula:b8ef18f5-0b3e-4467-8228-5385c23c085e}} CDM and still lead to a large {{formula:93ff811d-3b94-41c7-bcd9-39eb439a03ab}} .
| r | f1c4cb41e3ba56280b3c342755f05670 |
The first inequality leads to {{formula:b0b64f2d-7eef-4e5b-8c0f-4b699a3f827d}} . Thus, the upper bound on the number of workers is {{formula:2ebba50f-f677-4523-bb37-fb24dbc26de0}} . Since {{formula:df47fe8c-5755-4c59-8c15-d4cf3bfae468}} , the second inequality can be written as follows: {{formula:22d55249-36c1-4163-b869-d0e70087136c}} . Hence, {{formula:d0515482-42be-4a83-849f-e2106824b3d8}} . Thus, the upper bound on the number of number of cores (threads) is {{formula:1a1f325d-2c46-4525-9997-1eea4dade25a}} . The convergence rate for serial and synchronous parallel stochastic gradient (SG) is consistent with {{formula:bf124e06-8352-4b36-b7d6-c8b07bf5a782}} {{cite:c4d9f253ba0ab10409a4d3d8e34f85ff2202082d}}, {{cite:e461e830d80c4dfeee4732911e7960c2c3c56a71}}, {{cite:d993e221bde6dba333f993fad2ebc14e420ea4c5}}. While the workload for each worker running DPSGD is almost the same as the workload of the serial or synchronous parallel SG, the progress done by DPSVG is {{formula:6af365be-124f-4e02-b8e0-5f02c489e1bf}} times faster than that of serial SG.
| d | 64e4b09ca0621b281ef182d5016d67c9 |
Our {{formula:c912ac4e-2488-48c6-b1bc-5e1bf13e624f}} -GNF with `The First Law of Causal Inference' are implemented and publishedThe {{formula:5b9d45da-32d0-4bb2-a32b-70a5c55d44a1}} -GNF code in supplemental materials will also be published at https://github.com/username/rhoGNF by adapting the baseline code of GNF {{cite:abb4c2735d9c02bc6fd3dcd8a72c3081261684cb}}https://github.com/AWehenkel/Graphical-Normalizing-Flows and UMNN {{cite:04ab545c2ca441be7e29683a13f5a1dcafcc182f}}https://github.com/AWehenkel/UMNN to model the strictly increasing transformations used in {{formula:808de7dc-95bd-451d-8d5b-00447fdcb86f}} -GNF in PyTorch {{cite:64147670e0ac22ccab7a91675d0823e642967b78}}.
As normalizing flows are developed for continuous variables, we use the Gaussian dequantization trick from c-GNF {{cite:e5935829afc9c05f60511d3f66a70bd8ae56cf4a}} to model discrete variables into {{formula:8c02deb7-8a33-416b-96f6-38f96a8e8f31}} -GNF. For the experiments, we present three different settings:
(i) simulated dataset with continuous outcomes,
(ii) simulated dataset with binary outcomes, and
(iii) real-world dataset with categorical outcomes, i.e., the IMF (International Monetary Fund) program impact analysis on the degree of child poverty in the Global-South region consisting of 67 countries.
| r | 0673cf63aae908f9529bd4294bbe0d88 |
Higher spin gauge theories have attracted renewd interests
in the study of the AdS/CFT correspondence {{cite:722d8c25a713659df142b1f49caf3c08347a045a}}.
Higher spin gauge theories have been conjectured to be dual to simple conformal field theories.{{formula:a95df862-8da5-47b5-8ff2-8f9e74dbe611}}A bosonic higher spin gauge theory on a three-dimensional AdS space (AdS{{formula:40a1d594-6155-4380-9707-ee73564585a5}} )
{{cite:96ebca8a1c1c8c0724c7421d94149f27648bfda1}}
has been conjectured {{cite:9fb70ec0b67e10d21b5572b48d166ae6c6e18e95}} to be dual to
the 't Hooft limit of the {{formula:148a9b33-f35d-4def-96d5-737867beb850}} minimal model,
while
a Vasiliev's higher spin gauge theory on
AdS{{formula:e3601f39-feed-4bcf-b9c1-a61525920581}}
{{cite:bd8e165727750f19583cf1b46bf5e1c1a781a5b4}}
is conjectured {{cite:47b69dbda0a6345135b4c4daf2cf4e178549f06a}} to be dual to three-dimensional {{formula:412303a3-1dac-4d5b-8583-616e2608763d}} sigma-model.
Our models on AdS spaces are much simpler than them
and actions are given in this paper.
It is interesting to explore the CFT duals to
our models.
| d | a5371fda55cc6e2ee1452874402822a0 |
Following the work of {{cite:da0f53a395f9bebafd9af538c6d673aeba565d77}}, we have shown that we can reconstruct continuous surfaces based on (small) point clouds, where their implicit prior leads to surfaces that are smooth and interpolate well in space. This contrasts with, e.g., slice interpolation as is often used to obtain dense voxel masks. INRs are continuous, allowing us to represent the vessel surface at any arbitrary resolution. This could facilitate seamless blending of separate arteries for, e.g., CFD analysis {{cite:cf775a0643bff416e47143421b026c51b694a531}}.
| d | 4075fd0234b3acb0058c861fe23e7e48 |
Note that we use {{formula:5fa6897f-2e10-4915-8ecc-31ee7bda3655}} to denote the {{formula:b2d57620-1e98-40bd-9af8-0e4d6b32cef8}} -norm of a vector {{formula:dd8ad38d-8b8b-4bf1-b91a-6b3dfa8e7f0f}} .
It is clear that {{formula:d68c3f5e-c280-446c-9a87-2739f125caf6}} is a Banach space. Moreover, since functions in {{formula:ebec0c1e-e68f-4f74-b059-064ae2d697cd}} have summable cosine coefficients. we have {{formula:5e8599a7-f4e4-4cbd-9a91-cbe1aa2437e4}} . When {{formula:3fd07ddd-e5c9-4de8-ae7c-816240c1189f}} , we adopt the short notation {{formula:f427abe3-29b0-4509-ba48-14fece9c708c}} for {{formula:69296675-1b61-4d50-942f-25d59356d36c}} . Our notion of spectral Barron space is an adaption of the Barron space defined in the seminal work {{cite:cf2d04ae8e5b89a37b26fd16ed664846ed89230d}}; see also the recent works {{cite:b1c8f75e106fa633a0aa98f1365d57ab97d49fb6}}, {{cite:9998d71569039de3265134ec888570df266fe210}}, {{cite:b92bca204d352b8af9c59b54dd141555797725dd}}, {{cite:6be6bf0bd568595a2d956318fe3920b16ed1794e}} on other variants of Barron spaces. The original Barron function {{formula:968e1647-7908-42c6-bc2b-83006b60d56f}} in {{cite:cf2d04ae8e5b89a37b26fd16ed664846ed89230d}} is defined on the whole space {{formula:b8378813-02ac-4514-8908-44e5b9af389a}} whose Fourier transform {{formula:b97ca2ed-f8db-4343-9ad2-44cb602c6805}} satisfies that {{formula:d94cdf4f-cef9-4983-8043-3924d23af61d}} . Our spectral Barron space {{formula:aab5e75a-7df5-40ec-8eb7-73fc84e762dd}} with {{formula:65023f9d-e9db-4f6b-9728-4fa66f0500c8}} , defined on the bounded domain {{formula:41cc3a35-bf37-49b2-ad72-c598f6d23490}} , can be viewed as a finite domain analog of the original Barron space from {{cite:cf2d04ae8e5b89a37b26fd16ed664846ed89230d}}.
| r | 837c1069263429294194c3462a725fda |
During the survey, we found that some methods start using Generative Adversarial Network (GAN) for data augmentation recently, which achieve better results than traditional methods. For example, DAGAN {{cite:75a5a28f8a8154253d4350bab5f6adb20e98ab6f}} succeed in generating augmented images for human face as shown in Figure REF , where only the left top one is real image. And after training on those augmented images, their model perform much better compared to those methods only using the real images. Inspired by these methods, we raise an enlightening question about this.
| i | d3dcf4d5f7d1b19c4df6f954761f54af |
The block bootstrap technique is one of the nonparametric methods that can be used to simulate from a stationary time series {{cite:28c892d556acc58803fa9ba420980d28faef6b48}}. In this method, blocks of the original time series are created using a block length parameter. The simulated series is obtained by resampling blocks of observations as opposed to resampling individual observations. The block length is an important parameter choice and the technique in {{cite:f1a4cbac3a9496fa83898ec26a0213d107852c36}} can be utilized. Though the previous method is developed for univariate time series, one can obtain optimal block lengths for each component series in the multivariate series and compute an average block length at the end. The block bootstrap method does not require the distribution of the error terms, avoids small sample estimation problems in parametric models such as VAR, and requires selecting the one block parameter. In practice, the choice between a parametric or nonparametric simulation technique depends on the length of the {{formula:24450141-19ce-4088-b4df-2ec80bceaaf0}} segments discovered by the chagne point method in Section REF and also the estimated model order {{formula:8c054442-4e4e-41be-83c7-dec5fd91b072}} in the VAR bootstrap described in Section REF . Parametric resampling methods face estimation issues when there are many parameters to be estimated with few observations and this is further discussed in Section REF .
| m | 178cff62150a0ebd7bbf770049692622 |
where we have separated the linear operator {{formula:20ec5857-28e5-4890-90d3-4515dd876f49}} and the nonlinear operator {{formula:93bf95fb-07f8-4e81-9633-57ab1f9b4af8}} , with {{formula:3d2156eb-b683-45f1-a248-073f3484e9dd}} and {{formula:206d2251-dc47-4ad7-a734-d38f4acafae5}} denotes the convolution. Additionally, we have that {{formula:ba7bcd34-946e-4da3-b752-5ee4b36d76c1}} is a linear diffusion operator such that {{formula:4ba44153-0a71-438a-acef-822d31cccbea}} , which coincides with the standard M-dimensional Laplacian ({{formula:739bf188-9199-4123-8225-3a2d36eafbd4}} ) if the diffusion matrix {{formula:50e5e0c3-a29f-4d5d-a25a-47bfeca6665a}} is the identity matrix. If {{formula:788eb95f-a98b-443a-884c-c9ecb2621c92}} , we are considering a nonlinear Liouville equation. We assume that, if {{formula:a7a2e338-1045-414f-8790-f81c4e93d984}} , Eq. REF describes a hypoelliptic diffusion process, so that {{formula:7d6b3bbc-1a13-4fee-af0b-9b8c31198a2d}} is smooth {{cite:82312f2bc1b6cd54f80e331cc00d996505df4df3}}. In what follows, we refer to the case {{formula:100d8c8c-e8bc-46cd-b5cb-1ce3e2409df7}} . Conditions detailing the well-posedness of this problem can be found in {{cite:c8f8c8ecfa4c54189f0bd7e9373e1de8e81b3428}}.
| r | dba88ca1334171a3b1cf2e2c96b2a68c |
Dynamical effects in the coupled-ring lattice are another avenue for further study. For example, the transmittance jumps in Fig. REF (b) may form hysteresis loops under an additional slow modulation of the input intensity. Such designs may also be useful for limiting unwanted dynamical reciprocity {{cite:9843855eb05d131c334a3ba47d7d5e46b018ab77}}, as the nonlinear isolation is provided by topological edge states localized in both frequency and space. Small amplitude signals with sufficiently large frequency detuning from the input could propagate via the qualitatively different bulk modes, and might thus be efficiently filtered or suppressed.
| d | 4d7cb2f46958553051f9a4f2c28f6336 |
We are unaware of any prior work assessing transformer-based {{cite:664caee730e42a85e0f9ef6a444a351889fb4720}} DNNs with EEG data (raw or otherwise). This is perhaps consistent with the ineffectiveness we observed with the randomly initialized full architecture (3.) and could imply that effective use of this powerful emerging architecture requires pre-training (or at least enough data, given the better looking SSC performance). Future work should continue to evaluate this architecture, particularly as it appears to be more widely applicable than the NLP applications it was originally proposed for {{cite:5307741f62be894d8fda175d349a8dcf6475ef18}}, {{cite:fec19747830b2f39913a7164ac8c1d5beef485d1}}.
| d | 829cf5be00a04ee1972b6e9c1bcef84a |
In {{cite:bb29e3971e603ede7e22c4f7d86a8c0d65b7cb7a}}, the authors introduce Multi-Head Attention has several attention layers in parallel. The output of attention layers is a weighted sum of the value, which the weight is computed by softmax function of Scaled Dot-Product Attention {{cite:bb29e3971e603ede7e22c4f7d86a8c0d65b7cb7a}}. The attention outputs are independent that are concatenated and linearly transformed with the expected dimension. The multi-head allows for attending to parts of the sequence differently. Fig REF is overview of Multi-Head Attention. The authors recommend the Transformer architecture that has the encoder-decoder structure to build global dependencies between input and output. The Transformer Encoder including a stack of multi-head self-attention mechanisms and feed-forward networks can map an input sequence to representation features. In this paper, we use Multi-Head Attention and Transformer Encoder as the embedded layer to generate sequence representations. We also employ the pre-trained model RegNet {{cite:2eebb518286817acd67a77e1dbdb8b1cd12497d8}} as the backbone for the proposed network. We use the weight of RegNet with 1.6GF architecture on ImageNet dataset {{cite:93595edd842e5b875a3e7f668cd7aa162f635015}} to extract feature of images. The pre-trained model takes the input size of the image as 112x112x3. The backbone is extracted with 888 features by the flatten layer of the pre-trained model. We reshape the backbone to (batch size, sequence, feature) and fed it into the Transformer Encoder. In this work, we opt for the length of the sequence to be 64. In addition, the backbones are connected to the Multi-Head Attention mechanism of the Transformer Encoder. We concatenate all backbones, output of attention mechanism, and Transformer Encoder module to get final representation features for the expression classification task. Dropout layer with 50% information and dense layers of 8 neurons are used for final output corresponding to 8 expressions of human. Fig REF describe overview of our architecture.
{{figure:90c3e180-1745-42ce-9b16-e2b6d4ab530c}}{{figure:d18e3464-e7d3-4df7-9153-2b99dc062b1b}} | m | 0652f50bf7451bd14d38ef2b130771ff |
We compare the proposed LaptSNE algorithm with vanilla t-SNE. COIL20, COIL100 and PenDigits are small datasets with no more than 10000 samples. MNIST and Fashion-MNIST are large datasets with thousands of samples. The scikit-learn package was used to implement both algorithms {{cite:db345ea12817ad9aadee1ac936306bef730f846e}}. We integrate the LaptSNE algorithm into the package with gradient descent implementation.
We present both qualitative results and quantitative results in the following subsections.
| r | ce36d2274efb6116fbb5a0ffa355c19a |
The typical time-latitude diagrams for the dynamo models were shown
in Figures REF and REF . The shape of the simulated
sunspot cycles in 1D1 model can be seen on the right panel Figure
REF . The simulated sunspot cycles for the 2D1 and 2D2 models
are shown on the the Figure REF . We can conclude that the
shape of the simulated sunspot cycles (and, perhaps, the associated
Waldmeier relations) is directly related with the spatial shape of
the toroidal magnetic field evaluational patterns. For example, in
the 1D1 model the maximum of the butterfly diagram is very close to
equator and butterfly wing is elongated toward the pole. In such a
pattern of the toroidal magnetic field evolution the decay phase of
the sunspot activity is shorter than the rise phase. The opposite
situation is in the models 2D1 and 2D2. The physical mechanisms which
produce the short rise and the long decay of the toroidal magnetic
field activity were discussed recently by Pipin and Kosovichev {{cite:ceac68fe3176a441ec22d35022dec2b0c0ac37be}}.
{{figure:4fe7d9ac-84bf-4a19-804a-5daefc7d1f82}} | r | c032827db4e923fcea13494224aea3c6 |
2) We now prove the claims on the superlevel sets using the {{formula:4e95953a-13fb-46dd-92ce-6d6bfb3b036a}} and {{formula:4315b986-8032-435d-a910-2f6fe0d7d0f6}} s of a sequence of sets in the Kuratowski sense (see {{cite:cf8db30002630d177ba640b8be3d9e8727095370}}). Setting the latent space {{formula:babcf5dc-227a-4f8b-900a-1a575a011028}} in {{cite:d21a1c432e7dd3c8a0ca6e483c49f150d4406537}}, the following set inclusions are obtained:
{{formula:3eefdd25-751a-40ed-bfee-c0ea75a54866}}
| r | bb8579c52999183fd7bf1ea9f9e86bfc |
Following the method of {{cite:c58af16d0510c9e4917d6af34eefdacd38a8fd0d}}, {{cite:c1851f521c1d89fae4e2eee5af4f3a966b680f8d}} to remove the stiff term from this equation, we multiply through by a multiplicative factor {{formula:95e72d29-0f06-427b-be2c-762e58cdd962}} and introduce a new function {{formula:d92429f1-d9af-4799-b9e2-ae5db9fcdb0a}} , where {{formula:33cf6373-39f3-459e-8bb7-fd3f5a102a05}} and {{formula:39db284e-3589-48fc-bc36-2c92a669fb61}} take the form
{{formula:1f02b161-6686-4ded-ac1e-d2fe64daece2}}
| m | 38cf615fc4b3b787fe33ebd4011283bb |
In this section, the values of {{formula:d747cab2-4cdc-418d-960a-86956422399f}} and {{formula:8d4a6113-2706-44f6-9aa3-3465a7a12702}} obtained in Section and summarized in Table REF , will be compared with those reported in previous works {{cite:adcbed41ab2e464741b48d113327dff6bf266ad0}}, {{cite:0ef089fb81a28e80a96bbe6c9e06763796b5c52f}}, {{cite:ba737eead125027960f2be5fc336cd2c403a7d8e}}, {{cite:cc9a4a94b0ec35c6f061848f84e266d7860545c0}}, {{cite:e1b1c25d7b6e1b2ac2f57deef28f7137a9c1abd1}}, {{cite:6cb4612ba3ed0baa5a0d4c937158b6cac023f434}}, {{cite:e5d9ba21da1d59f2ba41504025f16f1974417783}}, {{cite:42006e89e7e258502883bc112ee79e1192153c37}}, {{cite:e910c0ec7dcf69a8b42a68e1654b876263bce351}}.
Furthermore, the urban scaling exponents {{formula:4d9eb4e4-69d9-4d38-b070-3bffcd9e529b}} will be estimated by introducing the numerical results of {{formula:1e38434f-37d4-4e22-b7dd-f6875fe66fcb}} into the relationships linking {{formula:6ba5802c-45f7-4ef6-8997-0d862c47b708}} and {{formula:c5f6a960-99ff-4ac2-8ac7-77b4c4fceaac}} worked out in {{cite:9450e3ac3cdb3189b4ccc0280b2c2639e5277999}}, {{cite:f3a9e41ee5a01d2e21fecf1e98c9c1a6081c4fa5}}, {{cite:9ea8ec119e84c604e8710ac6e22c8aa7e2573c66}}.
For the sake of the discussion, a brief summary of previous studies dealing with fractal measurements and scaling models of urban areas is reported here below.
| d | 6c7642f661a5a2663c00e8a5faab18e1 |
The GP then performs inference as seen in section REF .
However, before inference can be done, the transformation and kernel parameters, {{formula:8eaa4e59-866b-476c-b3ef-b695eff66dde}} must be learned.
In practical use, the covariance matrix {{formula:4ae587a3-f196-4ee2-bd54-bb186f2d4365}} is approximated using the KISS-GP covariance matrix ({{cite:f18e6e3176c79dea8b5106c7e6cb01d4ed203b92}}, {{cite:be7bbd57f61fc28a8525102c66d2826b83854adb}}).
This is chosen because it allows for {{formula:645c2b65-4127-49e5-9eb6-9ad765481175}} scaling with training data.
| m | 4d79f94f001eda9a30d62e810ed7ce55 |
Here, {{formula:51b53222-b042-4386-b53d-9e0054cb836e}} and {{formula:e2858397-03a0-4f21-a5a4-a897af88ed83}} denote the expected loss with hypothesis {{formula:58f3de40-c4e2-42b1-873d-4e9853f4d888}} in the source and target domains, respectively. Considering that the disagreement between labeling function {{formula:3549871a-1b90-447f-83c8-22fe5e812212}} and {{formula:8c999958-a15c-4a97-822a-8ca58287317d}} , i.e., {{formula:6a8e0034-3897-4491-b234-250d2bca8ced}} , can be small by optimizing {{formula:252bfb1e-cf12-4508-94e5-5c689f905180}} with the source data {{cite:796ee9de9f659a3e29cf5b470fce26efcc385710}}, the UDA focuses on minimizing the cross-domain divergence {{formula:37da4ecd-9a4b-4587-b25f-836261d621aa}} in the feature space of {{formula:58034564-6afe-4106-8015-ffefe7c7454a}} and {{formula:e0f05993-76e8-4b29-afa8-7ace60a9025f}} .
| m | cbe74b1218e3521f9a413c3f6ed3aa07 |
The process mining discipline emerged around 20 years ago {{cite:e81dd76f2b6ac7095af047df1c89325771b838c2}},
and today there are over 35 commercial process mining tools (e.g., Celonis, Disco, UiPath/ProcessGold, myInvenio, PAFnow, Minit, QPR, Mehrwerk, Puzzledata, LanaLabs, StereoLogic, Everflow, TimelinePI, Signavio, and Logpickr).
Many of the larger organizations (especially in Europe) have adopted this technology.
For example, within Siemens over 6000 employees are using Celonis Process Mining to remove operational friction and increase automation.
Despite the widespread adoption of process mining and the availability of easy-to-use commercial tools,
the process mining discipline is relatively young and there are still many open challenges.
In this position paper, we focus on three questions particularly relevant for IoP:
| i | 5a8e10556a80c3b4290fb0b01302f41d |
proposed by {{cite:e3acc2841c34549abf1e0215704025c9d01b4c99}} and the Gaussian ansatz
{{formula:df835035-92f6-4be6-b41d-ac19b1ca1250}}
| r | f96150bf313542374bf90ac6c5ba2a98 |
In this section, we present the experimental analysis to examine the performance of our proposed CUSBoost algorithm. We have used datasets from KEEL-dataset repository {{cite:8cd9062133632b3af3abd25cfe36cdc79db345b5}} with different imbalance ratio. Table REF show the datasets details .
{{table:68d788a0-fd7e-4de7-9f4d-4cbc3ac82004}} | r | b015db11c0d7ea8fd14f8eb1f37a2e91 |
Readers are referred to Proposition 6 in {{cite:1fe7cfd95fa0be0f4eb3adf6063770b98750bf9a}} for more detail.
We should note that the important premises for us to use this available result are that the objective function of (REF ) is convex, continuously differentiable in {{formula:e7abcd0a-a223-47d1-8f78-e452c4c3cb22}} and the constraint set for each {{formula:56360187-c51c-4b89-94a3-589cb35f3c60}} is convex and compact.
Furthermore, by extending Proposition 1, we can prove that the intermediate solutions {{formula:cff9f5ff-4026-4347-a6e0-83f4a1b67bc3}} in Algorithm 1 at the {{formula:9e0437ad-d820-4467-a9fc-3c3b16613217}} th BCD update are always of rank-one:
| m | 5b0ba9a50388bab81f8b818a3b11dbd8 |
In this paper we have shown how the known relation {{cite:d0932d6350b54519c5cc0af8758ae942c91035b4}}, {{cite:55984649241cbab8226248d94ee28c321956f160}}, {{cite:8227587682c074decb1c6f6f792b92e2c1b4de9d}} between modular invariants in 2d RCFT, Lagrangian commutative special Frobenius algebras, and topological boundary conditions in 3d TQFTs, can be recast in the following form.
A three-dimensional theory {{formula:fc8957c4-f6fe-42f5-98ca-85dc05f8d762}} , constructed by starting with a Chern-Simons theory and then gauging a maximal one-form symmetry (or, in the non-Abelian case, performing anyon condensation of a maximal non-invertible one-form symmetry), behaves non-perturbatively as a theory of gravity and indeed is holographically dual, in the standard sense, to a well-defined (rational) conformal field theory. The bulk theory {{formula:c88519a3-150c-4bed-9a3d-80fbe7b2e955}} has a number of interesting properties. First, it is background independent: the full non-perturbative partition function is computed by choosing any three-dimensional manifold with the correct boundary conditions, with no need to sum over geometries (in a sense, the theory automatically sums over all needed geometries). A similar behavior has been observed in examples of full-fledged string theories in AdS{{formula:a46c21d9-aeb1-4827-ab8d-dff952bf0c22}} {{cite:77d5df61cea4ce7442a22ad2a39415d5ec8e839c}}, {{cite:f3333fa5082040fdff3def8140443d9ed5233cd7}}. Second, {{formula:639dd9c6-eced-48e7-b2f5-0ac14b5b1b00}} is a unitary theory of gravity: its partition functions with fixed boundary conditions are equal to the partition functions of a unitary 2d boundary CFT. In particular, the partition functions with disconnected boundaries factorize. Third, {{formula:a0af7ca6-8c7e-4844-8912-3dbcc926ca15}} does not have any bulk observable, rather, it is completely blind to the bulk geometry, which follows from the fact that it is trivial in the bulk. This is what one would expect from a holographic theory, once the full non-perturbative path integral has been done. Fourth, the bulk theory does not have any global symmetry: bulk symmetries are precisely removed by gauging the one-form symmetry.
| d | 9bcbd9c8bd53abd9d9eff9475ea000f4 |
A secondary advantage of using 2.5D inputs may be that ConvNets that are pre-trained on larger data bases available in the computer vision domain (such as ImageNet) could be used. Potentially allowing the ConvNet optimization to start from an initialization that is better than starting from Gaussian random parameters {{cite:47d93fcee5d00773779df9ab60d2845695fee571}}, {{cite:af59da228dbca05b6f599afd05ca3441861ad394}}.
| d | 073f55fe8bc1fd0201a813a0754e7dc8 |
Thus, a conceptually simpler {{formula:e2ad3a4d-01e2-4401-bdbd-59240c94ba89}} and perhaps more attractive {{formula:852ba499-6435-4d17-9371-58eaf04efaf9}} approach to realize our predictions is to consider a gain medium consisting of a continuously pumped superconducting qubit which is weakly coupled to the same resonance as the strongly coupled qubit (which for example happens if {{formula:dc966f65-bf8d-4d54-a2ee-ca4629466364}} ). In Fig. 2, we took {{formula:3ad6987e-9fdd-4046-a92a-f7236251dc86}} , and {{formula:27d258c0-1055-474d-97bd-d952e8c5271d}} . Thus, for a single gain qubit, threshold is reached provided the quality factor of the resonator is above {{formula:8e97d330-a08b-4d90-bdcb-afd8034c6f8d}} . There are two advances that would support reaching larger g values: the rapidly increasing coupling constants that have been realized with superconducting qubits (see Fig. 1 of {{cite:98bb190d4d2560607f49e2bd53178f6ee2624ce8}}), and early estimates in this field suggesting the possibility of {{formula:2dc88349-57cb-4db6-bf4a-d303671fc249}} values of roughly 20 {{cite:39fb9206d5e13afbe820c82142d5abfb942f23de}}.
| d | 7fcc88374394ef7abef1855351db99b9 |
One of them is the ICARUS-NESSiE experiment (SPSC-P-347) {{cite:0cead21dd17c91a8673fa14068e92222f02289df}}. It is a joint proposal for the search of sterile neutrinos with a
short-baseline neutrino beam based at CERN. In the following, the new short-baseline neutrino beam facility at CERN and the NESSiE detector concept, as well as the physics
reach of the experiment, will be discussed. The detail on ICARUS LAr-TPC detector and techniques have been discussed elsewhere {{cite:ac3d99b7b52011e7210dfd84cc7570f39d9d1e84}}.
| i | fcd53a96c32b70bf60a4a252e508fe90 |
On the methodological front, our work introduces new tools to the study of adaptive experiments. We show weak convergence to the diffusion limit for sequentially randomized Markov experiments using the martingale framework developed by {{cite:a73cbee75e4abc9565a29c7360401d0f6b112459}}, which hinges on showing that an appropriately scaled generator of the discrete-time Markov process converges to the infinitesimal generator of the diffusion process. Our analysis of the regret profiles of Thompson sampling in the diffusion limit relies on novel proof arguments that heavily exploit properties of Brownian motion, such as the Law of Iterated Logarithm.
| r | da9cc212cec2da7a3cd1125df9cabe77 |
We now restate thm:kexpr and show the proof. Note that thm:kexpr is different from Theorem 2.1 in {{cite:19637bfacec46394fc4730b429e325a0c6d58c9a}} because we allow repeated elements in {{formula:ec2f4bd2-ba92-442f-9a33-61d3ac826388}} as shown in eq:equaapp while they focus on all possible permutations of the input sequence.
| r | d5dcfe6427d998ae919976d1f342e205 |
Binarizing the synaptic weights is another important improvement which helps optimization in hardware implementations of deep SNNs {{cite:0eb6b3515a68e089fe29c7809541e2919e8ec30a}}, {{cite:1aa51f561aaaa3e6f13e984f14fc00364cb4f8a6}}.
Current Binary SNNs are the converted version of pre-trained BANNs {{cite:3e287b55c5339f8e32efd869be2aa03e0b8a4276}}, {{cite:0add1aa877d2eea158b86b5fee97f0e2cdb0b292}}, {{cite:cb3a3e6f14bbbda2fcf6dfb8712886e20994f5b3}}, {{cite:f32025f7d26558d2208674585c6423cbd449c6e4}}.
They train a BANN by using traditional BP and then, convert it into the equivalent BSNN with rate-based neural coding.
Here, we developed a CSNN with binary weights, which are the sign of real-valued weights, and employed the proposed learning rule to directly train it.
The forward pass is done with the binary weights and, in the backward pass, we updated the real-valued weights.
The proposed BCSNN uses single-bit of memories for implementing binary synapses and employs only one full-precision scaling factor in each layer or each convolutional filter. Therefore, the network size can be reduced by {{formula:bf49f8e6-c7cc-4e27-bf2b-a7b78da1a97a}} compared to a network with 32-bit floating-point synaptic weights {{cite:ede82f3f10efacd8e566de94587862cb84813e60}}.
Also, due to the use of single-bit synapses, the multiplier blocks that impose high load of floating-point computation to the network can be replaced by one unit increment and decrement blocks {{cite:ede82f3f10efacd8e566de94587862cb84813e60}}.
The evaluation results shows that the BCSNN has a negligible performance drop compared to the CSNN, respectively {{formula:c9533c30-bbcf-4825-a665-ef13d15d75ab}} and {{formula:a19e6a59-f426-4ad1-8628-2da08ff04c29}} accuracy drop on MNIST and Fashion-MNIST datasets. While it has more advantages than the CSNN in terms of hardware implementation.
To the best of our knowledge, this is the first implementation that aim to directly train a deep structure of single-spike-based temporal SNNs with binary synaptic weights.
However, one of the most important challenges we face is to make the network deeper to solve more complex problems such as CIFAR10 or ImageNet classification which can be our future topic.
| d | 9c5503e2d65a8ecb742468887baef5e4 |
One issue preventing our protocols from further acceleration is the Kerr nonlinearity correction term {{formula:f7433801-5297-4290-977f-b5ae8fc088a7}} to the resonator mode dispersive Hamiltonian {{cite:f695c79f3c6ef681f51a6b70c61d58674f7cec1c}}.
While our methods are designed to work in the linear regime, increasing the protocol speed requires fast-growing driving power, and accounting for nonlinearity becomes essential.
However, in the weakly nonlinear regime, i.e., where driving power is well below the first-order dissipative phase transition point {{cite:53758224cbdcf3c08f2a82098582bdb52af644b1}}, we empirically, in both simulation and experiment, find the effect of nonlinearity can be largely mitigated by including a mean resonator frequency shift {{formula:a781e9b3-e93b-4650-9746-6dfa5ba257e8}} {{cite:f86f0e877679bd3266a461d88ada53c90ab627be}} in our protocols, where {{formula:3938da25-5df1-4e9f-85d3-4e51181d7222}} is the equilibrium photon number in the resonator mode.
If the drive exceeds this dissipative phase transition point, not only does the microwave output suddenly increase, we also observe the transmon qubit becoming excited in a qualitatively similar way to a previously reported result {{cite:8e2a5d6822d796f89a4aa1ef33ed28253f88cb5c}}.
This result is shown in Fig. REF , where we stimulate the resonator mode with different amplitudes and durations and measure the remaining ground state population.
Our results support the theory {{cite:0ac3ff017d147e3eaa564f42c40d3306078a8307}} that the resonator phase transition and the qubit excitation coincide.
{{figure:0fcd8992-4613-4e08-8cfe-685080856fe4}} | d | 503c648e206291394df82019571bf93a |
To drive the system to a nonequilibrium state, we incorporate reservoirs with differing chemical potentials at its boundaries. We assume a weak coupling to the system (Born approximation), high-temperature memory-less reservoirs (Markov approximation), and that the bandwidths of the reservoirs are much larger than those of the system, which leads to frequency-independent system-reservoir interactions (wide-band limit) {{cite:1d3611edccc44e159854a58630ce46877ae70704}}. Tracing out the reservoir degrees of freedom leads to a Lindblad master equation for the reduced density matrix {{formula:aebb8ac6-995c-4494-98c2-21ed90242211}} of the system {{cite:5b0a270457796bb0271800643c7fe58bb4c65755}},
{{formula:35752181-42a0-47b4-a3d5-074a9610b921}}
| r | af18b9597200bc693b6f476d107517de |
With the explosive growth of user-generated images, it is also desirable to perform online continual learning for BIQA, where there is no distinct boundaries between tasks (or datasets) during training. Under this setting, Desideratum iii@ that requires no direct access to previous data seems too strict to satisfy. It remains to be seen whether this desideratum should be relaxed, allowing the widely practiced replay trick {{cite:37e57853271b0530326b307586271bd620764c7f}}, {{cite:29c19004ba68f663d5f327f98b7d069e5d3826b0}}, {{cite:50158e9b88143b18bdc09bf9ba04394fc28fb9b0}} in classification to be leveraged.
| d | 2bb9fc8351c467f8041e83798344e44e |
In spite of this fact some physical effects of the pairs of complex poles can still be traced down in
the behavior of the trace anomaly on curved backgrounds. Under certain consistency conditions {{formula:a88659f4-573c-4b3e-b828-cd9f2a906238}} -theorem establishes
that the coefficient of the Gauss-Bonnet term of the anomaly {{formula:ee498284-3a42-433c-a089-0b2fe551936c}} must evolve in a monotonically decreasing way under the renormalization group flow {{cite:a37d98e21aa87f1cb059b8f7490730e0b112bff9}}. However, in the case of the UV asymptotically free theories analyzed in this paper {{formula:89445c32-f46e-4c33-b056-c28454356d1a}} is positive in standard infrared regime whereas in the UV regime it can reach negative values {{cite:ec91fce4b696785b7f08cacebd534f32056c96c4}}, {{cite:2ea8bf7173c6f42df4d8c1e87d0d46ad89241a2e}}, {{cite:94efd35f686460a09d4e530e9d1884098fc0f061}}. This breaking of {{formula:00b5772f-0b20-47f2-80e4-9af80567377e}} -theorem raises some questions that require a deeper analysis.
| d | 13eb745b83aaf8e40dd712b42f306d0a |
Ab initio calculations: Density functional theory (DFT) calculations with the projected augmented wave (PAW) method were implemented in the Vienna ab initio simulation package (VASP) {{cite:57008cf014a7d5d9de27950203374546b61bf426}}, {{cite:b5144da82804f6e78839dfa91a8898253ae759a3}} with generalized gradient approximation (GGA) {{cite:2b21fd37fac423f3890abe049c605eb6f879da90}}. For the irreducible Brillouin zone, {{formula:089e0f1a-5b66-40d6-a688-99acec304d5f}} -meshes of size {{formula:1baba4d8-2b7e-4bd1-b9fb-aa3fcc29f099}} were used. The spin-orbit coupling energy scale was found to be less than the typical linewidth of the photoemission spectra, so non-relativistic calculations were performed for both the ferromagnetic and non-magnetic states. For comparison with the photoemission spectra, the Fermi level of the ab initio calculation was optimized to match the experimental results, giving an effective hole-doping of 0.1 eV for the ferromagnetic state and electron-doping of 0.07 eV for the non-magnetic state, of ARPES relative to DFT. The Sn-terminated surface spectral function calculated by the WannierTools package {{cite:64d4eafb952a37704ed7198880a9332506a92ecf}}, using a tight-binding model generated from maximally-localized Wannier functions {{cite:6435e9719615b0ed67ab2ddcbd172c65b09301d2}}.
| m | 9a974649403c7a0e1602cc53e1433632 |
There are many potential avenues for further work. One might look for
non-spherically symmetric solutions of Euclidean biadjoint theory, and
also interpret the spectrum of existing solutions we have found in
various numbers of dimension, including their relationship with the
Lorentzian solutions of
refs. {{cite:df2813895df4600b14d92c876137d366a751ba0e}}, {{cite:c5639e606cc0228421cfe64d84a348aac64f0446}}, {{cite:79091660d706d62a040aacf64b14cc0b8d5ff342}}. Examining
how general our methods are – in terms of mapping out the known
moduli space of gauge theory instantons – would be useful, and a
first step in this regard would perhaps be to try to make sense of the
more general ansatz of eq. (REF ), as noted
explicitly in ref. {{cite:7baf1e17fccadbc09a05974576b2bbddd0ef8eaa}}. Finally, we note that
twistor methods are ubiquitous in the study of instantons, and have
recently arisen in the context of the exact classical double
copy {{cite:31b10a3f6e6fc09d1351e600e8b3134aff08ca94}}, {{cite:15aff7a1e8bdc4fc50dbaab32add9cf872083195}}, {{cite:07d1b973d2a62032594d706183fd4185c1a70dbe}}, {{cite:42ba1f4e96d961af048f803a4b4dae4c397ed2d2}}, {{cite:71105e1e0a6e7f0387704d761153b60a1170d5aa}}, {{cite:2a3272f177ac17b3379541ed62c9edb8633ae6e1}}, {{cite:48d7236eaef7c8c940cedde64055b24b24785616}}. Some
sort of twistorial description of the (anti-)self-dual double copy is
surely possible. We look forward to reporting on these various topics
in the future.
| d | 0f884e470a79335583a9a98ea15ef29a |
For future work we suggest investigating the combination of our approach with other UQ approaches such as out of distribution detection {{cite:24d9f574c56c05a11529cd2424a443bbc614dbed}}. For this, we believe that it is possible to generalize our approach to consider also soft segmentations by adapting Equation REF adequately. To further improve the sensitivity and precision of the intersection/union of segmentations in the calibrated ensemble, it might be useful to adapt the choices of loss weights {{formula:58f5cd75-fa0d-48cd-b1ad-96dcbc713ae6}} accordingly. We also believe that knowledge distillation might be of great help to reduce inference cost and facilitate clinical deployment. For this we believe that theoretical considerations and clinical implementations of our approach are needed to determine the value of UQ based methods like ours in human-machine collaboration. Furthermore, it would be interesting to see how our suggested method of pretraining on unlabeled datasets using pseudo-labels performs when being compared to other pretraining approaches like self-supervised learning {{cite:3049d33f249b235df67a1459b1f27f1873844242}}, {{cite:32afd7ba0b5949455140896a0cb38ed1d967afbe}}. We also believe that our method could be extended to incorporate the impact of the uncertainty in the segmentation into Radiomics-based classification models using such segmentations, or even be extended from segmentation problems to classification problems like Radiomics-based classification.
| d | 47904f3adb5096dfc989981cce6e34a3 |
In this sense, the TCC is a weaker condition than the de Sitter swampland condition (REF ) which rules out such cosmologies. Interestingly, the above time scale is the same at which the back-reaction of infrared cosmological perturbations indicates an instability of de Sitter space (see e.g. {{cite:21edf102f57e3b92084b084c42f0add2a4a528c1}} for a review), which in turn is the same as the quantum break time of de Sitter space in the approach of {{cite:480abe55462600789dce5cbdb68ce1f0778d427e}}.
| d | 7f64b07e4a7658db9c2d70b0c0f09f45 |
In this paper, we shall study Linear Complementary Dual codes (LCD codes), which are linear codes that have a trivial intersection with their orthogonal. LCD codes were first introduced by Massey in
{{cite:350f7ee0fb7b661c1aac8152390d0b0906023601}} and were used to give an optimum linear coding solution for the two
user binary adder channel. These codes are also used in counter measures for
passive and active side channel analyses on embedded crypto-systems. For a detailed description of this application please see {{cite:85083fcbe04f5489c60d09371f60cf17e67e2cc1}}. LCD codes are asymptotically good, it is shown in {{cite:93f7d0babc5607a5110953b9b5e870dde09714a2}} that they meet the asymptotic Gilbert-Varshamov bound. One of the main goals is to construct LCD codes over finite fields that also have good error correcting properties. A result of Carlet et al. in {{cite:f446e401fd9f4f2f7e0d39b4d6db9409b168546d}} gives that over any finite field of order {{formula:ec3671fc-f26e-409f-a73d-a7fb010c6164}} the existence of an {{formula:832f6aac-81ed-4092-965c-3205c934ea60}} linear code implies the existence of an {{formula:911832b6-1a76-4dd8-8b1d-3608e08aa3b6}} LCD code. In general, the limits to error correction may be more restrictive for binary and ternary LCD codes than for linear codes, as LCD codes do satisfy extra conditions.
| i | 5be0693f598d3e958d80333fb65e6203 |
In this section, we will compare the performance of spikemax losses with spike-rate loss on three different neuromorphic classification tasks. We use SLAYER-PyTorch {{cite:751cdbbf0f8dc2f61bff8a2f69882762677a3383}} as our SNN backpropagation framework. Our loss methods are implemented on top of it.
| r | b00f59df1a080d622dc097b878ff794f |
Together with the above, and motivated by recent concrete examples present in the literature, where the bound for the viscosity/entropy density ratio (REF ) can be violated (see {{cite:c84eff8174657b95a97caf4d4576036249e3470a}}, {{cite:1797c50a4f21a599118f75268a870a556270f268}}, {{cite:aa89024d0cd7ae238a2b648690604ca3fa2f6705}}, {{cite:48eb64f641c06b8b10c5b73f0ebed4c6c0495ad9}}, {{cite:5083f9768c076cc3e90fc463eccdf8c29f432af5}}), we analyze the shear viscosity {{formula:47558693-dfba-4c2c-8def-675480018bb7}} for these solutions following two procedures. The first one, through the construction of a conserved charge as well as a suitable election of the Killing vector {{cite:b4c97cd0c41cef8a80a7ac514fd2ee50dfde66d1}}, and the second one, via Green's functions and Kubo formula, given by {{cite:bb9dc35c8c204082263dfb0a848ae61b0dfabf5c}} and {{cite:8db007544d7f42529468f2824c20347ebcc59732}} respectively. For both techniques, arise a new concrete example where we obtain an expression for the shear viscosity {{formula:e62bfc5b-c152-4a89-8fcb-b5599f6289a4}} of the dual gauge field theories, allowing a violation of the KSS bound.
| d | fc3edfeb7aaeafc62a55e79f6e89c069 |
for some universal constant {{formula:fc0fe0d1-cbdc-41a4-adcf-f64def80ceb2}} . Using Theorem 12.2 in {{cite:486266ddc844ed18a51ae0a6f599db41141f88bb}}, we have
for {{formula:72481de3-4c35-4a3f-aa97-6e211fc24608}} , where {{formula:7b2256b9-c132-45ce-8688-91a60c74fa1e}} ,
{{formula:82989bb9-9b1b-46af-8224-a294f6a3fc97}}
| r | 1ef9b45b0c3a11e7e21d5385387fccdf |
In this article we study the general characteristics of two type IIIb solar radio bursts and one U burst with stria structures present (typical of type IIIb bursts) observed on 22 August 2017 with the LOw-Frequency ARray (LOFAR; {{cite:e3899373814e7b3494f6229407fa257840a757af}}) telescope in the frequency range of 20 – 80 MHz, including dynamic spectra and imaging observations. This gives the spatial information of radio bursts and relates it to the height, size, velocity, and energy of the electron beams responsible for their generation. In order to better understand the physical properties and evolution of the solar radio bursts, we used the data in X-rays from the GOES and RHESSI satellites and in the extreme ultraviolet (EUV) from the Solar Dynamics Observatory (SDO).
{{figure:9bc909c7-2b51-4d19-86d4-ecc82b5548af}} | i | f06c7b1356ac6aaedda0d9d7855c92ae |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.