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The {{formula:16a89007-266b-4a5e-b300-07fe0d6eed6d}} gravity is a modified gravitational theory in which the standard Einstein-Hilbert action is replaced by an arbitrary function of the Ricci scalar {{cite:e4f805495d6472b76ba78d83a30903be8e8810d9}}, {{cite:674ad41aece911f6726f0c4ae79d65bae9ffb45d}}. These theories have received considerable attention in the last years motivated by the fact that they can explain the observed accelerating late expansion of the universe {{cite:d7b29ef1b9471aeeb04384abcf3ff4137ef44342}}, {{cite:ba5c1661990b30aff2c0969bcba34a8772d5c4fc}}. There are several studies on {{formula:f4995362-77a4-40ab-971a-e57efe3a7644}} gravity, such as, solar system tests {{cite:693e4f907d093590557d4ae9a3f5c612ef0aa119}}, {{cite:730325fd2bed47190fb606879e5f0e300cc92521}}, Newtonian limit {{cite:ce5bc7082af3aace25d14bb7058c6f0bef4fc016}}, {{cite:03cb7d37ef00ed4b4dd743509dcbfa1b44833a19}}, {{cite:e1109f45b70d34781726edbf326723e6b8038fa2}}, gravitational stability {{cite:5cefc434f95c7a4521720284f030eb68d78fe71d}}, {{cite:853c6129d7d331dab1ad395a857a2767a125abde}}, singularities {{cite:d84e69d21974e946498141836b6c817bb85416ab}}, energy conditions have been used to place constraints on the theory {{cite:c8b151b78fec4c9dba5cf74c796d51701c35bfa7}}, {{cite:5318903ae41bf1304686b32850340f9f3b6af557}}, cosmological perturbations during the inflationary epoch {{cite:ded4e7699fd12c480e3846ef61c8fb875d56a7bd}}, gravitoelectromagnetism formalism in the context of metric {{formula:4a0a0720-ac1f-439f-ab86-97fcec47ff0e}} theory {{cite:e35d01264bf44f1875f100c56b0a3859eb5bacd7}}, among others.
| i | 1002a42ddf5b6d294c01066f29940fbe |
Beyond graph representations,
Ogay and Kim {{cite:d95c2263d0baa4562272f0d56a3c74e853a9cd3d}} proposed to represent a motion planning algorithm as a random process that is controlled by a heuristic as a distribution of random variables.
A machine learning method then learns to relate the obstacle distribution and the heuristics to better control the motion planner.
Gaussian Mixture Models have been used to represent collision possibility in high dimensional configuration space {{cite:39a8a9b5bffbcd27af899cda959ad051d30e5756}}.
Ichter et al. {{cite:ba7a7c469c877532948c84b3bc2f95d5153a5b9d}} proposed to sample configurations from the learned latent space conditioned on the new planning problem.
Kim et al. {{cite:87c1532ae44299e3d31d0c22c868c715b1b252f0}} developed a novel representation of planning problem instance called score-space, based on similarity in score space, they can transfer knowledge from previous problems to solve new task.
| m | d6775610a452dbfc9f87ff151d5aced6 |
In the Standard Model, in terms of CKM matrix elements, {{formula:aa3ee7dc-a760-4d71-bb3f-2450cc2b2b73}} The equations below are written assuming that there is only one decay amplitude, ignoring possible small contributions from other diagrams {{cite:6e8ac9e38e5222cf54d5b7ea2842f10b29177d53}}, .
The decay time evolutions for initial {{formula:8e16677b-de00-4a6f-b0c0-6fbd978600ce}} and {{formula:2c6dca04-56e8-4f87-917a-3d27d6151cff}} are {{cite:5bec8b81dd9cada50b80e3660178cdced78e1352}},
{{formula:d78b1e99-0d07-4b15-8c33-7427bbabd715}}
| i | 35ffe85683c332cdc60edd43f8dc5330 |
Our model also computes an artificial label for each pair of strong and weak augmented unlabeled samples (i.e. pseudo-labeling {{cite:75379598979df2a8f2b6a965678a4375d4c866d6}}, {{cite:099199450c4443a7a0e9d09f2c013dbb3c1d1917}}, {{cite:690a63dc7545be8c42c4467329ab66f1aa598264}}). This label can be obtained by computing the {{formula:42d2b69c-72f5-49c4-93e6-fa326eebfc1d}} function over the averaged model predictions for the {{formula:68e4394b-5484-4768-87fb-d0c9b3c38a4d}} classes, for a given pair of associated samples {{formula:05606c63-4bab-4c98-8fe6-5ba0ae90b58c}} . Similarly, an averaged model confidence can be computed as {{formula:1b88bdb6-dc48-4856-9710-9d0049f3d108}} . Then, for each mini-batch our method minimizes a self-supervised loss function with respect to the feature extractor:
{{formula:9aa40a59-4487-4bdf-a4fa-932ce8d883ce}}
| m | 4aed64aa83964e4cdabd206dfd496bce |
To make progress in positive characteristic, where the landscape is distinctively more complex,
it is best to adopt a more restrictive definition (see Remark REF for a comparison).
Graded Lie algebras of maximal class {{formula:29c6ba54-ce90-4083-8520-faa047f704e2}} which are generated by {{formula:16817375-9702-4a6e-9f7d-c61fbab41fb3}} , as in {{cite:fbcee0cf856a112f0e1fdc45c683b7bd85352fff}}, {{cite:628512702a472bcc58495b605185b3d76e1cdb4b}}, {{cite:7fe776363324871992bf0021546aca905be591d6}}, will be called algebras of type 1 here.
Then, necessarily, {{formula:df8d1f21-e871-4f58-a22e-801ebc61a33f}} will be two-dimensional, and {{formula:1d1e2538-9ef5-43ab-930e-e2bd94bcead4}} will be one-dimensional for all {{formula:f6d1ec56-d689-4c42-aa31-a15bc12aa3e2}} (under our blanket infinite-dimensionality assumption).
We define an algebra of type {{formula:56140e14-2f7f-4dd5-9a5e-04ad96c509d7}} , for {{formula:5ebe004e-63e5-47eb-8c3d-878b4d8dfe50}} , as a graded Lie algebra {{formula:c3da92c0-cd0b-45cd-b645-934b9642979a}}
with {{formula:89170886-49ca-4ce0-b870-6100ceb53f88}} for {{formula:88f7d402-9929-41d5-9a85-7f45d1c5414c}} and {{formula:d686614e-142f-4f76-8a3a-e16f9ba52f50}} otherwise,
such that {{formula:ec7bca70-e3c2-4894-afda-43e55047d091}} for all {{formula:9edfafe7-6458-4a6f-add5-82cc5804a668}} .
Such {{formula:e09c5dca-2478-4aec-a3d5-569908034acd}} is a Lie algebra of maximal class, and is generated by {{formula:dfd8061a-c271-4c0a-9fb9-1d2fcb0ccee1}} and {{formula:b3d41cf6-2f69-49c2-80e6-a907f1e114ab}} , both one-dimensional.
However, beware that the latter assumptions alone on {{formula:40316bb9-c1e0-41f3-8c1b-5b3e350d1160}} (of infinite dimension) are not sufficient to ensure
that {{formula:c2322431-bd90-457a-bf5d-c91625023d5c}} is an algebra of type {{formula:2cd72fc3-6e9f-4159-bb08-93a7d1770ccb}} , see Remark REF .
Thus, {{cite:dbc3ff2770ff7e3062f83d7f9bba24894514b3b5}} showed, in particular, that over a field of characteristic zero there are precisely three algebras of type 2,
up to isomorphism of graded Lie algebras.
| i | 281934e7f2577be9cc3ae8e7df710996 |
In the following, we should discuss the mass spectrum of vector bottomonia.
As listed in PDG {{cite:63bd7775363ad9539b8c5982fd0b2830e45c2c5f}}, there were
{{formula:88af7ad0-7820-492d-903f-dc723957ae79}} , {{formula:f9d520e4-d7de-4d89-87e6-e9b2270e5007}} , {{formula:cfeeda0f-7e8a-4361-85f6-3a432f4e9ede}} , {{formula:ef3841c8-f910-4fcb-bc0d-e431e02ee62b}} , {{formula:5dcd97d6-fc1f-4ebe-af4f-d4c7e7e62bb4}} , and {{formula:f51fc799-d3ce-439c-9063-ed84b1b2209b}} . We find that they form a Regge trajectory
as shown in Fig. REF .
This Regge trajectory satisfies the relation {{formula:169c4534-7aac-489c-bb5a-613b1b2a07dc}} {{cite:130190cb3bcbe9d9ce0313d12bdef292663810d1}}, {{cite:e7de48b9a37422fcaaa64c387753771389026cde}}, {{cite:5149af09c6377058c94afd39430f2a562db49d5f}}, {{cite:b934a33e20cbe8c225749678739a128cfd637bd9}}, {{cite:dc1a3f42d113550534ebeb00bb32c76817ac7ec5}}, {{cite:52722737c3723abb11ac8d6f145a9c8378521b51}}, {{cite:b9d76b7de80ffcf7fb11c04aed84afba359c7e32}}, {{cite:6188b0fe1de2209aa46dd845132f33769d5cf41d}}. Here, {{formula:9eb9f8c4-69cb-4b5f-88eb-82f5b75fdc29}} is the mass of the ground state, {{formula:3cb651cd-0a8a-4e67-8e01-1565dc859acf}} denotes the mass of the radial excitation state with the radial quantum number {{formula:fde05efd-ec21-4948-a246-a812f179115b}} , and {{formula:0bf62265-af9c-4f3b-ae27-e3a30434c8cd}} GeV{{formula:2a835ec5-a6f6-4799-b060-3f29be2aa4af}} is the slope of the Regge trajectory.
Although the {{formula:b5272bd3-6722-48eb-adf3-94ba4f9fe188}} is suggested as the mixture of {{formula:68a81a73-65c6-4b40-b16f-19ecada53069}} and {{formula:142d3e3e-e254-45da-900c-9a968a637221}} states of bottomonium, the {{formula:3a2884fe-61f5-4426-82bc-0ee3b009502c}} has main component of {{formula:06e75635-5546-4a37-958e-a164cf0ca3eb}} state. Thus, we may take {{formula:1edb2262-2969-46dd-9227-3af493848d1c}} and the predicted {{formula:3392c6b6-0b12-40c9-8630-ea4ac98662d8}} and {{formula:e4130d8c-c2c9-4473-9fb1-a9de2cf5ce95}} {{cite:d65371ec16f44bde6fb0b31079e8730bc1abbb15}}, {{cite:b6c752534666c717e1251ec76b5d508380514257}}, {{cite:f55f3863802fc540c0ebd7acc7d64827cd44c492}}, {{cite:d5d9f3865e925f2fb5edf8b2004384716bded723}} to construct
another Regge trajectory (see Fig. REF ), which have slope {{formula:ae5fc336-d3d6-4263-b170-8e89bfcb47dc}} GeV{{formula:ce8c1b28-0e58-47d2-bfe8-1e7b0125c390}} . This slope is similar to that for the {{formula:2c3d2408-2bc5-4ad7-ae1d-602d740ad295}} -wave bottomonia.
Thus, searching for the missing {{formula:9d7a6cd4-52bc-4a14-89e6-e7ec1f38f578}} and {{formula:768f6728-59eb-4c63-b447-f5518db62879}} bottononia in future experiment will be helpful to test this Regge trajectory behavior. It is obvious that the present work of studying the {{formula:a6f5f525-87ab-441a-b355-e18443b4fc1c}} shows the potential of finding out the {{formula:d1b7b0c4-8641-47da-a27b-dcf5a0bc826c}} bottomonium.
| d | 6aa91030d62b3cb5fb594d18518f1356 |
In the jet distance range from 0.2 mas to 1 mas the component position angles (PA) listed in Tab. REF are in agreement with {{cite:f62e0a909a685856e783a3bcaeeb2ef09f71565c}} within the errors. For example, the PA of component J6 is {{formula:f4ce0b44-676b-4f1c-a31a-121d88bad951}} in the model while here we find {{formula:c8e1528f-eb2e-4a1a-815c-1b7095a62916}} (86 GHz). The optical polarization data arise from a knot at unknown distance, but judging from the agreement of the PA of our innermost knot C2 of the 86 GHz map and the PA of the model {{cite:fb44f00c8d170ea2b0193f693ac2bdac707b61e6}}, it is possible that the optical emission region is not far from knot C2.
Beyond 1 mas our PA values agree with the earlier model of {{cite:fb44f00c8d170ea2b0193f693ac2bdac707b61e6}}.
| d | 02bd052a79770778699dd27388640bbe |
where {{formula:0f5a777d-c16f-407b-b5bd-a3c0ca13960f}} is the location of the maximum of the RW potential (REF ), {{formula:a0353699-d4e0-4b52-a807-baa854f55ca4}} . {{formula:c7596771-c18f-4edf-b5d2-75df967956bc}} are the WKB correction terms and {{formula:cdba95c2-ecdb-40da-9c4f-85c1fad8f818}} is the order. The corrections {{formula:553e0e41-8d73-4f97-bcd0-3dbc69bbf316}} are given in {{cite:eba660d385445fd635e30c426566e2fdc6fc1725}} and {{formula:5415e7fb-c53f-407a-a471-b02fd2698d3a}} can be found in {{cite:a5367484ac16963e2a5088a15010f738fa3e707d}}. Solving this equation, we obtain the modes to the 6th order, which we present below in Table REF . There, we provide the QNM complex modes for different values of the overtone number {{formula:3de84557-ff03-43ef-8480-14bc93210e1f}} and the angular momentum {{formula:cd4c59f0-11da-42ce-ae44-59d27b1e9850}} . As indicated in {{cite:a5367484ac16963e2a5088a15010f738fa3e707d}}, the WKB method works more accurately for lower values of {{formula:c0774f00-85a1-481b-9aec-e64f12fb8487}} and higher values of {{formula:313f1875-4a11-4c00-9d10-8c952e116379}} .
{{table:230a0a28-85ec-431d-b308-56974b528728}} | m | 7faf7df23cb49fedfd82929373632f1a |
We also simultaneously fit {{formula:2e93d972-4c3c-41f7-8413-ce1291556ad0}} to the nonprompt {{formula:d39595cb-82fc-4b80-8c3d-a7b1719e6082}} data
from ATLAS {{cite:a9dd958c45079049e443ce2e6397d113b67d0c82}} and CMS {{cite:ed4cefb2b61e5f1e8bd88ce11fec07e57f1a2b8b}}.
This is possibly problematic because the experimental (first) errors
of {{formula:3b4c7264-ae06-48e2-afe5-1b9533e64cd2}} in Eqs. (REF ) and (REF )
from the individual fits do not overlap. In other words, the agreement
of the underlying ATLAS {{cite:a9dd958c45079049e443ce2e6397d113b67d0c82}} and CMS
{{cite:ed4cefb2b61e5f1e8bd88ce11fec07e57f1a2b8b}} data, gauged with respect to our universal
NLO GM-VFNS predictions, is marginal. In fact, the combined fit to the
{{formula:df3bf21c-5e0f-4bb3-93e2-3b45858037b7}} experimental data points yields a minimum {{formula:bc568e59-ac31-42eb-bb27-c8ab5a118a1b}} of
{{formula:abb72429-95c4-4706-9919-1123c00cd9fc}} . Following a recommendation by the
Particle Data Group {{cite:5a8d0eb28435f6f1fdc723a5246e2c26ad67ac27}}, we thus rescale the original
Gaussian error of {{formula:7af2f0ac-36a7-44e8-a2bf-72320e2fb256}} with the enhancement factor
{{formula:29b731b0-f91f-4b3f-aed6-9cfbce248654}} .
We so obtain
{{formula:604a711e-4a5a-455e-b53c-84662ccdb3e2}}
| r | b1e55230a2970a7a98c38fda559545d3 |
These considerations pose the problem of the degree to which EoS constraints are driven by the data, rather than by correlations between different densities imposed by the EoS model. Under that light, it is interesting to consider the effect of folding nuclear calculations into the inference of the EoS.
Figure REF shows that the J0740+6620 radius measurement does not inform the EoS below {{formula:1f4cb6a4-f623-42af-9f9c-01567a2a065d}} , something also confirmed by {{cite:d34a5f5d87756add5756105e7211a4e2973e9957}}.
References {{cite:a04a0d772b5d9355326218eaa7718f5f5034c04c}}, {{cite:62597232dbdc3815141ab8ec2c2949ecfe40c0b6}} further show that our GP EoS prior is designed with no strong correlations between low-density {{formula:bad83aeb-bee9-47c2-819d-90f264f22261}} EFT information and high-density physics.
As such, we do not expect the J0740+6620 radius data to offer new insights about {{formula:03ceb643-90c2-4dfa-a657-d9da68e54125}} EFT predictions within its regime of applicability, i.e. 1–2 {{formula:36183c7a-3c3e-4dd5-8741-77f6c57acb7b}} , nor do we expect {{formula:258623f8-1e38-40ad-a564-7b06ac250038}} EFT predictions to influence our conclusions about NS matter at high densities.
In contrast, the parametric EoS inference in {{cite:e036e35428d661293a19f3bbf2b201c658cb7c06}} is sensitive to the {{formula:17dbbc0c-1c27-4ebf-a45c-f9e52a63764d}} EFT calculations they condition on up to {{formula:0229e732-5219-4d6e-99c0-8b937820a3d5}} even at the highest densities probed. Figure 7 of {{cite:e036e35428d661293a19f3bbf2b201c658cb7c06}} shows that the NS radii and pressures they infer with both of their parametric EoS models have some dependence on which {{formula:1f336154-c28b-4d84-ab08-6351af951683}} EFT calculation is chosen as input.
This suggests that statements both about the validity of nuclear calculations based on astrophysical data and inference of
NS properties after assuming a specific low-density calculation
must take care to avoid introducing unwanted systematic modeling assumptions through the choice of high-density EoS representation.
| d | a77255941cd1f41efe3dde2465ccbb62 |
It is interesting to know how far an approach such as this can be taken. It is possible that different state spaces could lead to classical simulation algorithms for other quantum inputs. If we are interested in simulating quantum systems, then we do not directly care about simulating systems with non-physical cylindrical inputs, so we might consider other state spaces of different shapes, with the aiming of finding ones that grow slowest when undergoing interactions, but contain as many quantum input states as possible. We know that a convex hull version of twirling {{cite:2706d7de55695972389704e0576e13bac3f01062}} can be used to argue that an optimal state space must respect the symmetry group, but other than that we do not have systematic techniques for finding such good state spaces. Another possibility is whether coarse graining can significantly increase the permitted measurements. For instance, if it were possible to write down a non-trivial family of entangled states that are separable with respect to block state spaces consisting of entanglement witnesses, then they would be good candidates for entangled systems that can be efficiently simulated classically for any single particle measurements. We do not know if such examples exist.
| d | 16ddd65303b6dab5b2085bbbf04b93ec |
INCV {{cite:a8156e9cf50e75201a6994484ebe25512c00cac5}} iteratively filter out noisy examples by using cross-validation.
| m | d5c808c81926d10ad658fab26a01998c |
Societal impacts. Image segmentation has several applications, including autonomous driving {{cite:14cd314dbda52f6ccb7fd9ef2fdae9424b086733}}, medical image analysis {{cite:fdecb747c4e728a5b874def3f61420cb5ea712c3}}, and video surveillance {{cite:1c89f9a7634c60dfbda53c56d45aa1b7d89d54a2}}. Although we have not focused on any specific application in this work, we describe some potential societal impacts in regard to image segmentation in general. Autonomous vehicles lead to lower greenhouse gas emissions, improved traffic safety, and frees up time for people {{cite:db120f067f3fdfeec85226c77cb68563655b593a}}. Automated medical image analysis can be used to aid doctors in identifying sick patients {{cite:1fb265298b7422783b0b47eb875df128494fc12d}}, and video surveillance can be used for crime prevention {{cite:b7f777a1b4af84e0aa052491ac4df5666a0aa5ff}}. Video surveillance could have potential negative impacts as well, such as being used for compromising integrity, mass surveillance, and data harvesting. However, the models considered in this work are trained in the weakly-supervised setting and lack the ability to discriminate based on specific human traits. For deep learning in general, the training of huge models could have negative environmental impacts, and it is important to asses the task at hand whether they are outweighed by the potential positive impacts that the models can provide.
| d | 19d0e14a8d823dae3f38bffd6e0cd363 |
Magnetic resonance (MR) imaging is rapidly becoming the dominant technique for image-guided adaptive radiotherapy because it offers better soft tissue contrast than computed tomography (CT), while avoiding radiation exposure. However, due to the physical nature of the MR imaging procedure, the scanning time can take up to tens of minutes long, which seriously affects the patient experience and leads to high costs. Therefore, accelerated MR imaging has become a hot research topic, where reconstructing images from undersampled {{formula:f4daf498-55cc-4c00-9545-069c4575108e}} -space measurements is a standard strategy. However, the aliasing artifacts caused by insufficient sampling often affect the clinical diagnosis. Therefore, the recovery of high-quality images from undersampled {{formula:268a1044-13b3-4a77-8703-1ed097053d18}} -space measurements is the ultimate goal when accelerating MR imaging. Currently, mainstream methods for this include MR image reconstruction and super-resolution (SR). The former aims to remove the aliasing artifacts caused by undersampling {{cite:ec8027803a79a0674f3d5d8960e21051653d9668}}, {{cite:016968b4a79f69cb478473a0a182f9cb55270c2c}}, {{cite:f1368545cda3636aee03b2a073208ea0c3aef152}}, {{cite:6e6618cdd78e7ac08dca795193a9bc43231d159e}},
while the latter enhances the image resolution {{cite:2ac528c0f7b16f8397031b67bada485938c56f8d}}, {{cite:df7513b2107255a8b6498d3501f8971a9b5df851}}, {{cite:1b697da7eca10d09254cc333a8a24f8bd3359d19}}.
{{figure:cffd2575-1058-40e2-8857-6ab15d03c23b}} | i | d250a994346972640ff46f9e8ee7e8a9 |
AIB is compared with VIB {{cite:4695b3e6061a77e49dfb9727be1f576a24016f83}} and NIB {{cite:34f29ddabede43a78e13b49a6bd057c3a018b828}} on a synthetic dataset {{cite:b443ff04fc05dbc315f54235be06a89beca616b0}} and two common classification datasets MNIST {{cite:aaafec02e8e9b0a9bdf082a9d6b257ad8283acb4}} and FashionMNIST {{cite:6dc615d055ec27e08dc42583d839b61d950559d5}} by varying hyperparameter {{formula:b91faa70-d544-42f7-bc6c-adb712d49afe}} . We adopt the typical DNNs trained with the cross-entropy loss to show its representation ability and robustness (denoted as “Normal"). We also employ the popular “dropout" method (denoted as Dropout) with dropout rate as its regularization hyperparameter for evaluation. We still call the trade-off curve relating to “dropout" as the IB curve for convenience.
| r | 37c6bc9ecfa4d0e9fd18a57ddfc18264 |
The models are trained with Adam optimizer {{cite:cfccf969bbe38ad0b861d18b35cf4b02af582463}} and teacher forcing.
We use linear warm-up to increase the learning rate from 0 to {{formula:a1cb72ca-9993-4584-b7b9-11d77ce14ac2}} in the first 200 steps, followed by a 200,000-step cosine decay down to {{formula:d405560e-5230-404a-82c2-cc65e363b339}} .
Model parameters are initialized from the gaussian {{formula:516ed3ca-662e-4a1b-b93c-e77f3e8ddce9}} .
Using a batch size of 4, we can fit our MuseMorphose into a single NVIDIA Tesla V100 GPU with 32GB memory.
For all three loss variants (preferred settings, AE objective, VAE objective) alike, the training converges in less than 2 full days. At inference time, we perform nucleus sampling {{cite:9850f18e5a0408462fc3cd6efec3ee19f74f53f6}} to sample from the output distribution at each timestep, using a softmax temperature {{formula:40f93c54-62cf-4d7c-b17f-82a0eaa8d6dc}} and truncating the distribution at cumulative probability {{formula:3187081a-bfca-40be-a996-a09b386d840e}} .
| m | 6a1b2d0ad4bde360a9cf51670cb1ae58 |
In Table REF , we compare the performance of our best method after distillation with transfer learning, semi-supervised learning {{cite:ec36c2034efaad60d983fe2dd2462a295f2da092}} and DatasetGAN baselines. The transfer learning baseline was initialized with pre-trained weights on semantic segmentation of MS-COCO {{cite:8ffdf27dbcd87f27b124811df26573b473f205de}} dataset. Our method performs better than the baseline methods throughout all the datasets.
| m | 80a780bcda30a59c637e9e6998d4ac63 |
We have only considered gauged supergravity with {{formula:d0abbb5a-9d97-418c-870e-44cb5870f5b8}} gauge group electrically embedded in the global {{formula:da78af20-a6b1-4e33-8318-5b549e3f8852}} symmetry. It would be interesting to study magnetic and dyonic gaugings involving also magnetic gauge fields. In particular, performing a similar study in the case of {{formula:8a4d82ca-b4bf-4ecb-a374-4846c21c276b}} gauged supergravity with the electric-magnetic phase {{formula:fc1835a2-fdc1-4aeb-8e57-2f46771fbbe3}} , see {{cite:689487d774174158958bfe71f029e7de1a84a6a2}} and {{cite:4e35cf48ff80aa59230b400a4d39bccc8b5ab068}}, {{cite:c9bbd50ccdd6b2dff751b8cf369b8a1ac0a76d89}}, could be of particular interest since in the omega deformed {{formula:8f1e59a3-3e42-4bae-9b2a-094b5fb526da}} theory, the structure of vacua and domain walls are much richer than the electric counterpart, see {{cite:c2616dde7b4d1ad858a1c5a74e33d82b4866cb89}}, {{cite:7452a86163d49a47b8bc01ad081186a5be3d9baf}}, {{cite:a04fe67f9eb1c03ae92acf17716da0c9836a1e45}}, {{cite:9efb218340acce63fec3306e0577b2ad7deaff95}} for more detail. In addition, the study of genuine {{formula:6b11c09e-cbeb-444a-999f-17bb342020bd}} gaugings which cannot be embedded in the {{formula:40ddd33a-66c4-4821-afa6-08197474caa8}} theory is worth considering. In this case, the gaugings do not satisfy extra quadratic constraints coming from the truncation of the {{formula:935b4fa5-82a4-45a7-8c29-4a2ca12f57fe}} theory, see a discussion in {{cite:0030f9f043cba415f7e624f3d167e8606c7502f5}}, so the corresponding solutions cannot be embedded in the maximal theory.
| d | 246603f220f8133b66db338f0ded93c2 |
Second, the proposed sequences constitute a partial unitary matrix with a column mask
through arbitrary row selection,
whereas the ZC sequences of prime length form a deterministic matrix with low coherence.
While the coherence-based recovery guarantee of the deterministic matrix
is limited by its theoretical bottleneck {{cite:dd4fa6af357b8fb8c8e3a6f2fbb1aebf4154168d}},
our partial unitary matrix can present theoretical recovery guarantee with higher sparsity,
which ensures reliable CS-based detection theoretically for more active devices in mMTC.
In summary, the proposed non-orthogonal sequences can be a good option for uplink grant-free access,
supporting any number of subcarriers and providing theoretically guaranteed performance for CS-based AUD and CE.
Remarkably, our GA-based design offers a new set of non-orthogonal sequences
with many advantages over the ZC sequences of prime length,
which are known for the superb performance in practice.
| d | 24628be702363293cbc5acadb16e6589 |
This proof can be extended to the case of the arbitrary {{formula:7514682e-1b7d-4cf2-b742-1ee61a72cf3d}} , too. Then, the most appropriate way is to show that there is a correct limit of {{formula:59e9d87d-37c1-487f-bc5b-9199c606e53f}} defined via (REF ). Application of the following known limit relation between the Laguerre and Hermite polynomials {{cite:69fee976a968cd6d24c7bf6daf0d74efb3c5d49f}}
{{formula:56ce72ea-10cb-4379-8217-0ca2ae8fe766}}
| d | 5b6ea17971d3f1fdc022979a2e9cd84e |
In some scenarios, an intelligent attacker may attempt to launch an adversarial attacks to fool forensic algorithms {{cite:a0ac543428adaac59158e6ceee3808b023a5f82a}}, {{cite:4329ea9d72b5c72f3e7007a6992fa4b91430f328}}, {{cite:24e41eecc791c9db927e478dd3b853d7d846ef4a}}, {{cite:c8753d556b7a2565cb1eb54cb36091ad942e856c}}, {{cite:ed53b711105b2d8e2390cc6c63efb26595038b2e}}. Many adversarial attacks have been found to be able to fool deep learning based algorithms {{cite:7fa7426931aa26dc0fdc72bc70ec1868e6396284}}, {{cite:f8c817c0478302c47b689aa0a690a04d3521a027}}, {{cite:6c68eb28dcca56456ff69669a673dbf0615db2db}}, {{cite:6aca3d293fc13c8709181d2abdccf514153fab7e}}, {{cite:b5157bb6680ec717a1c5550e5f454891b8a28944}}, {{cite:77ab7174338d866711238b5cd7a553ac85ecbe66}}, {{cite:2cf4e58278a9cce73082879b3a4ee977ea038431}}, {{cite:ae318f51e33a603593f3d27fa713c4139045b250}}, {{cite:bead7cf732964b36e53ea5378b0dca89f8ed555b}}. Researchers have already demonstrated that fast gradient sign method (FGSM) {{cite:228a74deed76225ae287028ed1d74f644c506a7e}} and generative adversarial network (GAN) {{cite:052ffd0a1f0b305692cb94e30ec2b42255c2a8af}}, {{cite:2192e43f0c51d54d50f562f1c3d5d3a426d9cc7d}} based attacks can be used to fool forensic CNNs. Therefore, it is important to understand the capability and limitations of the adversarial attacks.
| i | de04a9e6ce685d8fb85f988f781a06c5 |
For lane lines detection, the method was tested on KITTI {{cite:03d82607ad779809ed9cc0a731bd01131b4a909b}} and Cityscapes {{cite:02761ff642722c4db060a91863e59b32ae0395ae}}. For general traffic lines detection, The proposed method was tested on the Berkeley deep drive (BDD 100k) {{cite:d670a925c6fd4be961005ebce34f7811cfd2c707}}, KITTI and a self-recorded video. These results of general lines detection cannot be compared to other methods due to lacking metrics. At last, the BDD 100k dataset and images from a self-recorded video are used for testing the localization method while passing free spaces.
| r | a1434d243d2b6f85b5759b4338e70f47 |
We compare our method with an extensive list of recent works on efficient video recognition: AR-Net {{cite:478ea0bf01eb8f6921cdf6865d8f29e117f80abe}}, AdaFrame {{cite:a7c6777d09ba031ad40524219dfb674d957024f2}}, LiteEval {{cite:f16eed5d5217a5f20273b481e0de5484a4947d80}}, SCSampler {{cite:8cf426dee003122bc42f447db1f4e62ebd4298c6}}, MARL {{cite:cfb36375dc0284a246b55ffe28411ecfb141a88e}}, and ListenToLook {{cite:ed77bf86b397034c7fd32108a7be0b66268c06eb}}.
AR-Net uses MobileNet-V2 as the sampler network and adaptively chooses a ResNet architecture with varying depths as the recognition network. The method is additionally evaluated with variants of EfficientNet {{cite:9ea3e081971f170c59ef931a75e134ae2122889f}} as the recognition network.
AdaFrame and LiteEval both use MobileNet-V2 as the policy network and ResNet-101 as the recognition network.
SCSampler uses MobileNet-V2 as the sampler network and ResNet-50 as the recognition network. MARL uses a ResNet-101 as the recognition network combined with a fully connected layer as a policy network.
ListenToLook uses MobileNet-V2 as the sampler network and ResNet-101 as the recognition network.
Finally, ListenToLook (IA{{formula:14b4177b-26e3-4f2b-8d09-7ff7691ddfd3}} IA) uses two ResNet-18 for audio and visual modality respectively as the sampler. The same architecture is used for recognition network.
| r | 17324edf8bb2b954c3c2a29eb7f06b42 |
We have seen how PermaKey, by focusing on local predictability, is able to reliably discover salient object keypoints while being more robust to certain distractors compared to Transporter {{cite:eebbf862c0880bd4262809e661cffdae7fe1621e}}.
However, it should be noted that PermaKey can only account for a “bottom-up” notion of saliency {{cite:d4be311155896a34ea58ae5f5a06b88c00307c1f}}, where salient regions are determined purely from the observed inputs, without also considering task-dependent (top-down) information.
Therefore a potential limitation of this approach is that it might capture objects that are not relevant for solving the task at hand (i.e. corresponding to “unpredictable distractors”).
However, we argue that this way of extracting object keypoints in a purely unsupervised (i.e. task-agnostic) manner may allow for greater re-use and generalizability.
In particular, the same (overcomplete) set of keypoints can now be used to faciliate a number of tasks, for example by querying (and attending to) only keypoints relevant for the particular task using a top-down attention module as explored in {{cite:742f493433425bc79da38ad84923bf409ad80442}}.
In that way, the same (redundant) representation can readily facilitate other tasks, such as a “new object” acting as the key in Montezuma’s Revenge, without having to re-train the bottom-up vision module.
Although we have not explored this direction here, we believe that this could be an interesting direction for future work.
| d | 6dfa51e0da10a6401315552c892bc994 |
In this section, we aim to improve the data efficiency of existing detection transformers, while making minimum modifications to their original designs. Firstly, we provide a brief revisiting of the existing detection transformers. Subsequently, based on the experiments and analysis in the previous section, we make minor modifications to the existing data-hungry detection transformer models, like DETR {{cite:2d4276f7aa4bc719c821bb436043d488a64e19af}} and CondDETR {{cite:0e1d018cb05ad5091426765220f9f75cc263c742}}, to significantly improve their data efficiency. Finally, we propose a simple yet effective label augmentation method to provide richer supervised signals to detection transformers to further improve their data efficiency.
| m | 3a913d9095b7f9d4128d5cf2bd59773a |
Because of its random-walk nature, the local dynamics of Gibbs sampling suffers long auto-correlation times when equally likely states are separated by an extensive number of variables flips. As a consequence of long mixing times between such states, statistics become heavily biased. In the initial phase of DBM training, when weights are small and randomly distributed, these issues are minimized. Interactions between nodes in this `high temperature' regime are weak, and are well approximated by a mean-field theory {{cite:cdb3a7ce06e03f3c73d7a34d0627b2092fff1b96}}. In this phase, CD works well without much bias, and is the reason mode-assistance is really not necessary early on in the training.
| d | df3671988652772c889092be572ae382 |
The P-N junction is one of the fundamental building blocks for modern electronics. With recent discoveries of atomically thin materials, layer-by-layer stacking (vertically stacked) or lateral interfacing (in-plane interconnected) heterojunction has been reported, {{cite:a8dbc7ba31a7c6bb775878d9446f6f5b3a19483e}}, {{cite:d476740bcfc9b3f8fdc66c45c56abd6629b3292b}}, {{cite:f730531570884b90507f432162ac584ba41e567a}}, {{cite:420ba94fc1c4b7c7bd8070c5edc4b22dc19cd549}}, {{cite:2d77f86044aaf1c767824efe66270c81420aa5b9}}, {{cite:c2ac6b30d2781e36c8fbe4474728fef3c080ba46}}, {{cite:f102c951c13dd3e5687dbff553a43f00447c17e1}} which indicates the traditional semiconductor devices can be scaled down to atomic thicknesses.
| r | c90c6ae8bab4815decbc73cbf4ba2ec4 |
The likelihood analysis for each data set and cosmological model is done using the MCMC method as implemented in the MontePython code {{cite:72e1acf8544bfa6a16753393047715ddb3df0b6d}}. Convergence of the MCMC chains for each parameter is determined with the Gelman-Rubin criterion {{formula:6a394905-c254-4038-8a1f-1067caa17d70}} . For each free parameter we assume a top hat prior which is non-zero over the ranges given in Table REF .
| m | 63c79c79e237d22ef40394e1f8eb720c |
Most of the previous studies on the design of phase shifts in the RIS focus on the sub-6 GHz or narrow band systems {{cite:e94943040286388556c36b5b44503914e615cc69}}, {{cite:3c283425dec6003415243918e67d3e2f292dc068}}, {{cite:c9c7b4c460a2d50d965152daec9888dc78a16988}}, {{cite:550a15baa071df34beffb8bf3aa50a7fab9414a4}}. In {{cite:e94943040286388556c36b5b44503914e615cc69}}, with the aim of maximizing the spectrum and energy efficiencies, the authors proposed low-complexity algorithms to joint power allocation and phase shift design. In {{cite:3c283425dec6003415243918e67d3e2f292dc068}}, a semidefinite relaxation (SDR) based scheme was proposed to solve the phase optimization problem with unit modulus constraints. In {{cite:c9c7b4c460a2d50d965152daec9888dc78a16988}}, the fixed point iteration and the manifold optimization based algorithms were proposed to obtain locally optimal solutions. In {{cite:550a15baa071df34beffb8bf3aa50a7fab9414a4}}, the phase shift was designed by phase extraction operation by exploiting only the statistical channel state information (CSI).
Moreover, only a few contributions have considered the wideband scenario. For example, in {{cite:253c20fb22dc5d8a1a96a62cea3fcad5baf37245}}, the authors considered a RIS having a few randomly distributed active elements and proposed compressive sensing and deep learning based reflection matrix construction schemes with low training overhead.
| i | aaaad2f4aefa1497d13b3d4be004fb88 |
In the standard LBM for fluid flows, the evolution equation reads {{cite:48eab936cdd4a381ac42ad70f351318939c9ee2f}}
{{formula:de593b01-c83a-4a95-aedd-a462ae3c92dc}}
| m | 1832c221d72687ae5c1598cabb574bd5 |
with {{formula:3b0d838f-35d7-48ad-936d-5a0d171985a6}} the weight function, and {{formula:c0ecd94e-8408-4668-968f-513a9b95b495}} the quadrature weights. The error is given by {{formula:6985d13a-7f5e-4830-8d03-5abad183951f}} , for {{formula:514054cf-758e-41b7-a112-88d655d0519a}} , and the pair {{formula:469ad3b0-4c89-4e33-b3d7-e475980bf1d0}} are the Gauss-quadrature weights and the nodes based on the parameter distribution
as proven in {{cite:2f68429f2c36e1f7f83a37939f1e7099a316ce2f}} (p.180, Theorem 3.6.24).
| m | 7bac7227ce709d69e9a63a94ba3a1e5d |
Recent studies on graph neural networks (GNN) bring a new structure for model learning. By viewing particles of the object as the graph vertices, the dynamics is modeled as the interaction between the vertices pairs {{cite:1a7281d3917ad945d83acfbdc2797c560043fc38}}. The future object state can be predicted through a sequence of `message passing' blocks, which mimic the transmission of the interaction from one graph vertex to others. Compared with those general-purpose network structures, the GNN encodes the prior knowledge on how the interaction may transmit inside the deformable objects.
However, as most of the machine learning based approach does, the GNN model relies on simulation for data generation. Thus, the sim-to-real gap still poses a significant challenge for the model to be adopted in robotic manipulation tasks.
{{figure:91b7319f-eedf-483e-9c98-6cea8378bd56}} | i | 1167c5b6d1313e5880a923e217109bdb |
Filtering methods update their belief based on the past state and current observations of visual and inertial modalities {{cite:836accb4849c36eeeedacccf51442cad5b34fed0}}, {{cite:a2c30dba3bc254dd3d4336f72ea4e29a3d0edb8a}}, {{cite:33d1a551b4a923667b28c96c6d1c09904972a500}}, {{cite:fc94172688b9c481362c65d3119d262b6833b2b7}}. "Learning" within these methods is usually constrained to gain and covariances {{cite:8c36d512f131a94bd8261fdced7e34f6d67831c7}}. This is a deterministic process, and noise parameters are hand-tuned beforehand.
Deep leaning methods are instead fully learned from data and the hidden recurrent state only contains information relevant to the regressor. Our approach models the feature selection process explicitly with the use of soft and hard masks. Loosely, the proposed soft mask can be viewed as similar to tuning the gain and covariance matrix in classical filtering methods, but based on the latent data representation instead.
| d | 01b68d57eebb9691df3cff61362bc468 |
[leftmargin=*]
Additive white noise perturbations are constructed as {{formula:6fdbbb54-7d3b-4d4d-ac87-5e706f5a6159}} , where the additive noise is drawn from a Gaussian distribution {{formula:3e30bd1d-4df7-4850-ba0b-ced9603db692}} . This perturbation strategy emulates measurement errors that can result from data acquisition with poor sensors (where {{formula:efb466fe-18c7-47f5-a521-d9f9c1277262}} can be used to vary the strength of these errors).
Multiplicative white noise perturbations are constructed as {{formula:2b3a4b80-0e25-4305-8102-edee42e236fd}} , where the additive noise is drawn from a Gaussian distribution {{formula:adc60a25-dbee-45f8-b2df-4f9dd6962a2c}} .
Salt and pepper perturbations emulate defective pixels that result from converting analog signals to digital signals. The noise model takes the form
{{formula:5ebc5088-e8ba-4636-94fc-63631d00cf15}} , and {{formula:ba2399b2-60ed-497b-af54-fb6c2debd5d5}}
where {{formula:1811f632-2541-4d35-b301-38bbfcc92b82}} denotes the corrupted image and {{formula:cf877870-c6c8-4aab-a7cf-23b753196e99}} and {{formula:b056cc5d-ace1-433d-90eb-5e9d314af803}} denote to the minimum and maximum pixel values. The parameter {{formula:28ac6c51-9550-44e8-a020-29abb1665759}} controls the proportion of defective pixels.
Adversarial perturbations are “worst-case” non-random perturbations maximizing the loss {{formula:9751a544-a33c-4e17-a8cd-ff702ef5682f}} subject to the constraint that the norm of the perturbation {{formula:28ba2743-0204-4b8f-a0f5-826ab39397f3}} . We consider the fast gradient sign method for constructing these perturbations {{cite:dc97ff7bfa8f3cdb72fd52cb1c472b9bd760a3b9}}.
| r | ac10f02e7cbf4b850524bbcf93186230 |
In this work, we employ the Wide Activation Super-Resolution (WDSR) model {{cite:d8a03188ed7a777a09f78b7a49531a44895230af}} as a building block to investigate architectures for joint denoising and super-resolution.
| m | b4d6945a5b84aa17fea69a1c89ad90a9 |
Recent years have witnessed rapid development in self-supervised learning and it has achieved success in both computer vision {{cite:3b0611af13e6fde2da154fd0534ad38e2481e9cb}}, {{cite:08511c5fdde133a596f7f4eccbeb14034ff88162}}, {{cite:ebe64fbf83cf7ec24b07152d8a02a3f154d0a231}}, {{cite:1bde711a6504c79dee3169acdf894710a604a66a}}, {{cite:af92ddf45a086f85d7d585c445d0c6ef859b66ae}}
and speech processing domain {{cite:d94be798f1d5850e896dcc12b2f3512c35cc8889}}, {{cite:da175e611800473bea93124c7f2eaa5f257bd87e}}, {{cite:b3833d4b97c449b209da6cec55e3c3e2ec3836a5}}, {{cite:f8c5a9d1c8273008fddc1202c7ccbb7f4aa20a69}}.
Different from supervised learning, where labels provide an explicit discrimination task for learning, self-supervised learning methods employ pretext tasks for model pretraining.
It enables to learn general representations from rich unlabeled data and to finetune the model on labeled data.
For audio and visual representations learning, previous studies leverage the natural synergy between the audio and visual channels of the video for cross-modal self-supervision. AVTS model proposes to learn general audio-visual representations via self-supervised temporal synchronization and a contrastive loss {{cite:90364764344c11de7f0f7584335adb61a2b8dbf7}}. XDC leverages cross-modal audio-visual clustering for self-supervised learning {{cite:ac85019fa4081bce7eaf70a2cf317ecb8afd0567}}. A contrastive learning method for both global and local audio-visual representations has also been proposed {{cite:8628e08349b213030378e2040b201da7bd030afb}}. Particularly, a newly proposed method by Shi et al. extends HuBERT {{cite:b3833d4b97c449b209da6cec55e3c3e2ec3836a5}} from speech to audio-visual speech data {{cite:9af157ed7bd64633cd317f833d05e3411742cb0f}}. AV-HuBERT
is trained iteratively by alternating between an offline feature clustering step and a masked prediction step until the model performance is no longer improved. It has achieved state-of-the-art performance on downstream tasks such as VSR {{cite:9af157ed7bd64633cd317f833d05e3411742cb0f}} and AVSR {{cite:fa2bd5f74a7a8ee67f16ed9507d3a38fb12661a1}}.
| i | d74a1623af3731769d833c8bed7a870f |
In this subsection, we perform a variety of experiments to validate the effectiveness of SRKOCL in continual learning scenario. In the first set of experiments, we compare the performance of our SRKOCL algorithm to the state-of-the-art approaches on different benchmark datasets in continual learning literatures via three evaluation metrics: average accuracy(ACC), forgetting measure (FM) {{cite:c802d11707d0736e48f821483e91810c3f51c4d9}}, learning accuracy(LA) {{cite:addf23f6fb734bd44c86e1737258432775e79679}}. The average accuracy denotes the classify performance on all of tasks when the learner finishes training on the last task {{formula:7442fe93-6638-48a4-a492-b420be8842a1}} . Forgetting is used to evaluate the model’s ability to maintain previous knowledge when the new knowledge is obtained, that means, the smaller this metric, the less forgetting. Lastly, learning accuracy is applied to measure the model’s ability to learn quickly.
| r | 660e4709341aab71dafd84db54e4f163 |
As a good theory should explain as many observations as possible with the fewest possible assumptions, it is logical that SAMs should try and extend the lesson from cool-core clusters to lower masses.
In this case, however, Occam's razor does not cut it. {{cite:28cb30d22cd4296e4b9c715032a6b21560fbc4a5}} and we have shown that we need a different criterion to explain the quenching of SF in galaxies.
We have not modelled the processes through which BHs quench SF. Hence, we cannot comment on the physics of BH feedback.
We remark, however, that the criterion required for the initial quenching of SF is different from the one required to maintain it shut down afterwards.
We can, therefore, make the argument that quenching and maintenance correspond to different feedback regimes.
In fact, a criterion for {{formula:317a88a0-e4ca-4585-96a7-1f9dace96164}} arises naturally in models where BHs accrete at the Eddington limit, so that the accretion power grows with {{formula:b3740d0b-bfc6-4c6e-8230-e2dc860f2495}}
until it is large enough to blow away all the gas in the host system {{cite:970883650faf90ac0d775bced5d27a6182888e2a}}, {{cite:5bdba2d87ab53ac38c5a7bf1ac6767ba5d78f221}}, {{cite:390f0435091206b639941dbf9b82b4d9384b97da}}.
| d | 94abf57ed6282f043d0c2ed84ab730f6 |
Since the birth of theory of stability, which was first proposed by Ulam {{cite:e1301c6692cf9af8d2ae53eee0d5555c1c7fde4f}} in the form of a question and after the first answer due to Hyers {{cite:562b0411792ffcece148e2afc62b6bfc4f345172}}, many results have been obtained for many functional equations in different spaces. In this work we are interested in the case of reciprocal functional equations.
| i | 12119aa176f5398f369be199f9ecca21 |
One of the reasons for using nonlocal scoring rules is to address particular problems where a local scoring rule is not considered “suitable". For example, Ignorance is infinity if the forecast assigns vanishing probability to an event that obtains. {{cite:cf84341b06dd2de4c9c9c1bcf0cf732c2a4a1388}} emphasizes that the use of Ignorance implies the value judgment that small differences between small probabilities should be taken very seriously and that wrongly describing something extremely improbable as having zero probability is “an unforgivable sin". {{cite:415037d6e14f3d58f59da9737cf48b181de9d88a}} pointed out that forecasters should replace zero forecast probabilities with small probabilities based on the uncertainties in the forecast PDF. Not to do so means reporting the improbable as the impossible. Within the Bayesian framework, Cromwell's rule states that the use of prior probabilities of 0 or 1 should be avoided. Assigning zero probability to events that are possible also contradicts to Laplace's rule of succession {{cite:e91ab5c75e2c6edcd4cc8026c6866444099ebbe8}}. In the insurance sector, the premium is inversely proportional to the probability of an event occurring; zero probability would suggest free insurance.
| d | 6a94360f99bd23f839678d3cb23f82e3 |
In this paper, extending the construction of {{cite:21edeacff241113caed8b97e0a61b8b335add983}}, we gave a formulation of the classical double copy with a generic, curved background spacetime. Apart from obtaining solutions of Maxwell's theory defined on curved backgrounds, our formulation makes the effect of the background spacetime on the gauge theory source much more transparent through the deviation tensor that we defined in (REF ). For an arbitrary Killing vector of the background and the full metric, the result is given in (REF -REF ). Choosing a flat background for a solution with a non-zero cosmological constant yields a constant charge density filling all space in the gauge theory due to the general property presented in (REF ). The effect disappears when the background is chosen to be a constant curvature spacetime, which can be explained due to the vanishing of the deviation tensor for a suitably chosen cosmological constant (REF ). Furthermore, we studied two different realizations of the Lifsthiz black hole, whose background is not maximally symmetric. While the contribution to the gauge theory source again turns out to be a constant as described in (REF -REF ), it is removed by the matter fields in the gravity side, yielding a vacuum solution in one case.
| d | 9d2c3cfdbc198db984f9c885dae45af6 |
From this holographic argument one may wonder if the two boundary theories: (i) a CFT coupled to a gravity and (ii) a BCFT, are equivalent as depicted in Figure REF . The purpose of this paper is to argue that this is indeed the case by presenting evidences of the equivalence by focusing on two dimensional (2d) CFTs {{formula:f4d5f8f2-2306-49bb-8bef-d4e153881d0e}} . We call this equivalence the Island/BCFT correspondence.
We will show not only that the calculation of entanglement entropy matches between the two, but also that the energy flux reflection in (ii) the BCFT, can be obtained from (i) the CFT coupled to a gravity. We will also identify the 2d gravity realized on the EOW brane in the case of pure AdS{{formula:f3b3f002-d7c4-40eb-9553-4dae91ca96f6}} gravity dual.
Finally, we also consider bulk one point functions, which are a part of essential information of a given BCFT. We will show that to obtain non-vanishing bulk one-point functions in BCFTs we need to modify the prescription of {{cite:7d44710ff099e7baa906c074d6272cbe629a41f3}}, {{cite:6189b06944ce21148bed6d151fcf256b060d4ee0}} such that we turn on non-trivial background matter fields. The Neumann boundary condition of matter fields imposed on the EOW brane induces this non-trivial matter field background.
{{figure:d18d2b32-a84f-408c-9457-86d38ee9d5cf}} | i | 361f6bde38e5412beb2e4e22e839f9d8 |
In Table REF and REF , we present evaluation results for zero-shot adaptation performance on unseen speakers.
In short, Grad-StyleSpeech outperforms other baselines.
Notably, our model outperforms the modified version of Grad-TTS {{cite:2a6acf2fc9a796fd3feed94dca7477d9b06f61c5}}, showing that such any-speaker adaption performance is derived not only from the diffusion models but also from the hierarchical transformer encoder.
Moreover, in Table REF , full model outperforms others in speaker similarity measure but shows bad performance on the character error rate due to the low-quality samples in clean-360 subset.
We believe our method might show impressive performance if we train it on the dataset containing more clean samples from diverse speakers.
| r | f79053a734561b9dddf66524039d922e |
Machine learning methods primarily address prediction or classification problems, and have been included in statistical textbooks {{cite:22bd60cc65feeae217703160015a1f5d41e2fa62}}, {{cite:15747c19ded59073cb2f00393c6cef5175c2c27c}}, {{cite:573dc3f389ced43d874a33a0b1ab8af7f6d0bf8b}}. On a high level, there are two broad categories of machine learning methods: supervised and unsupervised learning. In supervised learning, the predictors (i.e. covariates, features) {{formula:aae87593-ff7b-4e8e-beef-90505d05c664}} and the outcome {{formula:5e3a3ab5-99f8-4f0f-b688-9ca4367d9ffc}} are both observed. The goal is to estimate the conditional mean of an outcome {{formula:aa346178-8797-49c7-a9f5-219d2d0ba1cc}} given a set of covariates or features {{formula:74c3ad64-4af6-4bf5-aef6-1c1ce8f9ff13}} , to ultimately predict {{formula:5943f277-3fd0-4a5b-9bf5-cc08ec491265}} . These methods include decision trees , random forests {{cite:cb805fac5488aeca4ba7ab3c35a8bd93d303d8cf}}, gradient boosting {{cite:0ee04ccc9f583444c1f04d1be825ab02c2d852fa}}, support vector machines {{cite:5dee5ce7c86751fe9678fb446d9821235916ae58}}, {{cite:f00f0db14e14cc255ecbb3d4d3e450ded7a55276}}, deep neural networks {{cite:1af0b73f53f64217616d86ea739db0a222d4af3a}}, {{cite:d91fa43670440992bb62c48ebbcbb1f621314b88}}, ensemble methods {{cite:717cf229fb67677a0093dc46f4dd91f4d1e4d534}}, and variable selection tools such as LASSO {{cite:92b880968a0792aee290c2c104e595a727cf93f9}}, {{cite:212d74a760b63209b03448ec5ebacc44728b9fb4}}.
Regression trees, and random forests as their extension, have become very popular methods for estimating regression functions in settings where out-of-sample predictive power is important. When the outcome {{formula:890c063d-5ecf-4c42-a7b2-ed42411dedc0}} is an unordered discrete response, these supervised learning algorithms attempt to resolve classification problems - for example detecting spam emails. In this instance, a machine learning algorithm is trained with a set of spam-emails labelled as spam and not-spam emails labelled as not-spam, so that a new email can be classified as either spam or not-spam. In unsupervised learning only features {{formula:c6838351-9035-4273-924f-bcd5ee9cc724}} are observed and the goal is to group observations into clusters {{cite:c7ef469d1c73ec6c636d4e1e3409e65e2babcc2e}}. Clustering algorithms essentially group units based on their mathematical similarities and dissimilarities of features {{formula:adc25e95-b518-4e30-87c3-70b016ca6af1}} . These tools can be used for example to find groups of basketball or soccer players with similar attributes and then interpret and use these clusters to form teams or to target coaching. Deep learning methods are another general and flexible approach to estimate regression functions. They perform very well in settings with extremely large number of features, like image recognition or image diagnostics {{cite:082f97a934fc0799154a86a4594fd196bf27e334}}, {{cite:495e9f7341349d55a8906300774cdf44c1532d0c}}. These methods typically require a large amount of tuning to work well in practice, relative to other methods such as random forests, and as a result we will not discuss them further in this article.
| m | 692842789518ab73b929fd2a6cd64aee |
In this paper, we compared several readily-available methods for assessing HTE in CRTs using a neutral simulation study design and then used a completed CRT where we imposed selected missing data patterns to compare their performance using real data. The key findings of our work are as follows. First, MMI and B-MMI had the lowest bias and highest coverage across the settings we investigated, with B-MMI being the only method to achieve nominal coverage rates across several scenarios considered when the imputation models were approximately correct. However, when imputation models were strongly misspecified, imputation approaches performed poorly, and were worse than CCA in several scenarios. Second, using an imputation model with only main effects for the outcome, treatment, and covariates resulted in especially poor performance when targeting a non-null interaction estimand. This is problematic as imputation models with only main effects are the default specification in many software packages, such as the popular mice R package {{cite:d07daf9e376d5c87ffa152720550f09ee0b44af8}}. Third, including more interaction terms almost always resulted in better performance in the simulations, so in practice, it may be safer to “overspecify” imputation models when enough data is available to justify doing so. Future work should consider whether such overspecifications maintain good performance when the smallest necessary imputation model is more parsimonious.
| d | 27f41a341c268f171dab296b868d46e4 |
Other FL Algorithms.
Many FL algorithms have been proposed to tackle the limitations of FedAvg. We plan to extend FedTuning to the following scenarios. (1) Participant selection. Compared to the random selection of participants, guided participant selection that considers clients' data utility and device utility can improve overall training performance {{cite:5f102c6e35851b9a8724ffe5a284288b3991f8a3}}. Popular alternatives are to only wait for participants that are finished before a deadline {{cite:d90fd0aaf5e407f7868d0aae7f94d5918a19f5f7}} or only wait for the first {{formula:67f4b722-1fb4-4dc4-8b80-155aecb96c45}} participants {{cite:1f98c5ff5b3a5cdc69526fdd41d6ab1f6bb013da}}. (2) Adaptive training passes across participants. Due to the heterogeneity of clients, setting the same number of training passes {{formula:61bf7a78-d921-4f67-b4fa-385b273ae1c9}} for all participants on each training round is not optimal. To support different {{formula:266a7aee-70d1-4ea8-89a2-67e0fc54e7c6}} across participants, FedNova {{cite:23f1942c88e6a4410d387ba99a75f602773aa1b5}} relies on re-weighting of aggregation while FedProx {{cite:5dc952c079cea5fd12c1ce642b98f075e41bff38}} adds a proximal term to stabilize the convergence. (3) Aggregation methods. In addition to FedAvg, many aggregation methods are available, such as FedProx {{cite:5dc952c079cea5fd12c1ce642b98f075e41bff38}}, FedIR {{cite:58aa1b2ee6e49199e7266b7fb7a97f3150c16dd3}}, and FedMA {{cite:03a34d4d1aa38b92831caf0917a659641331c4bc}}.
| d | 4a38d81d7707881fcba0afcf0da8bb9b |
Learning strong and discriminative representations is important for diverse applications such as face analysis, medical imaging, and several other computer vision and natural language processing (NLP) tasks.
While considerable progress has been made using deep neural networks, learning a representation often requires a large-scale dataset with manually curated ground-truth labels.
To harness the power of deep networks on smaller datasets and tasks, pre-trained models (e.g. ResNet-101 {{cite:c2655a7a5499d4e05672d6036ed542b1e318d1c1}} trained on ImageNet, VGG-Face {{cite:0f313001f35f53daac8f374b9738ae444efe17c3}} trained on a large number of face images) are often used as feature extractors or fine-tuned for the new task.
| i | 6f35af0dc6c30ecf42a2b05e1df757c2 |
In the image classification task, DCNNs learn to generate the predicted distribution of image class by extracting the features of an input image{{cite:d567a2ea634ed296e940481729145a0826384c25}}. The learning objective is to minimize the difference between the class distribution predicted by DCNNs and true data-generating distribution. To measure the difference, many loss functions have been proposed, such as mean square error loss (MSE) {{cite:21c611839e76e26e685da8712b79993fa33db946}}, hinge loss{{cite:d3ff312371ce70266a1bbba85ec079392a3a5b5a}} and cross-entropy loss (CEL){{cite:74dee42a5fda54aa9303c774cbb4dc46eb1fd340}}. These loss functions play important roles during the training of DCNNs. Compared with MSE and hinge loss, CEL has excellent convergence speeds for training DCNNs {{cite:983bb7b8af2f806392542d7d55aa4c95101d93c4}}. Therefore, CEL is a reasonable loss function for classification tasks based on DCNNs.
| m | 66267b7556f08a8bb15c12ff45b9c1c0 |
Training artificial intelligence using curriculum approaches, from easy to hard, can lead to improved results in a wide range of tasks {{cite:eca19f707ffbfc1aa405fd6c9f9369cdad18f0cc}}, {{cite:52771194d5fe3dd6832837ceb415af31c079e7f1}}, {{cite:0fea3d71ba52434a80cbbeaf1d01122a03a3053c}}, {{cite:61b0f6dc4bd2bcb9247e2a35ea6e6598dce29995}}, {{cite:2a7dc76f55b05ef1d96714bf2e9d3400947778bc}}, {{cite:3a725170349b3f7f7f520a5e26cc0874170d622a}}, {{cite:a5ce6f27bb4efb50ae1ffd8e213840da9b83d3cf}}, {{cite:9066a9994cc36784b2126e26cadc1641752dd7d8}}, {{cite:fa6edc5f17fd39d9a5e11c2c0be2453322e67fc4}}, {{cite:74e920e52452a78faffdf5d0867f75c0b6e55029}}, {{cite:22ec20a271fcdd4debd14badc544f2f56279dc61}}, {{cite:3feab081ab32976c70866d87dd937ee331f382a4}}, {{cite:b8305d644f80b43dad3741c7c660a19504c38558}}, {{cite:cfc36fb846a17b3bdd89344b6fc32fb67c6a043e}}. Still, it is not simple to determine which samples are easy or hard, and the available metrics are usually task-dependent. Another challenge of CL is finding the right curriculum schedule, i.e. how fast to add more difficult examples to training, and how to introduce the right amount of harder samples at the right time to positively influence convergence. In this section, we present our approach for estimating difficulty and our curriculum sampling strategies.
| m | 63a037014ef3e009cbd98c5181c3bb3d |
Over the last two decades, quantum physics has experienced its second revolution giving rise to new quantum technologies. Thanks to quantum control, matter can be manipulated at the single particle level by exploiting quantum resources such as entanglement, superposition or squeezing of states in various platform registers with high fidelity {{cite:fe49e51d0b7c1a80c0e9253e9f07c2ab65cf1f85}}, {{cite:fb0e76febcea7b548c48123ba0f1bde3e0374cf9}}, {{cite:faffad160e9b979980f3b4e4aa22a88af29ba461}}, {{cite:9924690b4889824e89135d20f1b09b3a76831efa}}, {{cite:94aebd383451d95b4fff7397c74e93784950e848}}. All the progress indicates that quantum physics will offer outbreak for the future coming in a wide variety of forms, from quantum cryptography {{cite:96f13865eca51a3b7b6543ee8c3817b2c082751e}}, quantum sensing {{cite:b51396d08de2d83315cc6674997dd4925b22d111}}, to quantum computing {{cite:a04c37b2e98fc74668676303ea1910748274d1c2}} among others. Some examples of technologies emerged in this second quantum revolution are atomic sensors providing unprecedented high resolution and efficiency in the detection of external fields {{cite:b4e0cb4b87569b4837540e18981a94da3b2128a9}}, {{cite:af62a2f62afc6748a6179f1161f9b50f849f02dc}}, {{cite:a636b34e4f102827afc0bddc12ac96e71111a7cc}}, {{cite:a17c59c9cafeed174fc81731903275b84d9744e1}}, {{cite:3877caf3458bfdf4039efd9f91e4792d291c5f45}}, quantum channels {{cite:084526eabdc68c1f0eebe07a8cb21cfbc67db8fd}} that make uses of entanglement for unbreakable communications {{cite:f3c562886f64cb1da4e3386621549524f06a956e}}, or quantum computers that use superposition to execute parallel-processing computations performing specific tasks with higher efficiency than their classical counterparts {{cite:894ff318ddf01e9a4d8e8734be73839577c43acc}}.
| i | 43846659419038935794b61d7667b49e |
Moreover, quantum algorithms can be utilized for cryptography, search and optimization, simulation of quantum systems, and solving large systems of linear equations {{cite:4724f669e02451a885721f96cc1dd791ec3de624}}, {{cite:772e07cf5930e4bad416554138489202eae44503}}, {{cite:570abdb14d94abd3cec15b0f7520926cb7455f98}}, {{cite:9ce2b0f1861698d458137053060cabaf92beddd5}}. Especially, the quantum walk (QW) algorithm, a quantum analogy of the classical random walk, is one of the fundamental methods in quantum computation {{cite:1ec45bfc71cdbbee61eca8916d3cc88b73dd0158}}, {{cite:412412f1c2fbf0636e82c5d7d1bcf717505cca2a}}, {{cite:f3c922959223bc5847b79d6e388189578554f77a}}, {{cite:8aa2e8652fd62873a3e47d1ad7ae4388d0699e35}}, {{cite:275f616369bc9093f711b909ee2935663e680b6a}}, {{cite:2fd8d940d68fdc7277fa596748ae84ce51036a85}}. QW-algorithm can be employed not only for searching and sampling problems but also recently, in quantum cryptography {{cite:5a510aa65e2f72183072aa76923788949356aee5}}, {{cite:ba72e0754c85ece5e1d1898ef2b92cf0d475ee0e}}, {{cite:7af957fc84158e8ab72b77ca0e14605bd91b4761}}. Lately, quantum walk-based random number generation (QW-QRNG) protocols are introduced in {{cite:19079b2fd01d5eff67abc7a782ce513ea38f978a}}, {{cite:f8e6e3c076b3718896c8dda9469f6527e2f952ab}}, {{cite:48c0295700eb86c21436f5b97a6951f8cb7d8544}}, {{cite:31c44e6a31c83cd6d3f2e20f2db9e1dbaa18d20f}}.
| i | 454fe6ac231fa44ffd343a8eb56b44a0 |
The core of DCM approach is that
the test statistic
{{formula:3c9028f5-73fe-469b-862c-cffeadf83b60}} in Eqs. REF and REF
refers indirectly to
the reduced Chi-square
{{cite:7c38df2f63919c36ab459ed386557d9ed2c5254d}}, {{cite:68b91dd502307888c9dd385a2131f18d22e2f2c8}}.
Our DCM computer code
dcm.py minimizes {{formula:21ed736e-1690-40a1-9929-dd49aafac705}} .
For any data,
the possible
alternative nested models
that can be tested
with dcm.py are
| m | e6c600028b6e7fc88a129c2d941624fe |
In a hard freeze forecasting context, a proportional hazard model can be applied to build a joint model for all study locations using explanatory variables like longitude, latitude and elevation. From the parametric relationship, predictions for any location can be derived. If we want to take the model a step further, one could add random effects to the exponential part of {{formula:f1dc2c49-fae8-4182-8831-21b04cd4f9a3}} , e.g. a Gaussian random field that captures spatial and/or temporal correlation {{cite:122b5a9015dbe8d754bdadf20e724f4905bf4768}}, {{cite:3336a59ba1d9ad0e47510fac7737aa0c7e7d8b34}}, {{cite:509093b2b589c661c50495525089680e8b1a5b54}}, {{cite:b6460015e51fb3698f248a0f9ad7499561c8caf2}}. A fundamental assumption in the proportional hazard model is that the hazard ratio of two individuals is independent over time. If this is inappropriate, one can consider a Cox model with time dependent regression coefficients {{cite:5b94d02e5cdcbf5bc461c27f1ceab6fb7634e625}} or an accelerated failure time model that assumes that the effect of a covariate increases or decreases during the study period by some constant {{cite:f92f2aedbecdf94363173a60f7ccdc5299f6a93f}}, {{cite:9b8b1ebf67eb97d85a4616602158b952bbb56577}}. There also exist survival models where the hazard rate is estimated by using neural networks or other machine learning techniques {{cite:8a9e1bd84229e68839f317da7a0b8fc7eda4288f}}, {{cite:c981a1424a0c9c2020b52a5ed5740cd0f4e3c5cb}}.
| d | cbdcd07310f49582c4dd649a8418064a |
To test the generalization capability of the proposed approach, we perform training on Dataset 1 and test on Dataset 3. The F1-score drops down dramatically to 33.05%. In order to understand this finding, we visualize each dataset using PCA (Figure REF ). It depicts that, although Dataset 1 is mostly linearly separable, Dataset 3 is not. A linear kernel that performs well on Dataset 1 fails to provide good performance on Dataset 3. If we use RBF kernel, it overfits the data and produces worse results than what we get using linear kernel. Similar trends are seen in the performance of other two state-of-the-art approaches {{cite:5b6646227226468739e489e40a1c2f4df325c0e6}}, {{cite:f1b3384170fc387774923d24dfab4405dffd4e25}}. Thus, we decide to perform training on Dataset 3 and test on the Dataset 1. As expected better performance is obtainedWe report the result using all the features in this case. with F1-score 76.78%. However, the other two state-of-the-art approaches fail to perform well in this setting. While the method by {{cite:5b6646227226468739e489e40a1c2f4df325c0e6}} obtains F1-score of 47.32%, the approach by {{cite:f1b3384170fc387774923d24dfab4405dffd4e25}} achieves 53.02% F1-score when trained on Dataset 3 and tested on Dataset 1. Below, we discuss about this generalizability issue of the models developed or referred in this paper.
| d | 489b7c0af72ef6a42ff5616a43d1ca1e |
2.3 Complete intersection and Gorenstein dimensions. The notion of Gorenstein dimension was initially introduced by Auslander {{cite:71efe4558951e80c88f109259d81ade7376f2ed2}} and subsequently developed by Auslander and Bridger in {{cite:57e8cb9db08548f16ba68d11f9731fca4c0e6fe9}}.
| r | 3b8cfc75651e426eb8ba08aea1bbc65b |
Limitations: Despite the promising performance and an applicable trade-off nature, the time cost at reverse diffusion process could be expensive due to multiple steps (100 steps in our experiments). When evaluated with 512 trajectories on the ZARA1 dataset, Trajectron++ needs {{formula:94d1e046-fd31-49f7-8a0f-cbc8e5db2522}} but MID will need {{formula:d895cc3a-f541-4e02-8d06-b0c399dc7d15}} with 100 diffusion steps setting.
Fortunately, many recent efforts have been made to significantly reduce the sampling cost while keeping the high generation performance {{cite:2167317bc2724bf6ba685fad9e7fe4581cfdccef}}, {{cite:2aec39b457e3d3b478877fe1705684ca157a2401}}, {{cite:f9c0a9e8630f1526dfa2eb7d5af9d857fdedc169}}, {{cite:31bfe98aac8bb8390490eb2d74c5fe724b1112e4}}, {{cite:dc9b95cb316187f9944b1292afc5c7e588f59a0c}}. However, plugging these methods in our MID is not trivial. We leave it as future work to build a more efficient system.
| d | 4709a77886d7a2219b4c00e1ae13930c |
Contrastive Loss {{cite:9dc56f1435a2dd6f01510ddb25e85b823ebf0706}}. It construct positive and negative pairs to learn joint embedding. A set {{formula:f9b99761-2b9b-4293-b757-e2b8e2fd1aeb}} is formulated comprising of training pairs {{formula:e31f05b3-fc62-4bcd-a026-312eb041ff9b}} using d-dimensional face ({{formula:40b8aa25-7f2a-4d6b-b794-c009118173db}} ) and voice ({{formula:72c7946b-3cf5-463d-bf23-cc2966ca2b31}} ) embeddings. Each pair has an associated label {{formula:6d25447e-2f5e-4c93-b802-34831cdff440}} , where {{formula:f66508fd-2d57-45ed-8a91-831d61adcbe1}} if {{formula:8cc45453-69bf-44d7-bdb4-25e68b2bcac3}} and {{formula:d98ec87a-bab9-4a5b-a544-984015bc211f}} belong to the same class and {{formula:1b637d16-fd1e-4a68-bd96-db928fd10697}} if {{formula:9b9ee8f6-366b-4397-bcd3-b58feb374bda}} and {{formula:dcbb7c95-6347-4ec2-a50c-a8079d1bf2eb}} belong to different class.
| m | b12dc0035dfa201381edc72d85eb5c58 |
At about 50 years ago, vacuum pair production has been investigated in many original works {{cite:ebf0b9e327a7fc197586d9f8e7be9b3e852092f4}}, {{cite:bcb59392b2c5e3faa8e9d454763c63426473d1f1}}, {{cite:03763685f8b5f46024f39bdf035557b52dafa8b2}}, {{cite:856c99978107c65d69a0c045b61caf78b7774344}}, {{cite:88976ec6b2786c3abf8c66509fc601dec4a21859}} by using simple but very important fields such as constant electric and magnetic fields {{cite:ebf0b9e327a7fc197586d9f8e7be9b3e852092f4}}, alternating electric field {{cite:bcb59392b2c5e3faa8e9d454763c63426473d1f1}}, {{cite:03763685f8b5f46024f39bdf035557b52dafa8b2}} and so on. Recent years, many theoretical analysis and numerical calculations have been performed based on previous researches, see Refs. {{cite:42bc82d3346c09e17567a588f843c6cf6235a141}}, {{cite:3899a5e758cd1f0bb315da9466c40e0c8f482ac5}}, {{cite:796e2ea3e3a04a59d447f3004b56f5bb2c4ba6d7}}, {{cite:6ef4789492eff8c78c9fea65cd8e64c9d23169fa}}, {{cite:11361e2a28f4a097bc96bcaec82b5d928a993038}}, {{cite:7d147d88234208e02db5ee69b6cd0607edb98801}}, {{cite:a0bc3a4acf2a3e859de433c6dc451b0b5cd15f46}}, {{cite:3ca1adb73ee7815d23dda1dbfe1d0dc42120ef57}}, {{cite:59d6901f5b3ebf73443594ddc429535fcc18bda7}}, {{cite:e34a0dec4751842b90fb63ff77fdb82ec07d3160}}, {{cite:a16b609d83a60cb940c8bc851e005b0caefce2b6}}, {{cite:4f9ad44e19ae461c0c4f5a0978d7ab36de194c99}}, {{cite:e16df0c3032bd37bbf65a96349473d0a21531cde}}, {{cite:41b1b23e2d9cf89e8a600e351838bb0fc153394e}}, {{cite:1fdc8c9b0dd422035681c434301292af4b344be4}}, {{cite:8301e8ba9f03bff635a41e11f7c01dfffdaa1cd5}}, {{cite:7acdebfb8b32f682cb69d28e4e276a2f23522ef7}}, {{cite:fda74be6ae524a07ab6f5d9a4a550fdb659ee0cb}}, {{cite:838cd386f696e0fa7bd480ec64468a49e7e5a78f}}, {{cite:e42a4cc9a4f63e7d21fcb79292fdf3bfd8525353}}, {{cite:e924cd50c344cd1ea640b646ff8faa444943c32b}}. The momentum spectrum and number density of created particles are examined analytically or/and numerically under both spatially homogeneous {{cite:42bc82d3346c09e17567a588f843c6cf6235a141}}, {{cite:3899a5e758cd1f0bb315da9466c40e0c8f482ac5}}, {{cite:59d6901f5b3ebf73443594ddc429535fcc18bda7}}, {{cite:e34a0dec4751842b90fb63ff77fdb82ec07d3160}}, {{cite:a16b609d83a60cb940c8bc851e005b0caefce2b6}}, {{cite:4f9ad44e19ae461c0c4f5a0978d7ab36de194c99}}, {{cite:e16df0c3032bd37bbf65a96349473d0a21531cde}}, {{cite:41b1b23e2d9cf89e8a600e351838bb0fc153394e}}, {{cite:1fdc8c9b0dd422035681c434301292af4b344be4}}, {{cite:8301e8ba9f03bff635a41e11f7c01dfffdaa1cd5}}, {{cite:7acdebfb8b32f682cb69d28e4e276a2f23522ef7}}, {{cite:fda74be6ae524a07ab6f5d9a4a550fdb659ee0cb}}, {{cite:e924cd50c344cd1ea640b646ff8faa444943c32b}} as well as inhomogeneous electromagnetic fields {{cite:796e2ea3e3a04a59d447f3004b56f5bb2c4ba6d7}}, {{cite:6ef4789492eff8c78c9fea65cd8e64c9d23169fa}}, {{cite:11361e2a28f4a097bc96bcaec82b5d928a993038}}, {{cite:7d147d88234208e02db5ee69b6cd0607edb98801}}, {{cite:3ca1adb73ee7815d23dda1dbfe1d0dc42120ef57}}, {{cite:838cd386f696e0fa7bd480ec64468a49e7e5a78f}}, {{cite:e42a4cc9a4f63e7d21fcb79292fdf3bfd8525353}}, {{cite:b1f279d04c7c4fff5de2108774a68b38400cdca4}} with many different field shapes. Recently, Fedotov et al. have reviewed and summarized the key theories and progress in strong field QED in the past decade {{cite:e0c773f0f246ae2de22b05398dff8a9338e01617}}. These investigations enable us to understand new and challenging phenomena occurred in pair production process.
| i | f7ee3a8640ee61959a5df2a38623b2c0 |
The computation and evaluation of magnetic trap properties are based on current density. The technique used in this paper is Galerkin method {{cite:d60b5f145c50163963aa4b345eefefed7f2ee4ce}} or MoM {{cite:332496b4dc1c9b30e1689dd6f1d52a665ea925cb}}, {{cite:cc94ad978731c099b9fa1accd1053b3b30860ca9}}, see Appendix . This applies to realized traps, as well as to fundamental bounds. Conductors are assumed in the form of highly conducting surfaces {{cite:e1c158324e1b9c0a0b580b31a8c3f2eb7fa53bb6}}.
| r | 10272ff6dd6db04e7bd23efb5b18eefb |
A conceptual feature we wish to convey through our work is that the one-loop method used in our of calculation of critical exponents in § is possibly more convenient than using Feynman diagrammatics to do the same, as performed for {{formula:d5edebd9-34df-4abc-ba4d-bda2f004382a}} in {{cite:83644d2f64ffa4c0617d1c220efad6da72b5dd7e}}, {{cite:e998e65033fb0f8f6c0e4016669a2bd13c31ca9c}}. One important question which remains to be answered is to estimate the contribution of higher loop corrections to the critical exponents.
| d | ec9d7058332035a63a72e0c44c212737 |
Intriguingly, the recently published works {{cite:1acd7fddbc9f2ad5e612a184fb8894afe757d593}}, {{cite:121426629c23b5f49e03efc2839673df5fcfe768}} have
revealed the physically important fact that charged black-hole
spacetimes with regular event horizons can support massless scalar
field configurations which are non-minimally coupled to the Maxwell
tensor of the charged spacetime.
| d | d716dc6672ea1df05b0acb82832f117b |
However, a systematic method to construct a generalized hedgehog ansatz
which is not spherically symmetric but keep all the other nice properties of
the usual hedgehog ansatz alive has been developed in {{cite:d9cfb0d5073a2ad70623c4842bce65f659ac7141}}, {{cite:e57706b00cfef55795de3a6d048872982ddea3f3}}, {{cite:6c422e714045f26ab12d397da45c52f373714e0b}}, {{cite:bb86159b2ad8df4effc4091220d9f19e9cb73b79}}, {{cite:d67a710c083a469695bfe0dc73137828f28de6b9}}, {{cite:1cd7502a3114391b8c0d4a4229accc14ec1611e3}}, {{cite:a11ec321f69a4c24e18149c46408575b49474780}} for the
Skyrme model, and such strategy has been proven useful also in the
Einstein-Yang-Mills case in {{cite:05096097fd47a9e2574b7f576f9e30cf2a3b6f22}}, {{cite:291ef73a5d9630690a2c8420ebbdcd97fff3d28f}} and {{cite:9be8e6f19974d16ca8a66a59732f9bc72fc7d38b}}; and generalizations thereof {{cite:d553fbfe0d0bef19be4d09dd2469765f976c09f6}}.
In the present case, we generalize this technique to the case in which
the Yang-Mills-Higgs model is analyzed within a flat region of finite
spatial volume. We construct the first genuine analytic examples of
non-homogeneous and topologically non-trivial condensates in the
Georgi-Glashow model and in the Yang-Mills-Higgs-Chern-Simons theory in {{formula:603765fd-ebd9-47cf-9842-9ba58f3f5677}} dimensions. Such solutions possess a novel topological charge and have
non-vanishing non-Abelian magnetic flux. Moreover, many relevant physical properties can
be computed explicitly (such as the energy density, the total energy, the
pressure and so on) in terms of the volume, the coupling constants and the
topological charge.
| i | 957ad647dc21d30d3e0a899206a979dc |
The first two initial centroids certainly are far away from each other. We can find the two farthest samples by calculating distance from all samples to all samples. Unfortunately, this is a very time consuming process. However, we can reduce this computation if we consider only the outer samples of the dataset because outer points contain the first two initial centroids. To get the outer samples, we used the Convex Hull algorithm {{cite:01d2130a5d43588cfe053acf28f3d06166ad8256}}, which provides the smallest convex containing all the samples in the data. The polygon contains the outer samples which is presented in Fig. REF .
{{figure:1249ae8e-da66-4a60-9763-ed8defee686d}} | m | 30ac076825310ef43c5bcc93ac0921c6 |
Further, we experimented with combining language-independent and language-agnostic models. In the context of this paper, we incorporated a simplistic combination - if either of the combined models predicts a conversational turning point we consider this as a positive signal.
Analysing the results, we observe that incorporating the sequence length and the BOCP {{cite:f7d3007b34a7db11d9a99a34f1a1ddfd7feecb8a}} with all linguistic models can yield a substantial improvement. By combining the sequence length with the Neural Learning-to-Rank model, we improve the performance to 0.25 micro AUC and 0.30 P-R break-even point.
| r | dbf735ab439d84cddb29afe6e787037e |
Related works.
Several works have focused on extensions of Atl{{formula:56a680b6-0362-41f6-a012-81bdb3f8f343}} to incorporate more
powerful strategic constructs.
Among them, we recall Alternating-Time {{formula:a9a55288-8af3-4083-82bc-8eb4494f8e01}} Calculus (A{{formula:b0b3da45-0d57-4bda-bd0d-f1f97062514c}} Calculus, for
short) {{cite:fa9fae3bcdbabe20a7e2b1420c88cb3ac1fb422f}}, Game Logic (Gl, for short) {{cite:fa9fae3bcdbabe20a7e2b1420c88cb3ac1fb422f}},
Quantified Decision Modality {{formula:b2259f05-986d-4933-8f1c-c2e21dd4a627}} Calculus (qD{{formula:3469421f-be11-4f10-9df9-933e0bfb7b13}} , for
short) {{cite:c19e602848873bc653066670dd26c92b4e3edc83}}, Coordination Logic (Cl, for short) {{cite:3e74fa8392f11eaa28c8d143a99a553a5c22d27d}},
and some extensions of Atl{{formula:c43e0c4f-a305-4755-aeb1-f3edae480bf8}} considered in {{cite:45820d4abb242e5bc868a2dee4da6e3446615076}}.
A{{formula:2f099a78-9402-4cca-85c2-f6d65884f7f7}} Calculus and qD{{formula:05e1a871-ed1f-47ac-a3a3-05139477ccaf}} are intrinsically different from Sl (as
well as from CHP-Sl and Atl{{formula:cd09f9b1-de79-4642-9921-aac73032372c}}) as they are obtained by extending the
propositional {{formula:e2b0966f-dec4-42ec-9c57-9a5a4c7a4632}} -calculus {{cite:377eaca2a72fd0f8e6c7de04ae68c9ac09f6f70a}} with strategic modalities.
Cl is similar to qD{{formula:7ae7814d-3ec5-4de8-b2dd-4970598a3e5f}} but with Ltl temporal operators
instead of explicit fixpoint constructors.
Gl is strictly included in CHP-Sl, in the case of two-player turn-based
games, but it does not use any explicit treatment of strategies, neither it
does the extensions of Atl{{formula:9c4d3c95-91c3-49be-bf1d-ab12320bdbfd}} introduced in {{cite:45820d4abb242e5bc868a2dee4da6e3446615076}}.
In particular, the latter work consider restrictions on the memory for
strategy quantifiers.
Thus, all above logics are different from Sl, which we recall it aims
to be a minimal but powerful logic to reason about strategic behavior in
multi-agent systems.
A very recent generalization of Atl{{formula:a2f826a8-075c-4593-a4f7-587c09c29a01}}, which results to be expressive but
a proper sublogic of Sl, is also proposed in {{cite:045ab5b755d68a3bbaee64e339fb0978fff0cea9}}.
In this logic, a quantification over strategies does not reset the
strategies previously quantified but allows to maintain them in a particular
context in order to be reused.
This makes the logic much more expressive than Atl{{formula:5857386f-ab09-41bb-82f1-34aa21212b42}}.
On the other hand, as it does not allow agents to share the same strategy,
it is not comparable with the fragments we have considered in this paper.
Finally, we want to remark that our non-elementary hardness proof about the
Sl model-checking problem is inspired by and improves a proof proposed for
their logic and communicated to us {{cite:adcf04e0e2e46bf809ef68656a53755eb85dc461}} by the authors
of {{cite:045ab5b755d68a3bbaee64e339fb0978fff0cea9}}.
| i | e7f29942bc908c49cd0f7e3e250a636f |
As indicated, we must still remain open to the possibility that the {{formula:cd5aee35-8abf-4ce4-aa1d-dd312e5c607b}} and/or {{formula:6a2bb14c-3355-416d-b53c-49d0d4b4df58}} measurements are affected by some kind of (unknown) systematic errors, although some of these possibilities may be on the way of being ruled out by recent works. For instance, in {{cite:bd224e6dda64df34de259693ec45839cff10e9d5}} the authors study the systematic errors in Planck's data by comparing them with the South Pole Telescope data. Their conclusion is that there is no evidence of systematic errors in Planck's results. If confirmed, the class of the {{formula:9f550751-813f-4f06-b735-54f7b0bdf8ff}} RVMs studied here would offer a viable solution to both the {{formula:482b5be7-d386-4b4f-af0c-6eb8c59d35bc}} and {{formula:d161877b-58bc-4db4-8597-cc3ce557d85c}} existing tensions in the data, which are both unaccountable within the {{formula:54fa3f04-cb2c-4bc1-9aa5-4727c0a20ec8}} CDM. Another interesting result is the “blinded” determination of {{formula:61c2adc9-6724-477a-bc44-053ee0da5f9c}} from {{cite:5ee882f01c4b7210087939b19dfd7fb2898e6e3c}}, based on a reanalysis of the SNIa and Cepheid variables data from the older work by Riess et al. {{cite:215404f4b9ecefd1b99db02c56804efc87bb8fca}}. These authors find {{formula:98db6d36-6bef-4157-b95f-2e22bd3b028a}} km/s/Mpc, which should be compared with {{formula:cb27a903-3b52-47ac-9cb3-f26c48d22573}} km/s/Mpc {{cite:215404f4b9ecefd1b99db02c56804efc87bb8fca}}. Obviously, the tension with {{formula:dd20f818-bff5-40b9-9b11-30eb8c8cfac9}} diminished since the central value decreased and in addition the uncertainty has grown by {{formula:4f0edd01-e23a-497d-89a3-3ca48f7063c3}} . We should now wait for a similar reanalysis to be made on the original sample used in {{cite:6b2bab36d28e38592260bef4c457e6301ebdab7f}}, i.e. the one supporting the value {{formula:981d129f-33c3-44c9-8cf7-4b90e39cc91b}} , as planned in {{cite:5ee882f01c4b7210087939b19dfd7fb2898e6e3c}}. In {{cite:46e62e5171a57c0c56edc463a2a62fb6878e1924}} they show that by combining the latest BAO results with WMAP, Atacama Cosmology Telescope (ACT), or South Pole Telescope (SPT) CMB data produces values of {{formula:af2b6c0a-2dcb-495e-b3b9-a549d64785f6}} that are {{formula:335eea3b-df50-477d-9ce2-1ec167dfb660}} lower than the distance ladder, independent of Planck. These authors conclude from their analysis that it is not possible to explain the {{formula:a770e73c-ab25-44bc-84d0-27576ee39438}} disagreement solely with a systematic error specific to the Planck data. Let us mention other works, see e.g. {{cite:fb1212307c25b36a4eb07a21682fb23ca8facb85}}, {{cite:4e156794a555e9214534a0ead2e8b45b84550017}}, in which a value closer to {{formula:0883c081-bb26-4624-8c13-361c37cd7c53}} is found and the tension is not so severely loosened; or the work {{cite:08b16c93190ce16407629bb647935d0fb0ab9c71}}, which excludes systematic bias or uncertainty in the Cepheid calibration step of the distance ladder measurement by {{cite:6b2bab36d28e38592260bef4c457e6301ebdab7f}}. Finally, we recall the aforementioned recent study {{cite:aabe0117171e76aa954ad3641d5c263078899891}}, where the authors run a new (dis)cordance test to compare the constraints on {{formula:bcdb36a5-9d5d-4a90-8be5-668cea3a21ca}} from different methods and conclude that the local
measurement is an outlier compared to the others, what would favor a systematics-based explanation.
Quite obviously, the search for a final solution to the {{formula:8150698d-e0f1-4215-9ea7-6f9cf1c83922}} tension is still work in progress.
| d | 14f8e91fc14e574d85678f06124a8889 |
The reconstructed image is the minimizer {{formula:c50b4718-03c8-4406-8b96-eb5e7405a788}} of the variational model (REF ) with this data-fitting term, where {{formula:549319bf-551b-4276-972b-f502be64abdc}} is the observed image.
There are plenty of approaches for denoising problems involving Poisson noise. For instance, one can perform some transformations that reduce Poisson noise to Gaussian noise - see, e.g., the Ascombe transform {{cite:b9c43359e1d0f1a189bae80d80b1fc6036d57536}}. However, such a procedure has its limitations, as it can be efficiently applied only in the case of high signal-to-noise ratio. The reader is referred also to {{cite:b4806492059a840c27a19cff2c643938ebb97f8b}} which proposes a remedy in the situation of low signal-to-noise ratio. Iterative methods for denoising and deblurring images perturbed by Poisson noise can be found in {{cite:a90410e1346587fcfa17c15654526be56f116a82}}, {{cite:6e4a5b35eed21ba62739736ac32a4168a295a027}}. See also {{cite:347fd716bacd7a5768d3921faa73d2f93e741aa6}}, {{cite:1e77e06c6c5674e3e5234f3b7f7a9151a981a275}} for more general settings in infinite dimension.
Since our focus is on variational models, we recall that quite popular formulations are the ones based on a total variation penalty (e.g. {{cite:48b3f9464750e8cafb2b43829006e82b8676666b}}) and on an {{formula:c9ff304b-862a-474d-a20c-27e2750b3e53}} -norm (see {{cite:110d568f1a2df0bb97acc6d1c0e5ba737c78b367}}). The former model seems to be unstable when dealing with very low intensity values or when choosing the regularization parameter via cross-validation. Thus, a series of papers {{cite:cf5bff93d9d91c84458c3f622bb0ddec8700388d}}, {{cite:c3b4b2a8222195dcd890d0c3ef13512a9d8f0ea9}} advocate for employing the so-called logarithmic total variation regularizer, that is the total variation applied to the logarithm. This model overcomes the shortcomings mentioned above, but displays instability and slow convergence when addressing high intensity levels, thus prompting research on hybrid penalties, cf. {{cite:e7bb469612a347dd2961d79d6607dd179b1c356b}}. Our study will also consider the logarithmic total variation penalty, as it naturally arises in the context.
| i | 19bfa314095a2ce1584a4804a661c8f5 |
Though GNNs have achieved great success, they are usually data-hungry, which requires a big amount of labeled data (i.e., molecules whose properties are known) for training {{cite:c4527fa80bf893249c35a1d99ae06fccd5d97cde}}. However, the labeled molecules usually take an extreme small portion in the whole chemical space since they can only be provided by expensive experiments or DFT calculation, which restricts GNN based development. To gain further promotion, as shown in top left part of the Figure REF , there are still many valid molecules in the chemical space, though the properties remaining unknown, that have some benefits in terms of their structures. If we can effectively leverage these unlabeled molecules, it could be potentially helpful to improve the performance. Therefore, in this paper, we aim to explore semi-supervised learning (SSL) by fully taking advantage of both labeled molecules and unlabeled ones for property prediction.
| i | 4026008ad69c0966ca2dfe9ed4bf0e10 |
Actually a natural configuration of the B-LSSM includes another relatively
light {{formula:dee8f00c-9975-43e7-ac3e-4451bfdde451}} -even Higgs {{formula:a7ec38e2-d662-44d1-9080-1206b3b1ba6f}} , with mass {{formula:dcc95eb3-6db0-4550-a629-66644b1ca7b7}} besides the lightest
Higgs state with mass around {{formula:9408770f-4614-4f7d-8e30-a47b1de99150}} .
This fact was exploited in Refs. {{cite:00f5b8df139409202141eb29367cd1f8daa53540}}, {{cite:18f2bd39acd43d5d1541606f0046a4329a3fb021}}, {{cite:5cbdac47b72d2fef4146fb108c10b7fe9d7c28c2}}
to explain potential Run I signal for another Higgs bosons, such as {{formula:492cdace-98e8-47a7-8571-b5243e8328ba}} {{cite:8bf2a44c521a660ca594c02db0ab3dde486da6cb}},
{{formula:fcad457c-18ca-4e4a-8b33-64e9696ce25d}} {{cite:8710f64b9860ae35a985b9a8c2f99677ba98e71d}}, {{cite:c6d052aec6e238ba447af6d84f1cd99ca2a3569e}} and {{formula:10bf000d-e844-444c-b154-246d6839a9d0}} {{cite:086be476b20c9f20828909b1a62f1f13014171ef}} decay modes.
In the MSSM, two {{formula:b78a045c-4708-4e16-bf90-355bdf8c1e25}} -even neutral Higgs are obtained through the mixing
between the real neutral components of two {{formula:372007cb-7c61-4d03-889e-37b69ec2cdac}} doublets.
It is well known that those radiative corrections from the third generation quarks
and scalar quarks drastically enhance the theoretical prediction on the mass of the
lightest Higgs. In the B-LSSM, four {{formula:6e8d9117-87dd-4481-b8a1-51884bdaf481}} -even neutral Higgs are given through the mixing
among the real neutral components of two {{formula:a8279275-6e7a-4d13-9f08-66ce776cac11}} doublets and two singlets.
For this reason, there is not an upper limit on the mass of the
lightest Higgs at tree level.
| r | 6c09776449695dd30ad62513c52a8aaf |
Another practical advantage of our solution is that allows for efficient experimentation on reward shaping.
During the development of an agent, the designer can define a shaped reward such that the goals in the environment are more easily satisfied.
However, reward shaping, is a trial-and-error iterative process {{cite:e908aea7a760f9345a094fab7ad1356a5359c74e}}.
When the shape of the reward is changed, say to remove shaped rewards that are introduced just to accelerate the learning, the value function is changed and the policy risk to collapse.
By adopting our hybrid BC-RL training policy, one can avoid such collapse by training an agent with BC, and 'protecting' the old policy while the new value function is learned. This is a practical and easy to implement approach that allow for faster design iterations.
Although we believe that this holds true for several environments, this has to be tested on a diverse range of cases and policies.
| d | ea86dc44d055dd5c9321477a2a3d1a7c |
It may be noted that, as in {{cite:6c6cf1ceb8ef3b1dd04714f420a5701816fd8a4c}}, we first represent collision as a cascaded process in which the effect of collision
on lower order central moments successively influence those at higher orders in a cascaded manner. That is, in general,
{{formula:d974a8a7-8cc1-482f-b8f5-9dc77894bef5}} .
Furthermore, the form of the source term is derived to rigorously enforce Galilean invariance.
The explicit expressions for {{formula:b41617aa-cc39-44ef-aa34-1b4f9d94f6f4}} and {{formula:98f29ae7-2302-40ab-b9f3-a20d0aedc24d}} will be determined later
in Secs. and , respectively. Since the main focus of this work is on improving the collision (including forcing) step with features independent of inertial frames, we have only considered the standard discretization for the streaming operator. However, as discussed in the Introduction, other types of discretization schemes could be considered to improve the order of accuracy.
| m | aa4932a35c4cbe475f8e7731638c75d9 |
HODMD is an extension of the well known technique, in the field of fluid dynamics, dynamic mode decomposition (DMD) {{cite:c0515f90f822d504e5a82f1eb39e0f9100e78286}}, generally used for the analysis of complex data modeling non-linear dynamical systems, solving different applications (e.g, {{cite:3cda4fe692854cfd454c374c1174bb3982b8a652}}, {{cite:36c792825b013aaaea1b30acb6ea7aa7f06e7d84}}, {{cite:584d8ec7a6d70771f2f3ac63c6d723626c886411}}). Similarly to DMD, HODMD decomposes spatio-temporal data into a number of modes, each mode related to a frequency, growth rate and amplitude, as presented in the following DMD expansion
{{formula:366810f2-4b06-4da2-96eb-9927a0d4a8fa}}
| m | 24c7d2af1280437fa708be93dc83783e |
In this section, we show the result of proposed OOD detector with subset scanning and ODIN as detailed in Section . We first compare our result of OOD detection to Softmax Score {{cite:57fdd4200fe5789b74d42d7e531fddb94e603cab}} and ODIN {{cite:1137675615727e47ff17718bc18d9e4c9330e533}} in Tables REF for OOD samples with different collection protocol and in REF for OOD samples with unknown disease types. We further stratify OOD samples based on skin tone for these approaches and report their performance in Table REF . We show in Figure REF the detection performance of our proposed method on individual layers across our network and further stratify these performances across skin tone in Figure REF .
{{table:d2de6aa0-49fc-4c8f-a487-f611cf80732d}} | r | 442cb4c2f74dc771d9b549719f6b6579 |
Inducing and imposing hierarchical tree-like inductive biases in sequential models has garnered increasingly significant attention {{cite:a3cd5be2ef459d6cac2f6a10e344db1090b67e10}}, {{cite:a8f34dccaf67d9890092ebf22026d6c452aa4a04}}, {{cite:ecc887db587e9bc2f1ae7dbdfa16e7529ac3d799}}, {{cite:fc004ee2188b954af8ee6afb8fc63a934686fbd2}}, {{cite:2d912a0f2bd9f2329163efecd3cf729f8018a43b}}, {{cite:39f6f27b95a2b3f34c6fef25d2884b992dd68dbc}}, largely owing to the promise of automatically capturing intrinsic syntactic and linguistic structures prevalent in many forms of sequential data (e.g., language, mathematics and music). This is reflected in recent works, i.e., Ordered Neurons (ON-LSTM {{cite:a8f34dccaf67d9890092ebf22026d6c452aa4a04}}) and Gumbel LSTM {{cite:fee4dd8c1312e7b14607b8ffc2e2a310370d38ce}}, which have shown that imbuing sequential models with hierarchical inductive biases is a fruitful endeavor. After all, learning with well-suited architectural inductive biases generally improves representation learning.
| i | 34ed0cc2e812538d71690960d70eb835 |
While the results discussed in this paper may have deepened our understanding of quantum computers and their limits, they have not explicitly resulted in any practical applications in the same way that studying Boxworld type correlations led to the development of device-independent cryptography {{cite:9f3e56f8555a57fce814b40fa08a0fa8c94db4f9}}. Can studying computation in general theories different from quantum theory result in practical applications? One potential avenue for this is blind and verified delegated computation {{cite:ee5ced8143d1ce5da82e0b6db1473bf1aa0c30bd}}.
| d | 1b69c09b0dbcb70d5bfcf8634658b978 |
The second benchmarking study is then performed on a large cardinality dataset describing an intrusion detection task. This dataset is the union of the normal and botnet data from the CTU-13 dataset {{cite:2c6649bbb7d6da3d5e0e4d8ec4e9a75bf3924521}}, resulting in hundreds of thousands of data records (Table REF ). In this case, we compare the best two evolutionary ensembles from the first study with C4.5 {{cite:8b1c0143e273a51a5d6f5bfd8e4cf3d7e2dbc1c1}} and XGBoost {{cite:19ef31f81d0f908fa8a2741060bb8ad401e15e82}}. The latter represent very efficient non-evolutionary machine learning approaches to classification.
{{table:619276f4-05ba-467a-b822-f27ccfc14829}} | m | 39b8d11a464bc620d250be9ce80a49a2 |
We concentrate on the critical {{formula:dc634e7b-bc0a-429f-9dd4-a8b79e4ef59f}} model, arguably one of the most well-understood CFTs in {{formula:49bad3b9-0554-49a7-8edd-0437b9a2b487}} , which also has extensive experimental applications {{cite:9e9b887abdb63225d5b12e313bdfbf0b8fdc94ff}}.
In particular, we turn on a background magnetic field localized along a one-dimensional line, which in field-theory language is described byThe {{formula:30874a6e-b3c8-4d5f-8899-3c307e38ab92}} symmetry allows us to orient the background field in the direction {{formula:c1686885-ce9b-4886-b443-80e1f2a65372}} .
{{formula:5f41ad7e-8bfd-4256-aefa-36acd9ce8e6f}}
| i | c6fb268a78cd0b1d800363b9cc2778ab |
Although considerable advantages of ISAC have been predicted, deep integration of sensing and communications still requires further investigation. SLAM can provide locations of user equipment (UE) and radio features in the propagation environment. These results help design sensing-aided communication strategies. Therefore, SLAM is a promising technology for achieving deep integration of sensing and communications. However, SLAM faces critical challenges in communication systems due to the massive connections and complex multipath propagation environments {{cite:bd991ee0c03f40401bb1b6f134b55f905b8915e0}}, {{cite:818ce68c955d32b1dcbd62fe6b8cedd53f8eaa1b}}. None of the existing works have realized the SLAM function under the 5G New Radio (NR) standard because of specification and hardware constraints. SLAM has relatively mature applications in the field of robotics; it is often achieved by leveraging the robot's sensors, such as inertial measurement unit (IMU), camera, and laser, which provide more landmarks than features available in typical communication networks {{cite:2c59239bbaec48e4df08eae6cb94d7a0b77c0859}}. Although the resolution of a radio is lower than that of a camera or light detection and ranging (LiDAR), a radio can cover a long detection range and is vaguely affected by weather and light conditions, which are the key challenges faced by visual and LiDAR SLAM.
Moreover, completing the complex task of realizing high-quality communication and high-accuracy sensing is difficult for a single network, particularly for a single user {{cite:9e99b50a71dcf39517b4f4cb647bf1e00593144d}}. Radio frequency (RF) signals designed for communication can help realize communication and sensing by completely reusing the communication hardware. Therefore, other devices in the communication network can participate in collaborative SLAM.
We aim to develop multi-domain cooperative SLAM mechanisms in the present study with the cooperation of multiple sensing types, users, frequency bands, and devices.
| i | a17550788a20c2b5bc5299a4ae5ace87 |
AGILE contributed in a significant way to the multifrequency
follow-up observations of the exceptional event GW170817 (MMA17).
Despite the Earth occultation of the LR at {{formula:6c52b8e2-6967-4ff7-a258-22e00c477259}} , AGILE obtained
very relevant X-ray and gamma-ray constraints on GW170817. As reported
in {{cite:17557146f202a54abb9567d19be4b4ec77684480}} and MMA17,
the earliest gamma-ray
imaging detector data were obtained near {{formula:aa03774b-02bd-4c07-a340-66c82b2a5599}} s. Table 1
and Figure REF show the results of the first useful passes
over the GW170817 LR. Of particular relevance to our discussion is the
upper limit to gamma-ray emission above 30 MeV obtained with an
integration of about 2600 s after {{formula:872d59e0-25a5-4e43-a594-a000d9d93c86}} , {{formula:7410d8ef-a4df-4cf0-bb6f-1e4130085ec3}} . For a distance
{{formula:348972d7-2965-4921-85f7-b6f1de4c3c65}} this translates to a limiting isotropic
gamma-ray luminosity {{formula:def79cf5-aef0-4d1a-a7b3-9755d8e454b0}} in the range 30 MeV – 10 GeV. It is interesting to note that the peak
isotropic luminosity of GRB 170817A in the 10–1000 keV band
detected by Fermi-GBM is {{formula:5c57b302-17ed-4737-981e-cd2c5f8ba508}}
({{cite:9e0266a900c76584ff2c1f416f619ee2bc5b6f8e}}, {{cite:bb0e36ca1874861ee77ab2a24700070b13c424ef}}; MMA17).
{{table:a7767f19-03d7-43fd-ad84-f239d171ca3c}} | d | 7150bcf18836035e773ba93d162f645e |
The local monotonicity of set-valued mappings is naturally defined as follows; see, e.g., {{cite:b647e02a3e5f8041d11b00cd6684806c55c05392}}.
| d | 206c08e468dad9a7ed114c9262f76ee6 |
where {{formula:4fc82e1b-90a1-4630-95ac-27f28eb7ff35}} denotes the Riemann zeta function and {{formula:48c98d53-9d22-4c04-b9bb-6287fde2bf90}} .
This article concerns the behaviour of (REF ) in the case {{formula:fc74f665-93fb-4b57-bf16-5e90f7ae5e9c}} .
Hardy and Littlewood initiated the study of the moments (REF ). Their interest in these
mean values arose from their relation to the Lindelöf hypothesis, which asserts that for any {{formula:d36a3ce3-597a-4427-acf1-d30715aa7d3d}}
{{formula:c580730b-b3ca-4412-976e-c714700358d5}} . In fact, they showed the Lindelöf hypothesis
is equivalent to the statement, for any {{formula:c8d73494-4afa-4a07-92be-8145299cdac3}} , {{formula:c0f84a05-3b54-4551-8d22-5cd85000909e}}
for all {{formula:a90b5a52-e81d-416e-88ca-f704eeb9c718}} .
The motivation for studying the moment {{formula:a5dd54ac-5ea5-4d74-81a1-b73ce74a4e30}} is that it seems that
it might be easier to obtain an average bound of {{formula:752bfeae-2837-4780-a322-0b5203a6424a}} rather than a pointwise bound.
In 1918, Hardy and Littlewood {{cite:933645f15909108c92a6bf9f653c7d0a0eee2dd4}} proved that
{{formula:2cf65792-2eab-4d54-8987-ee6a2d54a714}}
| i | c80053cc0d83a8e5cc122640b0aa2fd9 |
Ablation study. We perform an ablation study to understand the impact of different components of PONI. There are three key components that contribute to our performance: the object potential function ({{formula:8f80bcff-4fd5-4792-a8ef-b3b9849fd329}} ), the area potential function ({{formula:ac88f7de-196f-481b-b611-a34e695294e5}} ), and the fact that they are defined only at the frontiers (F-only). We additionally study the impact of using ground-truth image segmentation (GT). In tab:ablationstudy (rows 1-4), we compare the performance of our complete model with variants that have one or more components missing. The complete model with the 3 components achieves the best performance (row 4, tab:ablationstudy). When {{formula:0f2624c5-9e1f-4109-938f-f9c6b93a2dac}} is removed (row 3, tab:ablationstudy), both success rate and SPL drop by a good margin, indicating the value of goal-oriented search within PONI. When {{formula:09a9dfa2-23a1-4976-8019-a1e7d31cbeea}} is removed (row 2, tab:ablationstudy), the performance drops drastically which shows the importance of a good exploratory bias for ObjectNav, echoing findings from recent work that encourage exploration for ObjectNav via rewards {{cite:cadb88fa2fa94d7add9c021f79c82435f129f0fb}}, {{cite:aecc111c2229c3b4d500519c21a03fc6c8da8092}} and tethered policies {{cite:4e3f7a160c171ab368c9b1a1990bedb067dee72f}}. In row 5, we augment our complete model with the ground-truth semantic segmentation (GT). We observe that the performance improves significantly on all cases.3D semantic annotations are erroneous near the object edges. This limits the success with even GT semantics (see {{cite:33b62f3b239c181733ec49b2bde93bdaaf3e580c}} for more details). Since the image segmentation impacts semantic mapping and the stopping behavior for the local policy, segmentation failures are a major source of error for PONI.
| r | a18adfdc4b5ecb7fa61e4af94a357c12 |
We recall that if {{formula:9a4fb78c-5a6d-46dc-8d6f-53e310bbdd82}} is a very smooth point, then the unique functional {{formula:b5afacd9-9f01-44dc-b060-e4f45269a7c9}} has the property that in {{formula:c4ff404c-859a-4a25-9784-84a9056b2547}} , it is also the unique norm preserving extension of {{formula:a75fcf16-a15d-4d41-931e-2ac6e3bf88ac}} on {{formula:a0efb880-03f2-442e-a358-22c25aa79dc7}} to {{formula:7d560ad1-143c-44e4-935d-31719456d104}} . Thus by Lemma III.2.14 from {{cite:f9f6a827b76260a25f353b4337728cdb6552838f}} we get that {{formula:90a21e4f-479d-4042-a7c9-8898f66bc373}} is a point of weak{{formula:d09ec00a-ba4e-450b-8ba5-837172ec732f}} -weak continuity for the identity map on {{formula:4444f2f3-6fd6-4973-a97e-b8765d4459c8}} . See {{cite:30740083d2c4731651568d9c71c7edcdb42bc9d0}} for an analysis of these points in {{formula:13763f41-f2c9-4377-828b-4415894cdc6a}} .
| r | bc02591681c621684cbf2afe21bae925 |
Recent experiments on gate control of the supercurrent in metallic Josephson junctions {{cite:392eb346f7c2c13bab2f00807c757ea866363ab4}}, {{cite:ab1f7c90715208e43251a371c7bf15710dcde651}}, {{cite:341557d8277482eeb592fc71379d9035bdabe551}}, {{cite:502fcfc5785a90045e90de7954f78ea0226fb22b}}, {{cite:5b1b1bfb7b256b164b0b1032d222f71bdfe5027b}} have revived the interest in a better understanding of the role of quasiparticle injection from normal parts of the circuit {{cite:625fa4abc636772a31da0308cf55a7903a6a3bf6}}, {{cite:5f996db142c75043a06e557890bb68d0bf854bf6}}, {{cite:1787f0eba910a9bba768c7749ba7871587eb4864}}, {{cite:6b63a5e9f47a524d0c883413bcbd89ebcf8129fb}}.
Deliberate quasiparticle injection via voltage-biased normal leads has indeed been studied earlier and shown to have important effects on the supercurrent {{cite:782ccf42b88e75cbf1e9ad0afc4163150fa42e07}}, {{cite:d43f3978ecfb0311aff3143c1aa040526aa19827}}, {{cite:6ab66139fc9bbdf1ec4a1bda49b9bfd5967954d6}}. The possible reversal of the sign of the supercurrent upon increasing the voltage of a normal lead directly coupled to the junction was first shown, though not emphasized, theoretically in a long ballistic junction {{cite:3444c7f0c379110222464ba2e0e67b22860a2449}}. The resulting realization of a so-called nonequilibrium {{formula:61668c57-3022-4ad9-9d64-01142664cd1a}} -junction was pointed out in Ref. {{cite:00356d6bc76fa2973934357a8d7067ebb6b054f8}}, where a simpler setup consisting of a normal dot connected to two superconductors was investigated. Experimentally, a nonequilibrium {{formula:148b87f5-5ed3-43ac-a525-d141764dd8af}} -junction was first realized in a long diffusive junction {{cite:cacf07f898f8686dcaf0755d65c3aeafa73c9587}}.
Also subsequent work, both theoretical {{cite:4170bdf9cbd1e0ce258950a7255e30cd1c1fb64c}}, {{cite:cbcb6acda0305479b20d1b6588e80b5352185c18}}, {{cite:1447a2a383b6df01e7532aedc232134ac1d52775}} and experimental {{cite:c4f4f7e633c001ee67ba68c2a6caf82df01b93eb}}, {{cite:09bd0a8c513d65b186fc38b587a208ddcefd4258}}, concentrated on extended junctions. (A short ballistic junction was addressed in Ref. {{cite:1447a2a383b6df01e7532aedc232134ac1d52775}}. However, in that case, the effect is absent.) More complicated geometries, sometimes called Andreev interferometers, have been studied as well {{cite:66498ef1611d7ecb0d13b3de0da401fa5634b3a1}}, {{cite:57bea2854b3da6397e9c20097852b03ff283c18a}}, but all in the long-junction limit. We note in passing that equilibrium {{formula:dce1691c-9ecd-49a1-902d-28b73b2dcb6b}} -junctions may be realized in superconductor-ferromagnet-superconductor junctions {{cite:ae6b9192fc05133e16a4016c45fdb9eabcc1684e}}, {{cite:68208f53cbb3a4864058e2b78b3fa138953dd415}}, {{cite:9f28d24d472fbf84678202be0d216a49d7831841}}, {{cite:66d2b634b8120f7f5bb51e0e20e9008d06f2174e}}.
| i | b326cfad9f602c7a6548eafec5581e9f |
If {{formula:650fe78c-db97-42d4-9f88-ced02a917bb7}} is twice continuously differentiable in the classical sense, then {{formula:35cbf88a-fe2b-431d-bd6a-52ebe38692d6}} has gradient {{formula:9dbf7ceb-2353-44b2-9957-0ba5f5c005b9}} and Hessian {{formula:d4f25b93-fd41-4df2-a13c-1b125b4ced6c}} . We recall that if {{formula:d4b668bd-e365-4a14-bf6c-535306fdb724}} is a geodesic emanating from {{formula:2b66a494-2ac1-41f9-968e-8402bb5c8961}} with {{formula:ce13662c-f558-44fd-a243-4379abfc41f7}} , then the Hessian is the symmetric endomorphism of {{formula:183544a2-7e6f-4f38-8aaf-9a5eda374933}} such that {{formula:79a84af8-3162-42f9-9450-f78acdab3476}}
Now let {{formula:2bcfb5cf-ccbc-4ef6-88f1-da49e387a95a}} be an infimal convolution that is not identically infinite. McCann {{cite:8f297b3f2351a1cfe4af8261a44a3eaca12f550e}} showed that {{formula:a589d8c8-45d9-40fe-912e-2e674847f196}} is Lipschitz continuous throughout {{formula:3bfc5c04-bf6f-4a29-bf41-8f1b3f1b9a65}} . Furthermore, there exists a subset {{formula:a0b6d3d4-2305-4f82-af53-329d02f04dd1}} on {{formula:fc0a92fe-5c6f-4a4e-93cd-5340b857b9f0}} that has zero volume such that {{formula:6c1cee9b-a4ac-4c9f-a9e4-93044b3bbdee}} is differentiable on {{formula:2c33f7a8-b997-4eef-90e8-3cc1f43a85c7}} , and {{formula:e20f661b-e6d8-4109-902c-d31eafc26ea5}} gives the gradient of {{formula:239d1109-45f1-4897-8c25-30b13ea925a0}} . By Theorem 14.25 of {{cite:449cd609f2a7ec6e700e8c52dc5b0b02c3463817}}, {{formula:436e59b0-5aa0-4f4b-8179-1c241d68d1b9}} also has a Hessian second derivative {{formula:619072bb-4d93-4dda-8885-2fe6a0222afc}} , in the sense of Alexandrov, which is essentially a matrix of measures. The differentiability properties of {{formula:6917eb66-272a-4c4b-98ec-e90fe3ffce52}} concave functions were also considered by Cabre {{cite:2769208f46ede65e5340310c1a45b70786ac7f61}}, who computed the Hessian of {{formula:4329d4f6-3dd4-47b7-90c7-5daf68045b1b}} and found the Jacobians of various changes of variables which we will use later in this paper. For the moment, given {{formula:46d71f8e-6d73-4095-b79d-b14b9c6736c3}} , we take {{formula:a72d527b-9f9b-4965-afa3-fb099eb47166}} and consider
{{formula:755fd040-e2cc-4ece-8c2c-abc0809630ef}}
| i | 5942f85468c64e1785fd1b35c9ef61e5 |
Finally, we compare the WOT-SRSH approach with many-body perturbation theory in the GW approximation, where the self-energy operator is approximated by G, the single-particle Green’s function, and W, the screened Coulomb interaction {{cite:1c00a5c5297ee2afc24e32311f8083c40c624ea2}}, {{cite:519f39cb538afb732d7d59873a40144e41f9c374}}, {{cite:3366b9defed9c7e64a8595880551428a7c94fe56}}. GW is perhaps the most popular approach for calculating band gaps. Importantly, one could view the screened range-separated Fock operator in WOT-SRSH as an approximate self-energy operator, which neglects the temporal dependence of the self-energy {{cite:2d0928ed964f878846be115d860488ab03e54d90}}, {{cite:3366b9defed9c7e64a8595880551428a7c94fe56}}, {{cite:a8ec12d75c95514a1a93f89701621c79714ecfe2}} and uses a model dielectric function {{cite:2d0928ed964f878846be115d860488ab03e54d90}}, {{cite:0e7bcbdef766ffbd1b00409264d5a659c4b48659}}. However one does not have to view WOT-SRSH as an approximate GW scheme. Instead, as explained above the screened range-separated Fock operator is rigorously justified from generalized Kohn-Sham theory, which shows that no time-dependence is in fact needed in order to obtain accurate band gaps. We also point out that we only use a fraction {{formula:0abd8d84-1b40-4134-a0de-85edfa113c2e}} of exact exchange in the short range, rather than {{formula:1b6b9605-cc12-449f-b3c5-3b41cde661a3}} as dictated by a model dielectric function {{cite:0e7bcbdef766ffbd1b00409264d5a659c4b48659}}. In order to quantitatively compare WOT-SRSH to many-body perturbation theory, we examine one GW approach, the commonly used “single-shot” G{{formula:9769a5ee-b6b2-4696-bf7d-7c25c0f9df70}} W{{formula:ed2386d1-62d4-432b-b1ad-a7ae1e81724b}} based on a PBE starting point (G{{formula:0b473eaa-8422-44e9-bcef-218a1d9b1412}} W{{formula:b88e2fbb-2f45-4e80-81d8-831fae9a27fb}} @PBE) {{cite:8a87b50e3c62e51b34f5b4c766287176508a109d}}, {{cite:519f39cb538afb732d7d59873a40144e41f9c374}}. Even with such a choice, there is a spread of results in the literature due to various additional choices, e.g., plasmon pole models, pseudopotentials, basis sets, and degree of convergence {{cite:b02a529d7fc16b84d6e3dda7011f8d5d9111b4e7}}. With this caveat in mind, Ref. {{cite:9d611963c22b16a5dd45dc098858666dacd82d59}} reports that the MAE for band gaps calculated by G{{formula:5c01db65-1348-41ab-a196-315673d2df42}} W{{formula:a7529a77-d280-4021-83a4-21d74ef07fc0}} @PBE, for 7 prototypical semiconductors, is 0.15 eV. The MAE of WOT-SRSH for the same set is 0.06 eV. Of note, G{{formula:40304a9d-f324-4dbf-b974-063c3bc0c540}} W{{formula:616239d4-8839-47d9-b706-894c35cdf16f}} @PBE underestimates the GaAs band gap by 0.5 eV, an error that is significantly larger than the error in the WOT-SRSH band gap for any material in this study. Another study {{cite:bf4bd26987ed5cfab0482513c07d2de1435be00b}} reported band gaps for most of the materials in this study, with an MAE of 0.5 eV, which is significantly larger than that of WOT-SRSH. Experience with SRSH functionals which were empirically fit to match the G{{formula:74bc66a8-1513-4b04-85ec-53637b0e257a}} W{{formula:69539af8-eb28-40c5-933c-7658a5b64d64}} @PBE band gap {{cite:9d611963c22b16a5dd45dc098858666dacd82d59}} shows that the predicted position of low-lying valence bands sometimes differ from experimental values {{cite:bcc4298a1e8b128e660ebdd5a2f0cdc18574ffc3}}. Thus, it may be advantageous to use WOT-SRSH as a natural and well-motivated starting point for many-body perturbation theory calculations within the GW approximation, which may address this issue, as well as other properties beyond the band gap itself.
| r | 2608de612f0001f66863d3f9097a75ac |
In the context of the NLS, Gibbs measures (REF )–(REF ) were relevant to study a substitute for a conservation law at low regularity. Namely, one can show that they are invariant under the flow and that they are supported on Sobolev spaces of low regularity. Consequently, it is possible to construct global solutions for random rough initial data. This was first rigorously obtained in the work of Bourgain {{cite:698e4034be29c2d376d55f19c91fbe608d018864}}, {{cite:2e012c5b010583806437416a7790d0d907a04598}}, {{cite:7cf497e11600f4ad849e54814ceb80539d5af696}}. Some preliminary results were previously known by Zhidkov {{cite:5289d19cb2175adfc62974da5c9350de2512361f}}. This is an active area of research in nonlinear dispersive PDEs. We refer the reader to the expository works {{cite:87854de123c72e274bb9f0b7b9bf30dc73e5f7d4}}, {{cite:5638e4dfc62ef41fe33af30420a27e0b29c353cc}}, {{cite:ae526d8318db7845b3a67016848c2044960e0423}} for more recent references and developments.
| r | 248631d13e6b998eb730706b60d15497 |
On the other hand, multi-agent reinforcement learning (MARL) has also been explored for autonomous driving tasks {{cite:4b559fbcb6921e2f383011a2006ab92471eb4dff}}, {{cite:48c47eff0766265d0b110a3b525d411d674cfa12}}, {{cite:7d444ae23a17e6a1c819f0fa78478daa2f2640d3}}, {{cite:13b7172ede27e20eb3489c984718faca9a8636fe}}. In particular, in {{cite:4b559fbcb6921e2f383011a2006ab92471eb4dff}}, a MARL algorithm with hard-coded safety constraints is proposed to solve the double-merge problem. Also, a hierarchical temporal abstraction method is applied to reduce the effective horizon and the variance of the gradient estimation error. In {{cite:13b7172ede27e20eb3489c984718faca9a8636fe}}, a MARL algorithm is proposed to solve the on-ramp merging problem with safety enhancement by a novel priority-based safety supervisor. In addition, the authors in {{cite:48c47eff0766265d0b110a3b525d411d674cfa12}} propose a novel MARL approach combining Graphic Convolution Neural Network (GCN) {{cite:656caf583e0168fe8cdc965ff184de76ee40e693}} and Deep Q Network (DQN) {{cite:e58575c52e85acf0664b3a620a25238fed2a9e82}} to better fuse the acquired information from collaborative sensing, showing promising results on a 3-lane freeway containing 2 off-ramps highway environment. While these MARL algorithms only consider the efficiency and safety in their designed reward function, another important factor, the passenger comfort, is not considered in their reward function design. Furthermore, those approaches assume the HDVs follow a constant, universal driving behavior, which has limited implications for real-world applications as different human drivers may behave totally differently.
| m | 9c287886a4b6ce31741cbfed3ee421d9 |
BayLIME is a Bayesian modification of LIME that provides a principled mechanism to combine useful knowledge (e.g., from other diverse XAI methods, embedded human knowledge in the training of the AI/ML model under explanation or simply previous explanations of similar instances), which is a clear trend in AI {{cite:dffd577effa848914ce5f5d78eca3e279e658215}}, {{cite:3de12ac4216bec541897034ae1ebfe2bcefea7c2}}, {{cite:8faf546bb2ad547329fe41ac3d78ed364533d776}}. Such combination benefits the consistency in repeated explanations of a single prediction, robustness to kernel settings and may also improve the efficiency by requiring less queries made to the AI/ML model. That said, we discuss the following questions to highlight the practical usefulness of BayLIME.
| d | b18bb683af74525db7e710b82faeaf18 |
Each agent in each scenario has a different mission to complete: driving from a specific start to a specific goal. Traffic consists of the agents in training as well as the background traffic provided by SUMO {{cite:63dd32d9bb884af8fc2467ecc265b96987576d1b}}. The chosen baselines include two independent learning algorithms, DQN {{cite:34d0d746bf768a4ef4d46a1cbbe6653c2bca5ef6}} and PPO {{cite:f55d0a4c7ee8bad9579b5bb2f4923a6b47587497}}, four centralized training methods, MAAC, MF-AC {{cite:2378b76b900b8061097f719bcdfd178f79cf0ac5}}, MADDPG{{cite:3976aad62f655911d022cd923981e16abfc9c539}}, and Networked Fitted-Q {{cite:f7aca8c5bc54db5d08c3f5ec671c1f51114f2f1c}}, and a fully centralized method, CommNet {{cite:9cf42417f0682dfa44a0459f99c5c3756413583d}}. The observation, action, and reward functions are kept the same for all these baselines.
| r | 146f549251fcd8fddd39b6926dfb4111 |
Utilizing humanoid characters in a physics simulator to optimize motions is a promising solution because the physics simulator can guarantee the physical plausibility of the generated motions. Prior works {{cite:f46aaf7f3108242ecbf19b8e8da7b33821687af8}}, {{cite:8e7c5ad265c2ca8ca502380264e751d6fd04b32f}}, {{cite:ee39c7d4e01edb2bbd594e003feed985b8285f2f}} utilized reinforcement learning (RL) to actuate the humanoid character to imitate various reference mocap data for creating physical character animation. Inspired by them, Recent works {{cite:b4adb0c948eb45f6636856997e5cc860de54f0a6}}, {{cite:bc45d65fc5a77784e3ed28a516574c642823460c}} also attempted to utilize RL to imitate motions synthesized by deep neural networks, in the format of skeletons or SMPL {{cite:4b2052b1b8556ac4f226dcf7795a4472f4a4d4dd}} models, aiming at producing physically-plausible motions for 3D pose estimation. However, these methods are only validated on simple motions such as walking and talking in the Human3.6m dataset and cannot generalize well to complex motions or irregular motions. In addition, RL based imitation requires transferring synthesized human skeleton motions to humanoid motions, where a humanoid character should be carefully designed to exactly match the human skeletons in terms of both shapes and the kinematics tree. This limits RL based imitation to transfer motions between skeleton and humanoid with different shapes and kinematics trees.
| i | 1ea07c5b6f82dc85fded36ccef5d7992 |
Once the network is formed, we change the interaction potential, making the bonds permanent and thus fixing the topology of the network. Since we are interested in understanding the roles that topology and chain size distribution of a polymer network play in determining its elasticity, we consider interactions only between bonded neighbours, similarly to what has been done in {{cite:aec94e065d599e6ae642449cd73440e70aaab0b9}}. Particles that do not share a bond do not feel any mutual interaction, and hence chains can freely cross each other (whence the name phantom network). Two bonded particles interact through the widely used Kremer-Grest potential {{cite:03e817b01da72310574f097f8d8adca68fcb3267}}, which is given by the sum of the Weeks-Chandler-Andersen (WCA) potential {{cite:1eaedae270ee4d2f377b9c25e617627631b37d74}},
{{formula:29435b79-c75e-44e1-afab-61d72790e508}}
| m | 83cf3ee55a45a86d842f1af8455309e1 |
As shown in Figure REF , we develop a new deep network architecture for automatic portrait video matting. It recurrently estimates the alpha maps and foreground images. Our network can be distilled into four parts: (1) feature extraction, (2) optical flow estimation, (3) context-motion updating operator, and (4) upsampler. All parts are differentiable, and we train the network in an end-to-end manner. Given an input frame {{formula:4afcda45-042f-4e4c-b399-d94187b273a3}} , our network first extracts the context features {{formula:6c6b0af5-1e3a-4394-a4d7-ae25919cf346}} from an encoder pretrained on the image classification task. We capture the motion information by estimating the backward optical flow {{formula:00fdbd38-d4b7-4144-a4db-59c45bd59c74}} from the current frame {{formula:59f222c5-bb12-4d02-bcb0-85644ba511ee}} to the previous frame {{formula:6b2a6279-ffb7-4bc8-8e7f-39692e0a453e}} by the PWC-Net {{cite:a19f7aae82eb2dfa6967cadf39e44be1927b82a7}}. To fuse the context information and the motion information, we develop a context-motion updating operator, which integrates context features, optical flow as well as the features from the previous frame. Finally, we upscale the resulting features {{formula:b1083547-bdb9-4abc-a256-d8ba0af6155f}} and predict the alpha maps {{formula:dd47d924-0ecd-440c-a588-22bfa1af2a29}} and the foreground {{formula:d707614e-f24f-4ec7-881f-235c83cf5ab1}} . Below we describe the network in detail.
| m | 2e6fdf2f576fc74da640714395856386 |
We have chosen to use some derivative-free optimization methods because NCRS needs some adjustments for using deep reinforcement learning because of the variable number of inputs and outputs {{cite:c10d86e75bb35a890a888a86ef0db95e4e58e51a}}. They are the covariance matrix adaptation evolution strategy (CMA-ES) {{cite:9fdbb2f4270ef6b4d93410115999b5d66802bd66}} and covariance matrix adaptation MAP-Elites (CMA-ME) {{cite:13d5dd577346ea42aace1d3762afa3a90b0a2c8d}}. The latter is used to add quality diversity to the former, broadening the exploration of robot designs. For both training methods, we use the library CMA-ES/pycma {{cite:03f6e04068421ef68595269459f04c303bf6e77a}}. There are two training methods and three benchmark tasks. This gives a total of six different combinations. Because of the computational demands, each of these combinations was trained only once.
| m | 9e0b774ac574e0cb7e440b5b6e98e28b |
Duplicate Removal of Oriented Boxes. Although the state-of-the-art NMS algorithms achieve promising performances in horizontal object detection, their performances may greatly drop in the task of multi-oriented detection. To remove duplicates in multi-oriented object detection, RRPN {{cite:6a6bf3570f39f386dcb6446132bf5446d027c646}} adopt Skew NMS, which design implementation for the skew IoU computation with consideration of the triangulation to dense rotated bounding boxes or quadrangle representations. R{{formula:63bbcac0-c842-41cd-a769-264af3b5814c}} CNN++ {{cite:fd760a38e5b03bcec549ff42913d39bff98d50fb}} adopt rotation non-maximum suppression (R-NMS) as a post-processing operation based
on skew IoU computation. To apply NMS to polygon duplicate removal, Liu et al. {{cite:4e78dd4ac0e5e0f3c679d0e2b03a5e0b0686f330}} proposed a polygonal non-maximum suppression (Polygon NMS) which improves the traditional NMS by computing the overlapping area between polygons instead of horizontal quadrilateral bounding boxes.
| m | 405c2f9e0c891abc25b3d5c7570ff3d2 |
The restriction that the weight be at least 2 means that weight 1 forms are missed in this approach.Weight 1 forms are also missed in the modular symbols approach outlined in {{cite:a3ac3280591e1eedb349e0f16bcf545f5765f97a}} This is a meaningful issue as, since the proof of Serre's modularity conjecture in {{cite:df23ea242b9bb8e6477f6cd313a3b5342b4c5124}}, these forms are known to categorise all odd, two-dimensional, irreducible Galois representations over finite fields. The Fourier coefficients of these forms give the traces of Frobenius elements in the associated representations.
| r | ddadfc7fc0e8659328abb1bd49190451 |
The response of microstructures for use in multiscale simulations, structure-property investigations, and uncertainty quantification can be accurately modeled with graphs.
The proposed formulation used the topology of the data discretization directly instead of a segmentation or clustering of the image data.
This aspect should have particular advantages for image data where the segmentation is not obvious, hard to compute, or is obscured by noise.
Furthermore, it has a simple implementation and avoids the need for feature engineering, but can benefit from it.
The architecture draws on both: purely graph-based networks and permutationally invariant convolutional filters.
We demonstrated that endowing the widely-used GCN filter {{cite:b789578bca4fdc6d8a8a33e19749b7ca2581a2e4}} with an independent self-weight (as suggested by the reduction of the ChebNet) can significantly improve accuracy without adding additional layers and their parameters.
The independent self-weight allows for differencing the node data of the self and its neighbors instead of only averaging.
This can be seen as inferring edge features between the central pixel and its neighbors.
For physical problems driven by gradients this change to the filter is important.
We also found that pixel edge neighbors are more crucial for a predictive model than vertex only neighbors.
Lastly we were able to demonstrate that small, efficient graph convolutional networks can be effective at the task of predicting the homogenized evolution of complex microstructure.
This has significant applications in sub-grid constitutive models in large scale simulations, structure-property property investigations, and material uncertainty quantification.
| d | d1d1b5fc3140188dc4f4c3baf380ce99 |
If {{formula:673038a1-326b-4bfd-9ba1-7746dcc33ee7}} is Lipschitz continuous (in particular if {{formula:11f73d17-b6eb-40db-a1df-2aec43686254}} ), then our Assumptions hold true. Moreover, inequality (REF ) recovers {{cite:8532ae934d4306af37b219c34726ca4a586ac959}} but with the duality gap instead of the KL divergence. Obtaining a result in terms of KL divergence is hopeless for PSGLA in general because the KL divergence is infinite; see the appendix. Connecting the convergence of the duality gap to zero to known modes of convergence is left for future work. Besides, obtaining an inequality like (REF ) that holds when {{formula:f6279f24-f777-44b0-9499-e3c9b07fd508}} is just convex is rather not standard in the literature on Langevin algorithm, see {{cite:08034b968563e3a99bad85ff3e88aa663b57f977}}, {{cite:30b24b6c001b9c7f2b76e9e08a7983d05ed06287}}. Corollary REF implies the following complexity results. Given {{formula:9cbaee1a-7861-4c11-b3a9-82a3294a3ab4}} , choosing {{formula:2188122e-f466-4451-ae95-fad72e2e18af}} and {{formula:dd6c2eb3-595f-4ed3-a04e-229e22da25c7}} in inequality (REF ) leads to {{formula:aa465d43-482f-4fef-b474-966f1acfe77d}} . If {{formula:5b57c2d2-3983-491a-8429-6078f7bf2ed5}} (i.e., if {{formula:6e294f62-a3ff-4ab1-8d58-68e012b6ff01}} is smooth), choosing {{formula:a8441328-3e19-4b44-922f-a79246f7e23a}} and {{formula:084c8e2f-6b97-4f53-8be4-dbc80b518765}} in inequality (REF ) leads to {{formula:07c735da-3b72-45b6-b39d-391ccdaf610f}} . Finally, if {{formula:6660df45-cf7f-4805-ac6d-29867970072e}} (i.e., if {{formula:9de58663-2bbd-41ac-9fb7-08242acdde3a}} is strongly convex), choosing {{formula:739ffed1-931d-4be3-97d8-3c23f8299284}} and {{formula:e73f7c84-9ae7-433b-87f0-c4a33ce1b8de}} i.e.,
{{formula:2d396fa3-8237-4990-9a70-f895dac6680b}}
| r | fd9fd57d8aa84a228b45b595059435b8 |
The muon anomalous magnetic
moment {{formula:83cd38ab-7e96-4b05-82b0-83c8cbd5180d}} has become a leading
candidate quantity with which to test the Standard
Model. The latest experimental result from Fermilab
this past April {{cite:52b9ee2b366ae9f355e4609ce8962c7e12220a86}}, when combined with
the previous result from Brookhaven {{cite:c56c2fee315dad227afd5f95fdb02409132bbe18}},
now shows
a 4.2{{formula:ccf6349f-aae0-481f-af09-875989937dbb}} deviation
from the Standard Model prediction (for a summary of the results
from the {{formula:0949b9ad-7a42-4886-b25b-49d751ad12ef}} theory initiative, both
from phenomenology and the lattice, see Ref. {{cite:4b4a281e02d064cf32ab54c392d5d35a7a3a28a8}}).
The BMW collaboration recently found a smaller
discrepancy with experiment, {{formula:954e6bc4-be5b-4b2d-a72c-5dd3eb0859ae}} {{cite:b766da9c4981966716e640fa39e4c69821336b5b}}, when
their sub-percent lattice QCD
value for the HVP contribution is used
instead of the data-driven value from the Muon g-2 Theory
Initiative {{cite:4b4a281e02d064cf32ab54c392d5d35a7a3a28a8}}.
The uncertainty in the Fermilab result will only
decrease in the next couple of years, and it is important
for the Standard Model calculation, which until recently has
primarily come from the dispersive estimate,
to keep pace.
| i | 816d7a03a7a3ba53a8cbdf8869d38814 |
[itemsep= -2 pt,topsep = -1 pt]
Sum: this variant combines the features of source nodes and its neighboring nodes by sum operation, which is widely used in existing GNN works, such as {{cite:8b52b894093124cf43126e114ca84efa3699dd80}}.
Product: this variant updates each node by computing the element-wise multiplication of the node feature and aggregated features of its neighboring nodes.
Concat + MLP: this variant updates each node by concatenating the node feature and aggregated features of its neighboring nodes, then uses an MLP to encode the concatenated features, which is used in previous visual language-related methods {{cite:c3ee28edf008a3cebee60838131595620a52da72}}.
{{table:170b9870-73eb-4054-b6ce-98bb13716a54}}{{figure:c1e45dec-0e99-4d38-85f0-d46c4a5f40eb}}{{figure:553c112e-2b43-405f-89e3-1edcc14fcb20}} | r | 80c7235b134d925b95c7707efb976366 |
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