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Accuracy-throughput Trade-off:
blackTable REF compares the accuracy-throughput trade-offs of the competing methods.
As shown, at FPS around 130, Ours-BN-R18 ({{formula:5154a818-45d7-41b6-82ef-ef5207ff7b18}} ) outperforms BiSeNet-R18 with input size 0.5 by 2.3% mIoU. Likewise, Ours-SN-R18 ({{formula:56044f65-49a2-460e-96b3-65c2b42237b4}} ) surpasses SwiftNet-R18 with input size 0.5 by 3.1% mIoU. Comparing with the video-based methods like {{cite:273e132ee46f761d5de5654c193f741c0d446b1b}}, {{cite:eaf28fcf566f485ca92c968ef84859fd7c38b15f}}, {{cite:e611a47d84159986fb83c990f57030b1e21436db}}, our scheme achieves much higher FPS and mIoU. In particular, Ours-SN-R18 ({{formula:cffbbdd2-0c98-48f1-a1a7-730cc40ef8ad}} ) outpaces considerably {{cite:9ac14336a2a574a54c353d919f8ec4886db8a4af}}, {{cite:86e8716d982baee2e2a327c62f89a79b2d7e2a1b}}, which target also high throughput, in FPS at the cost of a modest drop in mIoU. Results on Camvid {{cite:fa5bf7184c09ae2fcec1cffec8827cdf910ebd7e}} (Table REF ) show that our method runs faster than the image-based schemes {{cite:ec990b821bba5707f3dc03eaff24017bcb8dab9f}} while achieving higher or comparable mIoU. It is to be noted that the other video-based schemes can hardly compete with ours in FPS, although {{cite:86e8716d982baee2e2a327c62f89a79b2d7e2a1b}} has higher mIoU due to the use of better backbones.
| r | 184ae408fe87192cc29e751cbb032579 |
Efficacy of IIR-SNN with shallow networks. As mentioned in section 4, gradual training is required due to spike vanishing at later layers for deep SNNs if direct transition from T5 to T1 is attempted. However, for shallow networks, if there is some propagation of spikes till the end, training with T1 following direct conversion from ANN might be possible. To validate this, we experiment with a VGG6 on CIFAR10 and the results are shown in Table REF . In this table, VGG6g denotes networks trained with gradual latency reduction and VGG6d denotes networks directly converted from ANN and trained using that particular timestep, so the result in the last row of Table REF is obtained by converting an ANN to SNN and directly training with 1 timestep. We observe that proposed gradual training scheme provides slightly higher accuracy compared to direct training in case of shallower networks, though it increases the training overhead. This is consistent with ANN domain results {{cite:3e901646292aeeac2970c197db821f89364a5533}}, {{cite:915e0567c71f7eb41704e899fdad0e24b597cd64}}, where the authors achieve better performing networks using sequential model compression compared to direct compression.
| r | 0741c948c4f306492d17b787170d3074 |
A fixed point is multiple if and only if it is rationally indifferent with multiplier equal to 1(See Page 142, {{cite:1f71ab73bb27f03cd0a3e323223ad37a235c79a0}}). This fact is used in the following proof.
| m | 913e2ce8064665359c402a10b62af177 |
We also train our model on recently proposed Spaces {{cite:4a56be2a819c55c33c67f06e89dab465dbf876b1}} dataset.
The dataset captures light field images of 100 different scenes using array of 16 cameras.
We use 90 scenes for training and 10 for testing.
We randomly sample 4 pairs of images from camera array as inputs and sample the target image from remaining cameras.
We use the same training procedure as used for training on KITTI dataset.
We show the results in Table REF .
We validate the performance with 3 different baselines using 4 input views (to create 6 pairs).
Further, we also show results when using 12 images in the camera grid as inputs to synthesize remaining images.
We combine neighboring input images depending on the position in the camera grid to create 18 image pairs.
The last row of the table show that the performance improves significantly when we use large number of images for analysis.
We note that the model is trained using only 4 image pairs and generalizes well when using large numbers of image pairs.
We show in Fig. REF novel view synthesis using 12 input images for qualitative analysis.
| r | d0adaaeca6969197a7d319b6281edcb8 |
To this end, we propose a Pose-guided Coarse-to-Fine framework, named PCF, for part-level action parsing.
We first adopt the existing action recognition methods, e.g., CSN {{cite:4cef9bfe844b448678e64c029429f61c0696e6ab}}, to predict the coarse action of the whole video, since it is the State-of-The-Art (SoTA) CNN-based model in the action recognition task. After that, we predict the fine-grained segment-level body part action instead of the frame-level action based on the persistence of human actions, which greatly improves the computational efficiency with less precision reduction.
Moreover, due to the ambiguity of body parts, e.g., the similarity of the appearance of the left leg and the right leg, traditional existing object detectors are often unable to predict the body part effectively.
To solve this problem, we propose the pose-guided positional embedding method which guides the detector to predict the part locations with human pose keypoints.
By encoding each human keypoints with different colored dots on the original images, the feature representations of different parts are more easily distinguished by the detector, which effectively reduces the body part ambiguity.
| i | 35b7b186d5d96404bbfd6ca9be4eaf8b |
In 2001, the NAGARA event {{cite:9e0dda49f4d379c5f53ee6444c244dee2834dff8}} from the KEK E373 emulsion experiment undoubtedly provided the first evidence of
the light double-{{formula:987ca154-d612-494c-a499-70f9f089f6b9}} hypernuclei {{formula:bd1672e3-e1a7-4306-a495-0c5f34aa7039}} He, demonstrating that the {{formula:203b6787-980a-4895-a3f3-1f33d0abd680}} {{formula:c2632e09-045f-4b35-8186-c16f8178a1b5}}
interactions are less attractive than {{formula:3e3c2d2e-ecc3-4364-a806-bdaacf5b920e}} {{formula:53ef2689-6601-4278-a06d-ab94b05fceea}} interactions. On the other hand, the feasibility of a light
{{formula:f88b75a3-8453-4693-9644-903f204f9e53}} -hypernuclei based on the state-of-the-art experimental {{cite:9c7a3a9d57b57f1542292a41d51a219bf4edf589}}, {{cite:54174419d0d693fea7f742c2c75ad841dacfbf7f}}, {{cite:29f16799c8374131ce65116838d9b325c78b37b2}}, and
theoretical {{cite:295aa7fb455416c84d62f1d320b94a6f0440cb1b}}, {{cite:ca5debb6936a461d3eafffca114a6f5454417010}}, {{cite:a9e08570f4505a04b2471efc583820a6529a8303}}, {{cite:0810ad96732d74b5c2e7fe511bc4cd53b4e3d2dc}}, {{cite:2faf7588711ee990080403df241b932a54c7254e}}, {{cite:1d29c9fcdd76fc008cb77092fbfd16d976302e74}}, {{cite:e45f5a32583e4bfb82657541f40e5609c13a084c}}, {{cite:5bff59e104d55da2fd8d60149c280319e0ec43cc}}, {{cite:12bb1e232d71913c5409b1de2d2f283543685a6e}}
studies remains largely equivocal, since they were first claimed in the 1959 experimental work of Wilkinson
et al. {{cite:f05c56cdf9352992caed8422cfa4d15379a5001a}}. This is primarily due to the current acute scarcity of {{formula:49c54f72-2fed-44cd-b87c-5df97b4fb66c}} empirical information needed to
determine the underlying character of hypernuclear interactions, caused by the non-availability of any {{formula:4244d714-9af4-47cc-82f0-39734b1e3ea8}} -hyperon scattering data,
either current or obtainable soon in near future. All that one finds in the literature are a few scattered upper bounds for {{formula:cb0ce4f6-e40a-4cda-a9b0-fcb4664b4750}}
elastic and inelastic cross sections from emulsion experiments {{cite:03e0005e95d827e445ea6d48029ea9af094bd039}}, {{cite:7971290e974f5bf6d6d30d1e902a94c3dfc25c57}}. Thus, it is no surprise that different
existing model analyses lead to substantially contrasting views regarding the nature of the {{formula:c6a939b1-7894-42bb-9cf0-d113c2ba371e}} potentials, ranging from moderately
or weakly attractive {{cite:9c7a3a9d57b57f1542292a41d51a219bf4edf589}}, {{cite:5bff59e104d55da2fd8d60149c280319e0ec43cc}}, {{cite:03e0005e95d827e445ea6d48029ea9af094bd039}}, {{cite:7971290e974f5bf6d6d30d1e902a94c3dfc25c57}}, {{cite:4e60a135fb6bfbcc27a783b4bfa59a37bee71708}}, {{cite:0fb1fc14dba6669b9b1c5cfa70d5515a411c7918}}, {{cite:6e603d11f7b79a16a047006fab343f0001282335}}, {{cite:297da5ed2dea583c9026c37b28211172eda6d582}}, {{cite:6d1c78768915e84a7d03932a59eeee3f705ebf49}}, {{cite:43472fb52a70b0e1e3a0e5a67a368491af236b48}}, even vanishing {{cite:868d6321a83abe663f2a5c1586ec0c343f311f65}}, to weakly repulsive {{cite:54d628ebcd11598d5ab0dca77abbcac6e0c0af0b}}. In fact, the KISO
event {{cite:29f16799c8374131ce65116838d9b325c78b37b2}} from the KEK E373 experiment in 2015, which undeniably confirmed the particle-stable {{formula:d3ae13cb-ab9c-4dc5-b863-9a996526040d}} -hypernucleus
{{formula:c12ef0f1-4ba4-4dc3-93c2-45f97042db75}} C (interpreted as the ground state of a deeply bound {{formula:9263e152-03be-4929-98d2-f58098caee10}} N cluster system with binding energy
{{formula:bf1b08e8-4f2c-4fa9-8b66-a58b28142231}} MeV), at the least corroborated that the constituent {{formula:cdf2351c-6794-41ab-ad23-f1486bf22a9c}} channels are attractive. Specifically, the updated
Extended-soft-core (ESC08c) Nijmegen potential model {{cite:20935fc317d92864fc2c12a8cc6c7c6d9d47fc68}}, {{cite:1ce09748edbe9f1c1e45b1fd4c4e11dd887271ae}} has predicted that the {{formula:d8d988ef-391a-4b73-a8cc-984ab9c0d0a1}} two-body
system in the maximal spin-isospin {{formula:ba573126-4ae0-4408-8c73-18a04d12f221}} channel is stable with {{formula:9edf9539-216a-46bf-8526-72de5c711e81}} scattering length
{{formula:ebb1475f-355b-4a5d-acf3-e9c7e1a71490}} fm, while the {{formula:781c979d-8ca5-4884-859a-9052f9cbec61}} channel is mainly repulsive with {{formula:bb213bb5-680c-4305-9c4f-e8f008d451a8}} scattering length
{{formula:e62f97ea-1c99-43b8-b6ca-8c7a9cf22621}} fm. With the former attractive {{formula:322644fe-2f05-4aa5-9c0a-2fd6d34f1326}} channel having such a large scattering length, the two-body system
was found to be bound, the so-called {{formula:a9326ee9-12ac-440c-b2dc-0ce8e781ef5e}} state, with an estimated binding energy of {{formula:691b9cf5-eda7-473c-a01b-f34cafb73a52}} MeV ({{formula:63e437b2-4339-4e01-afad-5eed4b5fa286}} MeV) with (without) taking
into consideration the latter repulsive {{formula:d0bb0e54-3357-4504-a7d3-62c3626bbfe1}} channel {{cite:1d29c9fcdd76fc008cb77092fbfd16d976302e74}}, {{cite:e45f5a32583e4bfb82657541f40e5609c13a084c}}, {{cite:20935fc317d92864fc2c12a8cc6c7c6d9d47fc68}}, {{cite:1ce09748edbe9f1c1e45b1fd4c4e11dd887271ae}}. In
a contrasting scenario, the recent SU(3) chiral effective field theory (EFT) based predictions from the relativistic
calculations {{cite:6d1c78768915e84a7d03932a59eeee3f705ebf49}}, as well as non-relativistic in-medium G-matrix analysis {{cite:43472fb52a70b0e1e3a0e5a67a368491af236b48}} have
practically ruled out the possibility of a stable {{formula:652b9ed1-3f1e-42a1-9cb2-4b5e1eb2f282}} bound state in the (1,1) channel, being constrained respectively by the
recent HAL QCD lattice results of Ref. {{cite:6044ae5977b10d747b136ed42244da5f003db786}}, and the aforementioned empirical upper bounds from {{formula:a163a056-028e-4ce9-8fc1-397d4924a203}} cross
sections data {{cite:03e0005e95d827e445ea6d48029ea9af094bd039}}, {{cite:7971290e974f5bf6d6d30d1e902a94c3dfc25c57}}, {{cite:297da5ed2dea583c9026c37b28211172eda6d582}}. Nevertheless, the Faddeev calculation
analyses {{cite:a9e08570f4505a04b2471efc583820a6529a8303}}, {{cite:2faf7588711ee990080403df241b932a54c7254e}}, {{cite:1d29c9fcdd76fc008cb77092fbfd16d976302e74}}, {{cite:e45f5a32583e4bfb82657541f40e5609c13a084c}} on the ({{formula:cc078b8b-3431-42a6-969c-a385e3303ff0}} ) {{formula:7493bc8d-99a4-4133-97de-223db3c7c975}}
three-body system, relying on the same updated {{formula:83f694e9-1a1a-41af-8887-da0ee673d842}} Nijmegen ESC08c potential {{cite:20935fc317d92864fc2c12a8cc6c7c6d9d47fc68}}, {{cite:1ce09748edbe9f1c1e45b1fd4c4e11dd887271ae}} as input,
have hinted at the feasibility of a deeply bound {{formula:22107c58-f419-4ab4-9b56-fd00347aac3b}} state implying a strongly attractive nature of the {{formula:5572389f-b955-40cd-bc92-ad9334b23526}} interaction.
| i | 4afdcab7a4ab62320465b425e1c1338b |
As mentioned above, all the complete analytical expressions have been obtained in {{cite:bb079a4cb070b3bb2b1e822ca9e5d8b4e704b3c0}}. Here we will only show the approximated expressions and we will restrict ourselves to the phenomenological implications of the observables computed.
| d | 7dda34a22b7fe29685aaf47880e0a1f5 |
Over the past decade, a number of optimization-based methods for point cloud upsampling/resampling have been proposed. For example, Alexa et al. {{cite:f3eef49f4f7d9d5032d1aed4a504330e44d56c32}} upsampled points by referring the Voronoi diagram, which requires the surface smoothness assumption and computes on the moving least squares surface.
Based on a locally optimal projection operator (LOP), Lipman et al. {{cite:e3ae60a191bd25f690434dfc7b7405a48345d17e}} developed a parametrization-free method for point resampling and surface reconstruction. Subsequently, Huang et al. {{cite:3e0c9638d57917df2fb472b2bb9e7606d6c7c766}} and Preiner et al. {{cite:7aca7e816bbbb2c47b2fe5a8128c3ceacc48ab63}} proposed weighted LOP and continuous LOP, respectively. Specifically, the weighted LOP iteratively consolidates point clouds by means of normal estimation, and thus is robust to noise and outliers. The continuous LOP can perform fast surface reconstruction by adopting a Gaussian mixture model. However, LOP-based methods assume that points are sampled from smooth surfaces, which degrades upsampling quality towards sharp edges and corners. To effectively preserve the sharp features, Huang et al. {{cite:cfc61e254dba1743c1d50e5501c1dec825068734}} presented an edge-aware (EAR) approach, which first resamples points away from edges with reference to given normal information, then progressively upsamples points to approach the edge singularities. However, the performance of EAR heavily depends on the given normal information and parameter tuning. By introducing the concept of deep point, Wu et al. {{cite:7e37df6bc14871898194bcc4acc02bebbf3ab38d}} proposed a method to jointly perform point cloud completion and consolidation under the guidance of extracted Meso-skeletons. The method can successfully recover regions with holes; however, it is sensitive to noise and outliers. Dinesh et al. {{cite:ea58a466a7f24232dfd08a463983b1767d531b4f}} proposed a graph signal optimization method, which minimizes the total variation of estimated normals by partitioning the point clouds into two disjoint sets and optimizes the corresponding coordinates by the alternating method of multipliers iteratively.
| m | 5070304042b0595b1b5dbaddcb9e1214 |
To address these shortcomings, we focus on finding ways of making networks fail using natural, interpretable features.
Several prior approaches have been used for this, each with drawbacks.
One is to analyze examples in a test set that a DNN mishandles (e.g. {{cite:cd143bd832362decc48a7468c8513bf0e4f77621}}, {{cite:f5c2e47cab073a471c6b6f8883c8d2382f0e3d2d}}, {{cite:5dcb58888e91f7c02e6b738e24f758c9fca92996}}), but this limits the search for weaknesses to a fixed dataset and is not useful for studying novel combinations of features.
Another approach is to search for failures over an easily-describable set of perturbations (e.g. {{cite:b2584b2457442dfb0aa22c75bc049277ac56e045}}, {{cite:28f2b660a6c732b96766651be837fc51e879deba}}), but this requires performing an untargeted search over a restricted set of changes.
Finally, one can use more open-ended interpretability tools to gain insights about how networks (mis)handle features and then use them to construct adversarial examples.
However, prior approaches for this (e.g. {{cite:c90205b7df9b3589c9492c6879bfd7afe8aa7f66}}, {{cite:b2c9b3677f1f588ffc4716481121dd207df66d19}}, {{cite:5d63549baffbde4594ab15ba3fe67e37ecb980b5}}, {{cite:f7bbb96854c9bf8c5741947fc70eebf3c61bf489}}) have been limited to proofs of concept that have relied on a human to manually construct adversaries.
| i | fcda9891c92d2c1de319c97a82fd810c |
We train a (pre-trained) ResNet-50 {{cite:ae15f5451d22cf3a767aed405392ce78d3e1e8a3}} model on the emphysema labels of the ChestXray14 dataset {{cite:be0cf0bdc88058eef629f3961f9c8dd0becd070b}}. Our dataset consists of 38,353 training (854 positive), 4,625 validation (88 positive) and 21,176 test (436 positive) samples. This dataset consists of frontal CXRs with unique patients in each split. The parameters that were used to train this model are described in our previous work {{cite:b4a5aa6edb9d42f97906c0049d653b52eeb51142}}.
| m | 1d16d48358156b174b906e2357f7b79a |
The term {{formula:1b3cca38-380f-409b-a732-77efe7b72079}} is an external current which determines
intrinsic firing rate of uncoupled neurons
{{cite:b28d44658ac1cf57eb31330adb40fb3c0edb3bb6}}, {{cite:d3ca7cbf7ad41cc650bb828ac3fe78f9c8721f6a}}. The values of {{formula:fd0068ef-3d82-4612-a718-674b373c89d1}} are chosen
randomly from the range {{formula:ad9edc87-31df-4c74-a131-9d5a49848ab4}} . This choice leads to
alpha-band intrinsic firing frequencies with a mean firing rate
around 9 Hz. Alpha rhythms are typically observed during
learning and task performance
{{cite:862de7b158f9a8b0e268371536672d066100299c}}, {{cite:5d1f662b75de1fab317f80315f816e7bf2d7e228}}, {{cite:c3b354cfcd742c50df905b96cffa0249661538cb}}, {{cite:411dbf6920ff77aca5649288b5b14e2809d91d9b}}. The term
{{formula:a573e3c6-9cd2-4dc5-a01b-0f0695f140ba}} represents the chemical synaptic current that goes
into each post-synaptic neuron {{formula:bd766657-ef9c-4f95-93d7-d0810c986cc3}} {{cite:7e8b9af9f0a7629c5bb351379b292758aa4f9e05}}:
{{formula:5b37c403-a5a0-42e8-85d4-e5f6bfef538a}}
| m | 90a57ce61d47996b6b7c25505db483cb |
Thus, in view of these results, we consider that the expected fate of the
turbulent clump is really affected by the wind-clump interaction, as compared with the
purely gravity driven collapse, despite that it seems to be the dominant
physics in determining the time evolution of the clump. This behavior appears to be the case in
general, at least for observed gas structures around 0.1 pc in size, as
is discussed in Ref.{{cite:624a4655c94f149d596d196f86a035816b7d6c54}}.
{{figure:e66eac31-7fc7-4276-9416-cd4b457b7958}} | d | 6f76c39819636dbbab233e7710589c02 |
We run simulations for the 40 innermost stars for which their orbital parameters are known, using the data of {{cite:7de3909ea806df804571228335d9e03c09d9b698}}, {{cite:db3ead6d597714ba65e32c1979bf3fd41e7c318f}} as initial conditions. We carry out our simulations by means of ARGdfcode ({{cite:40617497d1cca315d056037b06bb7627355ae315}}) which is a modified version of AR-CHAIN ({{cite:7dd89dcaf33c8dfbd42a2df1d4a1f02da96869c3}}, {{cite:d46c19921a864eb86b79dd58614d5a9977ffc6a0}}), a fully regularized {{formula:869e403d-be4e-4015-a5c9-ff4c07832640}} -body code with post-Newtonian corrections up to order 2.5, enabled to use analytical external potentials and their dynamical friction.
The semi-major axis of the S-stars lies in the range of {{formula:3aace792-13e3-4597-94ab-651737506d3f}} 0.005-0.05 pc and they approach very close to the Sgr A* where the relativistic terms could be important. For this reason, we made our simulations taking into account the post-Newtonian corrections of equation of motion up to order 2.5.
| m | a59b63327a441e2ec61968e93ec1b188 |
The second stage is depth regression. We use a stacked hourglass network {{cite:d3d4f2e2dd215b020b928e8e14396087130d6e3c}} with dense connections for regressing depth. Our stacked hourglass network consists of 3 cascaded encoder-decoder structures. It has the advantage of refining depth maps stage by stage when compared with mostly used single encoder-decoder of FCN-like structure in other depth completion works {{cite:65586743be6b235515344f79bc53059a14f86e24}} {{cite:1a4ba14cb6c5fd0f866656b92c66d40cdaf7c364}} {{cite:7baad4c0fadde67c814a3e4c50f3dc27b29adeb1}} {{cite:abac947ac77d5e303ab2f336d3bb5c3b32fb0071}}. The stacked hourglass produces 3 stage outputs ({{formula:fbbc1a4b-14f7-4e52-a8a6-7751a8a82b1d}} , {{formula:df788c45-4803-47bd-bfc0-a625b784d0ca}} , and {{formula:0d5f0b4f-76f6-4627-8cce-d89a6a4dd156}} ). We further use skip connection and densely connect each corresponding layer of these hourglasses and feed the regressed depth to every subsequent stage to enhance information flow. Finer depth is regressed at later stages. At inference time, {{formula:dcdcaf8c-fab9-4012-8945-cd93a50c4cf6}} is the final depth output. ReLU {{cite:3d6462a9ed22e8903feb70387713ab7a42ce995d}} and batch normalization {{cite:66217873be2fc254eaba92411e35673fb8e12648}} are adopted after each convolution in stacked hourglass and APC.
| m | 2f949e7e0fc01d6d5a6891c7a945f039 |
At finite temperature, we can test the prediction of both the discrete and continuum theory that the presence of curvature lowers the effective critical temperature at which the staggered magnetization undergoes a continuous phase transition. Because our cylinders are finite, such transitions will always be rounded due to finite size effects {{cite:eed3e663805033f95c77b18b7e8a20c8daaccff8}}, {{cite:4d1d705b4aefc1d743cac27ebf0fd14282156741}}, {{cite:7ca2885f78034341137449dae333d274a1b6167e}}.
| r | d790c416b89f60b72168482c831e1b63 |
In order to overcome the numerical difficulty of the penalty function method
near the optimal point {{formula:8891ffb0-4960-435b-a013-ce9791d7b7df}} of the constrained optimization problem
(REF ), there are some promising methods such as the dynamical methods {{cite:614930b0c6406bbbd3ec9275828a5aa03339de5d}}, {{cite:d4ba08911f85a5b5dfdb376c1bec6e948e7313cb}}, {{cite:3f1e2a7da33901328511fd07ba8ea63aab7e45aa}}, {{cite:5f16db27aa6f42e69ad08d8cb520228805164fb9}}, {{cite:6b5554eab98841e0fd74842e281f0909264036d6}} or the SQP methods
{{cite:81fe3e36ccfb097d1346de5622ff7f5272d21f4f}}, {{cite:acc0858fa0d332f88a521bcdfe8b134d1bbb291e}}, {{cite:a47eab58087e815184439f029e52ff2074f32514}} for this problem via handling its first-order
Karush-Kuhn-Tucker conditions directly. The advantage of the dynamical method over
the SQP method is that the dynamical method is capable of finding many local optimal
points of non-convex optimization problems by tracking the trajectories, and it is
even possible to find the global optimal solution {{cite:43d5c1aed2355429892896faf28dd5c239793ad6}}, {{cite:320aa90f81691a5da068f496e155fd7d5f738e9b}}, {{cite:7066283bd30952c630223bc7e7bd42d690653cf2}}.
However, the dynamical method requires more iteration steps and consumes more time
than SQP. In order to improve the computational efficiency of the dynamical method,
we consider a continuation method with the new time-stepping scheme based on the
trust-region technique in this article.
| i | afdee60bb3c70f7cd1f632caada4389a |
An immediate question is whether the equivalence persists in an interacting theory.
We could try to couple the spinning particle to an external electromagnetic field
and see if we recover the Bargmann-Michel-Telegdi (BMT) equation {{cite:0526d445cfa3c8d239fa329c1a3c2ebd92662ed9}},
or try to couple it to an external gravitational field
and see if we recover the Mathisson–Papapetrou–Dixon (MPD) equation {{cite:835bed7199434e864b7354c6130bb20c60c21795}}, {{cite:efcf2d1f3f0f396b1e7be0264d804dbc1b4741e2}}, {{cite:4c38c5ef1322048dcbe94bfb66d2f75045766b1b}}.
Coupling to an external field may not be a straightforward exercise
as it requires generalizing the spin-gauge constraints in a way
consistent with the U(1) gauge invariance of electromagnetism
or the general covariance of gravity.
| d | 4898be676cb747ddfdf47838a4e20524 |
Finally, we would like to mention an interesting methodological connection between our analysis and the
analysis of statistical discrimination problem performed in {{cite:503eb20ef8aa1d221f2a866c7a0405b713e9ca55}} (see also {{cite:33158d6cbc51dcd92f5e476c7a0cacb235d486ed}}). In particular, we need similar results form the theory of empirical processes and the condition (REF ) formally resembles the so called “margin”
condition often encountered in the literature on discrimination analysis.
| d | baa5fdc56e54c2bf259afaa8d3f0d4b5 |
There are a lot of observations data which signal us to an
accelerating expanding universe
{{cite:315581436e4c18516f995790bef2b9aa5a36de7d}}, {{cite:8af9fe0c172d7b98163328275368b2117f288ef3}}, {{cite:c5ac4c18e37eeb01a3c696b9da1ba4a4093d4c68}}. In order to describe
this current phase of the universe expansion, we need a strange
source of energy which is called dark energy and allocates
approximately {{formula:a1329d22-bf61-4c8d-be2e-4a58e9265484}} of the cosmos tissue to itself. WMAP
observations also indicates that the pressure ({{formula:5cb39d8d-082b-407e-974f-962ec1ab3a43}} ) and energy
density ({{formula:f810392c-0cb9-4704-a7ab-f716e89aac5f}} ) of dark energy are bounded to
{{formula:925b67b1-61c7-478e-ba3d-5f0f2692bac6}} , a result addressing a phantom type dark
energy {{cite:c5ac4c18e37eeb01a3c696b9da1ba4a4093d4c68}}. Therefore, in addition to the initial Big
Bang singularity, another singularity called Big Rip, can be
achieved by cosmos {{cite:d54e28f086140eb69ff2b88384ced5aae5c6bed1}}, {{cite:5c67429932089f8bbe5c878e4909549f9ee604ff}}, . It was argued that a cyclic universe may avoid these
singularities {{cite:fe1bbfc3bc1708af5280e339446d05c00a21d3fd}}, {{cite:1e7ae3d6921aee8ac9258f424ff6835cce3d859c}}.
| i | 2f7bd98c35c72535bd827846643abb5b |
Proposition 2 (Maximum acyclic induced subgraph (MAIS) bound, {{cite:f214bebde1a55f78f133788b5829813bf9e0272b}})
Consider a non-secure index coding problem {{formula:f37d975a-4319-4458-9d3b-f6e927ce6a5d}} .
The (non-secure) symmetric capacity {{formula:be0a4d5f-f0d8-46c1-bde9-5e41516a57de}} is upper bounded by the MAIS upper bound {{formula:00ff730f-bce3-4548-935b-5ed27535113b}} , which is defined as the reciprocal of the cardinality of the largest acyclic set {{formula:0b3e78d9-7e3d-4bbe-956a-2e8019316fb3}} .
That is,
{{formula:5bcb53f3-fd92-4b46-9824-3e212adfe445}}
| r | 41904ba189a2e6db5e43ed9c53f093eb |
Receipt Understanding Receipt understanding requires the model to recognize a list of text lines with bounding boxes. The performance of this task is evaluated on SROIE {{cite:0c796adc42cd2b27fa43c06b4413b1a56d7aa6cd}} and CORD {{cite:14e9eeb1116e89a32bf052dcf9b4ea17bfce2dac}} datasets. Like FUNSD, we use officially-provided OCR annotations and bounding boxes for fine-tuning and feed the output representations of GraphDoc to the classifier. The model is finetuned for 50 epochs with a batch size of 4 and a learning rate of {{formula:d509ce76-af04-40b1-93e6-0605b4675f53}} . The evaluation metric is the entity-level F1 score. Table REF shows the model accuracy on both SROIE and CORD datasets. Our model achieves the new state-of-the-art results on the SROIE dataset in the existing works of literature. We also achieve second place in the public leader board in Task-3 on SROIE just by single mdoel https://rrc.cvc.uab.es/?ch=13com=evaluationtask=3. Although UniDoc outperforms GraphDoc on the CORD, the parameters of UniDoc are larger than ours.
| m | dc00142345b8023bd5d5682a6b0058af |
Since the first version of GAN was introduced by Goodfellow et al. {{cite:7d102dc201fc90243f7c2e72902e0a677f367c4d}}, variants of GAN have been proposed to tackle different types of image transformation and super-resolution problems {{cite:733f2dcaa7839e16d05b6668b8486397952f14f4}}, {{cite:f2860e4a21757e3db8c92514b3a2450ce58a666d}}, {{cite:4771e708b2d87e3b787a130a86dbc826d59cd6d5}}, {{cite:bb15dbf86c8e2335ba95cbab77964ff726ab7c6b}}. The architecture of GAN is designed to be different from the traditional architecture of multilayer perceptron (MLP) or CNN-based models. In GAN, two adversarial networks, i.e. the generator ({{formula:325d87e9-364d-4c68-83d9-c64657e8161c}} ) and the discriminator ({{formula:1ccaa78e-5771-4e03-82dd-3edb95ef9243}} ), compete with each other. Here, {{formula:b588553e-eb6e-4bf8-a0fa-fb02fe39d2d4}} generates fake images similar to the real ones, whereas {{formula:68d9a9a5-9b2f-406b-9812-a75de229d915}} distinguishes the fake images from the real ones. {{formula:5bbb0602-5a10-4659-b2e3-5499c22868d2}} and {{formula:98d98626-3304-4cd5-b932-9543d4964180}} are usually MLPs or CNNs that are trained simultaneously. The goal of the training process is to make {{formula:25bf3af8-e4e7-4883-b7f6-44879aaeda9c}} generate fake images that are difficult to distinguish using {{formula:af472a8a-4313-4dd6-bb97-74461a522a94}} . This process can be expressed as a min-max two-player game with a value function {{formula:53c1a411-6fcc-44fb-83d1-ac861509e86e}} such that:
{{formula:a907e025-91e1-4ef2-8a70-ea891f9eafca}}
| m | f4e856dcfa4d6a1d05762c86133dc994 |
In this section we present the theoretical predictions for the {{formula:687c173b-bb9a-4149-92ba-10b9eeceff04}} -mesons total decay widths, together with their lifetime ratios. All the input used in our analysis are listed in Appendix .
Note that, we consider two scenarios A and B, defined
explicitly in the previous section, depending on which input
we use for the parameters {{formula:bd616c70-1445-4480-b874-2f6c120f2a69}} and {{formula:fe0ba5b0-de67-40a7-8e23-af0c9f6da9bb}} .
To be consistent with the results of both fits by
Refs. {{cite:514de14f8a142af6c57fbc211899bf3480d70acc}} and {{cite:0b30ca2639c07ba8955a72a71febbd517ae652b3}},
by default, in our numerical analysis the mass of the {{formula:9d17ae41-8731-4956-8bfe-118977417c17}} -quark is expressed in the kinetic scheme {{cite:53f27cd2d9c7fd0ea9a9abfdeb8de3d5ca9eb084}}, {{cite:d4f35b22c9ab8ea05a489eb5ad2f64b8bbee5212}} fixing the cut-off scale {{formula:983d9175-f9aa-473d-a75f-4c1dff91a313}} GeV, while we adopt the {{formula:e8adfb22-f856-419c-b0fb-fd65abcaedd1}} scheme for the charm quark mass {{cite:7fe265fd4f9ee451c7b875c4b419270cf9d0ef59}}, i.e.
{{formula:fcf72806-3195-48f2-919f-b58fc3dda2ab}}
{{formula:b2f5f1ff-74e9-435a-9983-07c975e5be8b}}
| r | 4bbeaddd56dfaa37bef0d3b89ee983da |
In Fig. REF , we compare the proposed MIMO-NOMA based adaptive power allocation scheme with four baseline schemes, namely the equal power allocation scheme and the fixed power allocation scheme in {{cite:a630e72dae01fa16367a104a7264f9acc3288f12}}, the best channel condition (BCC) power allocation scheme in {{cite:fcb27051264d78b00c6d89f1646b5688dd2e6523}}, and the MIMO-OMA based adaptive power allocation scheme in {{cite:b19bfdf017e4a5162aae1b36d72edafc01d76a4e}}. Note that the fixed power allocation scheme distributes {{formula:c53ec82e-2fbb-4cef-b362-25ecb8d2baeb}} to the {{formula:5454e740-11a0-4c74-b0e4-7289d2b330b0}} -th user in {{formula:3695215a-433a-4543-8df6-412884169293}} -th cluster to due with the SIC.
In the BCC power allocation scheme, except for the user with the best channel condition, the achievable transmission rates for all the other users in the same cluster are set to satisfy the minimum QoS requirement. Here, we let {{formula:cf210611-9cc8-42ec-af5e-d4245d2cee72}} bit/s/Hz.
From this figure, we can find that the proposed adaptive power control scheme has the best performance. This is because the adaptive power control scheme can adjust the power allocation scheme based on the channel conditions and system parameters. As the SNR increases, the equal power control scheme, the BCC power allocation scheme, and the proposed scheme almost have the same performance, however, the fixed allocation scheme has a clear performance decreasing. It is due to the equal power control scheme and the BCC power allocation scheme force the user with the largest channel gain to achieve the relatively high power compared to the proposed scheme, which can improve the spectral efficiency. However, both the equal power control scheme and the BCC power allocation scheme can not guarantee users' fairness well, which is shown in Fig. REF . The fixed power allocation scheme has a worse performance than the equal power allocation scheme, since the fixed allocation scheme allocates more power to the user with a weak channel gain, resulting in a lower power utilization efficiency. Hence, it makes sense to select a proper non-orthogonal power optimization scheme according to the service characteristics in MIMO-NOMA systems. Moreover, it is also intuitively that MIMO-NOMA can significantly outperform MIMO-OMA under reasonably power allocation schemes.
{{figure:df72a36a-b7d6-4096-ae60-85e2ed4ce8fe}} | r | 787cbf4120b9c6dc13094a96ac5de1ea |
General relativity has been highly successful in describing both, the weak field regime (solar system) and the strong field regime
(Black-hole, Neutron stars) {{cite:ed7f6cf7acebdeb212c52bc27694694d3c4e17c5}}. However, quantum theory of gravity based on the Einstein-Hilbert action and
quantum mechanics is not renormalizable {{cite:89921a8e770ba924e8d4183b5b822cc7f712b2f7}}. In the recent past, the study of quantum field theory aspects of general relativity and Supergravity has led to a few interesting results.
| i | ae6d9b5a744adf82eb94b147aabdc39e |
Exactly solvable models {{cite:0d20023005d99d4bb08428184af3962d8d37c181}}, {{cite:86d90f16c9115af97183fe86e1e3fb76a05b7a3f}}, {{cite:58f6afb7359236478432f871561c35f46e2d102a}} play an important role in statistical mechanics, providing us with the possibility to obtain analytical and mathematically rigorous results that are scarce when the physical systems are interacting. One of the first examples of exactly solvable models is the Onsager's solution to the two-dimensional classical Ising model {{cite:d7da32935b9b5f672e84f5fcc1374b1d9d83b285}} in 1944. Onsager used the Onsager algebra to obtain the partition function of the two-dimensional classical Ising model in the absence of the magnetic field. Since then, the Onsager algebra has become a useful tool to study many classical statistical mechanical and quantum lattice models, such as the chiral Potts model {{cite:6ee71a94b272b22b02bd630dd7238e097a0bcff2}}, {{cite:61498bfac2d92090743eb3916cc64b5b28e1bf45}} and the {{formula:4805e37c-e688-4746-97a9-5fe7899e90ac}} -symmetric spin chain {{cite:b241da714838a7614d3b4239f3eeb02392aaecad}}, {{cite:f459f14433eceed3de1863fef7ef193586469d49}}. In addition, the Onsager algebra is closely related to quantum integrability {{cite:8af9c240063229e1166055329719999b5d2bae61}} and Kramers–Wannier duality {{cite:67f8276b6bc6e57882a0eacc60c940b06a776c87}}, {{cite:748702840aba32ac5aa7e28d33893789bc321ae7}}, {{cite:8df49a91e3114d6b74ef426be8d44d675dfb32ea}}, offering many facets on understanding exactly solvable models to us. More recently, the Onsager algebra has been conjectured to be present in a series of quantum integrable systems at root of unity values of anisotropy {{cite:fa66c07316bb4702fd975ae755fb086781fb47c8}}, {{cite:d3d49487903deaa9c9ce9adf38445447d77ebcc2}}, {{cite:f4654f08f255b3de4952569f70839e36b0c00b5c}}, e.g. the spin-1/2 quantum XXZ model at root of unity with quasi-periodic boundary conditions For certain roots of unity, e.g. {{formula:c6842776-b5d7-4798-9a91-d9dd2d7b112c}} for spin 1/2 or {{formula:b3fb8426-3c00-44b1-baf3-042be68ca804}} for spin 1, the Onsager algebra can be found explicitly for the spin-1/2 XXZ model or the spin-1 Zamolodchikov–Fateev model {{cite:fa66c07316bb4702fd975ae755fb086781fb47c8}}, where the Onsager generators consist of local operators. When we are at other roots of unity, the Onsager generators are expected to have quasi-local density{{cite:d3d49487903deaa9c9ce9adf38445447d77ebcc2}}., hinting at an intriguing relation to the representation theory of quantum groups. The Onsager algebra is also closely related to quantum many-body scars {{cite:b82536e2e21f794357cd504d5d517eb963ba4114}}, a subset of the eigenstates of non-integrable quantum systems that have non-trivial out-of-equilibrium behaviour. The Onsager algebra can be used to solve the dynamics of interacting quantum systems {{cite:d3040d597c950757ca9a35a7b87e41e3ef77c739}} as well.
| i | a073a9eb6ce773a2d18c853a01193f6e |
Ref. {{cite:39266ff8e04890e0b636cbfe49801129c755e440}} treated doubly heavy baryons very carefully. They start from the heavy quark symmetric Hamiltonian in the limit of {{formula:9d797c94-a4f2-4339-8b6c-a83a673f88f3}} with {{formula:d51f43e6-5bbc-4fad-a5fb-2d59d625099f}} heavy diquark mass, and then, include {{formula:e71de381-e795-499c-b93c-328fede414ec}} corrections to improve the results. This operation causes mixing between heavy quark symmetric states. For instance, they explicitly showed mixing between {{formula:84f00cc0-ddc0-4190-b134-311c8b76df4e}} with {{formula:14956aed-a235-417a-945a-4aec9c39cbe5}} or {{formula:4ae89068-959f-42af-a44a-01b4a3c53165}} mix with the {{formula:bf82f953-a827-442b-a127-63a942ef0170}} with {{formula:524127cd-f7a8-4d6a-b54c-e357d6b75b7e}} or {{formula:e4b244bc-1070-43c1-a053-cb9d8ad48d0f}} , which is nothing but breaking of the HQS. This is a different problem we have considered in this article. They did not consider the case that the heavy quark symmetric states consist of nonrelativistic states with definite {{formula:54e55f52-a7d5-4888-97b5-633b19606f20}} and/or {{formula:50a30511-a563-422d-8a8e-7dbd02c3b920}} quantum numbers, and hence did not derive the realtions we obtained in Eqs. (REF , ).
| d | d99ca86b69d8d07aad6ef1526ce24044 |
Most of these methods are run on a single Nvidia A100 GPU, but some were not open-sourced at the time of this publication. In particular, TerViT {{cite:f8e44af1b31f09be586d332055845e658d33217c}} and LSQ {{cite:51d7ebb47ade2c9c51653409c5332169e1764ce0}} are estimated using LSQ's open-source ResNet-50 QAT scheme, and Mr.BiQ's runtime is reported on a Nvidia V100. There was no reported runtime for PSAQ-ViT-V2, so we estimate it to be 60 minutes based on PSAQ-ViT and our best guess at the runtime of the additional steps.
{{figure:0730bdbd-6ddc-4c47-bd94-d3ffbaba5824}} | m | b158770ba25f0a932726c2e86f699d1d |
To put this goal in context, in recent energy models for high-dimensional data {{cite:63ffba0343abab194c649366da9d809d1001c42a}}, {{cite:792d5747d7bae28b25e380e742187ecae110d0d9}}, {{cite:c6df02e305e277b4e9f6667c8fdf9f0eb9d6ad82}}, {{cite:46f64268af248480c6442d8f16d3b86c4e4ca116}}, {{cite:73ae901738b07a4c17c2f1ba81d1d09baf9fdd79}}, {{cite:5b57b52d388e7b7bba7e28d38f0543537c031290}}, {{cite:5d50f37a9734435dfac2cc838738ce0c6f6c5027}}, sampling using MCMC quickly breaks or collapses to a mode and chains longer than a few hundred steps were not reported. Thus, evaluation in prior work relies on samples from independent MCMC chains, where in addition there are heuristics like replay buffer {{cite:46f64268af248480c6442d8f16d3b86c4e4ca116}}, not supported by theory. In this work, we report FID scores obtained by single MCMC chains, the first result of its kind, which we consider as a benchmark for future works on long run MCMC chains.
| r | c92353d4be62bbc5d5f9dffb67f421ab |
Modern analysis of PDFs requires calculations of the
log-likelihood functions from thousands of experimental data points, and
scans of multi-dimensional parameter space with tens of degrees of freedom.
There are several groups providing regular updates of PDFs via global fits,
see Refs. {{cite:edef98751068d10ca840482679f97fa3cc256765}}, {{cite:441d0cf4d6deadbee1f8c8c8ed0191ee838a4cf8}}, {{cite:9f636b0629b9d83d737dd0a3ebaa377cc301811d}}, {{cite:f24c3941247dcced99e89eab556e60f5e4441551}}, {{cite:748bbb24392ef514b1bc002ce8f71f81ec82e1f2}}, {{cite:fef21cea42bfc81ba9a39993006dcd4d2f335d48}}, {{cite:b3fdfe069c80f0ecf803aaff91b90ae3bc0012de}}, {{cite:ec4d7be790e0db3a5ed9834a1154c4311a89f3b8}}
for recent results on PDF determinations.
The difference between those PDF sets is mainly due to the choice of the experimental data sets,
the theoretical calculations used, and the parametrization form of PDFs.
| i | 66af0574063b522ad1cfdaec400454b8 |
This work represents a step toward relating the properties of {{formula:38671084-9c8d-469e-8c17-d4d8c9ac2c31}} and {{formula:0669c152-14a8-423e-9e0e-a4339c44c90b}} to
those of {{formula:e68f1076-c96c-482e-8608-6a9dbdbf6db7}} and the associated acceptance couplings. As noted above, Markovian couplings
which are efficient in the sense of {{cite:78ef8c5950cca4c860d2455692beee9e0859bb8b}} are well understood in
only a few special cases. Beyond that, only a few additional bounds exist on the efficiency of
Markovian couplings {{cite:8872123222764695d84d986e30639efc2c62aa76}}. These questions remain largely open for MH-like
chains. A clear understanding of the set of Markovian couplings will make it possible to identify
better couplings for use in practice and settle the question of how efficient couplings can be for
this important case.
| d | 4ee2779407b5c49b59acb38edde57119 |
Figure REF a shows the AID of the different models and the analytical method of {{cite:1ffed0cfb5def904fa68d7d982391256e49d1e6d}} as a function of sample size, for one data generating distribution. Analytical estimates for some of the required parameters for calculating {{formula:072d45e2-f7ee-4673-aea4-3c87142b4ac5}} were not provided in the original paper, but we derive them in the Supplementary Material. While the analytical method and the linear CEVAE with a 1D latent variable perform better than the full CEVAE, all of them seem to converge towards the correct {{formula:bd622d84-7d8e-47d5-9732-f3bc226ab1b1}} distribution. We show in the Supplementary Material that the result is robust, as the estimates converge to the correct distribution for other data-generating parameters. Thus, overparameterizing the conditional distributions with NNs or using a larger than required latent variable dimension doesn't necessarily break the estimation of the causal effect.
{{figure:f3f6aea5-37a5-41c9-814d-81900232f451}} | r | 4b2a8c4c051efce4e59aae30f9c56869 |
Stein's method is a theoretical tool to obtain bounds on the distance between two probability distributions {{cite:d473462547dfebffc6ec053e0d14d82af855518f}}. It was first introduced to study queueing system by {{cite:a8bd21cb4bd6dba0eb6f4ec04ca3829aa89c8f25}}. Steady-state diffusion approximations for Erlang-A and Erlang-C models were investigated by Stein's method in {{cite:efb3f76a3fce3520fe09e60047b6c3a861b6282f}}. For load balancing problems, Stein's method has been used in different asymptotic regimes including large-system regime {{cite:93aa98398401e36ba0735c7f60f6307544997771}}, many-server heavy-traffic regime {{cite:790df84d6d3aa2f17f361269bf49f28813d2b3fb}}, {{cite:328414824a99572ea993452efcdd4c945fa7763d}}. In the traditional heavy-traffic regime, using Stein's method, a single-server system was studied in the continuous-time setting {{cite:198751533c6247670eececf6ca526ab064adfa8e}}.
| i | ea3ac6de17b045a990ec21e5c0035862 |
The solution to the optimization problem (REF ) is approached by its transformation into a convex QCQP that is solved by standard methods {{cite:aa1c14797ab2265b51ad57c7ee8675453d7fdf02}}, {{cite:d88f03afd9bba449822a103027ebbaca1a3813a3}}. The details are shown in Appendix . The Pareto-optimal set of points given by solutions to the optimization problem for the given current supporting regions (a spherical shell, a cylindrical shell, and a box) are shown in Fig. REF , after applying normalization
n̰ = 2 Rc̰2 PL ,
| r | 74bcc8cbb3998286050b80a214f42125 |
A common theme in both of these pathologies is that the effect becomes more prominent as the width of the network increases. Yet, the phenomenon of double descent shows that it is in this over-parameterized regime where neural networks perform best {{cite:14d6599cfc366a15cae7ab1056e9a5ebafab3557}}. Therefore, it is critical to understand the properties of wide variational BNNs — which we prove are considerably different from the true posterior in the mean-field case — if they are to be adopted in practice.
| d | f0f5c202d04072d8119b62e18428c1fa |
Computer simulations of these systems remain computationally expensive due to slow dynamics as very different length and time scales
are involved for the various species and as the number of microscopic species outweighs by orders of magnitude the number of colloidal particles. {{cite:1d8678a70ec12b0014faad332dd67366e6f27499}} Huge efforts have been devoted to speeding up equilibration in highly asymmetric mixtures by the implementation of (rejection-free) cluster moves, {{cite:968cd9eb1323cbbfe88be0f0efffbcb1a8556b7b}}, {{cite:74232ae82fbf1d0b53cfcfe4551e98515d6b8669}}, {{cite:1526de98a0c48290fff9c028f7e1b0ed2e64e887}}, {{cite:e7da62d3a9274545bae797aa63f3aa40e69ee0b2}}, {{cite:06bdedc3b000d5b0494882ef009160d9fc0efacc}}, {{cite:e038f24a29adfa019de726470cc11c3f8095dc57}} lattice discretization methods, {{cite:f69f0f59ecabfe52e0b93d6fb4260cb4896b6acd}}, {{cite:40f23e0b718a318820f178f5c276f9bbf91851ef}}, {{cite:07bb5ea3d4892b1b6d32fd946fb8b44f57b189f2}} or by exploiting a sophisticated field-theoretic description of the smaller species in the external field of a fixed colloid configuration within a density functional framework {{cite:686a8d200e3b4ed473dd789a80c5b9c5e264c68b}}, {{cite:80537118fde341363e5d5fd4e3541e0062ccbc60}} in the same spirit as the "ab initio" method of Car and
Parrinello for ion-electron systems. {{cite:bb39edb40473695f1215f1b23f58e75d0a76ee15}} However, all these approaches have their own limitations, and as a consequence higher densities, larger system sizes and larger size asymmetries are still unattainable, thereby leaving many intriguing experimental observations unexplained such as void formation, gas-liquid and gas-solid coexistence in like-charged colloidal suspensions, {{cite:958f00c2ee5c9f905e09d2571c3a8c6ca6d17df8}}, {{cite:7fa94cc5d8119757287eb271487edbac3036216c}}, {{cite:4981407ec3afd2176d0786138e30ef48b53d2908}}, {{cite:106a112d791e25d44b2adaeee67b690882c38a17}}, {{cite:f01f9cbe4fdf85fa04ef74777e4303890d67f724}} as well as hampering investigations of interesting phenomena like capillary wave fluctuations, long wavelength fluctuations of marginal colloidal liquids at their triple point, and density oscillations at the gas-liquid interface in colloid-polymer mixtures. {{cite:a6f43af9df69dae93e2b5d9ff44edf907a36e042}}, {{cite:883919d80e60ee4531013714ebc86e4d77c92168}}, {{cite:d2426d5afa0fed00256c479e68e074b1c6a6377d}}, {{cite:87320aeff71be9689a96b7510ea1883f2a48c298}}
{{figure:c21a7424-35b8-4df4-ba29-4f305b654608}} | i | 0e49b7b55d20373e14a8a49172863636 |
The contribution of our work is the proposal of the Stakeholder Influence Analysis (SIA) method. Its aim is to help firms to analyze an OSS ecosystem to identify its stakeholders' influence by the impact they have with respect to the requirements that get implemented in the OSS. We base SIA on social network analysis constructs {{cite:5828ac1cfe991db9a6fa05ef9373fdc4e2e13a63}}, {{cite:75562c1ac0aa586dd674d30064d2ed1e8ea0c7e2}}, {{cite:bcf31ffba3576ce5ed4e8bbb03d6ece9ce98f5aa}} that have proven to be useful in characterizing the influence of stakeholders {{cite:09690cbfbfb5c5e0be55b525dc117eb33887b73e}}, {{cite:9c3cfeea9148677992c4cd87f81c374f1e2f6c90}}, but also effective when analyzing a firm's participation in OSS ecosystems {{cite:9c3cfeea9148677992c4cd87f81c374f1e2f6c90}}, {{cite:cce559d5171958265995f5e658192d81dfb28fbc}} and requirement-centric stakeholder collaborations {{cite:db973f7463077e7e16e56cfd53383ef1f96d4d69}}, {{cite:a293ad8308df7147fafa9911b6ecaca4b659842f}}, {{cite:479750f6b994ccf9791e1a90ebd831bf82827542}}. An analysis approach used in an earlier reported case study of the Apache Hadoop OSS ecosystem {{cite:c5f35f47cce2167291f59ebf304a7ebcb4131f06}} is formalized to consider how requirements may be informally represented in multiple artifacts in decentralized repositories present in OSS ecosystems {{cite:f03b2c2b819d315d216a9acc43856a74d42ef256}}, {{cite:744291a0cb4346d7e1ceb1bb3f3a16653f4210af}}. The influence analysis is then operationalized with a stakeholder mapping approach based on earlier work {{cite:87a8a58fb1754a9909aacf597293987825aed529}}, {{cite:d6cdd0553c6143e48e8376beb96439beea72fe39}}, {{cite:bf32239fd116f47c364f8f58e1b749dd99d047d2}}. To demonstrate SIA's applicability and utility, we present a case study of the Apache Hadoop OSS ecosystem.
| i | ccbe3b0c6f388dbdff3ffc52dcbe3a8a |
For comparisons, we consider three realizations. First, we consider the standard DQN with one NN (target is a copy of the action network) and gradient driven updates, denoted as DQN. Second, we consider EDQL which is a NN (target is a copy of the action network) with error driven updates {{cite:0efefbd18197e7c9b5ced8cc5662bcc863996468}}. The training strategy for these approaches is identical to the one proposed in {{cite:0d8d0a9f54388af7bb15c2e8e6c982ab310d2559}}. Third, we consider the two network setup with standard gradient driven updates (G-coop). For G-coop, we follow Algorithm 1, however, we use the Gradient-driven Adam optimizer instead of the error driven update rule. Finally, we use the two network setup with error driven update and the coop strategy. As the two NNs are used to approximate function, from here on, we will refer to output of {{formula:f5c6b562-5ebd-4660-a9cc-56f7c5080b35}} as {{formula:18ca6e70-43b6-4e09-a46c-583266f3b2ea}} and {{formula:11b43e02-cf13-4edb-a584-74bb7dfb19c3}} as {{formula:7b925e53-1a16-4b20-9958-c74199af4207}}
| r | 28b6df5e0f09c1096f08f0e90659e6cb |
Regarding the superconducting qubit architectures, fixed-frequency architecture {{cite:450f9b9b4d201ec1e8ca391788f810ee936e5291}}, {{cite:ddd2947628ffe6ebb042fa88f28a5cb3ae2d2eb5}}, {{cite:471ff4d6d0a1e86364a53f6069fc29e3bb9e7c79}}, and the tunable architecture {{cite:e4be202135ab91b6ff34b1e4ab7ebdaab4bba175}}, {{cite:c5eace1e3aff65a553a7767d02dd7f134b70af6d}}, {{cite:96dbd5f0c66034565cd85123e03840f0764fa348}}, {{cite:6e57e574bf655cb55c5ad1ce1b230888e7bf9a66}}, {{cite:22892e2bdc91b04fdf8fe5cc5d919b4ca27a2e48}} are the two most common architectures used in the community. In the fixed-frequency architecture, all device parameters must be carefully set and fixed before fabrication to meet the design requirements and minimize unwanted interactions. It also accompanies unpredictable manufacturing errors, which is unfavorable to building large-scale high-fidelity quantum devices. The tunable architecture, however, employs tunable coupler to mediate and control the coupling between qubits. Hence, it is possible to tune the interactions between qubits to the desired value even after fabrication. Although this benefit comes at the cost of hardware overhead and flux noise associated with tunable qubits, its ability to dynamically tune the interactions make the tunable architecture favorable for building large-scale quantum system.
| i | fd3b890410326cfbac769caa459efae8 |
Notice that such separation between theoretical formulations and their practical embodiments is common for many classical problems in Bioinformatics. For example, computing edit distance is often replaced with computing edit distance under affine gap costs {{cite:a73ecff2183077947d058da6a811f358ee5cf09c}}, or enhanced with various heuristics as in the well-known BLAST aligner {{cite:1342db5c5c9f5602ba6d013958f5265ea2ef3577}}. Also text indexes such as the FM-index {{cite:0df26c3a15e458fa716c4b8ef8ccaf5b8166c8c2}} are extended in popular read mapping tools (e.g. {{cite:6e669b8bb31feca67322818d671a4bbd11dfdaac}}, {{cite:0d28065c8741966b353f255524ba2b9fa1927684}}) with many heuristics handling errors and mutations in the reads.
| r | 16b8137afb46e05d3b36d5325d3dfa8e |
The prox operator (REF ) can interpreted as a denoiser, in particular, the maximum a posteriori (MAP) estimator of {{formula:178ec392-aa11-4e51-af80-28d62d0475e8}} with prior {{formula:8e132a04-e0ff-49a3-b358-2d260a33d85d}} from an observation {{formula:cf5395e3-8128-4c13-b55c-113a1a3f3bfc}} with {{formula:3297c88a-112c-419e-abc1-2e8315ec908c}} -precision AWGN {{formula:9576f9c9-d050-4d72-a9ee-ae0140809582}} .
Leveraging this fact, Bouman et al. {{cite:ced46169a4bab04e41597ede7a186e758c3a2476}} proposed to replace ADMM line () with a call to a high-performance image denoiser {{formula:cbfac0f2-9bc1-4f24-a67a-5eabc5f12333}} like BM3D {{cite:9ceab4b3536da68cb407d11cf2f228510feb7425}}
or DnCNN {{cite:38525a51bb963e8e614921e8605c4791aa2c6c68}}, giving rise to “plug-and-play” (PnP) ADMM.
PnP extensions of other algorithms, such as primal-dual splitting (PDS) {{cite:e4e9284d67bd34616665653540a40efe2ef14e55}} and proximal gradient (PG) {{cite:349a12f8fcf39caed993a188eb7e2f735090a8ea}},
have also been proposed.
As shown in the recent overview paper, PnP methods have been shown to significantly outperform compressed-sensing-based approaches in MRI {{cite:1d8da4d0b91e5fbf5beaf0036cf8777fe88f8eb1}}.
Note, however, that when () is replaced with a denoising step of the form “{{formula:e53a644a-53a3-469e-b2a8-097553c6979f}} ,” the stepsize {{formula:9b8b14f7-eee1-4de1-9895-95e880357392}} does affect the fixed-point {{cite:1d8da4d0b91e5fbf5beaf0036cf8777fe88f8eb1}} and thus must be tuned.
| m | 833b28c7d72c11f221a8c95ea386ab44 |
We have addressed two very general questions regarding Fermi liquids: First, we have shown that LFL theory, which is often thought of as
being valid only at low temperatures, is fully consistent with Navier-Stokes hydrodynamics irrespective of the
temperature. We have shown this explicitly for the model interaction given by Eq. (REF ), which implies (REF ).
However, we have used Eq. (REF ) only twice: Once to eliminate the additional term on the right-hand-side
of Eq. (REF ), and once to ascertain that the model kinetic operator {{formula:10a0cda2-d7cb-4318-9596-d328215ae946}} is consistent with
particle number conservation. This, and the general structure of the theory, strongly suggests that an analogous analysis is
possible for a completely general QP interaction. Carrying out this program will lead to a qualitatively new effect, namely, a
component of the QP velocity in the orthogonal space {{formula:d76eaa2d-9913-48d1-859c-55537bae86aa}} . That is, physical particles and quasiparticles
will have the same density, but different currents. The resulting hydrodynamic theory will have a structure that is
different from that of a simple classical fluid and share some (but not all) aspects with a classical binary mixture. Among
the physical consequences will be a nonzero bulk viscosity, and an additional contribution to the sound attenuation.
Second, we have discussed the absence of a relation between the soft modes in the hydrodynamic and collision regimes,
respectively. With decreasing temperature the damping of the hydrodynamic modes increases and the hydrodynamic regime
shrinks until it disappears at {{formula:592df79f-90c3-4648-bda3-8443f8a0d1d1}} . At the same time, a completely unrelated family of soft modes emerges in the collisionless
regime. Their number is governed by the QP interaction rather than by conservation laws, their damping decreases with
decreasing temperature, and they are truly soft only at {{formula:12b7b52f-85cd-46f7-b92b-737302bb4184}} . Tables REF and REF summarizes the soft modes, as well as
the plasmon modes, in both regimes.
We have also discussed the special role played by the plasmon in a charged Fermi liquid, which is not a hydrodynamic mode
and extends through both the collisionless and the hydrodynamic regimes for reasons related to gauge invariance.{{cite:1e0250edf5e43aebfccbd8d6c35ec37abfe01c40}}
We have discussed 3-d systems where the plasmon is massive and its damping is independent of the wave number
in the homogeneous limit, see Eqs. (REF ) and (REF ). This changes in 2-d systems, where both the
plasmon frequency and the damping go to zero as {{formula:5eb68481-d2bd-452a-8100-17accd974857}} ; the former as {{formula:8e81f25b-37f7-4529-a5bf-0212cebfd38b}} and the latter as {{formula:c3690fff-3453-45e3-9409-ffb6c1e31708}} .{{cite:ccb44ab01dab4701414efb5a6010a89eaef00aa0}}
We also note that `Fermi liquid', in our context, can be interpreted rather broadly: We have not specified the temperature
dependence of the relaxation rate {{formula:002527df-a020-42b8-9443-3b41b838de5d}} , and we have not made use of the concept of `well-defined quasiparticles'.
For instance, our analysis of the hydrodynamic regime applies to what is known as a marginal Fermi liquid.{{cite:615e7c22fbf44f58eeaca1b240fd83745073cb7d}}
{{table:0285aefa-2f66-470d-9ee4-89284c54b3b7}}{{table:8ce8ae8b-3767-4c86-9920-1056bf4e7c62}}
The number of soft modes in the collisionless regime (or, strictly speaking, at {{formula:0a60349f-95cd-49d1-bba6-3ba31d56431a}} ), is to some extent a matter of
interpretation. In the {{formula:6a92bbeb-ec14-4716-9c1c-651bc3d4b88a}} -{{formula:bbf7e4b6-19a0-486c-8966-bf98828ecfc2}} momentum space, sometimes referred to as {{formula:4d091823-e560-449a-b4d4-7bc181a583da}} -space in kinetic theory,{{cite:77600906330abf88af056e91d3cce0a1552d9c8e}}
there is only one soft mode, viz., the fluctuation {{formula:0c5f36b1-7ebb-4114-a7a8-aca543773785}} of the single-particle distribution function, whose denominator
is given by {{formula:3c3a54a4-c7f1-4056-8245-b4f1ffd0810a}} , see Eq. (REF ). However, as a result of this denominator all of the
moments of {{formula:411be287-db96-45f9-a746-b5d5f7424d3d}} with respect to {{formula:e70ef8a3-4335-40fb-bb38-3e7a789934d8}} are soft, and in this sense there is an infinite number of soft modes. This
is true in a clean Fermi system; in the presence of quenched disorder on the zeroth moment with respect to {{formula:83aa6bab-c346-44c6-ac37-06977a319941}}
is soft, see Refs. Wegner1979, SchaeferWegner1980, Finkelstein1983, BelitzKirkpatrick1997,
BelitzEversKirkpatrick1998, for a review see Ref. BelitzKirkpatrick1994.
It should be emphasized that the spectrum of {{formula:1f9b728d-6aad-4266-9272-1a102cc30b95}} has a continuous part and, in general, {{formula:c43bf84c-b563-472b-bbdb-67f8897df46c}} -function contributions
describing zero-sound modes that are both part of the same spectrum (this supports the single-soft mode interpretation).
Our results are consistent with a quantum-field-theoretic analysis in Ref. BelitzKirkpatrick2012a, which kept only
the equivalent of the Landau parameter {{formula:77911a20-61d0-4c4f-8927-3ed7e870099a}} . It is interesting that kinetic theory, which uses quantum mechanics only
in the form of the equilibrium Fermi distribution, and the field theory are equivalent. Following Ref. Georgi2007,
we have referred to the continuous part of the spectrum as the unparticle excitation, whereas the zero-sound poles represent
particle-like excitations. We note that the unparticle part of the spectrum, while an exotic idea in a high-energy context, has been
known since the earliest days of the quantum theory of condensed matter, where it is usually referred to as the particle-hole
continuum. For instance, it gives the Lindhard function{{cite:ec2450099594eefe5617da53df5b058888219384}} its characteristic scale-invariant structure.
Neither the continuum nor the zero-sound poles are related to conservation laws, and all of them acquire a mass
at any nonzero temperature. Some remarks to the contrary related to zero sound in Ref. BelitzKirkpatrick2012a
were incorrect.
We have discussed only spinless Fermi liquids for simplicity's sake. It is well known how to incorporate spin in
LFL theory,{{cite:11d7c529c2288d67204c0a03f9ca4a6764d97262}}, {{cite:d47e74355eea8ff79846386ccd3cade6123f3086}} and the generalization in the current context is
straightforward. The spin channel again supports the unparticle continuum, and in addition spin-zero-sound modes
whose existence and number depends on the values of the Landau parameters.
The importance of the unparticle continuum is often downplayed in favor of the particle-like collective zero-sound
excitations. This ignores the fact that it has dramatic physical consequences. For instance, in the spin channel (which
we have not explicitly discussed) it is responsible for a nonanalytic wave-number dependence of the spin
susceptibility,{{cite:f02076de7f4e7346d81fd89ac9aa77f2269e1b22}} and for the ferromagnetic quantum phase transition to be generically
a first-order transition.{{cite:77a13a11078a64c821c40825c88d77b4cf38ddf1}}, {{cite:6f2a9888a34796a822fb0418e9021bc5858d973f}}
The origin and interpretation of the soft modes in the collisionless regime has been the subject of several studies.
The scale invariant unparticle continuum mode has been interpreted as the Goldstone mode of a spontaneously broken
rotational symmetry in Matsubara frequency space; roughly speaking, a broken symmetry between retarded and
advanced degrees of freedom.{{cite:ac34e7ca31177e196782cc803a6be07fbd2bdc65}} This is in analogy to Wegner's interpretation of the
diffusive soft mode in disordered Fermi systems known as the `diffuson'.{{cite:91fdbd4e38d5b000bbddacde37cc561f76beecc7}} Reference AlberteNicolis2020
has interpreted it as a Goldstone mode related to a spontaneously broken Lorentz boost invariance. The relation
between these two interpretations is not clear.
We have discussed clean fermion systems, but impurity scattering can easily be taken into account; see
Appendix for the relevant collision integral. It qualitatively changes the hydrodynamic modes:
fermion momentum is no longer conserved, and the density response is diffusive. In bulk metals the clean
hydrodynamic behavior we have discussed is very difficult to realize, since impurity scattering tends to
dominate even in the cleanest samples. In two-dimensional systems the ultraclean hydrodynamic
regime, where momentum is conserved, is easier to realize.{{cite:c5206b89ce045584f14c9451d125788b4db1b6d1}}, {{cite:ccb44ab01dab4701414efb5a6010a89eaef00aa0}}
Also, it recently has become possible to realize clean Fermi liquids in cold-atom systems.
{{cite:f471e99e76af4d218d3f371862e89c3f006ffcd6}}, {{cite:b7f25c0aafde4a49787d2f8e72c62e6864648590}}, {{cite:1d3151f4df63a21e72b8b5345c3250bc76173237}}, {{cite:2bd162dd3dfc095848a9b4f7730a688fa64ce4ef}}, {{cite:7a90291b6135a43b78c3d6d6dd7a4aae097aac12}}, {{cite:aa1d51b3a3083f00c5f4b0f9b12a3135c68e4e7c}}
We have discussed LFL theory at a level analogous to the linearized Navier-Stokes equations of classical
hydrodynamics. An interesting problem is the generalization of this treatment by adding a fluctuating Langevin
force. This will be analogous to the fluctuating hydrodynamics description of classical fluids{{cite:452d5f75c368d84784758da6b3459765020fdde0}}
and allow for the calculation of time-correlation functions in both equilibrium and non-equilibrium situations.
This problem will be treated in a separate paper.{{cite:32db3e41c9c0d991ec208abf462353d36f3a6244}}
| d | 41a1c4a2fd8b5f2e1ec7399d82372532 |
Figure REF shows the block diagram of the proposed DilatedSegNet along with its core components. It follows an encoder-decoder scheme much like the U-Net {{cite:1737650da40f7362fa1f0ce63e19d4596d739fe1}}, consisting of a pre-trained ResNet50 {{cite:dfe4e829b31c985f05a27a1d235ac861d6593f33}} as an encoder. The input image {{formula:e2a3b530-785b-472c-ae81-50c2706ba11e}} with a resolution of [{{formula:47515cf6-918c-4d89-9361-f0b612cf39f3}} ] is fed to the pre-trained encoder from which we extracts four levels of features maps {{{formula:277f12b1-0639-44eb-b94a-952b729a6bc2}} } with varying resolution of [{{formula:59c534bf-7f0d-4b6a-9825-9b0693f84fdb}} ]. Each of these feature maps is then passed through a Dilated Convolution Pooling (DCP) block, where four parallel dilated convolutions with the rate {{formula:ba77e280-658c-43ba-ac64-debca687a3c4}} are applied to enhance the field of view. The output from all the DCP blocks is concatenated and passed to the first decoder block, where the feature map is upsampled and concatenated with a skip connection from the pre-trained encoder. Next, it is passed through some residual block and then a Convolutional Block Attention Module (CBAM) {{cite:f88defe75fb8146e13f61c446173c4bccedfd7a5}}. The output of the CBAM is passed to the next decoder for further transformation. Finally, the output from the last decoder block is passed to a {{formula:69eb58bf-205d-418f-b37c-69d879b750e0}} convolution followed by a sigmoid activation function.
| m | 0b1ef7b35f399696c5ae67cca8dd0d79 |
Theorem 19 ({{cite:38b43084a5cfbf2c4d190baa6bcd1047006cbbf9}}, Theorem 2)
Fix {{formula:02f5ae2b-c7a4-4a56-9f12-0cf79a75a91d}} , a query point {{formula:892c5baa-3cf6-4906-ab84-cb8faa7ccab2}} , and a set {{formula:c85e8e81-86be-4041-bbc5-b411d280b867}} . Let {{formula:fa82fd2a-704d-49f5-b8c2-c799b0ec1530}} . find-smallest-in-set returns {{formula:98c560f2-4778-4d3f-b479-154fd9e4928b}} with probability at least {{formula:a55b2b77-f5c3-4bc4-8286-4e32e1b9371e}} in at most
{{formula:a4ccb222-70ae-4a57-bbf9-1ce0618843aa}}
| r | 1607a2e6b70e65c04db9e4bcf1277283 |
We do four sets of experiments on the YTF dataset. In the first experiment, we follow the same protocol as in {{cite:b4805efd68f834731504a1438d26a381753d7595}}. Specifically, the feature vectors of the faces in the first 100 frames of a video are averaged. The similarity is calculated on the averaged feature vector between two videos. This is standard protocol but on a model trained with face quality weight. it is called QW in Table 1. The second experiment uses the QWFA on first 100 frames. In the third to fifth experiment, we use the QWFAF with filter threshold {{formula:8d56eba3-34d2-4fec-a342-8928abb9ea4e}} . on the first 100 frames. If the average quality {{formula:2176b01f-a2c3-423a-8249-4a66146fc19e}} then we weight the feature vectors of qualities {{formula:dbe596b8-04b9-41af-a881-babd4ba1eef9}} . If average quality {{formula:c7673f61-97a4-4f15-a9a6-2f6164edc8d4}} , then we take the averaged feature vectors same as in the first experiment.
| r | 17c0806a008b5916ccd8f3475f977daf |
Reduced Order Modelling (ROM) is a
well-established set of different numerical techniques whose objective is that
of retrieving a low-rank representation of parametric differential models, s.a. Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), describing a relevant majority of models in physics and engineering
{{cite:935742026e8bdb403fe96cb740f0e9e53f015d47}}, {{cite:e087a7f109cb67d01f2d3bab1717069aeb54478a}}. Lowering the computational cost
of numerical simulations is a fundamental aspect of both industrial and academic
research activities and therefore ROM techniques have always been, since their
introduction, an important part of the modelling process. In its most general
formulation, ROM deals with Initial Boundary Value Problems (IBVPs) in which a
PDE is parametrised by a finite set of {{formula:650628e0-4fcf-45ad-b3f7-8c854b335a57}} parameters. One such
example is the following scalar, linear, first-order in space IBVP with
non-parametric, steady Dirichlet's Boundary Conditions (BCs) and Initial
Condition (IC)
{{formula:10765a86-2623-4c9b-9bf9-26b63ebea7ea}}
| i | 597c24704c4fd6cbee42e36381daea2a |
Throughout the present study, we consider the following class of dynamical systems on networks {{cite:647355ffbcc53848049ac35aae2b5e494eead4d3}}, {{cite:3d8446b65f606b88d89b73199174624d84a84ae6}}:
{{formula:8ac41b0b-266d-4554-9485-1a832e84f2a2}}
| m | fe9423f211827ef8ce292d3b51f47ca2 |
Clean encoder. Instead of freezing the weights of the clean encoder during training, we also experiment with updating its weights to reflect the parameters of the robust encoder with momentum to ensure consistent representations in memory {{cite:4c0ff827e2d551f4ae9a049421bf51cd7ec04ad9}}. The results are presented in Table REF . This modified implementation that updates both networks at once clearly beats standard adversarial training in terms of robustness, and slightly in terms of clean accuracy. However our proposed framework beats both methods in terms of clean accuracy and robustness.
{{table:ad594b82-3238-47ea-b256-a071365b0989}} | d | 2fead78fdf040642654f16a3cac91894 |
For both ELR and DivideMix we use the same setup in the original papers. {{cite:b7b140ab4f6b31d0327a516ecbff5dad3e37d8dc}}, {{cite:fcc5fb3f9fc5fc3da9ed5506a4e438b3df29200e}}.
| m | fc3fbbe2b7d4c328cdb6d17d94702cf2 |
Figure REF shows the overall architecture of acoustic environment transfer. In order to extract two features: (1) environment features and (2) content features, the source audio files are translated to spectrograms.
Spectrogram is a 2D visual representation of frequencies of
a given signal with time, while the color represents the magnitude or amplitude (see FigureREF ).
Spectrograms contain rich information of the audio signal,
including the frequency, the time and the amplitude.
Therefore, it is often used as a visualization tool for representing audio signals such as music and speech.
Also, it is widely used
for audio classification{{cite:22083bbdb73b2fd9befd5aeed2d0c153828b48fb}}, {{cite:853fb24129c5d8c5ea17125e702ab80cca915456}} and style transfer{{cite:6b2fc91935d82b66e02989a5f63d283b14032e8f}}, {{cite:ee7a5b8c5d28002260e9d25c81ef1a0a1007c57b}}.
| m | e244031290f8093e8b10d4c29e041b50 |
In practice, there is a need to automatically and rigorously model across studies the common signal that can reliably be identified, while at the same time modeling study-specific variation.
A methodological tool for this task is Multi-Study Factor Analysis (MSFA), recently introduced in {{cite:939d08ff28c3beb1bae290115e35e07dfdb8b365}}. Inspired by models used in the social sciences, MSFA extends FA to the joint analysis of multiple studies,
separately estimating signal reproducibly shared across multiple studies
from study-specific components arising from artifactual and population-specific sources of variation. This dual goal clearly sets MSFA aside from
earlier applications of FA to gene expression studies, such as
{{cite:c28290ca63f50a286d6add1dbf4d62a0f31ccd14}}, {{cite:f66b3071215acdc93ed7ef43e3c96242c4206f73}}, {{cite:ee18562675ec91159dc31c916c890093dcfddd8b}}, or {{cite:614ac907bf7e2cb850fcff41186cc907db80f487}}.
| i | 4846189253c2ce802b912512620732ac |
Our general analysis should be simply generalized to the asymptotically AdS black holes in GDT by gluing a flat bath. Since after gluing the flat bath, the whole spacetime is similar to the asymptotically flat black hole and cut-off surface {{formula:d648d95a-004f-4c3c-9a0f-f39b274ccdc5}} can be chosen to be boundary of the AdS space.
In this work we only consider the classical solutions of GDT. It is also possible to include the quantum effect which comes from the conformal anomaly following for example {{cite:dd52751521fb55ab3cefc213ca113c03a2888b9c}}.
It is also possible to generalize our results to single-sided black hole and consider a truly evaporating black hole. Some examples are {{cite:dd52751521fb55ab3cefc213ca113c03a2888b9c}}, {{cite:b82a3c5fb53c6386a9e74d614a68c69463022bcc}}.
| d | 34ea42f3aef880248c0700da6235bb5c |
This connection was first made by Dayan, Hinton, Neal, and Zemel in their computational model of perceptual processing as a statistical inference engine known as the Helmholtz machine {{cite:3e3a59523d8bd0263e53bf5d3c3dde439c1aeef3}}. In this neural network architecture, there are feed-forward and feedback pathways, where the bottom-up pathway translates inputs from the bottom layer into hidden causes at the upper layer (the recognition model), and top-down activation translates simulated hidden causes into simulated inputs (the generative model). When considering log-likelihood in this setup as energy in analogy to statistical mechanics, learning becomes a relaxation process that can be described by the minimization of variational free energy. While it should be emphasized that variational free energy is not the same as Helmholtz free energy, the two free energy concepts can be formally related.
Importantly, variational free energy minimization is not only a hallmark of the Helmholtz machine, but of a more general family of inference algorithms, such as the popular expectation-maximization (EM) algorithm {{cite:64c526aa38899c6a2bf0e6bab04e6b03df2daf94}}, {{cite:55b35ec4457e004ec7a1c0fd47286f0db90ead7b}}. In fact, over the last two decades, variational Bayesian methods have become one of the foremost approximation schemes for tractable inference in the machine learning literature.
Moreover, a plethora of machine learning approaches use loss functions that have the shape of a free energy when optimizing performance under entropy regularization in order to boost generalization of learning models {{cite:a693a9f2d537ea188b3ef8f893821d8f8b4432e8}}, {{cite:0889b1e47b18779b53704ae52f0525e58421a527}}.
| i | b39de185c94554bd3a8bcb5dfc9fa22d |
where {{formula:52991ab8-3882-42c5-8d46-144e63e2f649}} is a {{formula:b72d081a-dee4-48fd-9f42-547d97f98462}} feature vector, {{formula:a1d7a6ab-6bfc-4e3d-9bbc-fee69511835e}} is the corresponding {{formula:a8051d7c-33c3-43f0-9d67-a559650c4357}} coefficient, {{formula:1deb934d-95c7-4e9f-b02f-102ad13d2f06}} is the continuous response and {{formula:2e009c57-1c42-4c36-8b2f-c7535dc2e00f}} is the idiosyncratic error. Bayesian methods for estimating {{formula:f5e2308e-3627-46a2-99ae-f475a841c6c6}} broadly employ two classes of prior distributions. The traditional approach is to develop a discrete mixture of prior
distributions {{cite:24a452058fa4bd98165897b516638a8b0f8fa857}}, {{cite:da09c54d97970368cbe373da2e31060a11c89138}}. These methods enjoy the advantage
of inducing exact sparsity for a subset of parameters (allowing some components of {{formula:57abbaf0-1c24-4f54-a277-bc09eb9ff9a2}} to be exactly zero a posteriori) and minimax rate of posterior contraction {{cite:0e9ed92400c4a39f529cf7503843e12b7487613d}} in high dimensional regression, but face computational challenges when the number of features is even moderately large. As an alternative to this approach, continuous shrinkage priors {{cite:506ad4cff67dfb8a03abef42cdf6f49316da605b}}, {{cite:36c77bd676f551692ccda7a2b07bf848f7b3dec8}}, {{cite:bc94d63450b983287f8ff04f30c463fdd4edfc82}} have emerged, which can mostly be expressed as global-local scale mixtures of Gaussians {{cite:f059d91918195417ad9af12751ab4ed7892f09c0}} given by,
{{formula:01077527-0e92-4c2b-a5eb-c1835bc42435}}
| i | 6a695151861f04bb4e3ddf6022662db7 |
Hexagonal (h)DyMnO{{formula:f1f4fdae-b4d9-4c46-9d26-b5f91df7191d}} , with the largest rare-earth ionic radius of this series, features an interesting magnetic phase diagram.{{cite:afa1a2b803f41147f076fa98f6f66df8df04bfa8}}, {{cite:d45d5a9735ffc349657a6e1bbe33d5ef660302b3}}, {{cite:8292c3575b818c3576adb81845796d51278dce37}} In the low-temperature phase (below {{formula:0d01f41e-3bbe-47fa-b173-f426a1812c58}} 8 K) both the Mn and Dy sublattices are magnetically ordered according to the {{formula:aa2c5659-6b55-433f-86ff-4afd7648f1ad}} irreducible representation. At a temperature of 8 K the Mn moments undergo a spin reorientation transition and are ordered in the {{formula:b5bfc0e7-59f5-483c-95fd-562495ebe5a7}} representation up to 68 K.{{cite:8292c3575b818c3576adb81845796d51278dce37}} X-ray resonant magnetic scattering measurements also find a weak Dy moment in this temperature range, ordered according to the {{formula:41c4c78b-c5b4-45d7-9d61-9ccb01524f92}} representation.{{cite:d45d5a9735ffc349657a6e1bbe33d5ef660302b3}} This incompatible order, with different irreducible representations present on the two sublattices, calls into question long standing assumptions about the rigidity of the 3{{formula:49788631-7156-45f5-8213-12671a35d3c6}} -4{{formula:b5d6c08a-5e7f-4840-9b99-56ca886d3166}} interaction in (h){{formula:3e1cba7f-63f0-4434-b523-f2c4b382851a}} MnO{{formula:771a980b-c6b6-40e9-89dc-ef5541697638}} materials.{{cite:8292c3575b818c3576adb81845796d51278dce37}} YMnO{{formula:1faa3362-a8c6-4345-a1ef-43869ec823ee}} features magnetism only on the Mn sublattice and is known to order in the {{formula:9b2a7d6a-05d2-40c0-9c9a-c507e27f8f19}} irreducible representation below {{formula:363263ce-7099-4402-9a22-42809be73de3}} {{formula:aeb66397-24c7-4aa9-8ba1-eba154d72d8f}} 75 K.{{cite:ceea494384d084ec41933b88451bacb05680e7d2}} YMnO{{formula:aa2b7601-04fa-4a97-a4af-161e40a804ff}} has also been reported to feature large magnetoelastic effects{{cite:7f230ada2b617abd205fc86c7c4c7926ecff51c8}} and coupling between electric and magnetic domains.{{cite:d942a6392614607916cb8feb5245047dc370982b}} Compounds where magnetic rare-earth ions are partially replaced with nonmagnetic Y{{formula:a644a8fb-0f26-4bbd-aa91-4b7e233f6762}} ions, such as Ho{{formula:49ece68b-1db4-453a-81d1-f3b79ba401ff}} Y{{formula:ba87e182-fbef-4174-a099-02ac2b3f5ad6}} MnO{{formula:c0f048b1-28e0-44a2-9f72-fb4b5a3dbb8c}}{{cite:feeba6f73a15a190acf76458511c86ee40f4b344}}, {{cite:57f20eb5144ceafd77c6b42a6104b19cc54b7ce4}} and Er{{formula:4ab2fd44-64ec-4527-bfa6-120be897499b}} Y{{formula:b2a380ac-8baa-4822-afc1-84643e0dcabe}} MnO{{formula:e2d164fb-889f-48be-ba88-bb4509db558d}} ,{{cite:ce8c92d114aff3c15322a64f9a7a5ab126b99274}}, {{cite:5ccbba9228aaf1cda61f9857d1acea2e9527fa21}} allow for further examination of the role that the rare-earth ions play in determining the magnetic structure and open up the possibility of novel phase diagrams not observed in undoped compounds. We report single-crystal neutron diffraction studies of hexagonal Dy{{formula:59f19631-bda2-4536-9389-a3d77c2ee39f}} Y{{formula:8e5593c1-d7ff-490c-8997-6c66e723c109}} MnO{{formula:a491fb57-f975-4342-b39e-d8dbe72625a2}} (DYMO) and find evidence for a spin reorientation transition not seen in other hexagonal rare-earth manganites at zero field.
| i | a9cdf1c73707acee933e038eb10f8a73 |
Quantum error correction codes are critical ingredients for fault-tolerant quantum computation. In light of developing future large scale quantum computers, it is increasingly important to be able to design complex quantum error correction codes over a large number of qubit/qudits. Naturally, this points to the need for a simplifying framework that distills essential information from these complex quantum many-body states that are difficult to intuit for designers. Some pioneering examples have been explored in the context of quantum many-body systems and topological quantum computation{{cite:6bebf692db4e3d816d9463a4ef3020fdca9e0080}}, {{cite:fe811cc430b42f6ac404553ba18937da0351f058}}, {{cite:357f310bd836ef12415ddfe2d657b2aa68cf9736}}, {{cite:23e8b65e3a0346b61d7215e1fe2712b64147f192}}, {{cite:432cb68e7a8adb79fb57f8ca534edbf0c1b45e14}}, {{cite:db90b52273acfcb2e0f2b029cc6fbdad810710e8}}, {{cite:26d05b20e20394180e4b1d02b725ade0e441d389}}, {{cite:11d351ad62cb86443c1ff2aff39c6d2229b82714}}. These are often constructed over geometries that are sufficiently regular, although some number of lattice defects have also been discussed {{cite:f04dbecffa3e138bf516a79ba689034e0c66ad04}}, {{cite:a4114cb175fe374020828f71d1a803ce1a807025}}, {{cite:cfb9bb239bdf9668e193fdd761b3704baa20fad7}}, {{cite:f3ea7e51840ce1a65d1df7c207f3ac741c3083d5}}, {{cite:28ce24a47d8381fe447e1c06f8000ec66b5117fa}}.
| i | 5fadcfbcf39620eb72c7e70f952acf72 |
Traditional substrates such as Si are known to degrade the electron transport properties of graphene as compared to suspended samples. {{cite:ebb0cd9dfea5ceae63fffee3691321ff3b43bd8f}} Reduced transport properties are due to various scattering mechanisms. There is strong evidence that scattering in these systems is due in large part to various substrate interactions including interfacial phonons (which are taken into account in our work), surface charge traps, and substrate stabilized ripples. {{cite:6c3a70f43a2e923afd1dd3017b1a7b9adc69a99f}}
| d | 9cef5fdf4c0117b9f304f177890e477a |
LiDARs have been widely used for 3D object detection and tracking in autonomous
driving applications in recent years. The majority of LiDAR-based methods either
use 3D voxels {{cite:c7f072252df9d181c52d15904dd145d53c9c08c4}}, {{cite:df6550b34d1c763949aeb99cdb4a736b39a5d596}}
or 2D projections
{{cite:5b76cd067d989f29f48ac3880b5c8de6a61868c0}}, {{cite:19418f8375251e7081988ed9f1d096fd3fdd32df}}, {{cite:4862c6d2a60dc32d164887909e24d141169e7f85}}, {{cite:f73fde8de777301756c4e522b5d82af0ffd4bcba}}
for point cloud representation. Voxel-based methods are usually slow as a
result of the voxel grid's high dimensionality, and projection-based methods
might suffer from large variances in object shapes and sizes depending on the
projection plane. PointRCNN {{cite:11aa5f0e24f981570d932f1974f48773b826893c}} directly
operates on raw point clouds and generates 3D object proposals in
a bottom-up manner using point cloud segmentation. These proposals are refined in
the second stage to generate the final detection boxes.
{{figure:5097cc85-ff02-4aa1-92b3-e24a1ed946af}} | m | 1b7ab20b10a4c8ef443e82f406d92d47 |
The results of the small scale simulations in the range of {{formula:eae6537a-4b3e-4991-8adb-8d86e4124b5a}} have been discussed by {{cite:b74f53bdd070449c6c436a62712097b0a9f52e0a}}, {{cite:e5fa92d4a48ee8b42dde6fe9d1050e5bfd581856}}, {{cite:c6dfda4017dec425c821d32ea1ec8e4d1178337b}} and {{cite:32dcace8b2067f62437c4e2547d022a0d0c05935}}. Therefore, we do not introduce them here. In this paper, we focus on the large scale propagation of the winds driven by line force. The purpose of carrying out small scale simulations is to provide inner boundary conditions for the large scale simulations.
| r | 2e13b069294bea460ba05ac2cb1b53c1 |
We first prove part (REF ). Since {{formula:6f7e71a2-1b8d-40b7-93b4-8d9253fc6cc0}} is assumed to satisfy one (or both) of two conditions, we consider the conditions one at a time. First, assume that {{formula:5d1b2fbf-3d0b-4355-a559-1605a221b81e}} is irreducible when restricted to {{formula:dba467d4-6040-4276-baa5-e7660bc4e406}} . Then, the vanishing of {{formula:23d92584-337b-4b0c-abe2-735543e3a131}} follows from {{cite:89012b68806232b54a303a6e9c83c8fea69d95f3}}. Next, assume that the image of {{formula:95b33541-6593-4ec0-8ddf-857e133964ef}} has cardinality coprime to {{formula:ef2e74cb-9c87-46b2-b15a-447942b07153}} . Since {{formula:6724e43f-05e1-4b00-899a-3f2e3c1eb83f}} is a {{formula:6870a7ad-989e-42dc-95c9-40c30be05196}} -group, and {{formula:43107354-e08a-471e-a2b1-d3cfcc9b6996}} has cardinality coprime to {{formula:f2c7cac9-f5af-4898-a333-daa0ba8de094}} , it follows that {{formula:6fff96b7-9fa5-434e-96f9-4e0a3ac66bd1}} . As a consequence, we deduce that {{formula:228b693b-1372-41ae-b840-7d0bf010ffd4}} .
Part (REF ) follows from {{cite:89fa9703c151ce7e27ccc3baa69187e348f25f39}}.
| r | 06907563c95d130184ae4b5353365469 |
Computer vision models generally perform well on datasets where each class is well-represented {{cite:6df7ddc78960b58afedca4f3d2eb544703a56d29}}.
However, real-world datasets often have long-tailed distributions {{cite:7d94796d21881c3450044f96f138ab25aa04b652}}, {{cite:01b8a717809a4299f146718c973614c7d6e9c7cc}}, {{cite:4b75c0f709f8d6bad0d2daca2213808a09590521}}, which can lead to class imbalances.
As a result, the performance of computer vision algorithms on underrepresented classes can be inferior to the performance on well-represented classes {{cite:7d94796d21881c3450044f96f138ab25aa04b652}}, {{cite:ed1d6c59b91b63b05670300e8991e40cf032968c}}.
In some domains, recognition of rare classes is especially important, e.g. for the monitoring of rare animals in camera trap datasets, which motivates the investigation of methods for improving rare-class performance.
A possible method to reduce the performance discrepancy between imbalanced classes is to oversample the rare classes with new samples {{cite:04abe4ae93bacf9329db6bebbf21760e0042624e}}.
As finding new samples of rare classes can be difficult, synthetic samples can be used instead.
Generating synthetic samples of rare classes is especially attractive as computer vision algorithms have been shown to perform well on real test sets when trained on fully synthetic datasets {{cite:52e7036e9749dff91a17a7392c458078162fbb1b}}, {{cite:cc11e7dc0ca0b6132e9ec75dc3178e61166617bc}}, {{cite:3091168d10691f327c4c5ea3cde5038879bcdac5}}, {{cite:03dd0f3a88537a45e825a365d7abd6f5a4b08cad}} or on synthetically augmented datasets {{cite:379b7581fd4ea19843b8626101b2838b81e934ee}}, {{cite:109d1be09251e7b95a2e4a468c817375886a34c7}}, {{cite:bd9fcbf7374b9267061a96c11029b9414639bb0d}}.
| i | 94fb9876b018d82766804bda57aece91 |
A concern in applying a mean-field (single-mode) or a few-mode approach to
study time crystals and discrete time-translation symmetry breaking is whether
the lack of thermalisation and decay of the condensate in such studies is an
artefact imposed by the adopted approximations {{cite:d0add0467d33b88dd4f7f33932910f1a76395e81}}.
Thermalisation refers to a common phenomenon that many-body systems subjected
to periodic driving eventually reach infinite temperature, where no time
crystal can exist. On the other hand, describing a many-body system with no
more than a few modes precludes thermalisation and quantum depletion of the
condensate by assumption, raising concerns that the predicted time crystal may
not exist once one considers a more rigorous multi-mode approach.
| i | ba88e691ac8620008789942c955d7068 |
While our DSA framework is fairly general, a key limitation is that the scaling matrix (i.e., {{formula:35308252-659b-449f-8928-741aff3f2191}} ) in each component function {{formula:7d275c20-a896-40d5-85ff-b2748b9ad4d0}} needs to be the same. It would be interesting to see if our approach can be extended to cover the general case {{cite:9a95f1eb97aae43587495187911fb92950d2637a}} where the scaling matrices also depend on {{formula:63d826c2-4e3c-44e0-9129-eb7a2d929665}} Another intriguing future direction is the setting with dynamic communication protocols, wherein the gossip matrix also evolves with time {{cite:a14664f161423125ad2526cec565d91e997de297}}, {{cite:66ed00de259dfc814616e9125f4dc7285d4d8398}}. A third direction is that of two-timescale DSA schemes {{cite:13be8361a47e4c64d6e03672431b95a937c31908}}, {{cite:21256963a2f284b31f8a097ed3f37f79226a1911}}. On the MARL side, important algorithms like distributed Q-learning {{cite:1e40b5c2e092fd3c93e7c13a5ee244a139971fd1}} and its variants need more careful analysis and we believe our techniques would be instrumental for this as well. Finally, we would like to study the effect of momentum in MARL algorithms {{cite:f59a278980aed2222756ceeb1eeed43912a7edc1}}.
| d | de4d70d84f78ab2114598216e266b6bb |
These free energy practices are widely implemented in popular molecular simulation packages,{{cite:e8a3c880806766da8d7a4b7b75dd31478bc20132}}, {{cite:7672e5cb09247f064427d6a75369071294887c1a}}, {{cite:51eaed0b800113336e3b6ee83541ba93756dd655}}, {{cite:890aea3fcda6c0a1bd20d77a998539f0889f6b0b}}, {{cite:ae9afc0255c93be5d0931af6b3b64f5409f0fc63}} and, while generally successful and robust, their equilibration and convergence rates are likely not optimal. In addition their deployment and software implementations can be cumbersome and difficult to integrate and maintain alongside other molecular simulation algorithms. A recent study by Lee et al.{{cite:0de8470e0b7f43ab846ef57d209cc932e5cafd41}} discussed the downsides of multi-step free energy methods and called for a streamlined single-step approach that would more easily be integrated with extended ensemble and self-adjusting conformational sampling algorithms and non-equilibrium approaches.{{cite:d02d20d12bb5d393340546226b40d33c3658635a}}, {{cite:657cf0be017513f88237faa82880f444d5f0937f}} Lee et al.{{cite:0de8470e0b7f43ab846ef57d209cc932e5cafd41}} furthermore proposed a family of soft-core pair potentials and non-linear alchemical hybrid potentials that enable the calculation of hydration free energies in a single step in which Lennard-Jones and Coulomb interactions are varied in concert rather than separately.
| d | b034667f034bfe41580ffcaf08e24744 |
(5) Study of Basic Sampling Proportion {{formula:e71c804e-70cf-42ab-b8cb-7f5fc0b50ef8}} : As a trade-off controller between the image information completeness and the sampling rate allocating space, the basic sampling proportion {{formula:84db8f07-b357-4acf-ae1e-a2483b49c3d3}} is expected to make CASNet degenerate into a uniform sampling version in evaluation when its value tends to be 0 (lack of signal pre-knowledge) or 1 (lack of residual CS ratio allocating space). Fig. REF exhibits the average PSNR performances on Set11 {{cite:2c972b2ce6fc785984ab79f05b3c17c0ecbf096a}} and CBSD68 {{cite:4b4b859dafb2e30707537445fb701f6d9d828ec3}} under seven different CS ratios achieved by (a) our default CASNet version (trained in content-aware sampling manner), (b) the ideal version which employs the complete image for saliency detection and sampling in evaluations (trained in content-aware sampling manner), and (c) the trivial uniform sampling version (trained in uniform sampling manner). The default version (a) meets its worst performance of 30.95dB when {{formula:66138f75-74f9-4fca-8cb6-636fb877d7cd}} equals to 0 or 1. And there is a sharp increase (about 0.12dB) at the beginning end of its corresponding curve, which means that only a small proportion of the most important measurements can lead to relatively accurate saliency predictions and allocations. This curve then tends to slowly increase in the range of {{formula:2255275d-bb75-46b1-8c2b-3cedb8e4aceb}} , peaks to 31.08dB at {{formula:32dfa739-d854-49a6-be3d-aae8660c619c}} , and tends to decreases in {{formula:abce578e-eeb6-49ec-821a-3ab5cf82fd9a}} . We observe that our CASNet implementation (a) can even bring a recovery accuracy close to the ideal version (b) with a PSNR gap of only about 0.01dB and remain a distance of about 0.26dB compared with the uniform sampling version (c), which is also exceeded by the default degenerated uniform sampling one (a) with a PSNR gap of 0.13dB. These results fully verify the effectiveness of our four-stage CASNet implementation and show the importance of keeping the CS ratio diversity in the training process.
{{figure:547e696e-323d-4ebc-a8b6-60abbda25f76}}{{figure:d6d20c03-b37b-4e93-863d-7ea8850f1e40}}{{figure:ded2a51e-adad-4748-96b0-27b3e84eb2ca}}{{table:b7fe6e7c-7ebc-4226-9f0e-746a13693d40}}{{table:1eae5d97-b6ae-4913-9b1c-6443079e6dee}}{{figure:ca76095c-a310-40c8-a246-4d3151365c63}}{{figure:d096f47e-9af1-4e69-a01e-c1e2cefa2ed3}}{{figure:9eb0d353-c620-471c-810f-5c2c36691f42}}{{figure:9b433492-3577-4d80-bf4d-9bbef77d2a96}} | d | dd7145957f1a9cd9450f37f26603ec11 |
The Standard Model of elementary particle physics employs quantum
field theory in order to describe high-energy scattering processes generically involving a
non-conserved number of particle
species {{cite:5414e76af53d528436bd1f7fe2ccbb496b3b23ea}}, {{cite:29f0152798a6435782dc72ab4f79b3d168e0e94b}}, {{cite:2acc97c483cde8f45f95a494ff81600ad223dacc}}, {{cite:6a8dd40bea516b0f6e23e4522ed6113f832dc93b}}, {{cite:46586f7d4fc233c9dec6f8e4dd5d06572ea8fb70}}. The
primary object in quantum field theory is a quantum field. This is a local distribution-valued
operator defined over a certain spacetime. The Poincaré isometry of
Minkowski spacetime plays a key role in relating quantum fields to elementary and composite
particles to acquire physical meaning well before and after scattering processes. Specifically,
the Lehmann–Symanzik–Zimmermann reduction formula
links free particles with asymptotic quantum states
defining {{formula:191e5108-ff9a-4e73-961a-b1224fd1e560}} -matrix elements {{cite:8698b1019573f2b997e7f6dcb32ecb851f49d847}}, {{cite:46586f7d4fc233c9dec6f8e4dd5d06572ea8fb70}}.
| d | 6a9bd38a2af377ca7d2aac946d6fa64d |
For concreteness, we set {{formula:77d4ce6d-5fe8-4cbd-b37a-3992056acd13}} and {{formula:52603cd1-d7e4-4f0c-8c48-d4ed65bf0664}} in {{cite:b2d0327e23ab0a191b55f1218fde6e595ad4a421}} as in {{cite:4f8d082b076ebce1a3d9166b53a6a6e625dbbb50}} for a {{formula:701c4151-450b-45b4-a23b-c020a7fed7d5}} Chern-Simons matter theory with {{formula:c88a2109-7bcc-49e3-863b-2109c218442b}} and one complex scalar for the quasibosonic case, or one complex fermion in the quasifermionic case. The quasibosonic case should be naturally compared to {{formula:8a19a29d-3fd9-4129-8128-d6d27c88590c}} , as both {{formula:dfba666c-612f-44c9-a880-fcfd710f1426}} and {{formula:4f3d3d84-7bf8-4c25-a942-229475392462}} are scalars with {{formula:441737e5-dc4b-494d-b7b3-4b80e26ae8cc}} at tree level, while the quasifermionic case should be compared to {{formula:1466f179-ff41-4a0f-83d2-2dd0c6d5a833}} , as both {{formula:eb1974ed-25e1-4079-9e44-25aac087013e}} and {{formula:07c8a01f-43aa-41b1-80ef-0685b40191dd}} are pseudoscalars with {{formula:0abc0c85-f365-4bd1-a00c-787446761338}} at tree level. For all cases, the contact terms allowed by the Lorentzian inversion formula vanish. For the quasiboson and {{formula:c546d489-d161-4b40-8479-6eb8704c4e8a}} , the tree level correlator consists of a connected free theory term and a scalar exchange term, while for the quasifermion and {{formula:474a7198-73d6-4b6d-9785-1725a3cee4cc}} , only a connected free term appears. In our case both {{formula:eb94de5f-1351-4553-95bb-bd0a84d3b0f4}} and {{formula:a07e52dc-6455-46a3-b4f4-d3f0043f4945}} depend on {{formula:061b119c-4a0a-4b86-85c5-20161c36ca7f}} as {{formula:19d2e159-c2eb-4290-8ba9-39f0f7d3e9a2}} , while in the nonsupersymetric case only the quasiboson depends on {{formula:3e4bdafe-54de-4f30-a491-7bc7a3b142ec}} , and has the slightly different periodicity {{formula:b323c6ac-929e-411d-a596-ffab20d78207}} .The factor of two discrepancy in the periodicity between the ABJ case and the non-supersymmetric case is discussed in Section 6.2 of {{cite:f018d5bc02bdcad5f6fa67fe9495bf9c6df90ce2}}. For both the quasiboson and {{formula:1a9e2846-2c2e-4fde-be4c-6a8810fa099c}} , the exchange terms are given simply by scalar exchange Witten diagrams, though the physical origin is quite different in each case. In the quasibosonic case, {{cite:e08348c659acb477aa01ab315a3551cc1ff92b2c}} showed that for spin {{formula:f1fa1e5c-ce8e-4549-aabe-3a63fc27fdef}} single trace operators {{formula:f748f66d-5872-4f6e-980b-9e567071dfde}} , all tree level {{formula:17467a40-cb11-409d-b3b3-0cbe0975ee12}} were the same as the free theory except for {{formula:d0021c6e-426d-420c-9a02-acc15eefa454}} , which depends on {{formula:02d0f0b6-54f7-473a-8b3e-83f98acf64e5}} . The scalar exchange then appears so as to compensate for the fact that tree level {{formula:dad0fff9-8883-43e2-ad20-25a7b943f350}} is not given by the free theory result. In our {{formula:4ab6c35f-c36f-4ebb-aaf9-bbf3e39db271}} case, we found that the tree level three-point functions between two {{formula:5e9d77c8-3fea-47ae-8b7f-deebc804b944}} 's and a higher spin multiplet were given by the free theory result only for odd {{formula:49f360b4-4227-4be3-a39b-825c55ab978a}} , while for even {{formula:c3abe85d-8216-47b4-a520-b332cff758a3}} they are all proportional to the same {{formula:de4f5a69-9d63-41f6-8b3a-d9344edb2c88}} dependent coefficient. The contribution of the exchange diagrams for the even and odd spin single trace long multiplets, which at tree level coincide with conserved supermultiplets, exactly canceled so that only the scalar exchange diagrams remained.
| d | 481f61e9cd1525ae240ad918da331d34 |
The problem of finding an exact value of {{formula:3f571461-ad99-4332-a6f3-d1fdc174cc9b}} in a graph {{formula:cc615dc2-6c5b-4715-889e-fd8acf8e39b8}} is one of the classic NP-hard problems {{cite:9a4cbb9d0de0e4ad23dd1d72a2938c7cbeee9aba}}. Moreover, the problem is known to be APX-hard (e.g. see {{cite:abb4e76ff73c7bc79e6e669263d7a9e604aa22d2}}) and not fixed parameter tractable {{cite:fa56a7ced705b61590becf26d29fffd60b6e4018}}.
Hence, the problem of finding a minimum or
maximum weight smallest-cardinality dominating set in a graph {{formula:a4c82305-af3f-4df9-9364-a6f7ee4e7e5c}} is also NP-hard and not fixed parameter tractable in general.
Therefore, it is necessary to have efficient and effective heuristic algorithms and methods for finding small-size and light- or heavy-weight dominating sets in graphs.
Also, to estimate the quality of a given dominating set,
it is important to have good bounds for the domination number {{formula:183fdf2e-7317-41e1-b2bf-9e18fffafc3c}} and for the smallest or largest weight {{formula:0d21bed0-841b-44d3-ae9a-b6998d2d58d5}} of dominating sets {{formula:bb8010a6-6c74-4552-a754-10c0079de583}} .
The following upper bounds for the domination number {{formula:fcc144b1-ac42-4bb2-afbb-2d3c88cbed3c}} , which can be obtained using the probabilistic method, are well-known.
| r | 231176022d0522f290c1c8fdf23a4981 |
This paper has introduced a novel adaptive output layer activation function, which we have named ASTra, that can either in combination with, or separately from, our previously proposed GMN loss {{cite:334a535886acb67b17abbe023101c7a791b4af8f}} work to facilitate the classification of minority examples for extremely high IRs. We additionally introduced a novel use of metrics based on an approximated confusion matrix for performance monitoring during training.
The proposed methods were applied to the most imbalanced datasets in a recent extensive study of ensemble classifiers {{cite:111423a1b944a4b601d74901252cd5e5648eab66}} and achieved performances comparable to those reported in {{cite:111423a1b944a4b601d74901252cd5e5648eab66}} for RUSBoost {{cite:586919b5c589270dfc7b3fde8ff712af1cdd12d9}}, despite our restricting this initial investigation to the use of neural networks with 3–12 neurons in a single hidden layer. We emphasise, however, that for complex problems it is essential to explore the space of model architectures, since even in the case of a high IR the main difficulties may in fact lie in an insufficient model architecture. We also recommend a progressive exploration of the methods, beginning with the GMN loss alone, then advancing to the addition of the ASTra output layer activation function, as needed.
We aim next to apply our methods to challenging real-world imbalanced datasets requiring deep neural network architectures. Additionally, especially given the nature of the derivatives involved in ASTra computations, we are interested in the use of sharpness-aware minimisation {{cite:afef4b0f098f8d996a6f0572859a8fd32116625f}} to smooth optima and improve generalisation. Finally, we note here that it is our intention to open-source our code and to ensure its integration with popular machine learning libraries (Pytorch and Tensorflow).
| d | 855b1c860dd6a90d62d343eae8a80765 |
Random Fourier Features: The class of Fourier features methods originates from the work by {{cite:a02e70cf51a7ce5fd9e49dcd2b84ca4c37c7373a}}. These methods essentially use {{formula:976fde55-8eaf-491f-bf80-b2f31fb6443b}} to approximate {{formula:8ebf7b42-ad75-45c1-aca7-a19a1330a253}} , where {{formula:91139fcc-e497-4f93-a2bd-ee770ced75fb}} are basis functions constructed based on random samples from the spectral density, i.e., the Fourier transform of the kernel function {{formula:8d0f7253-7c96-4ebe-ba93-32755bac89e3}} . This low-rank approximation reduces the time and space complexity of GP regression to {{formula:37be93d8-fd5c-40fd-bcb1-dfa77b67ec02}} and {{formula:df4db64c-e46b-4878-bcdd-424bef597b1b}} , respectively, with accuracy {{formula:f860a155-9b6d-4006-9c4a-035f0b59911d}} {{cite:15bc03cfc35a189c57f4ff3f14ca57e9ad2702d3}}. Clearly, the price for fast computation of random Fourier features is the loss of its accuracy.
| m | 0fb396ec90926d41f537b1216064d259 |
All of the experiments are done on a single 12GB Nvidia Tesla K80 graphic card with 64GB RAM and Intel Xeon E5-2670 processor. We train the models at {{formula:448744d6-535a-47d4-8c73-d58ac679ab3d}} resolution with batch size 8 and learning rate {{formula:ade6e91d-6719-4b78-93f7-e95c826c74f0}} for 100 epochs using Adam optimizer {{cite:063718c1f8e63ae0b92c0f3b4c224bfbe841f5e0}}. For CycleGAN and MUNIT we train multiple models for each normal and disease pair since they can translate between two domains only. To assess style-based translation fairly between MUNIT and our model we evaluate reference-based translation only.
| r | a981b6c8c395a4d6a4f8e3fc67d78461 |
We propose two novel data-driven predictive models trained on the dataset: (1) Action conditioned tactile prediction (ACTP) and (2) Action conditioned video tactile prediction (ACTVP). ACTP and ACTVP use different representations of the tactile data. We compare these models to state of the art video prediction model SVG {{cite:7522ddf49aeb0d2c64b5710d9e79cdca67495f98}}, video prediction model CDNA {{cite:7f1267e07e2fade9758bea492e30fa35360a9477}} which has previously been applied to tactile prediction and the only existing bespoke tactile prediction model, PixelMotionNet {{cite:a37816003b768661915e8e4c419420c8725ca2ec}}. We adjust PixelMotionNet to include action conditioning and remove the optical flow layer to enable insight into the effect of these two features. We show that our presented model ACTVP had the best performance metrics. However, qualitative analysis and the slip prediction task show that ACTP is the best performing model. We find that optical flow and encoder/decoder methods result in reduced prediction performance. CDNA's specific method of optical flow, where a network generates masks and applies kernels to these masks, results in poor performance despite previous success in video and video-based tactile prediction with physical robot interaction tasks. Qualitative analysis and the application task show quantitative metrics like MAE do not provide insight into practical model performance for specific application domains. For instance, a model that performs best for slip prediction may perform poorly for pushing tasks or vice versa.
| d | a2a399dabf8b6b5d18ee51e19d749371 |
Our next result shows that {{formula:b4911fff-414d-40b9-aa1b-cbade012f84c}} converges uniformly in probability to {{formula:efa445ac-7468-48d1-b4f1-6c41f67f6aa9}} over the largest possible range where unbiased estimation of the later parameter is possible, despite the non-Markovian nature of {{formula:708af722-8e7a-4a1e-9a96-6588dd2779a8}} when applied sequentially over {{formula:0840fbb3-458b-46cb-b77e-85ce4b92beb1}} . The result asserts that {{formula:7d832d59-79fd-439f-875f-4bf9ed21ea07}} is likely to be a good approximation of {{formula:af1f704b-a6f6-415d-a00b-5a5a2c1d4917}} , uniformly for {{formula:6ae47313-175d-4f22-896d-687e1bf58873}} , when {{formula:f815597e-591c-4adc-938b-dfadb250d30d}} and {{formula:444324a3-6a2d-4c2c-8dcb-6ee221b8d337}} are large. The method of proof uses an approach by Hoeffding {{cite:6e65be58ee6505a649ee629599dd3fbbcebc83f6}} for the exact calculation of the variance of a {{formula:db8469ba-6f88-4864-a4e5-a02070b3c28e}} -statistic.
| r | bee447062ca8980e849487f3f240d8d9 |
Our first contribution is a modelling construct, where we reformualate the variance regularized form {{cite:5298eba124828b8b297f880ae6caaa2e11a4f895}} of our non-convex sum of fractionals objective as a mixed integer second order cone program (MISOCP). While the MISOCP form provides more scalability than the original formulation and guaranteed solution quality (Theorem REF ), it still does not scale to real world sized datasets.
Our second contribution is a pair of approaches that achieves further scalability by splitting the problem space into sub-regions and solving a smaller MISOCP over representative samples from the sub-regions.
Under mild conditions, both approaches provide global optimality guarantees (Theorem REF , REF ).
| i | 28a92b10af3941651b5bea0e7c4c26dd |
In this letter, we introduce a simple and modular nonintrusive Galerkin-free ROM framework for unsteady flows by employing ideas from POD-based and AE-based ROM approaches (see the bottom panel in Figure REF ). In our methodology, we first apply the POD procedure to generate a set of orthonormal basis functions. Instead of truncating the number of modes, we consider an almost full-rank POD expansion defined by 99.9% of the relative information content (RIC) measure, and perform an inner product between snapshots and the POD modes to obtain the set of POD coefficients. We then construct a plain multilayer perceptron AE for finding the embedding of these POD coefficients (which requires substantially fewer trainable parameters compared to those required by the convolutional AEs) to generate a nonlinear mapping between these POD coefficients and a latent space constructed with only a few parameters in the bottleneck layer. Finally, we utilize a recurrent neural network approach for integrating evolution dynamics of the latent space. In this modular way, we utilize the best features of all relevant approaches. Specifically, POD is utilized in ranking the structural content using a linear spatiotemporal decomposition, AE is used in nonlinear dimension reduction, and LSTM is integrated for the time series prediction. Following the established name convention of nonlinear PCA (NLPCA) {{cite:3dfa8c6ac837fc16090f0cda198ca3325758ac0a}}, {{cite:f9a41e113e8f90e1c67ac4b3ef9565f76623a2d1}}, {{cite:db6d8965017a77aa2850d94d99d4663d37286b43}}, {{cite:021fc85d6bbf3fe0d28180a76113f9c265e73711}}, we call our approach nonlinear POD (NLPOD). We highlight that NLPOD provides a robust end-to-end ROM data compression framework built using significantly fewer trainable parameters compared to CAEs. Therefore, our approach could be well suited for the digital twin applications, where fast transfer learning procedures are often desired when new training data streams are incorporated {{cite:4746a7bad3c1c87b3554e268c2d201b7f99ef1d1}}.
| i | 1a8a287575c295b18d76c7506a127b5b |
Before proceeding, let us briefly review the definition of squeezed states and ideal squeezed states {{cite:2d8a91d34d2423ab696fbc2dcf5d2b982463f85f}}, {{cite:60ccf2b749c8866efa6663bd49377ba66c371e81}}, {{cite:6ca1244ad2b7d01d7c1f187baa8616a85f0961a8}}. For two arbitrary Hermitian operators {{formula:021a5126-6c28-49d1-9911-eb93def4c08a}} and {{formula:d19aa81f-e0c8-470b-b8bf-67865e7c9152}} , the product of the uncertainties of the operators, {{formula:1f20726e-2a8f-4b76-abe0-2a10bfd37a9f}} with {{formula:73f1efbd-6dab-4294-85b4-fc59b1ecc2e6}} and {{formula:ae64d61e-c41e-4547-8d2f-f3da7b722173}} , satisfies
{{formula:d5950ffe-00c6-4fb9-8b6f-fbe175df8b38}}
| d | 4bab6719b3f05c04f1c582552fcb4b88 |
Related methods such as TRILL{{cite:3c1d54577bcb2cb63d653017a744e17674de6396}}, COLA{{cite:bf0c3456d5c7bc7f59671a890c9dc13cc57024d0}}, and Fonseca et al.{{cite:fba3559974bd9e0a0ef2de0226776b997316b7bc}} learn representations by comparing input segments cropped from audio clips. These learn to make closer embeddings for segments closer in time, while pushing away embeddings for remote segments. Though different segments could have different details, these encourage representations to become closer for the closer segments, even ignoring the details.
In contrast, we propose to learn representations of the audio segment itself with details.
| m | f11fea0307c9925efb816c89fc9e6830 |
As such, the forward problem of Equation (REF ), defined as solving the ODE system with given {{formula:3ccfc65c-daa2-4470-a1e8-329a56a56dd3}} and {{formula:6005c4ce-471c-4d8e-918b-d4feebe4c03f}} , has been resolved in the mathematical sense – despite of several known numerical issues in matrix exponentials for high-dimensional data {{cite:0e3b0a0ab26a9c4c601bb28e424cd02d644112f9}}.
| i | 4298d64b7f22621508aff29ced1b2dd7 |
Finally, we also consider the Fair ZSL protocol proposed in Section REF . Here, we compare our model with the E2E {{cite:0d653eae338a6d38f5d8c199a604c7c0df568040}} method and our implementation of the CLASTER {{cite:ca5f54a4b4779320d1c239e5d971c7bba5a79af5}} method. We again notice a significant improvement of 5.9% over E2E, which shows the robustness and generalization capability of the proposed method. It should be noted that we use the E2E model trained on 664 classes for comparison since the model trained on all 700 classes is not available. However, since we train on Kinetics-600, which has even less number of classes, we believe it is a fair comparison.
{{table:2fe8189f-edde-4ea9-badb-6950b0f3bbc2}}{{table:c494b7f1-6705-4dc8-87d3-4ce91c0ecfbf}} | r | 2fc31e0151a93f533fa59affe6a3390b |
Here we present the needed background material from variational analysis and generalized differentiation by following the books of Mordukhovich {{cite:c21c940c145eee31a3029c2d6ea86e302e52fafb}}, {{cite:8d0fdc89de57b3713be25e532ef3f88406f87d85}} and Rockafellar and Wets {{cite:6ea8b52da29ad5669fe14fb614d39cb1306cb328}}.
| d | 31c11b0b68d9f44e2407293307f34c2c |
We have proven that our simple evolutionary technique is a scalable competitive alternative to the reinforcement-learning algorithms {{cite:fbb463876855110835dc2851165e5034d38f768f}} and that it can achieve similar results even with a divergent-driven approach and with a largely improved efficiency.
| r | a2c541591f3b0918647aa41b1b0c3c08 |
Other techniques used are pretty standard in this area. We use techniques based on the famous sum-check protocol of Lund et al. {{cite:4b0cf81b6d07197e9e32439baa1e0c43a39ab6ba}} that encodes answers as sum of low-degree polynomials. In our case, where Prover sends only a single message to Verifier, a quantity of interest is expressed as the sum of evaluations of a low-degree univariate polynomial. Since the polynomial has low-degree, it can be expressed with a small number of monomials. Thus, Prover needs only a few bits to express the set of coefficients that describe the polynomial, leading to short proof-length. Moreover, to verify the authenticity of the polynomial, Verifier needs to evaluate it at just a single random point, the space for which he can afford. The main challenge in this technique is to find the proper low-degree polynomials to encode the answer, and in this work, we give such new polynomial encodings for the underlying sub-problems. Another standard technique we use is the shaping technique that transforms a one-dimensional vector into a two-dimensional array. On a high-level, this helps in “distributing” the work between Prover and Verifier as they each “take care of” a single dimension. Pertaining to the streaming model, we exploit the popular technique of linear sketching where we express a quantity of interest as a linear combination of the stream updates, which helps us to maintain the quantity dynamically as the stream arrives.
| r | d5847f67a1928ee6a7ac1cf33b416c5f |
Very short-term forecasting (VSTF): This class of forecasting involves time horizon from minutes to few hours, usually between (0-3 h) {{cite:6d15490434ed984cebc72ed495ab31736bd6d0c2}}. VSTF can help dealing with random changes in renewable energy generation which can be predicted only before a short period of time. It offers a wide range of applications in renewable energy resources (RES) such as wind and solar generation forecasting {{cite:7cac569e489e9e61f9a1019d73b5038ebab7e8cb}}, {{cite:f650b7a5b81853031a5458d8b917d508da2c1355}}. In this regard, Potter et al. in {{cite:105c668bdffb15d8630a387e0b356be463c9f842}} presented a 2.5 min ahead forecasting system for Tasmanian wind farms using ANN and fuzzy logic as a hybrid approach.
Short-term forecasting (STF): It involves energy forecasts ranging from few minutes to a few days ahead. This class plays a prime role in various grid operations such as dispatch scheduling, reliability analysis, etc. {{cite:4500e1989eac21883e7df978baad633b58643b85}}. Furthermore, accurate STF helps avoiding underestimation and overestimation of the demand and thus, substantially contributes to the grid reliability {{cite:838466af1bc01dd367bdad785d8f6b823a521038}}.
Medium-term forecasting (MTF): It is implied to horizons ranging from few days to a few months ahead within a year {{cite:9af561f11815bcfb850d52d4248e36c96501d072}}. MTF supports adequacy assessment, maintenance, and fuel supply scheduling in SG systems. Furthermore, it contributes to risk management using price forecasting and therefore, plays a significant role in evaluating the financial aspects of energy systems {{cite:9b5c0b7847192878451e33bb962e11f90fd50a8e}}.
Long-term forecasting (LTF): It involves horizons measured in months, quarters, and even years. LTF is crucial for load growth and energy generation planning operations over a longer period of time {{cite:3ef5892b2e42d5022fdc0b5fbf010ef0b7ad325c}}, {{cite:81e664c88fc8a39708fb28675581c4c443914f80}}, {{cite:3ef5892b2e42d5022fdc0b5fbf010ef0b7ad325c}}.
LTF helps removing the impact of random fluctuations arising in shorter term and predict the longer term trends.
In this context, Azad et al. {{cite:f04cb10f2cd34f911eff9e10e842601dee826e8f}} predicted the wind speed trends of two meteorological stations in Malaysia for one year using neural networks to manage the challenges posed by intermittent nature of wind generation.
| m | 603de6654c67190a8774f2d643d12100 |
Note that justification logics with interacting agents are not new.
Yavorskaya {{cite:d75e81518d1e0a4ff24e1caf0ab9c9218720fa25}} introduced the evidence verification operator {{formula:dfc0ae30-2a1a-4d26-ae06-f07e6f749dca}} that can be used by {{formula:03ee2f0e-2666-41d2-9800-4d798fa4b88a}} to verify {{formula:9fb7497c-3aef-494e-a3f7-046bf92d2f5c}} 's evidence, i.e. her system includes the axiom
{{formula:56299d54-d08d-4f70-a414-d51a9fa9afe4}} .
This resembles the definition of the complexity class NP as interactive proof system, see, e.g., {{cite:185cedb6adf9dd17609d30d3563d29f2d5f346db}}. There, the verifier is a deterministic Turing machine. The prover generates a proof certificate {{formula:5634c832-d585-4cbd-bbcf-c0ce7108d81c}} for {{formula:e7ca35ec-6bb5-474c-85ba-0095089c0614}} (where the complexity of {{formula:270a516d-0df0-45ad-8a80-44b55620f3ed}} is polynomial in {{formula:5648f410-c954-4131-8ab8-fc90b01639f7}} ), i.e. we have {{formula:498a3ec8-e504-4d59-a6e2-f38cbedb0b94}} .
Now {{formula:cee5fd61-6ec0-4ac0-81cd-754b2c5c8f60}} sends this certificate {{formula:33fbd85d-27af-4bfe-9528-3035d5f961aa}} to {{formula:3989c7a4-d569-4d22-856e-47b796cc5d3f}} and {{formula:a00e7707-062a-4eca-b4ef-6d5c748841a2}} checks it (which can be done in polynomial time). A successful check results in {{formula:99b44a5e-4677-4b30-8523-43efe0004b92}} being a justification for {{formula:2fbf1eee-5e74-451d-b9ef-00e3c657336f}} that {{formula:bcf18926-b999-41c7-b9d5-0fbf5b931407}} knows the proof certificate {{formula:3c0d6d71-bddc-4f96-a262-38a2a6fcacff}} for {{formula:5d1bc7dc-4432-41c0-bc35-3d39780bb1ba}} , i.e. {{formula:eb4f063f-b60a-4edb-9ded-575e6c71d1e1}} .
| i | 7156d48af9b30092b969be774b184a29 |
In this section, a cross-domain semantic segmentation approach using target point annotations via an active selection is introduced. The proposed approach consists of three parts. First, a cross-domain segmentation model {{cite:39bde7abee1649c5cca790d5b585f93aedc07d49}} {{formula:a4990fcd-dd16-40a1-9bbd-ff1aaa1f2c6d}} is trained using the labeled source data and the unlabeled target data. The model {{formula:57b37e99-18c4-4778-bc82-58062312bcfe}} takes each target data to generate prediction maps and entropy maps.
Secondly, an entropy-based uncertainty measurement is used to automatically select ambiguous patches in the target images and request for point annotation from oracles.
Lastly, a simple yet effective domain adaptation method using target weak and pseudo-label annotations to train a second semantic segmentation model {{cite:39bde7abee1649c5cca790d5b585f93aedc07d49}} {{formula:9dc0b8f9-410b-4fe1-9947-8f25cc215f3a}} is proposed.
| m | e4ec9e2e1e7e64e07eaea55ddf6abaf4 |
We found ephemeral regions to exhibit relatively high scatter of the rotation rates. The reason for this might be the governing role of the photospheric plasma flows on the proper motions of weak magnetic structures. Nevertheless, on average, ephemeral regions rotate faster in comparison with larger active regions. The equatorial rotation rate for ephemeral regions is 14.47{{formula:5a55ac48-aca4-4b38-a36d-726197f6084e}} 0.01 degrees day{{formula:fc0e8daa-dae6-434b-b278-112baf5d0340}} (the rotation frequency is approximately 465 nHz). This rotation rate is the highest observed within the convection zone and it corresponds to the depth of the leptocline layer at about 0.95 {{formula:043f947f-e980-465b-b9e6-4625483150e6}} {{cite:3e8a98dfe733855d0abd5c42e2a07ea105eaa247}}. Note also that this rotation rate is higher than that listed by {{cite:ee48ac3ac00ee48491afd81c42a84f2ce21148eb}} in his table 1. Thus, {{cite:ee48ac3ac00ee48491afd81c42a84f2ce21148eb}} found the rotation rate to increase with for tracers with longer lifetime. The tracers with the lifetime of about 1 day (100 frames with 720 s cadence) in {{cite:ee48ac3ac00ee48491afd81c42a84f2ce21148eb}} exhibited mean rotation rate of 14.11 degrees day{{formula:b6f92f70-8379-43af-9c9d-1c8837984bd3}} within 20–22 degrees latitudinal belt. For the same latitudes our fitting of ephemeral regions yields 14.23 degrees day{{formula:9242dcfd-313f-47e6-8ef2-19d0ca53c238}} . The mean lifetime of ephemeral regions in this work is of about 2 days. Consequently, our results and that obtained in {{cite:ee48ac3ac00ee48491afd81c42a84f2ce21148eb}} are in a good agreement: weaker magnetic structures are presumably anchored closer to the solar surface. We suppose that magnetic bipoles with a lifetime of about several days and peak magnetic flux of about {{formula:74a9d312-a210-4197-9770-d492a9625468}} Mx are generated and initially anchored near the leptocline. Smaller magnetic structures are generated within shallower near-surface layers.
| d | 25ae6110163ffa13807c806ec9dac6fd |
Synaptic plasticity is a powerful mechanism for unsupervised learning in neural networks, inspired by learning processes in the biological brain {{cite:1ee1a2ae745d745bd2a985273416de714764a121}}, {{cite:5aa0652e41e6a813b3719414209d69515d3014d2}}, {{cite:c61447665844d76bffdb19a95d91f3395ccf140f}}, {{cite:88182780192be85e371b704345218de506ec390e}}, {{cite:1644dcd6b4799e35236f2d793df8f1b65f8172c3}}. This process has been incorporated into spiking and artificial neural networks to enable intra-lifetime learning {{cite:776293abc99116d9085107776bcad4b4733f16d6}}, {{cite:2a238927cf7e9f6335f080027b7c7e4bb973572b}}, {{cite:8c268596f51d655e4561e1e6e9b67e0988ec0c87}}, {{cite:ed0556e005404f0d5ee87775a69282c1cda636f6}}, {{cite:8ed49174161015b9f2b3078b9eb8f78cb5ada3ef}}, {{cite:07d3a5500b62de99e66f0544eca9a1c49c6bea57}}. However, in this work it was shown that plastic ANNs struggle to generalize their behavior beyond the training time horizon. SNNs on the other hand are shown to effectively generalize to time on a cart-pendulum task requiring fine-tuned stability, and on a quadrupedal locomotion task where forward progress is rewarded. In the cart pendulum task, ANNs were evaluated with Oja's plasticity and ABCD plasticity rules, and the training time horizon was shown to have a linear relationship with the the average lifespan. SNNs evaluated with Oja's rule and STDP were shown to have lifespan divergence around a 400 timestep time horizon, where behavior generalized to time and the network was capable of balancing the pole indefinitely. In the quadrupedal locomotion task, plastic ANNs were shown to degrade in performance the moment after the time horizon was reached, whereas SNNs were shown to continue improving in performance.
| d | 8764f233c32b3cb116c764045e9a8fa3 |
where {{formula:cde45c9e-8624-4c2d-b2b7-19a6fb81f7f4}} is the number of networks and {{formula:230f54e5-a381-4b1b-9989-90955de2e64a}} is the average class conditional probabilities of the ensemble. However, we observed that the entropy score of a single sample {{formula:90f84a4e-de9c-4807-97fe-3cea4b195da5}} fluctuates wildly during training especially for high confusion score samples (see Appendix Fig. REF ). This is likely due to (i) the differences in the speed of learning of the ensemble on high confusion score samples, and (ii) flipping the decision on the samples from correct to incorrect mostly in the phase-III of training as observed in a single network via the so-called `forgetting' scores in {{cite:d51229b1e5657801174458e463184246e90350e5}}. To remove the noise coming from a single epoch, we average the entropy scores over training
{{formula:f5a7fdfb-d92c-44da-9aad-83af1eb31a20}}
| m | 2430e16efdd87de59928dc48262eeda5 |
The contributions of this paper are twofold.
We analyze the local and global convergence properties of an oracle-based saddle point optimization on locally and globally strong convex–concave smooth functions.
We derive a sufficient condition on the learning rate {{formula:6f8ef826-93b6-4dd2-ac01-91aa2b38c3a2}} to guarantee linear (i.e., geometric) convergence and derive an upper bound on the convergence rate.
In contrast to the abovementioned analysis for zero-order approaches showing a sublinear decrease {{cite:e9885f2cb43583fd66248232090746cec224f9ba}}, {{cite:ac3096bbf2b3b1d813acc5fc24f5f28eb66442dd}}, our analysis is for linear convergence; hence, the result is more related to the one obtained for a simultaneous gradient update {{cite:46041d198537d586cdf26be1366cb951ad8ae53e}}, {{cite:469277792dbaa51d3b55f1644f8b2719134dd027}}.
We show the condition on {{formula:99e6f859-376d-4f4b-a856-8f80fc0d44f3}} to be not only sufficient but also necessary for convergence on a convex–concave quadratic function.
This reveals a possible shortcoming of approaches with {{formula:c14ce1d0-beac-4219-8d2f-8c5dcbf6e3d6}} , which do not guarantee convergence but are employed in e.g. robust adversarial RL {{cite:3c81511b2f6a8ae79f964972f41514a9763f994e}}, {{cite:01f5c59202dd703a9804ee78272039cd827de10b}} or coevolutionary approaches.
The tightness and possible room for improvement are demonstrated in numerical experiments.
| i | 87ebc39b9acf140c12e9a566b3eea665 |
In the case of Enceladus, its much smaller mass precludes a scenario involving the migration of the moon over substantial distances. However, several scenarios propose that the small and mid-sized moons of Saturn are not primordial but rather represent a second generation of satellites which would either derive from the spreading of material from Saturn's ring {{cite:f086a488b6660d6afbc31a93d85081d7f4b0d67a}}, {{cite:e3b50679882f7448105e6c590cb2f0d4c14596d7}}, {{cite:36751dd195271521ac8ddfce56e21dc0c8fc0cdc}}, or from the disruption of a primordial system consisting of larger moons, akin to the Galilean system {{cite:5291350a7074a7716a2c760f6ca92861073dadf5}}, {{cite:c11c8b25626b6e5237208d3743c2b9f6cf003ea9}}. In the latter scenario, it is possible that the primordial moons were massive enough to have migrated over substantial distances in the gaseous CPD during their accretion. If, on the other hand, Enceladus accreted from material deriving from Saturn's ring, the relevance of our results depends on the origin of the rings, which remains highly debated {{cite:325f0f6b19ab6d0778b72127665d55471ab3f77b}}. {{cite:89a5291a5a2cfb20b931916784957de44ccf511a}} proposed that the rings could have originated from the tidal disruption of a massive (comparable to Titan) moon that would have formed in the gaseous CPD and migrated interior to the Roche radius of the planet. This scenario would remain consistent with the hypothesis of primordial methane accreted by the forming Titan and Enceladus, and is supported by the findings of the Cassini INMS instrument which identified CH{{formula:55ec3a9e-db35-4a0b-a171-52cec35e97f1}} , CO{{formula:1e99b162-81aa-413f-b45f-77c6f3f12716}} , CO, N{{formula:d7be5f15-081a-4e73-8120-36adf5ff5dba}} , H{{formula:8a5c67c1-874a-495b-b28a-48b3fff3efd5}} O, NH{{formula:8065db18-cd72-49ce-9976-82c1741f687f}} , and organics in the D ring material during the Grand Finale {{cite:97b2312077095bcbca71d7720a6270d35b1d93b9}}.
| d | d1a6f7ec7150aeafaf0858b5090a6728 |
Within our numerical calculations,
we obtain a sizable induced gap corresponding to almost {{formula:153bea49-c97c-491f-a2ff-d240c63759f8}} of the parent pair potential {{formula:5f2fb0b0-6046-4410-a0c9-72fa869dcd23}} ,
which is comparable to the induced gap of the planar TJJ {{cite:6dcaab01079b67c8545761de744c460eb167ad9c}}.
When we employ Nb ({{formula:09cfa85d-9caa-473b-acc3-7728c2bf3614}} {{cite:969c6b227c089110a218572dea433feb0e5a7460}}) for the superconducting segment,
for instance, the induced gap is up to {{formula:dabe9d81-3859-4380-8632-2b91903feb92}} .
The induced gap becomes larger with a larger SOC potential sustaining the PSH state and with higher transparency at the semiconductor/superconductor interface.
This property of the induced gap provides a guide for designing material combinations in experiments.
Although electronic correlations are weak in the thin-film semiconductor,
studying the instability of the flat-band MBSs against interactions would be an intriguing future work {{cite:b20d207da4dfd04d01bcbf0d053d325c55c9af1c}}, {{cite:1999c48ddbbe126effc9e25ff27efb797870f6bb}}, {{cite:cb7fa8f8d4657e7337313fab1f0c1b770d69edf9}}.
| d | 2585c56abb1e0f735d887f70ab100473 |
where {{formula:8eb9b43c-eefc-4e9d-aa2c-22e135e19a00}} is the position of the microphone, {{formula:794628b8-02b9-431a-a0e2-cc11068adf8f}} is the position of the {{formula:3cd08a39-e736-46c9-9036-bf8187e0a93f}} -th source, {{formula:84cb63b5-4cd8-449b-a1e8-204af7796816}} is the set of visible image sources for the reflections between {{formula:f686435f-c4e3-4b36-889b-0c40518f6fb0}} and {{formula:12d18785-69be-4ffa-8434-3d52be668482}} , {{formula:13fd1210-6973-41c2-bb13-9f9530b5a190}} is a windowed sinc function {{cite:f9a7ec85f18db5ccd6bed6d40d29a2069abc83fc}}, {{formula:f54eebf5-a406-4731-b2cb-00dbbcd6e8f3}} is the sample rate, {{formula:540f46d1-cd12-46bf-a8ff-8fe88dd71895}} is the speed of sound, and {{formula:3ee7cbf8-d470-4c07-a583-04437dbcb97a}} is the accumulated reflection coefficient between {{formula:13688b3e-01ef-43ec-9258-171d8ad75fc9}} and {{formula:c6a2b992-577c-44ed-99fa-dc278c3078a7}} :
{{formula:555b16dd-aff1-45b3-9fb2-41bba5aa66e8}}
| m | f0ccf8547f7d5bee0e199cff31d45e86 |
On the positive side, finding the canonical direct base from the meet-irreducible
elements (and vice-versa) is equivalent to hypergraph dualization
{{cite:1e1d60a0f021c5e3f36ba9f97f78ae31813d8155}}, {{cite:4afeb61cc625b7fa448bc5398f52fa03fd905930}}, {{cite:14dd4077ab5e8a91cc396fbcf0b6ecfd175e79e2}}.
Adaricheva et al. {{cite:6c8e39a7e0f5cb0705a563202b1af738c19dbb26}} obtain similar results for the
{{formula:73db3b58-2fc3-4bdb-b635-2c9d12c84e5a}} -base.
More generally, exponential time algorithms have been designed, see e.g. {{cite:0e5ba0aeabdf073f51a8d6e0c99f7d3047e85e17}}, {{cite:3b86b746a1bdf6cee61fbaf6092567fd815dbee4}}, {{cite:10a645237ff41234f9820f593ec6a688f1d20cad}}, {{cite:5f5fe7ca24ac42782e5283e1a1e333d6c5adcd65}}.
In {{cite:0ba5fbaad6d8a5f43bb6dfdbf62e21ce85472536}}, Wild shows that SID can be solved in polynomial time in
modular lattices.
The authors in {{cite:ca47829e90957f4e546c2b21632615290ea909fd}} devise output-polynomial time
algorithms for both CCM and SID in {{formula:095b9f79-99eb-4221-b17d-60e0c6f4df94}} -meet-semidistributive lattices.
Finally, it has been proved {{cite:27244c283d096028640c34e263d644daa8a808f1}} that CCM and SID
are polynomially equivalent to hypergraph dualization in the class of ranked convex
geometries.
| r | fc959a6e91f4a516e37d47385078edad |
We also perform transfer learning tasks on various datasetsThe link to Birdsnap dataset is broken or refers to a dataset with missing data, making it difficult to make a direct comparison.. The ResNet50 backbone was pretrained on Imagenet1K over 800 epochs with a batch size of 4096. By following the linear evaluation protocol in {{cite:781a2ae925a72976236fcf2c4c3c9446664b6494}}, a fully connected layer of classifier is trained upon the frozen backbone.
| r | ba4e10a1e6efad86b257b4fc9de568c7 |
We have seen that the leading soft theorems in gauge theory and gravity have natural interpretations in terms of the infinite-dimensional geometry of vacuum manifolds. This point of view has some natural extensions that would be interesting to investigate. For instance, the subleading soft graviton theorem is universally related to the stress tensor of CCFT through the shadow transform {{cite:1377db241c851432ab6e6eeefd7c9116c86788e9}}. The corresponding soft operator is believed to be connected to an infinite-dimensional space of superrotation vacua {{cite:f3d0a0634d6d4022eaf336ec65b1fa850c00fb05}}, {{cite:106c63b64604bb05c1bcf422de95e02afc6c5938}}, although there is still some confusion regarding the precise definition of the infinite-dimensional manifold in this case {{cite:ca903298eb0f02d56978bbcc39aeab4ccdff2f02}}. Consecutive soft limits at this order in the soft expansion do not commute, and it seems likely that the corresponding antisymmetric double-soft limit can be interpreted as curvature and might even be used to determine the correct infinite-dimensional manifold. The path integral on this space, with the metric determined by the antisymmetric double-soft limit, will likely relate to universal stress tensor dynamics in CCFT and might be used to compute subleading virtual soft exchange in gravity. On a related note, several recent works have studied an infinite tower of soft operators {{cite:9758c01f2134b491db7edefd9bf7f4000ca47c77}}, {{cite:8d24fe8bb96a6700f70a6a8d96ae72c7830d8289}}, {{cite:fb19333a229826546721c66ca5a41ed72f070311}} in the context of {{formula:4bc5af72-fb98-4e6b-b6c5-a3deac336b6d}} symmetry, and it would be interesting to integrate those developments into this formalism.
| d | 31e5892f55416698dcf7b6a5184c472f |
In a recent study of galaxies in chaotic environments at high redshift (Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, CANDELS) by {{cite:f47b4b832898d7d8663e759102d91a4ffa54ce46}}, a linear correlation between the SFR and the stellar mass was found. Although CANDELS galaxies are early-type at {{formula:0697a664-6282-4dfc-8cff-4ca40a208951}} between 4 and 6, it is assumed that its gas is very turbulent. In such a way, they are very similar to TDGs, which are being formed from a very turbulent environment. Therefore, a similar correlation might be expected for the latter. As can be seen in Figure REF , there is a linear correlation
{{formula:efce59dc-fe4e-4cd9-be56-ab764fdbe02d}}
| d | aabc571c89a740d5322efba0dfd9332e |
In {{cite:193faeb3fb16a4c8352f67ff0acb0af69df46241}}, {{cite:4ca5db159d98dfaefcb0b917901b793499469089}}, Asratian and Kamalian obtained the following two
results.
| r | 7842b179b1532924ba2b9588db44c27d |
The diversified requirements lead to a variety of registration approaches.
Some prior approaches {{cite:58ac5114ae8933f0de6307a38c2b79f4a64ee7d2}}, {{cite:6b38dd0ed9b034fa41707b8250d824dea030757e}}, {{cite:66ef8581d82763349b2b7bb1e13aed94b6928381}}, namely local approaches, focused on time-efficiency and accuracy. However, due to the dependence on matching local geometric features, these approaches are sensitive to the magnitude changes in rigid transformations, and thus fail to handle large initial pose differences (Fig. REF -a). On the other hand, global approaches {{cite:94feee266dc067b09c43cd581680b9993405a547}}, {{cite:5b322455df3b7684b1491c195582d927a2c7456a}} leverage global shape information to maintain robust against initial pose difference. `Nonetheless, these global approaches usually produce alignment results inferior to those of local approaches when facing distribution variances, such as partial overlapping (Fig. REF -b). Distribution variances affect the overall shape that global methods rely on, while regional geometries remain unchanged.
{{figure:993d0c96-3c28-463b-bf7d-8f1dd7f4df4a}} | i | 3d0c37654cb668823adfb728d889d10b |
There should be enough abundance for a certain element in the dense medium or the GRB ejecta, such that the element can be identified in a spectrum. However, GRB nucleosynthesis related to hydrodynamics and microphysics in the GRB central engine is quite complicated. For example, {{cite:a3f31f7ea5492a055033843dd62613d43bada5f8}} initially investigated the nucleosynthesis conditions in the GRB fireballs. {{cite:a38f2fe956482be91101405cf8a585b69a9d6637}} studied the GRB nucleosynthesis processes, and some metal elements, such as Si, S, Cl, Ar, Ca, Ti, and Fe, with their isotopes, were presented. Here, we neglect the rapid electron-capture process ({{formula:77136912-fa3c-4acb-bb4c-37affafa8141}} -process) elements because they have very small abundances. In principle, some metals from the GRB nucleosynthesis can be shown in the absorption spectra of the GRB afterglows {{cite:286db5390b7128438e5c24ea344c2d6002e4c863}}, {{cite:a4ca7c3eec3dd8da71eb5328f07a5ee4b56d9c2e}}. In addition, supernova explosion may enrich the GRB surrounding medium with heavy elements {{cite:06774964b886166973758b64337add6268a93f66}}. The {{formula:38ca214b-c4ae-4ee0-ac6f-0167ee25b3e7}} -process elements with their isotopes in the supernova explosion nucleosynthesis can be referenced {{cite:fa5e0f92b32b8a6c7d7321275626f66e75b04986}}.
Furthermore, oscillation strength is the other important factor for the detection of absorption lines. A larger oscillation strength number of one element indicates a stronger absorption. For the forbidden lines, a larger number of the Einstein coefficient corresponds to a stronger absorption. Therefore, one element with both large abundance and large oscillation strength/Einstein absorption coefficient number is expected to produce a strong polarized absorption line in strong magnetic fields. We
list our suggestions of the absorption lines in Tables 1 and 2Although some absorption lines may not be produced by highly ionized elements, we still list them because they are often shown in GRB optical spectra..
From the observational point of view, a large sample of GRB optical spectra has been obtained, and the equivalent widths (EWs) of the absorption lines in the spectra have been statistically analyzed {{cite:7582b29ab1764b86bcf200efb2e527cfcb324678}}. The species, such as SiII(1527), SiIV(1394, 1403), CIV(1549), FeII(1608, 2374, 2587), AlII(1671), AlIII(1855, 1863), MgII(2800), and CaII(3935, 3970), were clearly recognized with the effective EWs. In particular, CIV and SiIV have the rest-frame EWs of about 1 Å. Furthermore, some highly ionized metals inside the natal regions of GRBs were identified in some optical spectra, and the elements, such as NV, OVI, CIV, and SiIV, were noticed by {{cite:a4ca7c3eec3dd8da71eb5328f07a5ee4b56d9c2e}}. However, we note that some elements have small oscillation strength numbers: NV(1239), NV(1243), CIV(1548), CIV(1551), CIV(5801), OVI(1032), and OVI(1038) have the weighted oscillation strength ({{formula:9037498a-bee2-4629-9fd7-8d6cf5639fa4}} ) values of {{formula:8c6c7091-5041-44a4-9745-72f2c55d6d1a}} , {{formula:3db29029-f837-43fd-9ef1-bc10c97c9af9}} , {{formula:959f0e46-dbcb-4284-b04b-9aeb8b2a112a}} , {{formula:9023a5a0-7790-4e20-b211-8fbaa28700c0}} , {{formula:32fb6033-cf4e-4ca6-b8e2-b0fad20c140d}} , {{formula:5cb7412a-c59a-4369-8481-3660ba69c65f}} , and {{formula:c5bc2601-c8cc-41a1-a167-83a189e5bf88}} , respectively.
| d | 8dec7f385b32d419c16c0163ad95b71a |
Most of the work devoted to the study of critical transitions in ecology considers transitions
that occur due to the loss of stability via a classical bifurcation at some critical threshold of environmental conditions (e.g. critical resource concentration, atmospheric temperature, CO2-concentration) and often involve hysteresis phenomena {{cite:18daf498071d1b36b982b18a2822fbe6e957d7ed}}, {{cite:d12bc54098999e2fe28d276f9510029c2c598698}}. Linear stability analysis is employed to find these critical thresholds by constructing bifurcation diagrams reflecting stable and unstable ecosystem states, such as equilibria or limit cycles, for different but fixed-in-time environmental conditions {{cite:f5e1a2668c096c95b6def42daae125e8a5284907}}, {{cite:a41eb44d5ddfc7b861e3927cd202c5e8fcfee6c7}}, {{cite:b1dd3060a994b00d297d29bd43eebe815dba052b}}, {{cite:4d021278ea8250dbd1b3884dfef1afc9486f113c}}, {{cite:585665d51e1bf8030b6dfe677c3ff8aafe6dd9df}}. Linear stability analysis only considers
(i) small perturbations around the attractor to justify the linearization, and (ii)
time-independent (quasistatic) parameters which neglects changes of environmental conditions that might occur on the natural ecosystem timescales. Taking these two restrictions into account, one can identify
critical parameter thresholds at which an attractor disappears or loses stability and a regime shift or tipping occurs. However, variations of environmental conditions which are comparable to or even faster than the internal ecosystem dynamics can be present {{cite:7583ef74ac182322c30881042791fde1bb973e71}} and may even occur at unprecedented rates {{cite:6fc9cb478324aa4251306a5987f6f3e7009cd803}}. Most importantly, environmental conditions can change at a rate at which the ecosystem is unable to adapt its behavior {{cite:41e1e962366491f32c3ae550590e178c19067d71}}. Those environmental variations can lead to unfamiliar and often unexpected critical transitions, called rate-induced critical transitions, that cannot be explained by linear stability analysis {{cite:bb8e3f97ac144e417257b6e653ca41ae79bb32ca}}, {{cite:8be4c696a7fd16d4b2409e24bbf8486209a21797}}, {{cite:c0129a62f0055bedf346408f1f93065eab31bde5}}, {{cite:c71b3d4eab9a7ea85ad62ecd1b8e78900c28b642}}, {{cite:ee37b1b503b999251e9f51cf827320925c395acd}}, {{cite:c7d7f2db979a6d893a3e307290fe3c8af1f24be8}}.
| i | e2a65d91df4d23b72e43713d5796494e |
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