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We compare our explanations with two baselines based on occlusion (see Eq. (REF )).
The simplest variation is removing the word of interest and not replacing it.
We call this method Delete, it was first used in NLP by {{cite:ed322162311f2f7cdd3d151fe57e858a0c3c5349}}.
Similarly, we replace the word of interest with the unknown token <UNK>.
This approach is more tailored to state-of-the-art classifiers pre-trained with masked language modeling.
| m | 4bb07c49ad8caff15ba335800fa16992 |
There is growing evidence that the characteristic scales may be anisotropic.
{{cite:67665fb7d66ab4fd54f5aa1af9b0545512bae21c}} found a non-spherical splashback shell, the orientation of which
is aligned with the mass distribution in the inner region of the halo.
{{cite:d62e9e9a5f3079eeb17d96b2f5dcd8b15d1861cb}} found that the depth of the splashback feature in a cluster correlates
with the direction of the filament containing the cluster and with the orientation of
the brightest cluster galaxy. {{cite:46afeac6ad6c2cd1c4a1847cefef25c240ecaf2f}} found that the position of
the splashback feature varies with the position angle relative to the
neighboring structure. Such anisotropy is expected theoretically,
as dark matter halos are found to be better described by ellipsoidal
models {{cite:a375183154ec23178ec80848605b92cf39f9ab94}} and halo orientation is strongly aligned with the large-scale structure
{{cite:8a7fbab4ce16c3f8fbe9ed05e10f6d0208865ff7}}, {{cite:da91f77c5a81f1f7ca6589932eee90d3ccb8dc77}}, {{cite:5c0d37cb56498467ebafcbf1db2463854be6abce}}, {{cite:c9024492a1900ebbd91b32844f40400f93ddfbed}}, {{cite:344551be9010bcb65ea4867580f9bc81f4b8467f}}.
However, a detailed analysis is still necessary to understand and characterize
the anisotropy in the characteristic scales and its alignment with the
large-scale structure.
| i | 4f5e87e7c17ed6f800e75777ebb44f52 |
Firstly, while we have illustrated the effectiveness of our master theorems with two examples of different flavor,
there is no shortage of other signal structures that are of practical interest.
For instance, one might wonder how AMP behaves non-asymptotically when the signal {{formula:91a86392-2375-409f-91cb-7a881d28171f}} is known to satisfy certain shape constraints (e.g., having non-negative entries, residing in a monotone or convex cone {{cite:05a771c7025d30967c9c37e16b07e24bf72adb40}}, {{cite:dda19ef57d74ee0e3e6eaf9c720993b286139aca}}). In some of these cases, the natural denoising functions might not be separable, therefore while the decomposition in Theorem REF still holds true, controlling those residual terms is significantly more complicated.
Secondly, our analysis is tailored to the spiked Wigner model where the noise takes the form of an independent Gaussian matrix.
It remains unclear whether our non-asymptotic characterizations can be generalized to accommodate non-Gaussian noise matrices {{cite:f3d8091bd432e03dca1b326d80d8bb467f1e6188}}, {{cite:7f59b907027a75a22de333bd881a558e8a3a4f48}}, {{cite:b051be6aa73ac993a08f9dcfe4ef85dcc9c0666f}}.
Developing universality results in a non-asymptotic manner is an important yet highly challenging task worthy of future investigation.
Moving beyond spiked models, it would be of great interest to see whether similar frameworks can be developed for other models for which AMP is known to be powerful. Examples include sparse linear regression {{cite:19690398d2ea1e2947c04d2b3c4cc16dd8b84522}}, generalized linear models {{cite:1a6b3edc488943bf85b32863c5758a554aa44c7e}}, stochastic block models {{cite:153aea010ccb4356f71f45dc88f680d721ead037}}, among others.
| d | dd474157304b302a0bcab1e6800b5bec |
Besides presenting the values of the entropy for each case, we also
discuss the question about the transfer matrix dimension, which turns
out to be the major obstacle in obtaining the entropy for a given
{{formula:2f6c67a1-1d4e-4ef7-ac87-80605d93e868}} pair. Also, after collecting some figures for the entropies
we should deal with the task of how to extrapolate them to obtain
an estimate for {{formula:dae49ba2-da64-4545-a501-3d880ff6563f}} , from a set {{formula:27fb1360-bf74-443d-917a-e0c625b66306}} , valid to the
two-dimensional limit, i.e, where {{formula:f79b7628-b186-42f2-ad8e-960e8f26e675}} . For that, we are aware that
for critical two-dimensional isotropic statistical systems, presenting only
short-range interactions, conformal invariance predicts that in a
cylinder of width {{formula:5518e5a4-b0ee-42a4-b69b-c481bde1c396}} , the entropy per site must be given by the
relation {{cite:b6bb4dfecd6011e170f4a2b2aed88b635bfc113e}},
{{formula:610eb326-d425-4921-991c-f42ec55dd8c5}}
| r | 502a01c9bcbf8e4d9c3e5c417dc25364 |
The method of variable projection {{cite:b030f6b1886304197b1e6e289c8a4bbcff9573a3}}, {{cite:d0b5337e1efd62edc5d4363f691a3a13cf942197}} is a method for solving separable nonlinear least squares problems. It is characterized by the model being a linear combination of nonlinear functions, meaning
{{formula:6ff73799-d24d-4d8b-93f8-5837a264c67c}}
| m | cedf93cb2c1438aece9a6f57c0561882 |
A second type of extension into non-linear decision boundaries is utilizing information present in individual documents of the collection. K-Nearest Neighbours
{{cite:f25594d5a567bb87520dae436eb7c145b9b1ce19}}, Kernel Density Classifiers {{cite:db1853cb2299363c467603a36424c57e0fcc198d}} and Mixture Models {{cite:511cd7e9782cb881340493fbd79461afb74bc6e9}} are models that maintain parameters for a set of prototypes
for each class, and combine scores for each class from the prototype scores. These models can capture properties of local neighbourhoods in the documents
that would be lost with the representation of a single parameter vector. Kernel learning methods {{cite:d69f4312e19e3fecd672d95ad9e0a76dc209c6e3}}, {{cite:410113d6e15e2f21f12a67e3f4f5240cd50f6a3e}} use feature
transformations called kernels into arbitrary spaces that are not explicitly computed, but rather evaluated implicitly by the learning algorithm. This gives kernel
learning a great deal of flexibility in learning decision surfaces, but with a computational cost that is not always preferable over a linear kernel maintaining
the original feature space {{cite:dd5d28ed53b68f6096c243a82246b93b875ec052}}, {{cite:987e222c414a15da6691af7f2c6338f97b4b41b8}}.
| m | d612058b29c90c5ee4cc6c9ce5f6b25a |
The existence of dark matter (DM), non-zero neutrino masses and matter-antimatter asymmetry suggest that the standard model (SM) of particle physics, despite its enormous triumphs, cannot be regarded as a conclusive hypothesis. Very recently, muon ({{formula:11a99cee-eb66-43a6-b99d-47a7f6250f09}} ) Collaboration at Fermilab has reported the measurement of the muon anomalous magnetic moment {{formula:12a47494-0fb3-4b85-848a-28da2d757dcc}} showing a {{formula:93394fc5-991e-4db4-aead-92a87c271297}} discrepancy with SM prediction {{cite:49a4d6298615e25e8b254d94820ff7dc9b12f945}}. The difference between the combined experimental result {{formula:276631b1-9696-4d37-944e-dc8eba806252}} = {{formula:e97f2a0f-4380-4e81-b565-7993e5b12c09}} {{cite:49a4d6298615e25e8b254d94820ff7dc9b12f945}} and SM prediction {{formula:dd4695ef-c43d-46ab-bf6d-e8578c6e744b}} = {{formula:41dfe61c-3e64-43d8-9811-bfae58234c7c}} {{cite:f3da52641af391d5c2b6513213a3f456bc740959}} of muon anomalous magnetic moment is {{formula:ff8ed4b5-9505-4132-9d84-85e82df17e0b}}
which is a sign of new physics (NP) beyond the SM. Several models have been proposed with an aim to accommodate muon ({{formula:17c8f09d-ade4-493b-be70-71657f52ed19}} ). Although, there exist theoretical models based on discrete symmetries to resolve muon anomaly {{cite:ee5d3614284fc0dcd9704e012e34ed9626b775bd}}, {{cite:80aeffabdea8755f32a05567e0627d69b17cf778}}, {{cite:54ced26bc093c2539b5e084ef21694630b73be73}}, {{cite:16858f6b311474e30536a889112d21b8e7989c07}} but the most general framework include the extension of SM by {{formula:d9b8c76e-19fd-426f-bbd4-0cad899f6735}} symmetry {{cite:2d59ab5575ac939fad9aabeb041daeffd6a4c0d4}}, {{cite:0be823dc186d898ef0d618847637c114f7ff7415}}, wherein an additional gauge boson provide correction to muon magnetic moment at one loop {{cite:cd7088d56d445e950ec3a56566e28f18924cee23}}, {{cite:9b2a8dc6b18fee6929808abbbb93ab21a8a11f2a}}, {{cite:31ff85d99b154da6b179ba0eaf327e319ba14d0b}}, {{cite:6a45950c56f843aae52ac51b5445173388363d90}}, {{cite:f4c5a00f7335ebc4d84b200ef4efee14a71af175}}, {{cite:2072edd8a6c10820e43ac93fa690513cada64256}}, {{cite:1d86dbf27b614c2b989b698aa9030c71f9b900d3}}.
| i | f6a7d0a412e17f93de98b5a1c45e4a10 |
{{cite:2bb7aaa038e270d227ab3d25fa6143b508576cbb}} present data from the nanograv collaboration, analysing the dm time evolution of 37 msp at frequencies between 300 MHz and 2.4 GHz, 18 of which we analysed in this study. Again, the question of which instrument provides greater precision in dm measurements is pulsar dependent: lofar provides a much higher precision for PSR J1012+5307, whereas the higher-frequency nanograv data provide a much higher precision for PSR J1857+0943 {{cite:2bb7aaa038e270d227ab3d25fa6143b508576cbb}}.
| r | f4f3704ce344ce32238341517af463a7 |
To explicitly model commonsense knowledge,
relation embeddings based on ConceptNet {{cite:425cbacd3673fe14db0ce432391515e8e264ef40}} are used as additional features.
ConceptNet is a large-scale graph of general knowledge
from both crowdsourced resources and expert-created resources.
It consists of over 21 million edges and 8 million nodes.
ConceptNet shows state-of-the-art performance on tasks like word analogy and word relatedness.
| i | 05c0e609a5c723e27f2b8f819dd79372 |
We analyzed this evolution by calculating the fractal
dimension of the angular momentum trail. With this method it
is possible to reliably determine the onset of and the rate of
evolution in different regimes. A key result of our analysis
is that the evolution of angular momentum is neither diffusive
nor ballistic in any regime, as was previously assumed in other
studies {{cite:8054e3ab8dfb667e930105938c47faa277c254b3}}, {{cite:1ec8735c04f8f084bba81a221c23c958812a50fd}}.
This seems to contradict the results of the numerical experiments
done by {{cite:f923506c0e29b0b3eac904f845efe718e63f47b0}}. The reason for this discrepancy
is not clear, but we speculate that it arises from the low number of
stars used in that work.
| d | 48fb9978ea114d1d29fa6d368e1785cf |
Comparing with the results from the Breit-Wigner-type spectral functions used in Ref. {{cite:2abd61d280d1ed83f0abe3f7ebf021fad33dbfb4}}, our predictions with more sophisticated scalar spectral functions and higher order QCD corrections reduce the magnitudes of {{formula:e2e093a9-e48e-487d-a104-439b609f9a18}} and turns out to be perfectly consistent with the PDG average value {{cite:59af0218f93df034463bba29c4256ed17ac26b07}}, which is mainly based on several lattice determinations.
It is worthy pointing out that our results in Eqs. (REF ) and (REF ) obtained from the sum rules with the scalar currents are compatible with the recent determinations from the pseudoscalar channels {{cite:32dccc7f6dcfe9582b695442a76576b5b1f97ec7}}.
| r | c9e01d7183980456f2801741b38a3861 |
After acquisition, the next process was light curve median filtering (1-day kernel) to correct the systematic trends or transient variation. Any object with brightening of more than {{formula:92181d29-8c2b-4f31-a56a-a63647cf37c1}} magnitude after filtering is flagged as possible transient. The residual of the filtering was processed to get Lomb-Scargle periodogram as the key for finding periodic signal {{cite:9e9c7c4eefaa006a4f1fd9516aca0008a54490e5}}, {{cite:4559bd2438f45b2584b14578c033c3399fd24426}}, {{cite:12ad8b6dc9dc327ac366ec2e8ac66907cb234f2d}}. The period it self ranges from approximately 35 minutes (close to the data cadence) up to 10 days. Based on the established periodogram, the target is considered as periodic if the maximum power exceeds 3 times the false alarm level.
| m | 55dc5a941a47f0597e0c5c3eb759b52b |
Leveraging the recent development proposed by {{cite:e867e4cb6f34ca31c963b3cfccf2ca805e1e11a7}}, {{cite:a09072a10aff7860438200c1524421d3331ede7a}},
we suggest two modifications that correspond to the aforementioned observations:
| m | 310daea4071c977ef6db25f4f813c7fd |
Taylor expansion {{cite:1f37e855b990c1ddc5da7702a4af0373a871b1d9}}. Consider a DCNN with {{formula:6398b0b4-d84f-487b-befc-fc9ceb5fc5a4}} convolutional layers, parameterized by {{formula:c1ddef6e-7baa-4b59-8a88-d93d6354926d}} , where {{formula:c87b828f-69a1-455b-b393-baf3bf2df01f}} is the number of filters in the {{formula:b6c627d5-3f72-4828-95b3-4b7d8352c37d}} -th layer. Given a training set {{formula:da69010a-6a3b-4ba2-b3ba-f1841f6b16a2}} , the loss function is {{formula:517f84e3-28e0-4bea-a39a-a63b606a8db6}} . The objective of this pruning method is to minimize the loss change {{formula:3c3d4ecb-5104-4e8b-a5b4-16242a830de1}} when there are at most {{formula:121c26d1-be82-40ba-a924-196ad513d698}} non-zero filters in the network, parameterized by {{formula:dea4e392-e598-4f9a-9c0c-f1fd7f4f83c8}} :
| m | 9ec243c18892bd7422248b7ca5df166c |
In this study we compute the {{formula:c8ba4024-96b1-4169-b0ce-638575638796}} -variance for each possible line-of-sight direction {{formula:50097ae5-f283-42e2-b03d-d650e14be00c}} , {{formula:0da347b1-67a0-4cdc-b131-5f0de407a38a}} and {{formula:c6150a5d-19ec-4cf7-9672-0d1ba2261c6d}} . As shown by {{cite:ad26d6ba4918455f8565129c0420ccd8cc9b1b3e}} and {{cite:5cde0ecfe4af10c70130e22900997ee818679d34}}, the statistics of velocity centroids are very sensitive to the direction of the magnetic field in the regime of sub-Alfvénic Mach numbers. Although we use a weak magnetic field in the {{formula:06e33736-881a-419e-9f60-840e9fd77f2b}} -direction, the turbulence in our simulations is trans-Alfvénic or mildly super-Alfvénic (see Table REF ). The field lines are essentially dragged along with the turbulent flow, with the result that the turbulence remains approximately isotropic. Hence, we do not find significant variations of the {{formula:f55c0ac1-7226-4d3e-a2fb-74894fb1adfd}} -variances along the different directions. We therefore average all {{formula:7dd23870-0675-4e02-a03f-6290e459d055}} -variances of the three line-of-sights. Finally, power-laws of the form
{{formula:8c7da1e8-7254-4554-bb1e-c16b0043dbeb}}
| m | 6a687dade597f6435897485dad646870 |
that are linear in the parameter {{formula:246369d6-7da6-45c4-8845-8f9a66cd47a3}} , and where {{formula:4639e875-1f1d-4141-aea5-e66f990bc899}} is a vector built of nonlinear functions {{formula:64eb747c-5cfc-4fa0-8908-fd71e0b0ec29}} . Deep regression intends to infer the regression function {{formula:3bbc0cd9-454e-49bd-a3cc-d0463b509282}} , and it does not make use of the specific structure of (REF ). The level of complexity is controlled through the choice of the nonlinearity in the function {{formula:3a9b7143-c772-47e9-b2f1-c9ab799fb5f2}} as well as by the dimensionality of its input {{formula:4d5fb27c-9a56-4721-b1d9-facdd89b425a}} . Results of an uncertainty quantification for deep regression of problems of the kind in (REF ) can be compared to those obtained by a statistical reference method. The reference method utilizes knowledge of {{formula:79929037-e6a1-40d2-9802-f3f7c66cc993}} and the linearity with respect to the unknown parameters {{formula:954e45ce-8fc1-4464-8c0b-5a45ea539506}} . It consists of a Bayesian inference using the improper prior {{formula:bf6a7e6c-2781-47e0-bcab-0d3cdefc70a8}} , which coincides with the reference prior for the statistical model (REF ) {{cite:d2c08b2bdd7baf0a649beb5d242f7f1e8b923115}}. This prior is probability matching {{cite:408c2b4a23e7ab8e03fe7f999f3c2eabc291374e}} so that the proposed reference uncertainty quantification can also be recommended from the perspective of classical statistics. The statistical reference method provides an anchor solution against which different methods of uncertainty quantification for deep regression can be compared.
| i | f5019b11396084d7c9e2334fa6b8b6f6 |
{{cite:f74b3fec27d235fdb8580da1265707ad20a4e516}}, {{cite:4839a1bd27904309240c267737849ad8ac9cc354}}, {{cite:28a2a10b800b1858888e9eb711aded73301b24d3}} pointed out that mini-batch learning on distribution parameters was feasible if the batch-size was sufficiently large to be representative for the entire population. The available GPU(GTX1070 with 8GB memory) limited the mini-batch size to 150 for the STL-10 dataset and 100 for the Pediatric Pneumonic Chest X-ray dataset. For the CIFAR-10 dataset, the mini-batch size was set to 1000. The average number of images per class in a mini-batch equals the batch size divided by the number of classes(subclasses). For the STL-10 dataset, if each class is divided into {{formula:f75f37f2-5dcd-4916-987d-45eaded0d731}} subclasses, with {{formula:f1677d25-7483-44f6-9313-c163d1bc67ec}} or {{formula:d6f3b43d-f8f8-49a3-a124-fa080464b243}} , the average number of images per subclass in a mini-batch is only {{formula:bcdbbc34-4d5a-474a-9550-1f4726462695}} or 5, which is too small to represent the whole subclass. And for the Pediatric Pneumonic Chest X-ray dataset, the single channel images are too simple and similar, applying K-means clustering on the dataset is meaningless. So Algorithm 1 was only applied to the CIFAR-10 dataset in the following experiments. The number of training epochs was 400 for the STL-10 and CIFAR-10 dataset, and 200 for the Pediatric Pneumonic Chest X-ray dataset.
| m | 98c0ccdba3b76d92bc4b54147c645bae |
Tables below detail results per domain for the 5 multi-domain real-world datasets from DomainBed: PACS {{cite:2638c5939e65f0c6d100718efa0c792d3585d569}}, VLCS {{cite:4e9d3112bd364e9617501bd844ccdc380cc26ac3}}, OfficeHome {{cite:af50a6ba03040fab70fdbec09d51638622f88bd1}}, TerraIncognita {{cite:2bd7030a24acdd73fcddc15a94d5a15bc7da1f9b}} and DomainNet {{cite:8251f188d772b0ab3b92cd4cfbcc62eecf7e68c0}}.
Critically, {{cite:59e86d574db47816a2982cafac923257210342d1}} showed that diversity shift dominates in these datasets.
{{table:369e093d-7c43-46b8-811b-47524403b0bb}}{{table:e1fb7b47-605f-462b-afa8-8775a244b8e1}}{{table:1955ca5a-5b5d-4838-88fe-bde0b0b5830d}}{{table:ab2e366d-75c1-4545-b0be-10cb37846e81}}{{table:4d33e43a-c7aa-4025-a809-df08588ea91e}} | r | 98a22284d74e1f85e9099aca6e076e99 |
A large body of defence mechanisms have been proposed for the adversarial setting.
Adversarial training {{cite:b73d975d24d6906e5b669a9b90e468a3a678845a}} is one of the standard approaches for improving the robustness of deep neural networks against adversarial examples.
It is a data augmentation method that replaces unperturbed training data with adversarial examples and updates the network with the replaced data points.
Intuitively, this procedure encourages the DNN not to make the same mistakes against an adversary.
By adding sufficiently enough adversarial examples, the network gradually becomes robust to the attack it was trained on.
Existing adversarial training methods {{cite:b73d975d24d6906e5b669a9b90e468a3a678845a}}, {{cite:cb68b5ba18aaf1782775ca6753b42cd093ebbb36}}, {{cite:61b92c33e8e8702a3358ffe251626af13cf4fc5b}}, {{cite:9ae0b58f986537dc226a4dd90d94707cee66bbb6}}, {{cite:e293f5b5f7c7ce7dd92a4378680b67016e9d8fc6}} differ in the adversaries used in the training.
Another related line of adversarial defence methods focuses on regularizing the loss function instead of data augmentation.
TRADES {{cite:f64453eac843b85fa9767ff8f2de459efedc42ed}} introduces a regularization term that penalizes the difference between the output of the model on a training data and its corresponding adversarial example.
The regularized loss consists of a standard cross-entropy loss on the unperturbed data and a KL-divergence term measuring the difference between the distribution of clean training data and adversarially perturbed training data.
| m | 4278078bb9a86d300e18bae6cb24f7fe |
Gamma-ray observations in the low-energy gamma-ray band from a hundred keV to several MeV address various astrophysical phenomena; the nucleosynthesis and the explosion mechanism in the supernovae {{cite:585fc7c4794d7b1dd0242cbfe83902a6d704b6bb}}, {{cite:c97222a8b57aa7b36958b248e03d59ca73258de0}}, {{cite:7536a20c00f54ef318a105d0c590e758a4e42a53}}, the particle acceleration process in the active galactic nuclei or the gamma-ray bursts {{cite:b56d7dc4f746c7bfd94d7de6782b28803e618d1d}}, {{cite:7c6c1b237f126b13561d0d67d91e071f5a54106e}}, {{cite:ef472940eb7bc2e261e4cdc64ff7576b30df3daf}}, {{cite:963d365f7c52c9b42920a28fec7031197ac732ab}} and electron-positron annihilation line in the Galactic center region {{cite:9f3a741b8d077985628574da38233fd0e58cc7d9}}, {{cite:01ea366d808a05517a5f3a878c859dcf690e2947}}, {{cite:9f31b4d8ab74ec270e8527d19d30bd8aef8ad77c}}.
However, the observation in this energy band remains poorly explored compared to that of X-ray, GeV and TeV band, known as “MeV gap".
Even now, COMPTEL {{cite:f0790526eb957a83d3735565a7383a494edc15bc}}, onboard Compton Gamma Ray Observatory launched in 1991, is the most sensitive observation of the MeV sky.
The causes of stagnant in MeV observation are huge gamma-ray backgrounds from the atmosphere (albedo) and generated in the instruments by cosmic-ray interactions.
In addition, conventional Compton cameras like COMPTEL have unclean images according to the Compton circle due to the lack of the direction information of the recoil electron. Such pseudo imaging is not capable of background rejection and does not keep quantitative imaging {{cite:307905c0608984d9a0271b8ff7b8e335d2278ba9}}.
Thus, it was pointed out that conventional Compton cameras need the additional parameters of the recoil direction of the Compton electron in order to reduce backgrounds {{cite:e64329f485d3fbb4b44857632b92cd58d81f71ac}}.
| i | 5b626bf2645f929b06defe7d45b41db3 |
In high energy astronomy, Vaughan et al. (2003) show how nonstationary long-memory autoregressive behaviors, commonly called 'red noise', affects the variance of binned light curves. Some high energy light curves are spectacularly nonstationary such as prompt gamma-ray bursts and accretion systems like GRS 1915+105 with dozens of variability states {{cite:e5cb0fdf9fc2bd37f6322adc5d8d16ea7e324386}}, {{cite:0af512d8c4d4360d2225623a41508def60982acf}}. In such cases, local regression, wavelet analysis {{cite:582eca011d8141361f1ac5bdfe7e00bacd199874}}, {{cite:3f122699efcd2b2015029d0c043fefa95ed2d066}} and multiple change point analysis {{cite:dfc58b2b043d3d697e12507f9768de910d16338e}} might be effective analysis methods. The Bayesian Blocks decomposition popular in high energy astronomy is an example of a likelihood-based parametric change point modeling procedure for nonstationary high energy lightcurves {{cite:d3ff3f6745acbddc57f020ef1016b3b09598450e}} (§REF ).
| m | f2a75319c44f4d002471f5fe4f5b3973 |
To realize the full potential of this framework, described here are several topics for future research, including: incorporating cell-type specific neuromodulatory signals {{cite:d6db03fa9f7a17c97bae73a153e6f36302e678e4}} into the learning process; exploring the addition of glial cell dynamics {{cite:cd0b6b7cbd9c017dad47b131624d21e98252429b}}, {{cite:381505eabb4735c05c820883ebb7589c6d47a3d9}}; providing deeper insight into the learning capabilities of different plasticity rules in the neuroscience literature, such as the wide-range of existing voltage-dependent plasticity rules, rate-based plasticity rules, and spike-timing dependent plasticity rules; and exploring the use of this framework on robotic and reinforcement learning experiments. Another direction might explore learning the neural architecture in conjunction with the plasticity parameters, since architecture is known to play a significant role in the function of neural dynamics {{cite:d78c8616321db72642a0fcba1232d7c245f9be74}}. Recent works have explored learning the plasticity rule equation in addition to the plasticity rule parameters {{cite:3cc6739af061c9f17b4b63f87c4850860c4893e8}}. A differentiable plasticity rule search constrained toward biological realism may provide more powerful learning applications of this framework.
| d | 55b1179e3f20c95270e1cff13b5a62a3 |
The usage of synthetic data has been combined with real data to produce more complex scenes. These are applied especially for techniques that explore the generalization of their methods in non-expected scenes, i.e., using datasets not used in the training step {{cite:4172285a3f5f9e525ac206fdbe0d1dc11ac8a651}}, {{cite:6fd2e37d21ce7b6504bd5d1b708c77b8756962c4}}, {{cite:64930c452c0197641105e01078875b2a5fe59f39}}.
| d | b6aa78894fc2cfc3a28ed201be416ce1 |
As shown in Sec. ., in general, when the light coming from an AGN is {{formula:8e15b36e-18d8-435e-b8ad-b28455048f44}} 25% of the total galaxy light, most of the used morphological parameters and therefore the morphological classification of AGN host galaxies can be significantly affected. We found that the classification of early-type galaxies (elliptical and lenticular) hosting an AGN will be more accurate than when dealing with spiral and peculiar hosts. Difficulties in classifying late-type galaxies in comparison to early-types have been already observed in the past, e.g., when studying the effect of survey resolution and depth on the morphological classification of galaxies {{cite:b9f06871be47958f1419da1d225c936cd4a00dc3}}.
| r | 172aa6969c48a60e4deaac318e2b1807 |
Invertibility for real-image editing. Much like other GAN-inversion and latent space manipulation methods {{cite:621459918441255992c83efa6b1526c856887a09}}, {{cite:799bb5c6a67c9c9e44d43a8825758cb6ac9e52c0}}, {{cite:ba7dbb33de761f4f9430e49f1399536427d1f2e9}}, {{cite:30269ddd2484da1e24b0ad72230516ce3b2de379}}, {{cite:05dec2694fec0ed8952055c968316415f5efcebe}}, {{cite:98497f71c8c586112183a208ff58f27d108bf6fb}},
accurate real-image editing with paint2pix is highly dependent on the ability of used encoder architecture to invert the original real image into StyleGAN {{cite:7fd4fd4f7f0b5f9f91653d42401fd426e2b1e986}} latent space.
| d | a6dc0bde7d4128b3114b355be2dd559c |
A second follow-up question involves the supersymmetric version of {{formula:177884ec-1286-463b-afaf-f74474e75d34}} deformations. There are analogous deformations which are known to preserve both {{formula:2037aa18-3e67-4a4f-8d31-781be59af4ea}} and {{formula:ab67192d-2aac-44b5-82b0-da6b2ae064a5}} SUSY {{cite:9eae2e23547867eaf027480d2fb33ef04e0984fc}}, {{cite:8109a2aca06a40f8899d0191acaf8c3a846a574b}}, {{cite:f68a47a914c36d86cee6ba09ee721731aed62478}}, {{cite:b4b05602f6d0498321cc3c1b7e17407dbe177ca4}}, {{cite:f1738f5685b0cc9912a44113197e692f576e00ca}}, {{cite:9f9dad8e688a9e52ffbd720ad84f3c3273ff1b90}}. One would naturally expect an analogue of CDD factor to exist for S-matrices of these deformed theories as well. The existence of integrability and supersymmetry should impose very strong constraints on the quantum dynamics and it is possible that nonrenormalisation theorems can be systematically proved for these theories. Even if the undeformed theory is non-integrable, given the indications we have uncovered in this paper, one can reasonably expect some definite structure to exist dictated by an intriguing interplay of supersymmetry, integrability, and renormalisation.
| d | ad24cc70da9c343be0235d8f8a5e4b6a |
In Fig. REF , we show the {{formula:c7f441e1-5c4f-4ce3-a754-d8457244a2da}} favored parameter space on the plane of
the total branching ratio of {{formula:2fba36a8-68f5-4cb2-871f-1cab2800cb7e}}
and muon anomalous magnetic dipole moment {{formula:1c8895a6-4831-4e95-b0de-92de91fc1781}} .
As mentioned above, the main contribution to the {{formula:33df3820-fc3b-44a8-9c78-0952b386a1a6}} is from the {{formula:320667f6-dbbf-484e-b72c-7d5c63de6208}} boson diagram
and a large portion of parameter space can be excluded by the current MEG experiment.
On the other hand, the main contributions to {{formula:163a72f3-b0de-49f7-9c2b-dd7299a70572}} in the model are from {{formula:2329df08-13f6-4128-9753-5d2461b9a18c}} and {{formula:d27522ae-e647-4c41-aa33-57575b7ff31d}} diagrams.
The contribution from the {{formula:50557f03-dc99-489a-a588-83d3e221498c}} diagram gives a negative value for {{formula:7ba23505-2ddf-49a9-aa24-afaff6a33b79}} ,
whereas the neutral Higgs and charged Higgs contributions are both suppressed
for the current viable parameter space in the model.
One can see in Fig. REF , the total contribution to {{formula:bb5b6434-68c2-4f59-bb58-b54480259f7d}}
is not reaching the {{formula:26135caf-189e-4ee4-bef0-e378f8f48199}} region (shaded light blue) for the muon anomalous magnetic dipole moment measured at BNL {{cite:a84e16bef1624f193e6c332bb8c17f0096602a7c}}, {{cite:7a60c0021cd972050d9924a91436f481f8571945}}, {{cite:faa208f618c5a5d487e0fa63563dcf01640249c1}} and FNAL {{cite:731d6af42b64277bf29e97b0e0813df21347581b}}.
We expect the {{formula:5aa00afc-10e3-40bd-862b-96003e5189c3}} can be enhanced in higher loop diagrams such as the two-loop Barr-Zee mechanism {{cite:ffe236ddaaba9465c7c83336cebcfc1b7843511a}}.
Calculation of these two-loop Barr-Zee contributions is thus highly desirable but nevertheless beyond the scope of this study. We hope to return to this issue in the future.
{{figure:60189ef4-9549-496a-b0ef-a620802e86f5}} | r | 66e06d8a4acfa8e925e13e8966bc9f2d |
Neural networks performance is often compared to human performance {{cite:06a5fedd6d45bf5c917ca2405fa27caddedf106f}}, {{cite:1d97cea3cd93a34d5da29eff49f9db1d4ce38be9}}, {{cite:7fb8c64de217430754e9f3d4aba6e94c7dbdf2d1}}, {{cite:f2afd5d41a3c64faf60bc4301488536ec46e7fd9}}. A fundamental feature of human perception is that it supports widespread generalization, including combinatorial generalization (e.g., identifying and understanding images composed of novel combination of known features). Current CNNs are poor at generalizing to novel environments {{cite:3d78878bd0047163adefeb8e55e7cd17481449da}}, especially when combinatorial generalization is required {{cite:e14d3dc95f4e54563136031cf637419f66786f55}}, {{cite:7024e988d4d12727c67fc5501d559f618b733648}}, {{cite:ee1a0e51d8ad393129d56ea3c8aa5b610cf07c5f}}. Here we have shown that CNNs are able to extract latent principles of translation invariance from their visual world and to re-use them to identify novel stimuli with very different visual forms in untrained locations, which constitutes a weak form of combinatorial generalization. An interesting question is the extent to which stronger instances of generalization and other fundamental principles of perception (e.g., Gestalt principles of organization, {{cite:97dc15e6e36f8dbf4dd50d55aa228f377e537177}}) can be learned in standard CNNs trained on the appropriate data sets, and what sorts of generalization requires architectural innovations. Without the right training environment, it is not surprising that CNNs fail to capture the cognitive capacity of the human visual system {{cite:6f92850c53c22dfe272918b7272df32ed5e91e34}}, and the only way to address this fundamental question is to train models under more realistic conditions.
| d | 5e8795fa72d0c2dfaa97d9b97477c3b2 |
Large-scale dataset of high quality annotations is the fundamental ingredient to recent advances in supervised methods with deep learning, , ImageNet {{cite:f94c2facacea87bfd564acf4e23401655dbc6190}} for image classification, COCO {{cite:c284224ad5c85753b53957dfbb6b38fd54cd7135}} for image detection, and ShapeNet {{cite:1c7734aad873609d26e368c0e999f88163be26b6}} for 3D shape analysis.
Existing datasets for symbol spotting on floor plan, i.e., SESYD {{cite:6fc3b17c96cf90a5439f5d5a9f029267d1d350df}} and FPLAN-POLY {{cite:4f3a75cc721c67aaca54f9c3c1d7ff5946665bf1}}, are either synthetic, or inaccurate, both with only a few hundreds of samples.
Fan {{cite:916cb87742ec51d865ac072f7fbd6ddbc5346540}} built the first large-scale real-world FloorPlanCAD dataset of over {{formula:e28cd7e3-395e-4e74-a078-7601176b9b73}} floor plans in the form of vector graphics, and provided line-grained panoptic annotations.
| i | a66968cbd3fa56e20d2c541e371a86a3 |
Results on ImageNet: Results for CMSF-KM and CMSF-2Q are shown in table REF . Both variants outperform MSF baseline with a larger memory bank. This empirically supports our idea of bringing together far yet semantically similar samples (Fig REF ) by constraining the neighbor search space on the memory bank. CMSF methods also achieve state-of-the-art performance on both NN and linear metrics when compared to approaches with similar computational budget. We compare our method to other state-of-the-art approaches with 200 epochs of training in Fig. REF and observe a good trade-off in terms of accuracy and compute for the proposed CMSF method. Note that we train without symmetrical loss and multi-crop strategy which are known to generally improve performance {{cite:6daee35dfd2002c510d7f88c46a3268ee54655d6}} at the cost of significant increase in compute.
| r | 22a9c0ee3a14a212d042ee855f795942 |
dRGT theory cannot provide a unique source for both dark energy
and inflation. Motivated by this shortcoming of dRGT theory, and
also, the successes of pole Lagrangian in describing the Universe
{{cite:108e7cd3c075c8f8637146304256cfad77bad690}}, {{cite:99ad60336121411490e40baf97793662d42e75f5}}, {{cite:be41ee7e1345ffd249149306fe6e9c927d6bef7c}}, {{cite:0858b4e70fd6745eda9eebad1a7a13e81a90ee2e}}, {{cite:ed77be1bb21bff2f13857158200d58101cec25e4}}, we addressed some pole inflation scenarios in the
framework of dRGT theory. Throughout our analysis, we only focused
on power and exponential potentials, both of which can
satisfactorily produce {{formula:316c28a7-6ce0-453c-b35b-eea44b1f2e28}} number of e-foldings, required to
solve the flatness problem. Also, comparing the results with the
Planck 2015 data, it has been obtained that the established
model provide acceptable outcomes, although this results do not
lie within the {{formula:7ab047a0-3ac6-403e-8be3-864f8bb6cf97}} CL of the Planck 2015 data.
| d | b6ce32b255321ed66dd9d24a923ea820 |
[t]
Deformable Surface Reconstruction
[1]
Inputs: Template {{formula:16da6dfe-6564-4925-8ac7-d3f715f63eb1}} , matchings {{formula:75b39651-5570-44d4-b00d-fd86014d44e3}}
Output: Estimated surfaces described by {{formula:19b9a079-115e-400c-ace8-2c9ab2138f2f}}
Compute {{formula:6d7c90c1-d6e6-4a13-8b58-d6f459aacbd6}} according to {{formula:580d5b31-42ee-4a50-81bf-c9e38fe33375}}
{{formula:04310d8e-b33c-4787-b880-3f87cf1eef65}} Over-fit to template
Store {{formula:9bb82d37-6cbb-4e80-bf3a-d49fdcd81cf7}} {{formula:950c1163-be96-4f73-b4fb-814dc3014dcf}} Metric tensors of the template
Let {{formula:6655cc03-5013-45de-aec4-cad9fd333848}} Needed for eq:temp
{{formula:fe38c0ad-bb1b-47a2-b616-23e146f0228a}}
{{formula:25ea856c-f52f-43d6-97dc-8c46e0a65656}} Compute loss eq:loss with stored metric tensors
Representing the state of a deformable object alone is an open challenge {{cite:f1cbd0812222e0631e37e539e953691c69f7699e}}, {{cite:dac7a549b460cc8154541043ab5e8dea95cf0133}}. Most *sft methods represent objects using meshes, but an alternative is to use the explicit neural representation introduced by Groueix et al. {{cite:b304df7030cd7e539bed49c0f1cd0ae027647241}}. Such a representation encodes a surface in the weights of a neural network representing a mapping from 2D to 3D. Parametric representations are a general way to express a surface, and their great flexibility allows to control deformations with intuitive parameters {{cite:4dd096014019e1c0653a34a6ab24437da03b76fd}}. Given a parametric surface, we can analytically compute the first and second fundamental forms, Gaussian curvature, and surface normals {{cite:dee1bec5b3aeb1374dfb7433f14d28789c97412f}}.
| m | ea69eb8de59c162611f1b68a63313837 |
We study Witten's string cubic open string field theory on multiple {{formula:5f6d2d8b-630e-4312-bc9c-89809519cde6}} -branes {{cite:75df14d07507a85b177ffce2fe52a0ad4327d628}}, {{cite:aef8e437dda122e436e7bee55d78d9fbdf43de24}}, {{cite:6422ee7a8e3b371f2be26a10aadcd617bef86abc}}. On multiple {{formula:e3a88094-8413-4b68-9a93-a73ff5e4e965}} -branes the string field carries {{formula:8dd8f1d3-e3ed-4cc4-8f9e-d6cdb82330f9}} group indices and its low energy excitations are massless non-Abelian gauge fields and massless scalar fields carrying {{formula:fdc9c557-b4f6-4c9e-85b5-7fbefeca87bc}} group indices.
{{formula:1914d2da-8dd2-434a-8db6-260303a2778e}} -branes play important roles in string theory: They are dynamical objects with both ends of open strings attached, giving them non-Abelian symmetry. They appear as
{{formula:ef1dbae5-80c2-4af1-95d0-e96ff9ed72c4}} -brane solutions in supergravity and provide a theoretical background for the holographic principle, which now has a wide range of applications in various fields. Thus, it is important to develop string field theory on multiple {{formula:f2d21a5d-2c81-4e3b-be07-b70e285d3043}} -branes. Recently we studied covariant string field theory on multiple {{formula:b2e29e9b-36b4-41e2-8448-15ad58068d49}} -branes {{cite:45b89fccd1f3477cd911a3d43ee38f6b1cd478e2}} in the proper-time gauge {{cite:c446d81ec6c99f24b9046f6daa3c6aa500997174}}, which may be deformable to Witten's cubic string field theory {{cite:03601e21578a49f443d183967400985933412349}}, {{cite:8cc32cc6d1e38de2f37b074590173ea313789282}}, and obtained some fruitful results: On multiple {{formula:4ed8dbe1-957a-4d7a-8c5c-bba6b90f3a0d}} -branes string field theory reduces the
Bank-Fishler-Shenker-Susskind (BFSS) matrix model {{cite:809255b05d477aeed322c58bd9696dca0320c77f}} multiple {{formula:bebe2b11-4bf1-46dd-bf16-7ff77b42b1dd}} -branes (D-instantons) to the Ishibashi-Kawai-Tsuchiya (IKKT) matrix model {{cite:fdbe89cf6884646fe8acc43c292526d4cf81810d}}. Since covariant string field theory in the proper-time gauge is deformable to Witten's cubic string field theory, we expect that Witten's cubic string field theory produces the same results.
| d | 323302b37930960400a39d22ef60a2ce |
Network backbones have been computed using the `distanceclosure' python package developed by the authors and freely available at https://github.com/rionbr/distanceclosure.
Network plots have been rendered with Gephi {{cite:4a0a89a51bc734a4a0f0a261779358fd6a773dc2}}.
Distortion distributions have been fitted using the `powerlaw' python package {{cite:b054bf4a78da3f5efbe96e56e22a12da8b101b81}}, {{cite:3761c6c88cc11b7184dd42707db0ddb9dae6365c}}.
| m | 04bd833d6e4fb2a5ab71a7e5c1119d7b |
where, using the same notation as in the autocorrelation function, {{formula:c182ff16-9334-436e-a73e-eb04f025eeb1}} denotes the lag time.
The difference between the EA-TA-MSD and the EA-MSD (Fig. REF a) is a direct indication of ergodicity breaking in the
motion of Nav channels {{cite:ce1d02a51f273cfafcc972e99d181acd935da25b}}, {{cite:9214ac08fae334d9dce362cbefcc264b8fddc4d8}}.
In the context of our model, the ergodic hypothesis breaks down since {{formula:7849a161-c3c6-4925-8be1-d2352f6b2dcc}} .
In theory, it should be possible to use the ensemble-averaged MSD to extract
information about the exponents that characterize the motion. However, when the number of trajectories
is not very large (as is usually the case in live cell experiments), the estimation of exponents from this metric is
very poor due to statistical errors. This effect can be directly seen in the confidence interval of the MSD
in Fig. REF a. Thus, we propose here to employ in addition to the TA-MSD a robust metric such as the PSD.
| r | d67de377ae0491cd0eb83dafb3c4b192 |
In this article we shall be concerned with a
resource sharing game. Such games model
instances in which a common-pool resource (henceforth CPR), which is prone to failure due to overuse, is shared among several users who are addressing the problem of choosing how much to exploit from / invest in the CPR without forcing it to fail. Resource sharing games arise in a variety of problems ranging from economics to computer science.
Examples of CPRs include arable lands, forests, fisheries, groundwater basins, spectrum and computing resources, the atmosphere, among many others. Such CPRs are, on the one hand, usually regenerative but, on the other hand, subject to
failure when several agents exploit the resource in an unsustainable manner. Each agent exploits / invests in the CPR
in order to obtain an individual benefit. However,
it has been observed that actions which are
individually rational (e.g. Nash equilibria) may result in outcomes that are collectively irrational, thus giving rise to
a particular social dilemma known as “the tragedy of the commons" (see {{cite:bd19c2b3ef82a922f710c93d92c7f5c3c9664d07}}).
It is thus of interest to
investigate equilibrium points of resource sharing games,
in order to better
understand situations where such a social dilemma arises.
This is a topic that has drawn considerable attention, both from a theoretical and a practical perspective.
We refer the reader to {{cite:1c0046c581f92c744edbd8b7a29e91bcecf18e39}}, {{cite:9e14a7edfff6e42fed43bd2f8ffc98014cd03604}}, {{cite:11513e8954839d6176c526b825e65d7f8ac6e1e0}}, {{cite:ea74a403ae7194436c91fc3585229e1e886d6324}}, {{cite:62654c1680e53787c58a40f2131f4f86e26af14f}}, {{cite:7b6de2ba37d5b450a957040b7a9158fa1c782777}}, {{cite:e8aaaba881b3ff11023d5a37ac8ba292bdcbd08f}}, {{cite:9fbf3b2678790f81a9f7914113aef54d05091c12}}, {{cite:c31f1557c6f020ff188326bde6fd11feb528d440}}, {{cite:e67428c38293ca36e8ca61f3a53039de10add0dd}} for applications, variations, and for further references on resource sharing games.
Let us remark that most results in the literature
appear to focus on games
in which players invest on a single CPR.
In this article we investigate a resource sharing
game in which players are allowed to invest in
several CPRs, whose performances are
mutually independent. To the best of our knowledge our work appears to be
among the first to consider resource sharing games on more than one CPR.
| r | c663bfa9c6fe87a145c59da7ed8047d5 |
We propose an approach SOTitle to generate the title of the question post from Stack Overflow by considering both code snippet and problem description. Specifically, we combine the code snippet and problem description as the multi-modal input of the Transformer structure. Then we formalize post title generation
for each programming language as separate but related tasks and utilize multi-task learning {{cite:e889655da1bc6947d26e547ab03c7ea24612146f}}. Finally, we use the SentencePiece method {{cite:34e2f71ac83674d870b655d97fe81e9b5bb42c1a}} to split the code snippet and the problem description to alleviate the OOV issue.
We construct a high-quality corpus and this corpus contains 1,168,257 high-quality problem posts for four popular programming languages.
We conduct empirical studies on our construct corpus to compare SOTitle with six state-of-the-art baselines, including the recent post title generation approach Code2Que {{cite:e1cdd7bc4b3ec720049953bc250764174586c908}}. Final empirical results show the competitiveness of SOTitle. Moreover, we verify the effectiveness of SOTitle via human study.
We develop a browser plugin based on our proposed approach. By using this plugin, users can generate high-quality titles for their submitted question posts in Stack Overflow.
We share our scripts, trained model, browser plugin, and corpora on our project homepagehttps://github.com/NTDXYG/SOTitle, which can facilitate the replication of our study and encourage more follow-up studies on the post title generation for Stack Overflow.
| i | 3b512f1cf09265efbb4d552d76c8456b |
In this paper we study the high dimensional analogue of the non-lazy random walk.
We are specifically interested in going beyond Alev and Lau's worst case result {{cite:ec2b87499ec35885def58a4d2c670ed8b575444e}} and relate the structure of the cochain to its expansion:
| r | 200e36a5ce04cd5083392461b4420f57 |
The computed total and orbital-decomposed density of states (DOS)
in this lowest-energy magnetic state as obtained from LSDA+{{formula:be832f32-b4bd-41ca-9ee8-4fe11c60089f}} are
shown in Fig REF (a). The DOS of Fe-3{{formula:0f236ba4-e13a-4ce2-bf36-635f2c73a6f0}} clearly
shows that the majority spin states are fully filled up, and the minority
spin states are empty (see Fig.REF (b)). This is consistent
with the picture of the high-spin ground state of Fe{{formula:74b6c820-a80b-4c93-83c7-9ce322f60b17}} ions
(3{{formula:94d0b018-bc7c-44c2-8238-8cbd8c15d3f6}} ). The Mo-{{formula:71692325-e31b-4209-9faa-d1e45d76af40}} states (see Fig. REF (c)) are
found to be completely empty, indicating the nominal {{formula:f4b750fb-12a3-447d-8cf6-0a4a9690a29b}} non-magnetic
state of these ions. The O-{{formula:60da790d-f978-4003-ad67-abbf7f080695}} states are also delocalized and spread
in the entire valence band. The insulating gap of {{formula:06e6f5a2-256e-44f8-bfe9-b2bf8f1d7083}} eV is found
between O-{{formula:e85759cd-ee36-4ee8-9c26-5ae59fa0bb58}} and the Fe-{{formula:ba249420-8a5e-4fbe-9fcc-079683875282}} states, making this system a member
of the charge-transfer insulator in the Zaanen, Sawatzky, and Allen
(ZSA) scheme {{cite:8bd2b5a43cb62bb5f120a90786a95f5627709234}}, {{cite:780f8ba823f2c9ea8a0741816bab479c591964f5}}.
{{figure:787cb2e1-b990-409e-b646-a107185729f3}}{{table:837f92cc-d517-4e20-ae6e-1aa2c1cb8e42}} | r | 941c49a3bd2d9499099e01e81286adc8 |
The pre-training without cost-sensitivity allows the autoencoders to distinguish between the majority and the minority classes. It has been proven that autoencoders map similar values to similar ranges {{cite:56a5ab76d2b53c4f92f4e73eda798b4de95b5a8e}} and thus for classification in such severe imbalanced datasets, they are very useful. Autoencoders are extensively employed in outlier identification {{cite:8ee1d4a597956dde055f9e9aef1bbb13ce91e901}}, {{cite:f0859659080f2b1008dca11c244de8e85a4b1aa2}}, where an input with a substantial reconstruction error is identified as out-of-distribution, as the quality of reconstruction is expected to decrease for inputs that are considerably different from majority of the training data. The traditional AE-based pre-training is also favoured since it is highly stable and simple, as well as providing a decent initialisation to begin with. So, the retraining is to just fine tune the local models according to the proportion of the different classes present in the local dataset.
| m | 34cf3a8791488e6fd448c18107dc1327 |
Recent work on distillation has produced significant improvements over vanilla knowledge distillation {{cite:c8c877793339a317eb926a28a67c91cf5508598b}}. We believe that Knowledge Distillation with Feature Maps could improve both natural and robust accuracy of student networks. Adaptive data augmentation like AutoAugment {{cite:b38e5303388b34466ec9fba83bdb721629094942}} may also improve performance of both normal knowledge distillation for robust teachers and ARD. Finally, with the recent publication of fast adversarial training methods {{cite:3fac2ecd395f1baa1ea6aa3430c87bc92f95c328}}, {{cite:13ffadfcb9a5054202baecdcf25842d6c1095c95}}, we hope to further accelerate ARD.
| d | 42be7885a61ff4b5b4eaf3e0fc05b949 |
We study the dispersion relations of KAWs by numerically solving the full set of the linear Maxwell-Vlasov equations. Linear Maxwell-Vlasov theory has been described in detail in the literature (see, for instance, {{cite:f6a22e896ee645a066f02187dc8356c8fdddad38}} and {{cite:cb17e7b42b56548789e9a0ff697d77df994230b0}}). We summarize the relevant results here. Linear plasma waves are eigenmodes of the wave equation:
{{formula:c8718b2b-eed3-42ad-b8a4-bdd9e1de09db}}
| m | ce73818b65d88c06855e247242c46ada |
Throughout this paper, we presented MFSSA as a novel technique of dimension reduction of a MFTS. We found that the MFSSA problem is solved by performing VMFSSA and we also developed HMFSSA, presented in supplementary material, as another approach but found that it was more restrictive and not as informative as MFSSA. We also developed MFSSA to be able to handle functions taken over different dimensional domains to uncover a more dominant mean component for the intraday temperature curves/NDVI images bivariate analysis. The MFSSA algorithm is available for use in the Rfssa package {{cite:a7f4cd40aea932b193681058610edbd9fbdbcc72}}, available through CRAN.
Supplementary Materials
The supplementary material includes plots and animations of the left singular functions of our real data study in the manuscript, another remote sensing real data study example, and the full development of HMFSSA. We also include proofs of the lemmas and propositions of the manuscript.
Left Singular Functions of MFSSA
In this section, we build on the real data study presented in the manuscript by presenting the left singular functions. As mentioned, we apply FSSA to the temperature curves and NDVI images separately, We also implement MFSSA to the temperature curves and NDVI images together, both with a lag of 45, to obtain the following.
{{figure:7a3f5126-72cc-433d-8205-f44d31a97866}}Plot (A) of Figure REF shows all {{formula:c58047e1-f959-4673-8dfe-137aceefbf2a}} functions of the first four left singular functions of FSSA for the temperature data while plot (C) steps through each function in an animation. Plot (B) of Figure REF shows all {{formula:9a6dab0e-b342-41be-bac5-c22b78a53604}} functions of the first four left singular functions of MFSSA for the temperature data while plot (D) steps through each function in an animation. We see in the temperature data, that when MFSSA is applied, the mean component becomes stronger. We apply FSSA to the images with a lag of 45 and compare the resulting left singular functions for the NDVI images to those we obtain via the MFSSA analysis in the following animations.
{{figure:5f942bb4-9d9d-4077-9d40-95aca54e20f9}}Here, we see little difference between the animations.
MFSSA Applied to Remote Sensing Density Curves
To further show that MFSSA enriches data analysis of correlated variables, we use a bivariate example of near-infrared (NIR) and shortwave infrared (SWIR) images taken every eight days of a region just outside of the city of Jambi, Indonesia between {{formula:b9271183-f74c-44a2-abfe-50af9fdb8182}} and {{formula:b7c19705-73be-4571-8811-a4b8a4935a6a}} over the timeline of February 18, 2000 and November 25, 2019. The wavelength of the NIR images range from 841-876 nanometers (nm) and the wavelength of the SWIR images are within the values of 2105-2155 nm. NIR light can be used for imaging vegetation as it is used in the calculation of the NDVI measure {{cite:3ab94c9ac1bfdebfe59605e0a2d90f62a078a61b}} while shortwave infrared is often used for imaging the moisture content in soil where a lower surface reflectance (SR) corresponds to higher moisture content {{cite:62f7aaf6bc319839f48e55986d10198624fd77f4}}. As mentioned in {{cite:81c7ce4b22fc15c4484bbabed9c4610d1acd0030}}, it appears that this particular part of the Jambi province was a hot spot for controlled fires between 2001 and 2015 and this loss of vegetation over the course of about a decade will be reflected in lower NIR and higher SWIR SR values as time moves on. We obtain the KDEs of both the NIR and the SWIR SR images using Silverman's rule of thumb {{cite:ce493998bb9c6129d05481db90842dfb27cd1aea}} which we then project onto a cubic B-spline basis where the degrees of freedom are chosen using the GCV criterion. In addition, we replaced outliers in the SWIR densities with the average of densities from the preceding and proceeding days. Similar results, as compared to the following, still hold even if the outliers are not removed. Applying FSSA with a lag of 45 to the NIR and SWIR densities separately, where this choice of lag approximately captures annual behavior, gives the following exploratory plots.
{{figure:9ae8db16-4435-4a48-85b9-bd78f8443da9}}Figure REF subfigures (A) and (B) give us the right singular vectors and left singular functions of the NIR densities while Figure REF subfigures (C) and (D) are the right singular vectors and left singular functions of the SWIR densities. We find that applying FSSA to the NIR densities captures seasonality in the second and third components while trend is present in the fourth component similar to the NDVI results of {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}}. Applying FSSA to the SWIR densities shows that trend is a more dominant behavior captured in the second component as compared to the seasonal behaviors captured in components three and four. Applying MFSSA decomposition with a lag of 45 to the bivariate NIR/SWIR example, where this lag is chosen to capture annual behavior, gives the following exploratory plots.
{{figure:b72f95c8-08bd-4391-bab8-8ea35c28081b}}The bivariate FTS can be found in Figure REF subfigure (A) while Figure REF subfigures (B) and (C) are plots of singular values and w-correlation respectively. See that Figure REF subfigure (D) gives us our MFSSA right singular vectors which showcases the weights that are multiplied by the left singular functions shown in Figure REF subfigures (E) and (F). Since we are performing MFSSA, we obtain 45 left eigenfunctions that correspond to the NIR densities as well as another set of 45 left eigenfunctions that correspond to the SWIR densities. Notice the trend behavior for the NIR densities is present in component two as according to Figure REF subfigure (E) which indicates that adding SWIR densities into the analysis with the NIR densities created a more pronounced trend result as compared with Figure REF subfigure (B). To this end, we find that performing a bivariate analysis on the NIR/SWIR densities enriched our data analysis as expected.
HMFSSA
We begin this section with our discussion of moving from HMSSA to HMFSSA. As we clarified in subsection 5.1 of the manuscript, we need to assume {{formula:99e56cd4-0a4b-4c06-a0ed-231b85f4b3e8}} , {{formula:6adf2ce1-e8f1-4c58-8ed6-5d34a361bcd4}} , and {{formula:7ee55585-7f9c-4d31-8ceb-37c6b5610344}} 's belong to a common space {{formula:aaa6e9b9-9dde-4e6e-a954-0adda00af858}} , for {{formula:fcecc1eb-5b24-4f34-9473-29e5d3cb374c}} . Notice that while the domain for each variable is the same, one may evaluate each variable at different points along {{formula:1349715b-edbb-4aba-8c43-6fa70cb135b0}} . We present the four main steps of the HMFSSA algorithm in the following subsection.
Embedding, Decomposition, Grouping, and Reconstruction
We choose {{formula:37a570c2-5395-4edb-b2be-7d64d1003e82}} , set {{formula:e7e55861-bbb2-4b78-ae98-8f699dbec9e3}} , and we define the linear operator {{formula:f032946e-2f45-4970-9b1d-5a2bab374bdb}} given by
{{formula:b6bc302c-4ac2-486c-bc3d-7613dbde6c4e}}
which follows a similar form as compared to equation (5.1) of the manuscript. The operator, {{formula:bdc0b0e5-1472-435d-a94e-10eacc8612e6}} , is block Hankel, has rank {{formula:a0f45cf8-a641-49e1-9e05-fe93536097c3}} , and we have that {{formula:83b8582d-c472-4e1a-b278-d0ee016b2251}} . It is easy to see from the range of {{formula:878b7e02-fefa-46ff-9762-3b3ad327869b}} why all variables must share a common domain {{formula:99395123-bb1f-4e47-93ad-582ac76cf997}} .
Since {{formula:baeb1df7-9241-4381-baaa-476f94475578}} is a finite rank operator and thus compact, we utilize Theorem 7.6 from {{cite:f2bcda5dad2d3fead14933bcbd52566952549937}} to obtain the following fSVD for HMFSSA
{{formula:cc01e090-abfc-440d-899f-c5132b79cf83}}
where {{formula:a4fddbd1-f82c-4f0b-ad28-c13070c98250}} are the singular values, {{formula:d6f28d89-a1d3-4da2-a30b-268fb4ad0b0c}} are the orthonormal right singular vectors that span {{formula:96768e34-75d4-4bd4-b84b-7a917f85c5d5}} , and {{formula:c35af832-d502-43cc-bb75-b7b7b6ac9d77}} are the orthonormal left singular functions that span an {{formula:6dcf63bd-be00-4edc-b57b-bc6d76ce5145}} -dimensional subspace of {{formula:537ed1a2-2c2e-4517-bf93-c3aa2a071d63}} . Also notice that {{formula:10da8492-6bc9-4fc0-b741-a8548b034abb}} are rank one elementary operators similar to those seen in equation (3.4) of the manuscript.
The grouping stage of HMFSSA is similar to the grouping stage of other types of SSA where we form operators {{formula:7389ab59-7b00-4da6-892b-baae879b1837}} for {{formula:596a94e0-30ca-4451-bedb-8d9ffc2afd61}} . We finish by projecting each {{formula:c6019e5b-2a4e-40fc-bad4-799a1aa90bdc}} onto the subspace of block Hankel operators that map from {{formula:23632fd7-c2f5-4123-9cd5-4164051eb632}} to {{formula:365f92df-61d0-4044-a9ed-b40aaedff8ed}} to form a collection of {{formula:17025fa3-701f-4bc5-be59-308d36851f63}} reconstructed MFTS where the projection is completed blockwise using the diagonal averaging technique of {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}}.
HMFSSA Implementation
Implementation of HMFSSA is similar to that of {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}} since {{formula:ca6a0483-6526-4848-b44a-12eeff175866}} maps to {{formula:474050f3-374f-4486-9cec-28abab57b262}} . Let {{formula:0fc7c787-c815-471a-9f32-a5f0876e350a}} be a known basis of the space {{formula:9eb227ae-07a3-49a8-a857-c747a465c913}} such that any {{formula:5394a68a-2233-4e45-8fa9-78c3a596d51c}} can be projected onto the subspace {{formula:00e7abfc-a52e-4be7-b5da-4b43e8507165}} . As such, each {{formula:6f1e4df3-33ec-4bca-8c02-d181a3d2629e}} can be represented as
{{formula:45064518-bed9-4d75-a41d-5a2a1f2dd07c}}
Let {{formula:f043ce7b-8e7e-4c01-bcb5-2edbe7e47768}} be the {{formula:08390807-c6aa-4d8d-b101-4a54cde2e3de}} -dimensional subspace formed from the Cartesian product of {{formula:dce7dbdc-1cab-4032-a8cc-56dfd28f74cd}} copies of {{formula:a3effc84-ba4f-4b35-95fc-d8d2b5b24ed4}} , then the rest of the work in defining basis elements of {{formula:d04a3f78-32c3-41a3-bd96-0a855001a56f}} follows directly from {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}}. The work involving the expansion of the lagged vectors, the range of {{formula:ea46262d-074e-4101-b0f3-0779b3dfbe65}} , the definition of the coefficient matrix {{formula:780a55ff-461a-4c43-8311-0b7f51bfd8cf}} , and the HMFSSA version of Theorem 4.1 seen in the manuscript, also follows from {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}} except for the fact that we replace {{formula:ff3d26ae-f433-4b79-98ce-c14b706def7b}} with {{formula:e06869e8-2f35-419a-a335-83b260714585}} .
HMFSSA SWIR/NIR Study
To show that HMFSSA separates out MFTS behavior based on the covariate, we apply HMFSSA with a lag of 45 to the NIR/SWIR example and obtain the following plots.
{{figure:a30bec46-e361-493c-b377-2c473698c0af}}In this case, we have {{formula:5dca1e51-2e9c-40dd-8f83-63bc47538157}} right singular vectors that correspond to NIR densities and {{formula:e76f45d8-50c8-4ec7-95a8-2bb32fd36758}} right singular vectors that correspond to SWIR densities. It appears that the first component captures mean behavior of SWIR densities while the second component captures mean behavior of the NIR densities seen in Figure REF subfigures (E) and (F) which is confirmed when we compare with Figure REF subfigures (A) and (C). Rather than combining information to create a more pronounced mean component, HMFSSA works to separate out these behaviors by variable which is expected due to the similarity between HMFSSA and FSSA.
Proofs
[Proof of Prop. 3.1]
Notice that since {{formula:0b18dced-a7c6-404e-acdc-9b5e313bd8ae}} , then {{formula:4c24fc04-e8a3-4903-8bab-6fbf256b8d33}} is a rank {{formula:c19df4df-dc23-4d21-9b62-efbaa7b8b0bb}} operator and thus compact. As such, we have that {{formula:cdb39d9c-d54b-45dd-bb82-92e40cccea29}} is bounded. Let {{formula:7f92211c-4751-48c2-9a27-c3bf0874c08c}} and {{formula:f5124de5-41ca-4519-99dd-269ed7247f5e}} , then we have that
{{formula:b76e7fb9-08a5-496a-9898-5e60b615dbac}}
which implies that {{formula:f11dab43-f356-42f4-873b-f15cb3fe2c92}} is a linear operator. Now let {{formula:62f7b124-70b2-4a84-b875-4b388d33ea2a}} , then
{{formula:17afec88-2ec2-495f-b57c-b39e8dbaa019}}
and we have that {{formula:03b0f338-384c-4e29-9b6b-2d5e725d1e1b}} is the adjoint of {{formula:c3a6c8ad-7655-4473-b5b5-b0b025827379}} .
[Proof of Prop. 3.2]
Let {{formula:4c559763-9a8c-425f-9a54-cd6ce77c9eee}} be the {{formula:fbff8544-7129-43ee-9554-6616514e7d6e}} variance/covariance matrix for the {{formula:c4c39bd8-efc7-4686-b0ab-edc8b75cac10}} -lagged vectors of {{formula:92034b81-be8e-4fe1-ba97-d8b4c269f7e0}} . Since {{formula:d10ed5ac-6c64-4d13-9447-c230959d3d5b}} is a rank {{formula:a7660b55-2f18-4b16-be28-645226c46b4b}} matrix, the eigendecomposition of {{formula:14c13c83-2a88-4768-a593-94171b15d8e4}} gives a set of orthonormal vectors, {{formula:362dad9a-98b3-4b0a-8335-fea014e40ce4}} , such that for any {{formula:5aed82f4-4640-46a2-a8c4-fd6ce40bc126}} we have the expansion {{formula:c1e8d14d-95ec-4adb-862c-dbd9e1ce53a3}} . Notice that the set {{formula:e2816647-8766-4a19-aa16-138ff01f6aac}} are the right singular vectors of {{formula:bc6d22d0-6dee-48d9-b138-41e5dc4f9161}} , then it is true that
{{formula:bc6cac18-c607-46ba-a30b-5ec23c1dbd84}}
This implies that {{formula:f1e17196-9267-4506-93dd-160b1b4eec73}} and we have {{formula:4ef0838b-c191-46a1-8081-9be721f612e2}} . Now, suppose that we have some {{formula:4131f43f-3ff9-43c7-9f23-cabc61062800}} . Then we have the expansion given by {{formula:8e37d659-3561-4e8a-b1ac-c0d35284bba1}} . By Theorem 7.6 of {{cite:f2bcda5dad2d3fead14933bcbd52566952549937}}, we have that {{formula:db0246df-2105-40be-a097-d752b408a6ea}} has an SVD with the same eigentriples of {{formula:de26f2ac-6654-4eaf-bda9-13d08b1a27ee}} and we obtain the following
{{formula:b8b1b2f4-a94b-436a-bb2a-416cd53fc645}}
which implies that {{formula:c90d4e22-277c-40b8-b409-1ddbb249c687}} and we have that {{formula:03c9ba19-d1c7-4bd9-88ec-87b6bac131a8}}
[Proof of Lemma 4.1]
i)
Let {{formula:5ccbac08-609d-44c2-843d-837b5011156d}} , then we obtain the following elements of {{formula:b2e27940-eb80-483c-8362-9d391ea0d972}}
{{formula:c19e4bed-db63-4cf9-a142-4a6418578d2b}}
From this, we find that any {{formula:1a531f6e-92ca-4f07-878d-ccc222f8e54c}} can be expressed as
{{formula:4420ffb0-ef95-454f-a4ed-024023ee2a59}}
ii)
This part of the proof is a direct consequence of the proof of part i)
[Proof of Lemma 4.2]
The proof of this Lemma is almost identical to the proof of Lemma 4.1 of {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}} and holds without loss of generality.
[Proof of Lemma 4.3]
i)
Let {{formula:f6fd2e43-2adb-4d6a-9b09-5cb14eaf508d}} and denote the {{formula:6a53b8d9-2aa0-4c16-a8c0-03244db19a85}} element of {{formula:644a5d63-7507-492a-b048-746a8b517a95}} with {{formula:69669875-28eb-478c-b5a7-5977a55933f9}} , then we obtain the following elements of {{formula:f5a12fc4-54da-466b-8569-44c30298a804}}
{{formula:1cdbb21b-9067-4eef-9a8d-876aad32df7f}}
{{formula:479e92cf-46d2-4465-aee4-ceb3d7a35b0d}}
As a result, we find that {{formula:3ae4f10c-fbe2-4f0e-8fd3-ba70ba1ce0f4}} and the coefficients found in {{formula:a43d2ed0-abdd-4970-b029-dd304243bf6c}} are found in equation (4.3) of the manuscript.
ii)
{{formula:3ef013bc-3b70-40ea-95a3-3d9870627509}}
[Proof of Thm. 4.1]
This proof is a direct consequence of Theorem 4.1 of {{cite:064c5f86aa55acba292a6a9e46e0920e1ba423e0}}
[Proof of Thm. 5.1]
i)
Let {{formula:2b3e336a-107e-491e-9f2b-bc517932a0be}} . Then we have that
{{formula:a60cdf35-3f7c-4793-b731-4741c3729deb}}
and as such, we have that {{formula:fab234fb-2e6a-4bcc-a4bd-a9bcae6d393d}} .
ii)
Again, let {{formula:fac0582b-69b9-4863-b261-bb0b623d87b8}} , then we have
{{formula:43e6c773-099a-4a3d-9b79-939c42869054}}
This implies that the {{formula:191d409e-250b-4c68-8e26-64228412bafb}} eigentriple of {{formula:258d0d60-098b-41df-9908-93f4bc417753}} is {{formula:a353a4a0-a622-4fd8-ba22-6a1d6d4c1dcf}} and that {{formula:7ed4237f-74fb-424d-856d-dca41d3e16bd}} .
| d | 0f69c477dfeedff8dc44fd024d8a96ab |
Indeed, such an adjusted TB Hamiltonian fairly accurately reproduces the electronic properties of TBLG as obtained in {{cite:edea93e025037b8a5e6ff4fc0285bf32c71faec8}} as well as in experiments, e.g., in {{cite:2a0aabe498d212fa3d5d66512ab374b5a86ee69b}}, {{cite:0f2f7a4b9a0c98eb1fdf4e3744fbcf2d397d177f}}, {{cite:a5b7c409084ce8cd4b0b90bcc0f8c327784f6030}}. As a clear illustration, the almost flat bands near the Fermi level is perfectly reproduced in the relaxed TBLG in the vicinity of the magic angle (i.e., {{formula:4176b42e-48de-4a12-851a-536b03578816}} , see Fig. REF below) as experimentally observed (e.g., see in Ref. {{cite:2a0aabe498d212fa3d5d66512ab374b5a86ee69b}}).
| m | 08447716a49b9682459cfe76e38a5a74 |
We aim to modify the geometric rules of a generative model according to a few user edits. Given a pre-trained generator {{formula:bd9912ee-5148-4896-94ec-df8b6cb148c6}} , a user is asked to edit a small number of generated samples. For generative models that use an intermediate latent space (e.g., StyleGAN3 {{cite:f25087c3d2bd02d1df1cec46c44e894c4be9dcf6}}), we denote the intermediate latent code by {{formula:ea9f90bf-0d5c-4edf-a982-42fcf149ae54}} to make notations consistent. {{formula:b8ea7b44-7507-4f61-b72a-44ca7c475908}} denotes the sampled latent codes and corresponding edits, where {{formula:30f2af8d-e18d-49bd-8f06-3cfa5aac5fe1}} is the number of samples, and {{formula:1fe0908f-3877-413b-815c-2567f07db05f}} is the user-defined local warping function for the {{formula:5245d214-b579-4b6e-a504-8ad235adeca3}} -th each generated image.
We often refer to them as training examples as we train our model with these edits.
Our goal is to learn a new model {{formula:fc3e131a-498c-41ef-9539-9fb9314424fb}} , whose samples resemble the visual effect of user edits.
| m | 36b117b7bd8cfe1181f2baffb34df822 |
In Figures REF and REF we compare our results for albedo, normal, and roughness estimation to those of {{cite:0da20fcd02e7ac2b1e40c06baa970a9f63a89acd}} on the data captured by {{cite:0da20fcd02e7ac2b1e40c06baa970a9f63a89acd}}.
{{figure:3bf1dadb-ffba-4588-af72-1e4854465272}}{{figure:c477c791-3bfe-4d45-af1e-b50993298cdd}} | r | 7939b43f7b352dbfb8a4c291cd2902ca |
In this section, we verify the derivation of the achievable asymptotic capacity and evaluate the impact of the number of reflective elements on the data rate in the RIS assisted multi-user communications, the layout of which is given in Fig. REF . The parameters are selected according to 3GPP standard {{cite:2c3179a9bae1a222d124a5a16ad27eeb8e183626}} and existing works {{cite:3db3431ca0d42e54787064420f6a92b2030ad1e4}}. The height of the BS is 25m and the distance between the RIS and the BS {{formula:2fc4e81b-02cf-46e5-956b-54ab0ec91fd0}} m. We set the number of users {{formula:9a5f6852-6c30-44c3-9a88-7fe14ecbd2e9}} . The users are uniformly located in a square area whose side length is set as {{formula:e65f2a27-6de1-48ad-afc6-2337b0cb9e3c}} m. The distance between the RIS and the closest side of the square area is {{formula:411b7611-7f49-44c2-b7ee-d4a46fe2e232}} m, and the horizontal distance between the BS and the center of the square area is {{formula:2a85249a-fa11-43c8-a57c-85f5b83dee5b}} m. The center of the RIS is located at the middle between the BS and the square area with the height being 25m. The working frequency of the RIS is set as {{formula:d1b43344-9d34-4f63-91b3-5f3354e55626}} GHz and reflection amplitude is assumed to be {{formula:48ecfbe0-3396-4965-86c9-59ee8fd6961c}} . The length and width of a reflective element are set the same, i.e., {{formula:85e46df6-22c5-419a-8f0f-65fceb2d53d9}} m. Transmit power is set as {{formula:02ad92f1-6bfb-4797-ab4e-9f6af024c921}} dBm, noise power is set as {{formula:0b724911-a1a4-4e81-a093-10e1f4eec9ae}} dBm, and antenna gain is {{formula:c2d8c092-6cc7-4129-a8ed-83b31d787821}} dB. All numeral results are obtained by 100 Monte Carlo simulations.
{{figure:bf18ea85-073e-4692-9679-5ca79405ae3d}} | r | 20e1a3aaa0fb3759f443b9cb04c11f8f |
For the scenarios of Our-1B and Our-2B by using {{formula:ae697001-5eff-4220-b5d1-4b842e6b1da5}} , the branching ratios from the full amplitudes, look larger than the results from the scenarios of Our-1A and Our-2A by taking {{formula:7a9bb685-a6b7-4ef6-9f2d-950ffb2f6d93}} . Nevertheless, for a given photon energy cutoff, the orders of magnitudes from different scenarios remain the same. According to the Belle-II estimate {{cite:d2d734a409835aed2ec127458a426caea1d7d1c4}}, around 45 billion pairs of the {{formula:47e3e7b2-67fc-4fe1-83b0-394bc0d8e440}} leptons will be collected. Hence we anticipate that the radiative two-pion {{formula:cfda9e8f-4269-4d45-b83f-86b454ae3e07}} decay processes have the good chance to be measured by the Belle-II experiment.
| d | 8c5c4a7b1c39af0da39f1bcffebfba2f |
In Figure REF , four images from the VOC 2007 dataset are shown in order to compare between the proposed method and the a baseline technique (i.e. vanila ResNet-101 {{cite:7cd3f3766bc11ad0d6f2a975d3bb18f0e23352aa}}). The proposed method was able to predict most of the labels correctly as shown in the top part of the figure, while ResNet-101 exhibits issues in predicting correctly, particularly for the small objects.
{{figure:9be1bac5-30db-478c-acd1-5071a0ef192d}} | r | f6ad9bb645e2799dc1bfceb9cb0919dd |
In the homogeneous dust collapse case, all the matter shells collapse simultaneously to form an infinitely dense, infinitely curved
spacetime singularity. It was shown by Oppenheimer and Snyder {{cite:907eb1a8cf39bbe6c69160de26e5ddd3b7ecc375}}, and independently by Dutt {{cite:7d2942c6d23344352d543be005f6dc792b01a2ba}} that this singularity is necessarily covered by an event horizon, thereby giving rise to a black hole as the collapse end state. However, when in-homogeneity is introduced in the density profile, it has been shown to give rise to both the possibilities, namely a Black Hole or Naked Singularity final states for the collapse {{cite:9fe6d239973bfa40c409e730da372c3f1ddb1ceb}}, {{cite:8d9daa7bc0978a33e3ee25ad5d8ae87aa021176c}}.
This is essentially because inhomogeneity affects the formation and geometry of the trapped surfaces, and thereby the apparent horizon, that develops as the gravitational collapse proceeds. If the time of formation of singularity precedes the time of formation of the apparent horizon, there is a possibility left for the outgoing null geodesics to just escape away from the central shell-focusing singularity. If this happens, then the strong cosmic censorship is violated, i.e. the singularity becomes at least locally naked.
| i | cadc547d43f2c8a4e343f60d7835cf07 |
From the whole variety of shape spaces that can be built following this construction, a small number actually leads to practical algorithms and numerical implementations, which is an essential requirement when the goal is to analyze shape datasets. For curves, an important example is associated with a class of first-order Sobolev metrics on the space of immersions. One can indeed show that, after quotienting out rotations, translations and/or scalings, the resulting Riemannian manifold is isomorphic to standard manifolds (such as the infinite dimensional sphere, and Stiefel or Grassman manifolds) on which geodesic and geodesic distances can be explicitly computed. For curves, the additional cost of adding reparametrization invariance remains manageable, using, e.g., dynamic programming methods. A first example of such metrics was provided in {{cite:4f692abb849148d08ec135542416c0c2831ffd40}}, {{cite:cb8023e7d97c042ecf52bed311cdbcf762d973b8}} with further developments in {{cite:10268b67fd6b34d5bd7a11ea3f3ed2a8ee834831}}. A second example was then provided in {{cite:9415c5a4afffd8fe1e8d33a0b3551e29ce0d2832}} (see {{cite:929133b6e2e0dca04b1b3822fe991915eb24a993}}), and the approach was later extended to a one-parameter family including these two examples in {{cite:302e256e7f7d9aa945d2723881e938919d51f72e}} and {{cite:8f748af4a704ce3b724d561e50653f7bebc0d02a}}, chapter 12 (see also {{cite:f522a9ec9c4d5670bc3574ec246f7872b89f1f80}}).
| i | e669b0171b6e5e3cf9feb491b718cf2f |
Our second component is the Geometric target Spatial Transformer (GST), depicted in Figure REF. This is a differentiable non-trainable component, that we have built upon the spatial transformer from {{cite:1028c01e80fec48113dd3010e6b33e2e96e07d87}}. It applies transformations between different domain and target spaces, such as 3D to 2D and vice versa. The GST takes as input the pre-computed affine matrix to perform relevant coordinate transformations from the SA to LA. Specifically, we utilise it on the predicted SA segmentation to localize the RV in the LA.
| m | 18941bcf780c2231bda0f5c8e65124f2 |
It can be seen from the literature that the PI plasma system can support these conditions:
{{formula:d25f05f2-a412-44cf-a8ad-fee906f6add5}} (i.e., {{formula:f080a64d-9a74-4fa3-bfcc-8ea02c814849}} {{cite:b5973f15066256d0e4eb2711b328eaa333b14e95}}, {{cite:10ed663816b1b6f4843a2769b16ecde01c33b82e}}, {{cite:9c9a0862f760d86c005a4196a879411030d62395}}, {{cite:193c1530e67dbd92b6458be6001c9edfdd70977f}}, {{cite:27e3326ed9015d30117b77a43190e63fbea2abad}}, {{cite:26fe1e4bb388dd8aa0501a2f8ab96200981db5a5}}, {{formula:d36c486e-81bf-41d0-b1cc-32e7d26cc11c}} {{cite:83467bca9da636f5e8d8a87a5cde00bbba3d6c62}}, {{cite:422015763d0c349788bb70e62754fbbaf4cd21d6}}, {{cite:c0d8b356abfa9f508f06fc6e55ed9e5e6372dff2}}, {{cite:4162b3d085069df95e17e9cdea386921f72d1029}}, and
{{formula:0362cd07-3402-422a-b8cb-778975d61387}} {{cite:83467bca9da636f5e8d8a87a5cde00bbba3d6c62}}, {{cite:422015763d0c349788bb70e62754fbbaf4cd21d6}}, {{cite:c0d8b356abfa9f508f06fc6e55ed9e5e6372dff2}}, {{cite:4162b3d085069df95e17e9cdea386921f72d1029}}),
{{formula:4e025d0c-f7b1-40f9-9ced-f86cab6f7065}} (i.e., {{formula:d328e15c-d94d-4109-bb36-12c164b66e19}} {{cite:b5973f15066256d0e4eb2711b328eaa333b14e95}}, {{cite:10ed663816b1b6f4843a2769b16ecde01c33b82e}}, {{cite:9c9a0862f760d86c005a4196a879411030d62395}}, {{cite:193c1530e67dbd92b6458be6001c9edfdd70977f}}, {{cite:27e3326ed9015d30117b77a43190e63fbea2abad}}, {{cite:26fe1e4bb388dd8aa0501a2f8ab96200981db5a5}} and {{formula:cafd2e5e-1828-4005-90cb-04b39a8058a5}} {{cite:7756a0a1ba3f0bb3f93ba53c53724e01fbb0c312}}, {{cite:7adaee75d7c9990c8ba0bb54b4b43eb9a7f2644d}}, {{cite:ccb34a5cad9e5808eb5a2186ab71b36d345a9a00}}),
and {{formula:44647c18-70b7-47d9-a0e6-8358c40e3ea1}} (i.e., {{formula:8e6683a5-f76b-41e7-8f53-3d11f9d6c9c8}} {{cite:10ed663816b1b6f4843a2769b16ecde01c33b82e}}, {{cite:9c9a0862f760d86c005a4196a879411030d62395}}). So, in our present investigation,
we have graphically observed the variation of the electrostatic positive potential with {{formula:bde4c27b-6e87-4a56-9a6a-d2ed6a67aaa5}}
under the consideration of {{formula:3fe792f5-138f-4b17-a8d3-a85c3c92b224}} (i.e., {{formula:8e41130a-664c-41e4-aa00-012626f7cdfc}} ) and {{formula:e8c9d3c2-5415-429f-8160-f94406c56522}} in Fig. REF , and it is obvious from this
figure that (a) the amplitude of the positive potential decreases with an increase in the value of the negative ion mass
but increases with an increase in the value of the positive ion mass for a fixed value of their charge state;
(b) the height of the IASHWs with positive potential increases (decreases) with negative (positive) ion charge state for a constant
mass of positive and negative ion species. So, the mass and charge state of the PI play an opposite role for the formation of positive shock structure.
Figure REF describes the nature of the electrostatic negative potential with {{formula:c12102df-16db-432a-bfd1-4ea4cbfc4c54}} under
the consideration of {{formula:0d6c8cf0-416a-4cc2-b8f2-f61a320dc9a0}} (i.e., {{formula:842d6bc5-0435-4622-9e53-d10f6f62fcf8}} ) and {{formula:1150bcf5-b77d-48ee-b52a-021f70558e9f}} . It is clear from this figure
that (a) due to the {{formula:a96cbdf1-9448-45e6-abee-15faa46c56a7}} (i.e., {{formula:62dfb80d-449f-481a-b37c-d483d8899fb0}} ), we have observed negative potential profile even
though we have considered {{formula:7bfd0175-3a02-442c-9b56-a0f039f12107}} (i.e., {{formula:2948be4a-3963-4904-ab46-7b6bcc6cc6e7}} );
(b) the existence of the heavy positive ion change the dynamics of the plasma system; and
(c) in this case, the magnitude of the amplitude of negative potential increases (decreases) with negative (positive) ion mass when other plasma parameters
are constant. So, the dynamics of the PI plasma rigourously changes with these conditions {{formula:473d4ebd-44ee-4af3-8225-f25f67ce4b5b}} (i.e., {{formula:d35f4df3-5089-4da1-9cde-6cc3c6ff1434}} ) and {{formula:601b5bbf-46b0-48ce-9f53-006794e8f3fb}} (i.e., {{formula:b296b199-d883-4d32-a4f6-1e7f5413eda2}} ).
| r | 6025a168de744a39cd0c0c456a6cb6d5 |
In A-B effect it appears that magnetic field remotely affects electron wave packets asserting the action at distance. However the field theory was originally constructed to avoid action at distance. This problem has received substantial interest. To tackled this problem there are mainly two approaches have been suggested to avoid action at distance. These two approaches or interpretations are known as "the interpretation of electromagnetic potentials"{{cite:4b47606a87d2ee0d8bcb0f42e21c4c67280bed16}}, {{cite:43d67d00a293eea89b8c70fe3dc4de5b777bdf6b}}, {{cite:fc35c4058602d3de021185cbdce7c2110c7f070c}} and "the interpretation of interaction energy"{{cite:817a673e9e4e314f0a469618cda0459ac8dbb885}}, {{cite:278174dc6cc50012b2228f2f00f2f290330056d4}}, {{cite:16a2f1173c9a8bb247443d132533a711268de6fb}}, {{cite:f4b570ab5c7fc48f32240dbcacce17ebf86fc2e1}}. However it is unclear that which interpretation is the correct one. The possible reason behind the confusion could be that most of the studies presume one interpretation as basics of the detailed study. In particular, no study, to the author knowledge has considered direct implementation of the fundamental laws of electromagnetism to solve the problem. Thus in this paper the author first review both the interpretation in sections (2) and (3). In section (4) the author undergone a rethinking of the problem and developed a method by direct implementation of the laws of electromagnetism to solve the problem and to find physically acceptable interpretation. The most important advantage of this method is that it is implemented by direct use of fundamental laws of electromagnetism, so that it provides more natural and simplified explanation of the A-B effect. In section (5) the author briefly review experimental work carried out to verify A-B effect and to understand correct reason behind the A-B effect, followed by discussion in section (6).
| i | 88363b4c2a6a1ec09ed128fe084089c5 |
Our work supports model editing where the final ML model will encode the decision processes of not just the underlying data but also external knowledge. This ability can be leveraged to correct incorrect assumptions in the original data or encoded updated policies. On the other hand this introduces the ability for the model builder to influence the model outcomes which could intentionally or unintentionally introduce bias. The user feedback however is interpretable and transparent and user influence is in the form of a Boolean feedback rule. This supports easy integrating into a governance framework such as proposed in {{cite:379f137a9a6eb3944393faf49270c97ef9653e30}} where clear auditing of the original data, the feedback rules and the newly created dataset can be stored to transparently log the updates to the model and capture the lineage of the data. Post processing analysis to compare the original and the resulting model could also be leveraged to ensure unintended biases have not been introduces {{cite:2c14ceabd7cd6782141eab83a84f2b89f6ef1111}} along with generating an interpretable model comparison of the two models as proposed by Nair et. al. {{cite:c4a44eeaa01b9d2e2683ed7331835923f8fe6f2c}}. Additionally, FROTE achieves this while trying to minimise the model accuracy for other segments of the dataset. This is in contrast to human labelling or relabelling tasks where the downstream impact of the newly labeled data points may be unclear. Additionally, the source of the newly labeled data, their level or expertise, familiarity with the data are all opaque. One could argue peer reviewing a feedback rule set to obtain consensus among stake holders is relatively easy compared to ensuring a consistent view is being used among data labellers.
| d | 4ce605f75f59e26b8f0c0fb79f12b545 |
We apply the multivariate version of the Stein's equation {{cite:ba77e18bb70f53203edb41bd870048a55323a355}} as
{{formula:6a4617e8-159c-493a-9c90-6dcbcd8b1458}}
Here, {{formula:7670a64f-5166-4e57-ab5f-f4df0174b0c9}} be a solution of the identity which is induced from {{formula:1b20123e-a44e-4964-a185-3b8248a8918e}} as
{{formula:840ff09b-1745-4989-9731-73b9b2c50555}}
for {{formula:b6913f9f-6771-432b-9fc5-5a5c0ac9644d}} .
We evaluate the term {{formula:0c5f1c49-7354-4103-a523-3c6da25cd25c}} for each {{formula:faf04c90-6d78-4a91-9c14-6836f8e50fb0}} .
Let us define {{formula:a9bb022b-42c1-4d93-a27e-d377fc6d0a6c}} .
Then, we consider the first-order Taylor expansion of {{formula:faee9528-8f6d-44d5-87ea-d19fd88f0257}} around {{formula:43afc822-3aa3-4959-8f74-eb7fda1eb30b}} for all {{formula:e926d408-9916-4122-9cd2-10ab7f12e71f}} as
{{formula:be32f172-acb0-4d2c-9066-5c53d1ec38d3}}
Note that {{formula:f064efa7-a19b-4558-b695-ac2dac5c6cf1}} is an existing random variable as an inter point between {{formula:b7dfc22c-21f4-4cc6-9227-c7ccea7f477d}} and {{formula:6d66b1c1-51a8-4b4a-8e58-61e4cb249fb3}} .
By an iterative use of the Hölder's inequality, we obtain that
{{formula:fbcb1f2f-5097-41db-a368-74d0205f4b90}}
for any {{formula:1f178536-7b34-4b18-997c-a2b6c37d2308}} .
Similarly, the first-order Taylor expansion for {{formula:c3fa7243-aae7-40a7-9ba1-cbcc970c8049}} around {{formula:6cdca36a-9353-4e46-8674-04c563468d46}} provides
{{formula:a54c4048-cc6e-4d26-9835-215ec4f5efa6}}
Here, the second equality holds since {{formula:dbe424b7-9e79-451f-a40f-ee61dde207ab}} and {{formula:f74c4c11-f71a-4b49-8883-6243555bbeb5}} are independent by its definition, and the last equality follows {{formula:0d0e2026-953a-4662-bc16-cde397fa1498}} .
Similar to the bound for {{formula:1f0df25c-5101-4a45-a4d8-0ffc2c5f7c17}} , we obtain
{{formula:72fe2116-38e1-443c-a277-787f6505d840}}
for each {{formula:df3e78fa-3401-426e-807c-0079d7f3bdee}} .
Substituting the Taylor expansions into (REF ).
Let {{formula:41778a0c-7d7e-4c7e-8b4c-d89dc86a9052}} .
We obtain
{{formula:282fe9fa-26dd-47e0-a052-c9db31b98b41}}
where {{formula:495461ea-e9d5-4b4a-a0b1-f2888e1062e6}} is a universal constant.
Here, the second inequality follows {{formula:33cf5c0a-cb83-47f6-bd87-811126eeb5da}} , and the last inequality follows Proposition 2.1 in {{cite:ce05f4c0332a4c60c2eda43c46f3ef4b83e349fb}}.
| r | 5d571269998064869cd3c23a9735c527 |
The photometric and kinematic evidence for a nuclear disc inside the B/P
bulge of NGC 4643 is a clear demonstration of a pattern
{{cite:6cffb6e4729f179acae7c920315bda4fa2a76910}} and {{cite:6ac1a854de13560191440c8c24309281b2409be9}} suggested based on their
studies of edge-on disc galaxies: that the B/P bulges of barred galaxies
are frequently accompanied by nuclear discs. The case of NGC 4608, on the
other hand, demonstrates that this is not a universal
pattern: some B/P bulges contain structures much more like classical
bulges, rather than nuclear discs.
| d | 5d0f3589f53f75420fbd2808cb1c78f6 |
The methods we propose are exact in the setting of linear {{formula:b4e6993a-fe42-4fea-8d6e-d39caa4a8d42}} and Gaussian prior density {{formula:d7557dfa-5f8c-40fd-a273-7318cfeb95ba}} ; but,
for nonlinear {{formula:7373de30-3aaf-426e-bb4e-d1fe28f091a4}} , the Kalman-based filters we employ
generally do not converge to the exact posterior distribution, due to the Gaussian ansatz used when deriving the method; negative theoretical results and numerical evidence are reported in {{cite:d7071b54df7117ad8571922d44ee89b099fbdc37}}, {{cite:8fabcf69f5258880fee5a72eb4efd9182e18009f}}. Nonetheless, practical experience demonstrates that the methodology can be effective for problems with distributions close to Gaussian,
a situation which arises in many applications.
| m | 0c8851c520b477ab22743ce96a06a99b |
A liquid's surface tension is a crucial parameter, especially on very small length scales, for droplet spreading and wetting of surfaces {{cite:2d79eb9209dcbc49fc3f8fabad93cd66d5d7837d}}, {{cite:2e3a364dcb148f2b7f352ae2261030f6cbd12c25}}, as well as droplet impact and splashing {{cite:096ecc172810fc68ab3696dfc0db1f513200eb49}}, {{cite:2e8eecc4274c41697b8372f626a8ef2f88bae8ee}}, {{cite:c082569afe177b34905b291414a51ec240553db7}}, and liquid jet break-up {{cite:f1944984ba3ed4c083b787dc799a357d3e4c2ca3}}, {{cite:7ccbd2e01f52c8a22f48a9024584233e1ee8525f}}. A prime understanding of surface tension effects is therefore extremely important for applications like atomization {{cite:7ccbd2e01f52c8a22f48a9024584233e1ee8525f}}, {{cite:77f234f41fd7a1d89d5dc127a9e7f66b179d3647}}, inkjet printing {{cite:a87cddee70a4714e970e93be3e1d10e3b5c21230}}, film coating {{cite:371c8c9728226033d77de9bc7a7152a0d8bd5cff}} and many others.
| i | af0f8535f0d3b3800e4aa06004f6c7f1 |
where {{formula:adbd29bd-f1ee-4d14-af70-8715197213a0}} is the partition function of single core black
holes, {{formula:a0cf92f8-ef09-40b8-a7ea-9a3824046810}} the partition function of scaling black
holes consistenting of three cores, and
the dots stand for scaling black holes with {{formula:76d0ac9f-c221-430d-aa9f-87d019b3db49}} cores. We determine the holomorphic part of the partition function using
formula's for the degeneracies of black hole bound states such as
studied in {{cite:ae8186f04f43b9f05569a34a22e445f74393e8b8}}, {{cite:7a4e61e730c9028775885811a54e7d1db16bfd85}}, {{cite:6c45edeff59aa894de1b3ddd8fbd8527e91bcd60}}, {{cite:5b6d7c66d72c0f5c62870112fe9bda54f98a5c3d}}, {{cite:01d08026280714c4576dfc6d8c18141ae8093376}}, {{cite:4c39835a35c5b8b732fbbb5544f827f0bfc8bb40}}, {{cite:56e336b56ed3f13f0701ae7e60c2140f7017679e}}, which
gives rise to a holomorphic indefinite theta series {{formula:9b2700c3-756f-4d1f-97cf-3c01c876a5a8}} of signature
{{formula:306438f2-25e6-428f-b3b2-5a14e4b70aad}} . Since its coefficients grow polynomially, this demonstrates that the entropy arising from these solutions is
exponentially smaller than the entropy of a single center black
hole. This is expected since we have not included pure Higgs
degeneracies {{cite:7a4e61e730c9028775885811a54e7d1db16bfd85}}, {{cite:6c45edeff59aa894de1b3ddd8fbd8527e91bcd60}} or single center
{{cite:01d08026280714c4576dfc6d8c18141ae8093376}}.
We have worked out two explicit case studies, where we specialize the CY three-fold to a K3 fibration and determine
explicit {{formula:13938f1b-2685-4ddf-95a2-807fe3d56396}} -series for the partition function.
We do observe that the exponent of the
leading term in the {{formula:85f48e84-19c9-4238-92fb-9c7155a5eb0c}} -expansions is rather large.
| i | 39e60cfe3ff59704e2cf73e2251da30c |
[noitemsep,topsep=0pt]
GW190412 {{cite:e5865523c03cd9c730e8ea5f023f2b205a2ddd67}}, a binary black hole (BBH) with asymmetric component masses, showing evidence for higher harmonics in its GW signal;
GW190425 {{cite:561cd93fca877fcc9769489c076f436c0c0b39c5}}, identified with a binary neutron star (NS) merger lacking evidence of an electromagnetic counterpart;
GW190521 {{cite:4bd5791970b20ef096fdcaeced3af1c0885984bf}}, a BBH with a total mass greater than 150 solar masses, which is the most massive binary yet detected,
in which the posterior distribution of the primary mass is nearly entirely in the pair-instability supernova mass gap where BHs are not expected to form from the collapse of massive stars;
GW190814 {{cite:9eade34eab197301799027a3e50d842eb0e83a3c}}, a highly asymmetric system consistent with the merger of a 23 solar mass black hole (BH) with a 2.6 solar mass compact object, making the latter either the lightest BH or the heaviest NS observed in a compact binary;
GW200105 and GW200115 {{cite:2cb842731860f1212feabdedd600c842bfb4f9bc}}, which are the first detections consistent with a NS-BH merger.
| i | 844f645a5811875e83c7d58ff4523d93 |
In this section, we document details of the algorithm for the numerical simulation of equation (REF ). The computational domain is {{formula:0a7b631c-0ddf-499d-83c2-95988e42e38a}} . When {{formula:83ab5bb0-6381-4280-a15d-a8715bcb3b22}} is large enough, we can assume there is a periodic boundary condition in the {{formula:5a6df124-f5f7-48b3-884e-76773545ec6a}} -direction. Since there are non-penetration conditions in the {{formula:8a021cbb-44d9-4457-b78e-dce18b6bd26d}} -direction, we perform the even extension in the {{formula:c3b8c9e1-bdcf-4607-b1d6-9cee98c831f3}} -direction to obtain the periodic condition on the extended domain. Thus, we can use the standard Fourier spectral method to solve the advection-diffusion equation with periodic boundary conditions on the rectangular domain {{formula:d6c20af0-8888-40c8-8aa5-4ffd8d834d15}} . In the dealiasing process at each time step, we apply the all-or-nothing filter with the two-thirds rule to the spectrum, that is, we set the upper one-third of the resolved spectrum to zero (see chapter 11 of the book {{cite:c632076adfd19522e84fa349066ed51b22375712}} for details).
| m | 2697ca28c5e8a5178ef9744326d0767a |
Feature-wise methods. Intuitively, under-sampling the head {{cite:cdb4773a4ff7b50b8950ce4a013cc3a060cd336e}}, {{cite:0c57c523e0df2b964f4a982ddccf095a71a1858e}}, {{cite:d10fa4be4bf603d847e15a8be239d32972a91f04}} or over-sampling the tail {{cite:ec398c84442cb0c3f8d9de9498c9c56ff21be760}}, {{cite:0c57c523e0df2b964f4a982ddccf095a71a1858e}}, {{cite:049cdfc6519c01556cc0f1fcafa293645ccac850}}, {{cite:78d12ef1bd334e0c228c73ac24769b536cbbf5c4}}, {{cite:0a6dbdd7ac2c0efb5d6e901d954621438922fa78}} can improve the inconsistent performance of imbalanced datasets but tend to either weaken the head or over-fitting the tail. Hence, many effective works generate additional samples {{cite:e18b689a5d53c1bc8e0873a2226e4d4aeddc1e2a}}, {{cite:4bd6ece2eac9d4dc843588df813215945df18931}}, {{cite:8908f3f13dd3508ae179c497bcbf8a99d7a96cde}} to compensate the tail classes. BBN {{cite:bbe7e9e85d6b6509ea17884fdd67e9cbf4fa77e5}} uses two branches to extract features from head and tail simultaneously, while c-RT {{cite:b39c725961ad42237828a3f4a1f5d8d443c2749e}} trains feature representation learning and classification stage separately. mixup {{cite:22c70f42a2b34b0aeff171d8b511cf03c371481d}} and its variants {{cite:02a3d1d031d16953e28cd03bdf56b6634cee7a71}}, {{cite:a1525c31ef331f9317ec93894b08c633e7f41e4d}}, {{cite:afdebe03f7672abf20b3c0ff040deab51af3fd00}} are effective and easy-implement feature-wise methods that convexly combine input and label pairs to generate virtual samples. However, naïve mixup manners are deficient in LT scenarios as we discussed in Sec.. In contrast, our UniMix tackles such a dilemma by constructing class balance-oriented virtual data as describe in Sec.REF and shows satisfactory calibration as Fig. exhibits.
| d | 2310594167da5cb91d92b4e18fc861b6 |
The idea of neural networks dates back to 1943 when neurophysiologist Warren McCulloch and mathematician Walter Pitts wrote a paper on how neurons might work and demonstrated it using electric circuits {{cite:3f1449da09a87f95ff11f7d7adc4e5ea487ee926}}.
In the initial phase, the idea of neural networks and perceptron gain popularity (Rosenblatt {{cite:a4a64c8706407b7902da42deaff223af2cbd3257}}, Widrow & Hoff {{cite:4810851d59acb72887f95fca8b108e250ce96b4f}}).
Soon this hype hit a major roadblock with the publication of a book, “Perceptrons” by Marvin Minsky and Seymour Papert {{cite:380e3f2c6fb4bade49c23013a993360ae7175fa5}}.
The book concluded that perceptron could not be translated effectively into multi-layered neural networks and hence begin the `the AI winter'.
Fast-forwarding it to 1985, the work of Rumelhart, Hinton, and Williams {{cite:775ada8a90b77d514f3e21025838b9fd2456d42f}}, {{cite:9644974f6df9bc7bd3d32c70d8cd64b5fd2218ec}} gave new life to the neural networks.
Furthermore, improvement in the computation capabilities enabled the researchers to train large neural networks and beat the current state-of-the-art rule-based methods.
The first feat was the success of AlexNet {{cite:8b117076b99641345325031091f22c44d05f358c}}, which significantly improved on image classification task.
With the beginning of the `deep learning' era, neural networks have gained popularity in multiple domains, including object and face recognition (He,Zhang, Ren, & Sun {{cite:ec9959f094dba1413ba61316268ec2e70c470de1}}, and Lu & Tang {{cite:c1bc7dcd74158ba2831638ada53065233fb6b422}}), speech and natural language processing (Amodei, Dario, et al. {{cite:270579e3a028eac0f59082d816c9c81f3090cefb}} and Ferrucci & David A. {{cite:1fba399c0c99629469a6aee0a78aadce3da91bbb}}).
The networks are matching or even beating humans in complex cognitive tasks such as playing go or video games (Mnih et al. {{cite:27bc4308b796d48c523568569ec4aced80ea41dc}}, and Silver et al. {{cite:b99cdc6ef4bac7188981023eeebe0d21011becb3}}). The success makes us hopeful that it is possible to make computers smart enough to mimic human cognitive abilities with extensive data, better hardware, and more generalizable models.
In fact, some of the models have surpassed the classical theories in linguistics and physiology to achieve success.
However, such cases are rare, and they lack a complete fundamental understanding of how the model is learning.
| i | 7d0610d85fe02ccc2d749967589105ed |
Frequentist methods in addressing the piecewise constant signal de-noising problem include penalization methods like the fused lasso method {{cite:18720c935a78c8a8c5e8dc45808b9dc1c426c44b}} and the {{formula:e4daaf96-ef3c-48dc-a7bb-9563e1dd9c1a}} -fusion method {{cite:6ae117acc39dc79aeea9891b2c74444969987baf}}. The Bayesian equivalent of the fused lasso penalty is using a Laplace shrinkage prior on the successive differences {{formula:caf4166f-3edd-484b-bec4-73f572b87e08}} {{cite:5de7a82d7f71312599859bb80a9b29218bb286d4}}. However, the Laplace prior leads to posterior inconsistency {{cite:a67ae0faeb18d39c9d30f88de8491d8a61994810}}. To overcome this problem, {{cite:b6a4f959f60bb6e3b134a0e76f952e2c887c8b00}} used a heavy-tailed shrinkage prior for the coefficients in a linear regression framework. Motivated by this, {{cite:e944705d1fdb6ab275f59346ca1e572c9443f9f1}} proposed to use a {{formula:cf122f22-fca7-4895-bcfc-bf860bc2ea18}} -shrinkage prior for Bayesian fusion estimation. {{cite:02a1f4a0bbba31784fe796b75ac29b9532e6f1a6}} use a Normal Exponential Gamma (NEG) prior in this context, and make inference based on the posterior mode.
| i | 47fd47120ec059db55980bc50b54b81b |
Large-scale networks can be studied using stochastic geometry (SG) tools {{cite:2106767ecc31ffa2561fb8c93b92bbf71c3d3b77}}. SG is the study of random spatial patterns. It is a strong tool used for interference modeling in large-scale networks, and has been used to study several network performance metrics in the literature {{cite:c3112f48427e2c18a16ba3583319490b626f4029}}, {{cite:fb5808a32820ee03aaac66e1ffa2ab02c25fa4db}}, {{cite:ea5f64f8bc6ccd93b4bd6f6159afcdc2d043d3aa}}, {{cite:250051e38c8f2dbccb85cfce49ab8dbea5420803}}. In {{cite:c3112f48427e2c18a16ba3583319490b626f4029}}, the wireless network is modelled using SG as the Poisson point process (PPP). This led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. In {{cite:fb5808a32820ee03aaac66e1ffa2ab02c25fa4db}}, the coverage probability of cellular networks in urban areas modelled as a PPP is provided. The results are compared to the hexagonal grid model to find that the SG model provides a more accurate upper bound on the coverage probabilities than when using the hexagonal grid model. In {{cite:ea5f64f8bc6ccd93b4bd6f6159afcdc2d043d3aa}}, {{cite:250051e38c8f2dbccb85cfce49ab8dbea5420803}}, large-scale networks using non-orthogonal multiple-access have been analyzed using SG. Note that works in this area commonly use Shannon's channel capacity expression {{cite:23aacc4bbe5a9da1d8aaa0579be146c843ea8498}} to study performance which is not suitable for delay-limited applications.
| i | 4e45225b71113ea1d5730e7a2c4d4bbc |
Furthermore, as pointed out by {{cite:0b0038acfe3061ef9a53e0e494672ed5f5383b69}}, the actual level of assortativity may also vary within different pairs of node classes, i.e., there is a different tendency of connection between each pair of classes with two different characteristics of the graph. Thus, some pairs of classes may exhibit homophily within the same network, while others exhibit heterophily. In Fig. REF (b), we examine various networks from different domains for existence of diverse local patterns using {{formula:8a386309-3a71-4060-80ae-168fde80ad4c}} . In the two datasets, we witness skewed and multimodal distributions. We are essentially interested in how GNNs perform under different patterns, and further experimental analysis is provided in section 5.4.
| d | 2933c8f1ec58e9234d166fc57d58d39a |
This work belongs to a line of works that transfer concepts and ideas between the areas of formal verification and algorithmic game theory {{cite:15d075bfd5fc8ca21e65045650de6b524d3e3008}}. Examples of works in the intersection of the two fields include logics for specifying multi-agent systems {{cite:e979e159c7e8a8c420ab2d6c109798a527c70399}}, {{cite:08171b1eb3c69ed81d27dc86c1e6fc9488e58339}}, {{cite:8cb474efe301251d08f4c83dbb5ebcc2dadc07e2}}, studies of equilibria in games related to synthesis and repair problems {{cite:94945c0408e6e429c496fc2fcc30415f922abbc3}}, {{cite:a3686880bb0ef3cf6b7b569fd74c2e618e3c3681}}, {{cite:78d5e19cec3e52db1118879d88962c66df8b11cc}}, {{cite:be9cee4da4946467027da0232b89ea4afb0f3f40}}, non-zero-sum games in formal verification {{cite:816dae000b4141d1bf2c43192f2fb7c5460125d6}}, {{cite:db8741a1cf0a2a9490018ff25fdc76a4030ae451}}, and applying concepts from formal methods to resource allocation games such as rich specifications {{cite:0a7297bf4050938b8a72f0bcd002b6d39a087c5a}}, efficient reasoning about very large games {{cite:bb2cbf885d500b6f449f1df05660aa0d335e9e1b}}, {{cite:76b221a9ac60e8aa132a2e1181056439d6aa8b97}}, and a dynamic selection of resources {{cite:0249c5c141f67a844206c4dfe510b485a940099c}}.
| d | 34a08712ff5152c79df8e6503f80d0df |
To determine the motor commands {{formula:e79898f9-7805-4987-9bda-c974f765f9b6}} , we add noise to the activation of the relative output {{formula:db615948-b6ee-4310-8374-b5841e5791b2}} . Since the desired position of the joints are modified progressively, using white noise would generate extremely little movements and the arm of the robot would explore a small region of the joints space. For this reason the noise ({{formula:b7d6818c-f183-487b-88a3-1250f82ce312}} ) added to the output of the actor is generated with a normal Gaussian distribution with average 0 and standard deviation ({{formula:479e7b73-1b9e-4e04-b6cc-d773d090eb3f}} ) 2.0, and passed through an EMA with a smoothing factor set to 0.08. Moreover, to manage the exploration/exploitation problem {{cite:35a9d165337642d01a356cd2ed7fb91615af3ba6}} we implemented an algorithm that let the system autonomously regulate the noise {{formula:165b9302-b8ca-4d56-9fbe-d55f112c0cb3}} : the {{formula:6499fee6-67bd-4656-83be-c6d46ed3448e}} of its dependent on a “noise-decrease parameters” ({{formula:90533850-ae96-4f70-a959-d74e3c7dff88}} ) determined by an EMA (with smoothing factor set to 0.0005) of the success of the expert in achieving the goal for which it has been selected (1 for success, 0 otherwise), so that the higher is the competence of the expert, the lower the noise. The {{formula:26550614-c7e4-477f-91b7-1f89daad1a37}} of the selected expert {{formula:ca59da07-ccc0-4b2f-9643-2d120ca7b1c4}} at trial {{formula:fe8269bd-e723-49ee-8165-21707538e62c}} ({{formula:63d5bee5-ef34-4b53-9d74-c2e7ea949776}} ) is updated as follow:
{{formula:dcec8a04-47fe-4466-b178-4e0984a1b4ad}}
| d | 1ebbb623f048dfdfbe6713079cbf5541 |
The pseudopotential code quantum espresso (QE) {{cite:256aec4371031f8fa5a70ab5914e9d9df8e3c834}} is used to carry out linear response electron-phonon calculations. The electron band {{formula:9e921932-6b28-4e3c-b0cb-2ad741a56638}} - and phonon branch {{formula:428342b6-cca7-40e1-bb33-1676f06e7f25}} -meshes are Monkhorst-Pack type with 18{{formula:2183b284-bc8c-4840-9778-5364e901cb7e}} 18{{formula:e2a3e8e6-d0bf-4c2b-867f-a05490841fce}} 18 and 6{{formula:717e4cf4-a829-4cb2-8a69-38357e87b5da}} 6{{formula:af5f19c0-1d5f-4d43-865c-36a019dd3fa2}} 6 points, respectively. The optimized norm conserving pseudopotentials {{cite:defa80623fe0b9f1ca840fec9642f8bbb697e1d6}} were used.
{{figure:da0d5726-a9ab-449e-b14f-7279141db35f}} | m | 65eeee700bfc1318c54ccc3511309cb4 |
A preliminary version of this work was presented in {{cite:28a2d4cec4a04144600d3797701029c34ba3ee98}}. In this extended work, we introduce three major improvements.
| i | 8e2fd9897639630a4127d289b8bfc5c1 |
In this paper, we analyze both the hierarchical RNN-based and the
open-vocabulary candidate-generation approaches and propose hybrid
state tracking, HyST, a hybrid approach for flexible and accurate
dialogue state tracking, which aims to learn what method to rely on
for each slot type. To investigate the appropriateness of HyST for a
rich set of domains, we experiment with the recently released
MultiWOZ-2.0 corpus {{cite:b9849a1b650e9f7d93091f16fffd31fbd03c4503}} which includes single as well as
multi-domain interactions. These conversations include task completion
across multiple domains and allow for transfer of values between slots
of different domains, as demonstrated with an example
hotel-reservation and taxi-booking dialogue in
Table REF . When tracking dialogue state over the 7
domains included in this corpus, our baselines outperform the previous
benchmark for joint-goal accuracy (which requires estimating the
correct values for all slots of all the 7 domains). Our best hybrid approach
achieves a joint-goal accuracy of 44.22%, which is 4.1% (absolute)
higher than our best baseline, resulting in an 24% relative
improvement over the previous SOTA.
{{table:362e0742-df3d-4320-ac55-9d914df7ebb3}}{{figure:f6c89986-35f0-4f22-b0e9-5f23b517cbee}} | i | a7c1c00e18bfad8ddae32122f71f3f8a |
The reliability of the human annotations is essential, both to ensure that the algorithm can accurately learn the characteristics of hate speech, and as an upper bound on the expected performance {{cite:120e4d2cdcb1647322da4a9fde5516822dadd33c}}, {{cite:f6e4ce6cf187664af6a8798d6cc0c1067942e9cb}}.
As a preliminary step, six annotators rated 469 tweets. We found that agreement was very low (see Section 3).
We then carried out group discussions to find possible reasons. They revealed that there is considerable ambiguity in existing definitions.
A given statement may be considered hate speech or not depending on someone's cultural background and personal sensibilities.
The wording of the question may also play a role.
| i | e09c1298fb7f88076701e70bf529ad5e |
Electromagnons were recently observed in two groups of multiferroic orthorombic manganites, {{formula:7f5a0709-51c2-4fcb-af73-6997f4c3fc2b}} MnO{{formula:10871b91-81bc-4fb1-9499-7da277a9dff7}} ({{formula:abeaf57e-25df-4302-8653-689b527fbc97}} = Gd,Tb,Dy,Eu{{formula:a489bd2d-63f8-434f-a923-131d195b94ce}} Y{{formula:cce6ac27-679d-47c6-be2a-c5a7d6488fcd}} ) and {{formula:179c1df0-bb79-40fd-a61f-7c23fc021a31}} Mn{{formula:b4b0a246-c594-4830-a2ba-6344da7410b6}} O{{formula:1077648b-5e82-4496-af4e-5056ae32142b}} ({{formula:9995a6dc-b957-4c25-aa31-5611c142d4f1}} = Y,Tb). {{cite:b41ce9ff277ef67c363dbeaa1b4c741ce9df1ef6}}, {{cite:95f16e949ab4536e1294121e264eb0a4d89b3911}}, {{cite:2e3cab712e2b03e2de8cd4d2b4846271d394744a}}, {{cite:cbd19df9a2665e2c437abf7421cc896c3a6ffd3d}} Ferroelectricity in {{formula:db7bcc13-6808-4f9b-aacc-18faaf996f77}} MnO{{formula:ad8a3df7-4774-4769-a6c5-ff9d67bb29c2}} appears in a non-collinear antiferromagnetic state with the cycloidal spiral ordering and the magnetoelectric coupling originates from the so-called inverse Dzyaloshinskii-Moriya mechanism. {{cite:8e3d6ef02d8f24ec574ecfef927ec4abaaf96388}}, {{cite:2a20261ee91da5dc0bdd7a7f63bc4cd247bc6270}}, {{cite:3c50df53cc3c9a1e2a8d00c2a5213ad5b1962e34}}, {{cite:7fa4a6739704ca607a5570841f8241cdabd90582}}, {{cite:32881942f9ace93305d1607ced10ffd230946962}} In Ref. [KatsuraPRL2007] it was noted that the same mechanism can couple magnons to photons and that an oscillating electric field of light can excite rotations of the spiral plane. However, the selection rule for the electromagnon polarization resulting from this coupling does not agree with recent experimental data{{cite:2e3cab712e2b03e2de8cd4d2b4846271d394744a}}, {{cite:5b2afe86f159acd5b3a51bd59623f3dc0cd27871}}, {{cite:60144132c21032037837a28677384fbcb2af1be9}}, {{cite:9a22cf551595fdf173cabf14700d13f16e2d1bec}} and, moreover, the inverse Dzyaloshinskii-Moriya mechanism of relativistic nature is too weak to explain the strength of the electromagnon peaks in {{formula:a47bf830-1e52-462d-90bc-2745003dc6a1}} MnO{{formula:603c67d3-769c-44f8-ba00-52214fba7b17}} .
| i | 1476ae7d81fcb3061405394aa2934e52 |
We performed the scribble-guided segmentation on MSCMR LGE CMR images and compared ShapePU with other state-of-the-art PU learning approaches, including Transform-Estimate-Discard ((TED){{formula:a40a4cfb-65ca-48b3-beef-8b9b6302578d}} ) {{cite:7e4f4cfecf4d0e946bf6d0cbaf898ea2ef8f6e5a}}, PU learning with conditional value ignoring risk (CVIR) {{cite:7e4f4cfecf4d0e946bf6d0cbaf898ea2ef8f6e5a}}, and positive-unlabeled learning with non-negative risk estimator (nnPU) {{cite:b6120349570912eec2f035207e86917dd7c83c8f}}.
| m | 8de82965faee2bc37a4958f561a6c433 |
The claims about existence and uniqueness of lifts of automorphisms to {{formula:5cfc878c-4c0b-4e8a-9833-6092d721f965}} follow from Section 4.2 of {{cite:a5ab90cfbb6885f95c8c11249ab9d306701bb536}}, and a short version of the argument is Proposition 2.1 in {{cite:d9fcea3c5a7a973dc4c1809c3fc3e95771a1e010}}. The identification of prime order cyclic orbifolds with {{formula:1ab6f0b2-f0ad-45dd-aa44-354fdae4d79c}} follows from the main construction of {{cite:1651c7cb8ea79b532eebcca6771491257564e6ca}} for {{formula:48c20f78-f892-49f8-97cd-9c5b3c9f0958}} , Theorem 1.1 of {{cite:fbb7e71dd5b71c838b62bebfe267f4125fc1053e}} for {{formula:af566648-2289-4f08-b6c2-28174486c0a7}} , and Theorem 4.4 in {{cite:c9f2911c5dbf450aac3bc84230f21b004a9312fe}} for {{formula:7b72a6cc-2915-41f9-bf13-9b4cfc42fe25}} . The identification of order {{formula:0762d49d-34f7-47e8-be23-5d69c54dea55}} cyclic orbifolds with {{formula:27d5acc9-028f-4386-b4b2-1cd621e535bc}} follows from Theorem 4.1 in {{cite:c9f2911c5dbf450aac3bc84230f21b004a9312fe}} for {{formula:e1950ad6-9e49-425f-a6f3-caf052da8d57}} , and for the others, the result follows from essentially the same argument: it suffices to show that the weight 1 subspace of the irreducible twisted module {{formula:b269ad10-4c50-40aa-a09a-4a2264a4eebb}} has dimension {{formula:75c62064-f5b6-4bc8-b45b-2e98d27ee3bf}} , and one can do this by manipulating the frame shape.
| m | 0de3cc60a5de893f8ea94e93e8477b13 |
The Standard Model Extension which consider the CPT symmetry violation (SME) {{cite:5447a4b1efa7713d75b03ac09639c8180ebaea95}}, {{cite:c9dae80998da0a91796acf8206d447393cf3ecad}} is a proposal to explain some conflicts between experimental/observational data and the theoretical predictions of the Standard Model (SM) {{cite:c28b0ec17cb7b2dac4ccb630577d4ec33646d1c5}}, {{cite:638225bbdb71b2c19911328ca96df41bd8a325f2}}, {{cite:09f6420615c41e18b673112bb66c716a24636235}}, {{cite:9d538d3b8a91c4f8f5b4ff200af59646e4c6f03e}}, {{cite:8478d5d2e560514a716f30b90eb6c2ee57600a7d}}, {{cite:bd69d8375f44877fd5838ac4929862a708932273}}. The SME assumes that all possible Lorentz violating terms arise from nonzero expectation values for Lorentz tensors which are considered as spacetime background fields in a fundamental theory. These background fields give rise to preferred space time directions.
| i | 8eb1312bf7a70697c726f26872215e2f |
The equilibrium properties of spin systems with continuous symmetry (comprised of {{formula:19948342-474e-4ac7-93ca-da1194824a5d}} -component spins) and quenched disorder have received some attention over the years. They have been proposed and studied as models for various experimental systems, e.g., vortex lattices in type-II superconductors {{cite:e9189c07677224e718860976eb9fd547c45441c8}}, {{cite:32fb0c441e7dc93ed5382b0ad0366ef71048e4ee}}, {{cite:d4838ad60e82a4a1f5be0a8d1866da3910cb5472}}, charge-density waves in the presence of random pinning {{cite:cfcb2409c98c40617f8645d6b74d06319ddf9632}}, {{cite:77be601b7888ee31ad612088051170e085263fc5}}, {{cite:cc3536d075573f293025552fe25e97ef2f157d7b}}, {{cite:d978f128a9a078e25e5cac810d72eb6ff4d0bdbf}}, liquid crystals in porous media {{cite:454324bfd73d3747f4b125bb04b0145a1ad01b54}}, amorphous ferromagnets with random anisotropy {{cite:9d898d11ebad5f7ccb3ffb9dd3c19c58f3955e82}}, etc. These systems are highly sensitive to quenched disorder in low dimensions. Thus, interest has focused on how disorder affects the phase transitions in the corresponding disorder-free systems.
| i | 49d3e19066236a3c090b5c51946f28c2 |
We give detailed comparisons between our results and prior work in Remark . As a summary, {{cite:2812693fe795430a366892f4df1a62589a9c88b0}} obtain a relative error approximation with a running time of {{formula:533f1af9-1afc-4807-b527-315b9727feab}} , where {{formula:d6bc596d-62b8-490c-81c5-b4ad4e8ba5e1}} denotes the matrix multiplication constant, whereas our running time is dominated by {{formula:f99fb81c-3a37-48c3-8bec-22a663581dda}} and we obtain only additive error guarantees. Nevertheless, the algorithm we obtain, which builds upon the sampling scheme of {{cite:55d76cac9d04183989281babc49aaa06da41d139}}, is a conceptually simpler algorithm than the algorithm of {{cite:2812693fe795430a366892f4df1a62589a9c88b0}} and easier to empirically evaluate. Indeed, we implement this algorithm in Section and show that it is highly competitive to the SVD.
| r | e0bdd8a486ab9e0b5b020a37ad79c49e |
We find the resistance distance between nodes {{formula:65cd91ce-3a2f-402f-84cb-92b487d2cdfd}} and {{formula:476182b5-5998-47ab-94db-6adbbd3ea1c2}} , {{formula:03061b16-891c-406e-941b-792a07651833}} , by using the eigenvalues and eigenvectors of the network's Laplacian matrix, {{formula:66880ca1-e3a6-4333-95ac-f07b4624bbed}} , as {{cite:cb1b1bde958bda0c8136b7026f6b70175bc651a8}}, {{cite:2d8adf59902693921fd44ea4eeb0fd56b767fb8c}}, {{cite:b85c7fb4ab3be765d59759b1082c09829d1038c4}}, {{cite:0e19306d37c0eeb8be0bc5f15d6f734d81997ecd}}
{{formula:6833b377-b504-4a09-a2b1-b7ffa0d5b820}}
| m | cf47666fd3cd1782cfa72a8fa7cc4570 |
Assumptions REF and REF impose high-level conditions on two nuisance functions. Our theoretical results only require {{formula:47caa22a-cceb-4848-aa6c-e97c91566ff6}} , which is a mild assumption. For example, if considered parametric models for both Q-function and ratio function, then {{formula:a5c51d27-a3a2-42d2-9ba9-d2ec5307233c}} . If considered nonparametric models for these two nuisance functions such as deep neural networks, then {{formula:f91842c7-e5ea-4c5e-9768-b49b728d6706}} can be obtained under some regularity conditions. See {{cite:6f8aaade06b27b3d8673ce55885f9d2ec6bee1e2}} and {{cite:049860f24480fff830acbabf4b02a0b907199847}}, {{cite:23d24897b996818b8a7c3c5a1d76a6ff2416dc9f}} for the convergence rates of Q-function and ratio function by non-parametric models respectively. In addition, Assumption REF is a mild assumption, mainly for theoretical justification.
Then we have the following main theorem as a foundation of our proposed algorithm.
| r | 164010d0edd7363ee21d7401b8b885ea |
We reviewed defenses against adversarial attacks on machine learning applications in network security. We note that there are two major limitations in the existing research on adversarial defenses. Firstly, most defenses are designed to protect against attacks on machine learning applications in computer vision. Secondly, the defenses studied are usually designed for a specific attack or a part of the attack. A generalized defense model against adversarial attacks is at best still theoretical as research on generalized defense models is in early stages {{cite:b4dbf4f3966724b9496f620a9852a69c16b54589}}. Furthermore, our findings indicate that defenses against adversarial attacks are specific to a particular type of attack and are not necessarily transferable. Recent research {{cite:eee2e77b6d1d5a5aceaa626df20dc1abb6526754}} have studied the transferability in malware machine learning models in machine learning applications such as malware detection.
| d | cc4666a81cef8b69f19a070e4a9551c6 |
Depth data: Viewpoint-equivariant ITOP. We test DECA on the viewpoint transfer task, meaning training on one viewpoint, either top-view or front-view, and testing on the other one, unseen at training time. The comparison against available state-of-the-art methods {{cite:44b1fad96b5e60028b7dd38fa7fcdfdc79ed98ef}}, {{cite:37cb7bc4ed1cd4024dcc95a550ae4a536169cd8e}}, {{cite:b578c556d85b74c4260dc9f88d064d752de4691c}}, {{cite:eec3d1927e7187f14a0c05b4cc720f59903202a3}} are reported in Tab. REF . We consistently outperform other methods by a wide margin, thus making a step forward toward viewpoint equivariance.
While other methods provide only the best subset of viewpoint transfer results (Tab. REF ), omitting entirely the train on top and test on front scenario, we provide results for all the joints and all the viewpoint transfer combinations in Tab. REF . Our DECA achieves better results than the top-most of the other methods on many different joints (e.g. shoulders, lower body). In Tab REF , training DECA on top-view or front-view achieves comparable lower body accuracy. This means that when the network is trained on top view, where the lower body is mostly occluded, it can retrieve the occluded joints from previously unseen front views, and vice versa. This shows how our network has learned the viewpoint as a parameter, and it is thus able to generalize in a similar fashion in all the viewpoint transfer combinations.
{{table:fcd7b09b-efc6-45c3-b830-1d37ba78df73}}{{table:14ae1026-eaa2-41d5-b280-9f5da79e4293}} | m | aab07e7ab25c8f1322ff90ab8ccadca9 |
There exist multiple types of CNN architectures. In this work, we will focus on a deep learning architectures created specifically for medical image segmentation, as it is the case of U-Net {{cite:d8d40a5203e0191d513791dd102f6e741bccf9d2}} and its variants. The architecture has convolutional layers and is formed by a encoder that does the down sampling of the image using a max pooling. Then, the feature maps are up sampled in the decoder. Both stages of the architecture are communicated through skip connections to solve the degradation problem in deep neural networks. This architecture outperformed previous methods for multiple types of medical images. Due to its relevance in segmentation, this model is the base for the deep learning models selected in this study.
| m | ca6fd9f86ff1b1320435d337bdda3c79 |
+ Shake-Shake + AA {{cite:4b8c05e352a902340570b9cc24173c03dc076e21}} {{formula:c6f48ee0-d4b5-4dfb-b923-e665c3c18a07}} {{formula:32b952db-7f8f-442e-8523-14b4635e17da}} {{formula:51f2bc4e-86a7-4670-8602-8545ffa7d463}} -
| r | b7c03a8b1faa540add2add822773bbf9 |
The CADB leads to factorization problem only if one insists on having a unitary dual conformal field theory with fixed Hamiltonian. The puzzle can be avoided if one instead assumes the Hamiltonian is drawn from a random matrix ensemble. In fact, in 2D JT gravity, this is precisely what happens, the dual theory of JT gravity is not a single fixed theory rather an ensemble of theories {{cite:d1214f44a3a27929935b32ed2d96413fc8a88dd5}}, hence provides a plausible explanation why CADB exists from the boundary perspective. Even though ensemble average saves a potential embarassment, this raises puzzle in cases where we expect and know the AdS/CFT duality to work without any averaging i.e when a theory with specific set of couplings in the boundary is dual to a bulk theory with specific set of parameters (as in the original examples of AdS/CFT based on maximally supersymmetric QFT models).
| i | f5ea8fd0cb96c735ae512137e1b4c508 |
where {{formula:8efc2ac5-c47d-4ddd-874e-4c5891f0f34a}} is a box constraint set. Subsequence convergence to a stationary point was established under
the following assumptions:
(a) the origin is in the relative interior of the set {{formula:430dec55-53e7-4621-ae2a-62ac0fdb6b40}} ;
(b) the strict complementarity condition {{cite:aba62b374156cf93a97dba469f4b6e07d3b5547e}} holds for the above constrained problem;
(c) {{formula:56862006-adc5-46fd-a37b-b1454e5c3220}} is differentiable and has Lipschitz continuous gradient.
Moreover, the global convergence and linear rate of this algorithm was established for the quadratic programming, in which case, the augmented Lagrangian satisfies the KŁ inequality with exponent {{formula:3a7ca55c-9fa1-43ac-a3ff-d5296bbef959}} , by noticing
the connection between Luo-Tseng error bound and KŁ inequality {{cite:ccea0d49469adac64dde1a39877546bed3109e7a}}.
According to Theorem and Proposition , the established convergence results in this paper are more general and stronger than that in {{cite:826bdc9fbed07ca61c0ee1b7c92342041fa75344}} but under weaker assumptions. Particularly, besides the weaker assumption on {{formula:a2260532-6dae-4f7c-b2bf-c02bc5bbff35}} , the strict complementarity condition (b) is also removed in this paper for LiMEAL.
| d | eef86a9c6ac045912f0b99b6b503f3fc |
Proof of Theorem REF .
Applying Theorem 3.4 of {{cite:47a6b70317d8fbd831ee8a3ff39f065f640011b6}}, it suffices to
show that {{formula:f2186f9f-ea6c-4911-890e-f4d67fd0e9e2}} is Lipschitz continuous
with respect to {{formula:6d438a6d-e0ca-4a39-9220-c6b433bcf707}} , based on which we could bound
the global error directly. For any {{formula:47e2dda7-4349-4f2d-a23a-6c90ed40f850}} ,
{{formula:9860a264-92c0-4a60-93dc-9ea658d72807}} and {{formula:cf230193-2e2b-465d-9de7-13ab8ca6d115}} ,
let {{formula:852168cf-7a8f-4dfb-8be9-8d30a3e160dd}} . Note that
{{formula:97dc381f-4a18-4abb-9018-7805a2b2d3b1}}
| m | 5818c358b8377007903ee9c71cbb10c5 |
In the special case of a dual weak brace, the sum can be written in terms of the multiplication as it is already known in the context of skew braces, see {{cite:90d1e67c035f429aa800740496bbcc6ae0cf335b}}.
| r | a8a0b1a97bee691ecd738d5861b0ce11 |
Experimental results at the Large Hadron Collider (LHC) collected at a center-of-mass energy {{formula:00efce86-aa34-4f7e-ae22-ab83b44b7182}} TeV during the year 2015-2018
have been presented by ATLAS {{cite:e1da1c814204af4e4c65c4d040027d63bf64c041}}, {{cite:60cfb389b4c11d85b619f1f7d359763dcc221f38}}, {{cite:b54961b582cb5a3a6e55d826871e0e662dfaa581}}, {{cite:b2c0c533366d32aa3220a64f0454ec3d9c9dbd90}} and CMS {{cite:f6a31b3e206170119a28503a80c3a9dd6eadcccc}}, {{cite:969e86f6b376b1d464180ae917abc2134ec573b1}} groups.
No direct signals of new physics beyond the standard model (SM) have been observed at the LHC so far.
In many models such as the sequential standard model, left-right symmetric model, grand unified theories (GUT) and models with an extra dimension, there appear
{{formula:909e5b7b-d143-4564-a631-9d3d715b717d}} or {{formula:d952f799-e780-43b4-9a1f-aecb110fdc3a}} bosons {{cite:9f653037fb303206ee69a0346037e1fbb2ce7906}}, {{cite:4a8144ad9be3b7f2f0146f3b2ec8b541fa6e58ba}}, {{cite:c31dc476ba8c37553263eb420abb4016e0f46cbb}}, {{cite:7472dfe96efb6f4aa58790ae6a78154275fb1e0b}}.
Physics of {{formula:0779d62a-6f4d-49e7-8962-93a92f500567}} and {{formula:f04e0281-4e6c-41eb-8fc2-24379e9c66e9}} bosons at the LHC has been an important subject {{cite:03b921ba92563093e01d3dae0a7934e092bb560b}}, {{cite:50c9525a46419d00931535f203af1aec74b53faa}}, {{cite:9462aa2ba5749d3233f5a03b9acb70e1e8a0a20f}}, {{cite:92828d21f335118a10c9fa0cc2e03378c3e7ec48}}, {{cite:91e0ac58789dfc7ee56eea3fd47b7bd912c57c8b}}, {{cite:c8a5bf2ffd7852cd88967b7ef0ca3683a06fca9e}}, {{cite:9219ca4fca0ce55f7141c1c834fec66eefd490a7}}, {{cite:17e8f1b67787449de5672c0d70e476d995f573a9}}, {{cite:919dccd262552f9195bb2b8eaa140fa8a53cf870}}, {{cite:4c90ae69cbc613c95772c076e19e0bcb0445040f}}, {{cite:72e62538658e57925f2811695e04d3d813950786}}, {{cite:831c2e48fa4fb00a7f3742ae1db7811ea81a8c9d}}, {{cite:d00e5e774dd8f2f7e3e4fec8015d8530772f203f}}, {{cite:1a698bb09acfc01d6bb6603c282169c98333a2c4}}, {{cite:557eb83379b5660732c05c58ed43da9663f5be7b}}, {{cite:bafd5b30c70369324875aa28d31ab95cbed0cd69}}, {{cite:7d5a652b32b92ee4d56d8b5796e6a4ff8a6bc3e2}}, {{cite:74ad99ff9c3716410952bd952ba3f7dba6b105a8}}, {{cite:97adfb11d013453dc089d6f9107e00bb38449f24}}, {{cite:cbccb618abbca7aae9cc0ee576a6627d56a8b521}}.
| i | fd26b32ceaf65f3bd506a49a5aaa5bb7 |
Global Context based Methods.
As local context features could overlook the correlations between sentences and lead to redundant summaries involving similar sentences, global context-based methods rank individual sentences from the perspective of the entire document.
Discourse-based methods {{cite:8adab5012ea9b94aaf26b5fbff014766f4ad06e2}} construct a document's rhetorical structure and extract the sentences on the longest chain of the semantic structure, i.e. the main topic. Centroid-based methods {{cite:276e4057a11ad39b034eb80d778c7b8c492f8583}} cluster the sentences of a document through similarity measures and rank the sentences based on their distances to the cluster centroids. TextRank {{cite:94e6d0f181b8c132377e972f5c83e0577f69e8ba}}, as a graph-based method, is the state-of-the-art non-learning based method. A graph among document sentences
is first formed by connecting sentences using sentence similarity scores, then the sentence connectivity can be used to score the importance of a sentence. Nonetheless, the nature of these sentence based scoring methods could miss summary-level or document-level patterns.
| m | d3b206c3f64fad7dc7720dbdfaf715b1 |
We also find support for a violation of the conjectured conformal bound on the sound speed {{formula:2137c76c-ab5b-43aa-b693-3ea37af958d5}} in NS matter, {{formula:2f14a468-c9f3-42cb-bd5f-c76eba0baaef}} {{cite:9eace814acdb77f84f57fab4af2569ffa8ddeac8}} where {{formula:39347515-2a4e-4775-ac36-e71c6971eadd}} is the speed of light.
Such a violation indicates that the sound speed does not rise monotonically to the perturbative QCD limit ({{formula:234a5d37-19d0-4710-9a9e-98f3e9bafb96}} ) at asymptotically high densities {{cite:56876534be8d57a5538b1de3148cf707488f06b3}} and signals the presence of strongly interacting matter in NS cores {{cite:113c4033b1845453280e4d8581ff944217cd11d2}}.
The stiff high-density EoS required by the massive pulsar observations already put the conformal bound in jeopardy {{cite:9eace814acdb77f84f57fab4af2569ffa8ddeac8}}, but the softer low-density behavior favored by GWs and the NICER radius measurements help reach a Bayes factor of {{formula:d66a676c-0ae8-44c1-998c-05e6a905f245}} (mean and standard deviation from Monte Carlo uncertainty) securely in favor of a violation.
We infer that {{formula:240b8221-d532-4ba1-bb58-ddddb86b18bb}} reaches a maximum of {{formula:610898d1-1dda-4765-88ad-fe1ecdbe847e}} at a density of {{formula:12726f0e-7e60-42d1-a86d-9d3e450d8817}} ({{formula:cf6ae29a-3fc4-452d-b6d7-9dbbfd4ff5b8}} ).
| i | 090dd670cf644f82f27bd95a7d58ab20 |
As the presence of swirls of various sizes have been observed in the chromosphere and transition region the gyroviscous effect may excite low frequency turbulence. Observations and numerical simulations suggest ubiquitous presence of flow gradients in the photospheric–chromospheric plasma {{cite:cef0aa507c81b203e4f927c2d153232cf07307aa}}, {{cite:4109cf06b28cff3ae8ae1f588386a6f358faf178}}, {{cite:ceb754faa3468727ddd35a8f2f537e9ad2f18087}}, {{cite:248a73b45588920d69d5abc2ec937109fc733309}}, {{cite:d736f4a0dec06c6d97ce7750c972939024d75fed}}, {{cite:20b014bd7fbbf8acf98649f0252239acec493689}}. The typical vorticity of a vortex is {{formula:34f21860-d137-4ecf-a712-114b7cc555b1}} corresponding to a rotation period of {{formula:1a002d5c-6643-46c0-bfea-f737476e36fd}} minutes {{cite:b6bf426119ada577b9237ad2f0669557389428dc}}. Thus it would appear that the gyroviscous instability does not have time to develop since the growth rate ({{formula:82f4ad5a-c54e-43d2-a144-dab582de2ac6}} ) is very small. However, above vorticity value is limited by the upper limit in the vorticity resolution ({{formula:aff7314d-92fe-439a-8d99-39b9f2f7c3cf}} , {{cite:b6bf426119ada577b9237ad2f0669557389428dc}}). The numerical simulation gives much higher vorticity value ({{formula:7b7016f7-35e3-4cd3-87b0-9278f8250d73}} ) in the photosphere–lower chromosphere (Fig. 31, {{cite:20b014bd7fbbf8acf98649f0252239acec493689}}). The growth rate corresponding to {{formula:806525db-12ea-475b-aae0-02177a488cf3}} is one minute. Therefore, it is quite likely that the gyroviscous waves in the transition region will become unstable in the presence of shear flow given that the maximum wavelength corresponding to the maximum growth rate fits within the pressure scale height ({{formula:f666f351-9e33-493e-b250-192d5dff5daf}} ), i.e. {{formula:b8e08f0d-70f9-40d1-b6ea-f4c547437b84}} .
| d | bfd0d07b92f7387a02219b265170169b |
blackFinally, this paper is about the absorption of GWs from a distant point source by the
IGM. It does not address the fate of a stochastic GW background of a population of MBHBs ({{cite:933733b792fa0a54899f6eb996b6b284530a4063}}, {{cite:b2673584fdd756b9daab90f45eddb1bc7f561eeb}}),
which could result from the absorption and subsequent remission (i.e. scattering) of GWs from point
sources by the IGM, thereby removing their direction information but not necessarily the GW
power they emitted. Such a topic is outside the scope of this paper.
{{figure:3a0f476c-a1f5-425d-9124-20480feba2d1}}{{figure:2f1ce9e1-9dce-4d6c-b5f0-0bba382e9129}} | d | c67872e8994df26327646add32edd4db |
Fig. REF shows a real-world usage example of the full detection pipeline, including the object detector, pose estimation and the decoder.
Empirically, the system is robust towards varying perspectives, lighting conditions, dirt, etc., and provides reliable results for the decoded bitstrings.
Extensive testing in varying conditions is necessary to provide meaningful quantitative performance measures. Thus far, we have not observed that the method fails.
Approaches to further ensure reliability of the decoder include averaging predictions over time (at the cost of compute resources) and the use of checksums or error correcting codes, such as Hamming codes {{cite:f8673ce44c3254f4317a7b96ce5e69697fe21a68}} (at the cost of reducing the number of information carrying bits per drawing). Additionally, using spatial transformer networks {{cite:f51d510d76a3564256f4f50699f0a45a301a502a}} would make image rectification an integral part of the neural network architecture. This will remove the need for fixing control points in the vector drawing for this operation, freeing up these control points to increase capacity for number of encoded bits. Further, the spatial transformer can be trained end-to-end with the encoder/decoder to increase robustness against perspective changes that are introduced during image capture.
| r | 4365ad8674bf9afc93825877606584c9 |
The forward-backward splitting algorithm for monotone inclusion problems was first introduced by Lions and Mercier {{cite:f0110bdd315b9bc859ece2e8d0be7552b0e541d6}}. In the work of Lions and Mercier, other splitting methods, such as Peaceman–
Rachford algorithm {{cite:45f131dbe3a6bea3f65474f5c4fd2281702c8357}} and Douglas-Rachford algorithm {{cite:f173ed97283c235fbb57f02cc89308f707875181}} was developed to find the zeros of the sum of two maximal monotone operators.
Since then, it has been studied and reported extensively in the literature; see, for instance, {{cite:e41f3234bb3084caa35aefb761ce8f3c3a8f7a00}}, {{cite:ef6284ad8070138c46425878151dde43f02c76ae}}, {{cite:44eb797df60fb35f7b37db825edace3f358caa17}}, {{cite:bac070e0c59cc160b9652dd9cdff8fbdc0d650c9}}, {{cite:902bdd07cdfaae8c53fbc7f66b8f2dc45cff12de}}, {{cite:c5670da693216e8f342f7510a858398f2fce60db}}, {{cite:03646ce5567238e92830f7d993fe1712c0dd0cd7}} and the references therein.
Recently, stochastic versions
of splitting algorithms for monotone inclusions have been proposed, for example stochastic forward-backward splitting method {{cite:7944f883cd0ddb25bb9ba391faeab2e5b3965a9d}}, {{cite:9346581271f1bd2ea09d4ae4285b83785388bf7d}},
stochastic Douglas-Rachford splitting method {{cite:e2c6231381517ebea2ec298ea027d1b079bc6129}}, stochastic reflected forward-backward splitting method {{cite:d43e9cbe0661975bb430ee8afd9c9978c82fd116}} and stochastic primal-dual method {{cite:f08ab2817a74f7ddbb8e3a1f7194dbfa6f43533b}}, see also {{cite:922138596b49f334008e10b78a2f89b9fe68cf11}}, {{cite:b5140a988cc0ba357f32f9f491465d067353682d}}, {{cite:043298ed3fd7c5210bf7e23d6443416b4b2fd6b4}} and applications to stochastic optimization {{cite:7944f883cd0ddb25bb9ba391faeab2e5b3965a9d}}, {{cite:5ff523ced55b23450ece07b08c0f4eb9e906929b}} and
machine learning {{cite:f3e6ed295116b13e88c09621fb89fb9299ba4927}}, {{cite:24aaf13d5ccebc187f4c0fb6e01c0879d486e21f}}.
| i | d31cd6c155b5aae0e8b7fd37632a9e52 |
The BAMCBR module is based on the CBR 4R cycle defined by {{cite:c696fb87a7c190c08d5a5ffaf6639e15b15399bf}} that encompasses a cycle of continuous reasoning composed of four main stages (Figure 2):
| m | b742129c0355c3a6ea61fdd65766027c |
Recently, researchers have started building chatbots by training machine learning programs on transcripts of conversations.
{{cite:8d85fa2d1c50ef3bbaef76e0da173ce8b7dcc878}} ({{cite:8d85fa2d1c50ef3bbaef76e0da173ce8b7dcc878}}) presented a data-driven approach to generating responses to Twitter status posts, using statistical machine translation, treating a status post as a question and the response as its “translation".
Of late, researchers have built chatbots using Artificial Neural Networks (ANN) or Deep Learning {{cite:99cf46a3598b0110ca4674e1219a6ffb490a70db}}, {{cite:ea73920d27d52fbdc52cd12bb37a2c7046da75ce}}. ANN-based Seq2Seq models have been used by many recent chatbots {{cite:49c72fd92447ccdb54af2a3b513c407dc512da2c}}, {{cite:7af3a1db7790728b5ec867044ed11f45ea013c64}}, {{cite:c992488c1f8113af2ff8a2914fe02906c2d5fb25}}, {{cite:7ae03cd26fc4df0a244e33631f4ab7caee26557b}}, {{cite:40350d332a2c8b70b22a085c658c89218be5872f}}.
| i | c579a26b27c1dc50a63b79e98ff46a8f |
Architectures. In all the two moons experiments, the DeepMLP has 4 layers and 100, 100, 100 and 1 output units respectively. The shallow MLP has 2 layers of 100 and 1 unit. All methods were trained for 100 iterations on 50 datapoints. The MNIST plots are obtained from MLP classifiers having 4 layers of 1000, 1000, 1000 and 10 units each
and are trained for 500 iterations at batch size 100, reaching an accuracy of 95% on the entire test set.
For the GAN CIFAR-10 experiments, we use the architectures specified in the Spectral normalization paper {{cite:ad73efc5d18013a93766fce11e56428b6ace6b97}}.
Unless otherwise specified, we use the default Adam optimizer {{cite:3763d5845cd5334998ab5603a87345b1a1224090}} {{formula:a2d7912d-dd61-4983-8628-7dd9e851c9d7}} and {{formula:d63ed088-1419-4987-b608-cbb5c24f036a}} parameters.
| m | 294941344afd7eeec7e1df79cdcd9fb0 |
Here, {{formula:c3ab325a-2c23-488a-a73b-f4ce43567e7d}} is the {{formula:0cbcc4f4-60a8-454f-b738-38bde6d4b342}} -th Pauli operator {{formula:cad976e0-7610-4ac4-82be-b080fe168458}} acting on qubit {{formula:e9694e94-d9a7-4094-93f0-40628cec5a68}} , while {{formula:8f1781f1-d7c5-44df-9c95-9fbf2e7500f6}}
define local and bipartite time-dependent (coupling) rates. In general,
these rate functions may take both positive and negative values. The problem
is to characterize which constraints must be fulfilled by them in order to
obtain physically valid solutions. Interestingly, the resolution of this
issue leads us to consider all possible multipartite interaction terms, that
is, decoherence channels that involve coupling between an arbitrary number
of qubits. We also explore which rates emerge when the memory effects arise
from different underlying mechanisms based on coupling with incoherent
degrees of freedom {{cite:3d6a2397974c777db69bca3c715d235309d7ca6d}}, {{cite:b947844d139839bbcaaebed2f750163e3c85a464}}. The explicit formulation of an
operational (measurement based) memory witness {{cite:a00e280f08130898fd0b1a267b3a8c7906d09d89}}, {{cite:704e8f56dc493f673c482cb003f4a24fc98e3767}}, {{cite:bde8e7b69ec877f21f3453bc0d4ec530290e985a}}
further provides an alternative characterization of non-Markovian effects.
| i | fa9d2772bc6c954a2ef1657e07e3e2a9 |
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