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Related Work on Optimal Transport Frameworks in Machine Learning. A large body of related works apply optimal transport theory to address various statistical learning problems. These applications include generative adversarial networks (GANs) {{cite:42918b32cd96ceb917422488d459c73b882005c4}}, {{cite:6431cadb1901d4588a80b594cd0a9e673ab0d306}}, {{cite:b195257e90b47eb0750dc3843c44b4fcfee24635}}, distributionally robust supervised learning {{cite:432712a453cc6661e1e9041385330b3167860a63}}, {{cite:2ba851d635fe3f65fa27dd40feb05ed4acb6c9ac}}, {{cite:7523cca06eca9bbf78d6a32f7d4260e29a8bba7d}}, learning mixture models {{cite:3de591e02323bb34d88053a7e33860a129e4e1c9}}, {{cite:71137b495fca7275c11eb4b7dd78427bf9b16677}}, and combining neural network models {{cite:d6b5355c4238fb0d87a8c80cbb04126185de4b50}}. Multi-marginal optimal transport costs {{cite:a219db663df71058dd22a4788564b7bea68de4ba}} have also been studied in other machine learning contexts including GANs {{cite:75a696c1108f9bdd30dcd917ee32610086a7f66d}}, domain adaptation {{cite:435285caa27edb72e47f16be5a62d0d953b292e9}}, and Wasserstein barycenters {{cite:b5f78f499e5de756edb4b13aea9f92c185c77ecd}}, {{cite:79b1cbe3cbda2583c6fdf73cd0615b803fd13fca}}, {{cite:1f56b8b474aa8fae9b5a4643c4ec5a515d2a2fec}}.
i
5943016ba9f3128c993a4a3350189221
Among other similar works, in {{cite:3c3c7e1e74f2f64f855822178be7f74b40eb05bc}}, the authors study in the framework of Bethe-Salpeter equation, the production ratio of neutral to charged kaon pair in {{formula:ec84e6dd-863f-4a90-bfb4-396fe63b14cc}} annihilation below the {{formula:c1ec4f83-4923-4a32-9a13-8264ff427dc6}} mass by employing the two leading Dirac structures in hadronic wave functions as per the power counting rule {{cite:91c45f10b39c2c8969ded0ef1a98fef3db274a48}}, {{cite:87ce2e454c9f2fa5d861ce1caa39ef4ef5c8d620}} we had proposed some time ago. We wish to extend this study to calculation of cross section for each of these processes with the involvement of all the possible Dirac structures.
d
60d684924751e02bf14af67c33fba3bb
Full Connections. Beyond obtaining information from certain scales, many researches are exploring methods aggregating features from all scales. Kong et al.,{{cite:94e65fdfbd1ee00108a476dec9e93e0098c3288d}} gather features from all levels to a medium level followed by concatenation along channel dimension. For each level, they use global attention and local configuration to enhance and refine the combined features. The refined features are finally resized to the corresponding level and then element-wisely summed up with the original input of this level. Libra R-CNN {{cite:acda6a2116de822fb65eb0a0560921d2a9b75c27}} first gathers features from all levels to a medium level and does element-wise summation. After that, a non-local {{cite:01952381efee70898d7f19d532f4fa93730e408f}} module is applied to enhance the merged features. The enhanced features are then scattered to each level and element-wisely summed up with the original input. The above methods obtain features from all scales by gathering them to a medium level and then merge the features. However, a feature representation at medium scale is improper to describe objects at other scales. Therefore, the generated features can fit well the scale of this level, but may not fit well for other scales.
m
b953594e57fe289aca69677a5a95c3a8
Comparative analysis of MM speech synthesis model's results on U.S. English speech database is presented in Table REF . For evaluation of speech synthesis, experimental results Mean Opinion Score (MOS) and Mel-Cepstral Distortion (MCD) are the most commonly used subjective and objective evaluation metrics. Subjective assessment approaches are often better suited for assessing speech synthesis models, but they demand substantial resources and confront problems in terms of findings validity, reliability, and reproduction of results. In contrast, the quantitative assessment of the Text To Speech model is performed by the objective evaluation technique. The discrepancies between produced and real speech data are commonly utilized to assess the model. These assessment measures can only represent the model's data parsing capacity to a limited level and cannot indicate the produced speech's quality. The MOS is the most widely employed subjective assessment technique, which evaluates naturalness by inviting participants to rate the synthetic speech. MOS higher scores indicate better speech quality. MCD is the most commonly used objective assessment method to determine the difference between actual and reproduced samples. TACOTRON2 {{cite:c83af17ae16dc10bd2438a9b3fa20c4d0d4c3344}} DLTTS model performs better as compared to other speech synthesis models. Parallel TACOTRON {{cite:9bbee8f9c015d1e1e2f0c0b936441947e4573fcd}} is also the closest model in terms of experimental results, but its relevancy is much more than TACOTRON2.
r
31e5cbc1c738cdde8777d3d2ce573ff4
Built on the above foundations, we turn to verify if this bound is followed by the encoded information of {{formula:1cafbe80-0fdd-4395-97c3-7d523762a5ef}} in an arbitrary sub-system of {{formula:30848954-ba02-47b2-9001-4fd76bf575d5}} as well. The necessity to study this problem lies in that it provides an opportunity to glance at the effects of internal orders inside {{formula:611edc15-e177-49e5-8373-e09f28daf30c}} on the information thermodynamics link between {{formula:eb1f2cf4-4acb-4f50-a892-9c14a9a12673}} and {{formula:8d7ad6b9-c54e-4ffa-be6c-11c83e5824fd}} . Despite the substantial progress in exploring the physics of information {{cite:2e53be90d6045bf9c2749468cd957810431dcdad}}, the critical roles of these internal orders remain elusive. Exploring this problem may help understand information thermodynamics in complex systems, where the diversities of information thermodynamics characteristics might emerge on multiple scales due to heterogeneous elements and intricate internal correlations. As a starting point, the present study is limited at a qualitative level. Combining the 3-order multiple mutual information and the theory of information synergy and redundancy {{cite:3bfa64826bb7967c5dd62c7d5c6a8b690236aad2}}, {{cite:68d0ee15257d6ca05f8cfb5376943dc48eb21ad8}}, the proposed thermodynamics of encoding suggests an intrinsic difference between the non-isolated system with internal correlations and the non-isolated system of independent elements when they act as information thermodynamics encoders. Unlike those with independent elements, an encoder {{formula:f0ff73f0-acf9-4275-be77-cb0bb83517c0}} with internal correlations allows the encoded information of {{formula:e8447145-d852-4920-9dab-54d591bdc633}} in its sub-systems to exceed the information thermodynamics bound on the joint system {{formula:f46b2396-0cd0-4ce7-b059-8abee905be90}} . More specifically, the encoded information of {{formula:c8665e1f-8628-42d9-bda1-7ac93f3f853f}} in an arbitrary sub-system {{formula:a6089d66-faf4-4aec-aee7-1a891bba41c9}} is not necessarily bound by the irreversible work {{formula:751fcdb0-7693-4e15-997f-2c5a30895ecb}} from system {{formula:d1af2f30-7874-4794-8c07-ea57c0ee6def}} following (). This difference may originate from the nature of order inside the system {{formula:da890500-5d41-464a-8bd6-76fed6c942e1}} . There is frequently information synergy in the non-isolated system of independent elements; in comparison, there can be either information synergy or information redundancy in the non-isolated system with intra-system coupling. These theoretical findings can be mathematically derived utilizing the Yeung's inequality {{cite:70fcf310d408c7906a725a159ce24d900b6b373d}}. Furthermore, we have computationally verified them in an Ising model with a random external field and a real data set of the human brain during the perception process. Our analysis demonstrates that the stronger internal correlation inside these systems can create a higher possibility for their sub-systems to encode more information than the global one.
d
a3d6179a8cd1bb67a6ece9680073161a
As mentioned in the Related Work section, InstaBoost {{cite:b3b1a46091a91a2e4bc48f08727e345036db8c27}} relies on two operations - shift of instance segments and in-paint of background - to boost the performance of instance segmentation and detection. There are several key differences between PanDA and InstaBoost. First, in the panoptic segmentation task, a large part of the “background” in the instance segmentation task now belongs to the stuff superclass. The “background” in the panoptic segmentation images usually takes up less than 15% of the image, making it infeasible to use the same in-paint process. Secondly, the motivation behind in-painting the background is not explicitly explained and presumably to maintain the image's level of realism. In contrast, PanDA boosts panoptic segmentation performance despite losing image realism. Finally, in addition to the shift operation in InstaBoost, PanDA has resize and drop out operations which are shown to be essential for its effectiveness by the ablation study (Table REF ). The method proposed by Dvornik et al. {{cite:d3978fe01eae6b5821393fb647c5358a6a1c8828}} adds new instances to original images and avoids holes in the background from removing instances as seen in InstaBoost. However, the pasting of new instances has to be guided by a CNN-based context model to determine the location and class of instances to add, and that model has to be trained which requires data and time. Similar to InstaBoost, the method only applies to things classes which takes less than 50% of pixels in an image on average. Shetty et al. {{cite:48f8c28e0267bd65d9730e69abc93aaebdfd5569}} propose removal of objects to break context information and help deep models to generalize in classification and semantic segmentation. This approach relies heavily on a trainable CNN based in-paint network to fill the holes in the background. Data and time are needed to train the in-paint CNN network in this method. Additionally, experiments in the original paper show that removing large objects such as mountains makes it hard for the in-paint network to fill the hole left behind and indeed hurts model performance. In contrast, PanDA removes the large objects like road and buildings with high probabilities and we show that is essential for performance gain.
d
edce34111616f1da4a004f8400d181a0
Modern face recognition methods rely on deep convolutional networks trained on large-scale datasets {{cite:63ba37f79f3f112f6cf596e7503c09f7e2706a2a}}, {{cite:e9c7e472e34e5b5d36a47319ba86ab9468c9bdc1}}, {{cite:e4781723e3233235a521cd04a5ef582c15df73ad}}, {{cite:794a60d40eea784452606f6263af742edbcb1a45}}. These methods are now being integrated into a vast number of real-world applications, ranging from face unlock for smartphones and photo organizers to law enforcement systems and border control. A typical open face recognition dataset consists of web-crawled images of celebrities, leading to limited size and lack of balance in subgroups, such as ethnicity, age, etc. Training a state-of-the-art solution, however, requires enormous amounts of labeled data, scraping which may lead to privacy and legal issues. We suggest and study an alternative solution to using celebrity photos – pretraining the face recognition backbone on a generative task. Specifically, we first train StyleGAN2-ADA {{cite:68835b6ca2c190adf0ef1b1653d56232b6b0e9f4}} on collected unlabeled data (which we later refer to as an unlabeled prior dataset) to fit the face image distribution. Subsequently, we train an encoder (following pixel2style2pixel (pSp) architecture {{cite:e65ed27a06e816ab87fc063f863fa573c7aa8b47}}) that maps input images to vectors in the learned StyleGAN2-ADA latent space. Importantly, during the pretraining steps, no identity labels are used, so we can use diverse datasets crawled from the Internet without compromising privacy. Finally, we transfer the learned pSp encoder convolutional weights into the face recognition network and train it in a standard face recognition setup.
i
97e041bf92e9762840da32d5cb66b8c6
Let {{formula:3a3d677f-c61c-4b72-a0e6-96a5581298a0}} denote the composition of {{formula:d601ebe1-628f-4317-9a45-01ba542ab18e}} with the canonical projection {{formula:ec04f2b6-1b54-477d-9dc6-51fdf7ca682f}} . It is well known that {{formula:c5b774c7-417e-454b-a5c2-3aaad3977d99}} (also known as the level-{{formula:7e2d1636-8196-4a33-99aa-ada20578793b}} subgroup {{formula:2f4af29b-b86c-4fe0-9d8b-c4b070941798}} ) is torsion-free for {{formula:820cc9f8-bc3e-4307-bedd-20304c1ab242}} (see {{cite:8fbe266ad882cb8965f937f5fadacb3aea6a5224}}). Considering that the conjugacy class of {{formula:87c637ff-4759-4dea-84e7-ef4f142bb76b}} can be infinite in {{formula:ca93ff79-228b-44c2-bf86-067b977847fe}} , for computational purposes, we consider the set {{formula:8da2051b-d04c-490a-945f-7d280a762638}}
m
9ea591d6aec44067e7f13d19e11f1028
We notice that the total luminosity change during the transition is by a factor of 1.6, which is smaller than the model-predicted luminosity gap of 2.4, and could be related to matter leaking through the magnetosphere to the NS surface (e.g., {{cite:e4cf72c0fc75b5e80ecf3ec13277ab9fb03c3f18}}, {{cite:f9895e3892a9913297e9ef17363315d821c79612}}), e.g., forming some kind of accretion flow/channel to the NS surface (e.g., magnetic poles) {{cite:dd49c97a39cf7b7f5e3de8c41ea12ae814234a99}}, {{cite:9001ca5a986597b01304eb8714fb248a14a31677}}, as shown in Figure REF . If it were true, a reasonable prediction is that there is an enhancement of pulsation fraction (if the pulsation exists) around the transition, which is beyond scope of this work and will be explored elsewhere.
d
4adad41d2bea300142ca790ec965ca58
The Proper Orthogonal Decomposition (POD), particularly the snapshot method {{cite:a7207deb7278da2cf20f758b4c84f2d0fd6d4744}}, opened an increasingly popular avenue to data-driven reduced-order modeling {{cite:833e624ae1044c655d4d24f7f1c1dd38d9eac6f0}}, fueled by the increasing availability of high-quality numerical and experimental data. {{cite:be80fe3ee61f741da644ed2034dc554e0f30b1d9}} pioneered POD modeling for the unforced turbulent boundary layer, one of the most complex flows to start with. An avalanche of POD models followed for a myriad of configurations. {{cite:2a1f043862c8b8da0a61ddb941aa9c9b9479f07b}} proposed a low-dimensional model for the minimal channel flow unit for the purpose of physical understanding. She continued to develop an accurate high-dimensional POD model for the wall region of a turbulent channel flow {{cite:d711fd58b2923232790c8b1b80a588590406acb2}}. {{cite:ad99964367afc4fe931d55bab64376e8f319db48}} further proposed a pressure extended POD model with no additional cost and tested that on the two-dimensional square cylinder wake.
i
a24c450d8ace51aa7dd8ffe4abcd96cb
During the last century, telecommunication networks' theoretical analysis, design, and control have evolved together with the underlying technology. Starting with the circuit-switched telephone networks of the early twentieth century, through the boom of the packet-switched network that is the Internet, the advent of quantum computers requires a new type of switched network {{cite:2dc669914dbd63bf603d3bc20fe07ce257ec6d4d}}, {{cite:f918ea20dad3fe1de592828fee75a9ae1cc15820}}, {{cite:ba722cf6bdf5efc9c8756e087dcf4d1f06b3cd9f}}. In quantum computers, the qubit replaces the bit as the minimum unit of information. Qubits act as a richer unit of information that allows new computational applications and a new way of communicating by entangling the state of qubits at different nodes. This entanglement is a fundamental feature of quantum mechanics that has no counterpart in classical mechanics. When two qubits are entangled, no matter how far or isolated they are from each other, altering the state of one of them instantly alters the state of the other. This enables instant communication at vast distances. A Quantum network enables distribution of such entangled qubits between users, and several architectures already propose implementing such networks {{cite:4a2d87cc07d1f165c26a5b2d7235cfc92187ab0e}}, {{cite:5c25860b1dca9f0998971870aa220507fa680208}}, {{cite:88fd2fd719b12815ea44fa22da4d80735b903799}}, {{cite:969632a0f00f029d7e43655a0755873d36ed66bc}}, {{cite:f23c71b736f796363911d35363d41656b44ed33c}}, {{cite:8dbfd9243c5f1bf631c52f0c8cf0ac0ee2b41eba}}.
i
212a41241031b9f99d0b11c181416644
We now evaluate the impact of EMI on the system secure performance, with special focus on the cases with EMI-aware and EMI-unaware eavesdropper; these are referred to as EA and EU in the sequel, for the sake of compactness. The phase noise term {{formula:9254465c-1475-4db8-ad1e-68a60c47bdab}} for the RIS is modeled as a zero-mean Von Mises random variable (RV) with shape parameter {{formula:3f89e615-0dcb-464e-b43c-7341d2918d34}} {{cite:c75ba529a1037b4563f6b2cc4aa5b0eaaa628fdd}}, where a smaller {{formula:25919be8-a5bb-4060-9fd5-695f70a25474}} implies a larger phase error. For all figures, a carrier frequency of 3 GHz is used, so {{formula:4f5fe473-233a-448f-b7c9-7b54adc0816c}} m, and {{formula:865fe3ff-ea75-4bfb-ad37-d4046b409008}} dB, which corresponds to transmitting 20 dBm over 1 MHZ of bandwidth with a 10 dB noise figure, so that {{formula:80bedd47-8ecd-4367-bc3b-0186326a8ca2}} dBm. For all SOP traces, we set {{formula:745ae94b-51d2-4e97-9fd6-21c9cc3b8f3c}} bps/Hz. For Fig. REF , only the indirect RIS channels are considered, whereas Fig. REF includes the presence of both direct and indirect channels. For convenience of discussion, we define {{formula:5b65675b-21a1-4731-929c-43d940856f8a}} as in {{cite:c61d123aff16e0b743080f289908581cf609a87a}} as the ratio between the signal power and EMI power at each of the RIS elements. Monte Carlo (MC) simulations are provided to double-check the validity of the approximations made throughout the analysis. {{figure:e25b3a5f-4630-4bd7-8e7f-3f9729918dec}}
r
e4de2196f78ed0e98a48f83eb0566f45
The works in {{cite:cec018da422d69e33a21600a567b8528f19caecf}}, {{cite:f31bfe0218b538acedf57daeeb47e05f55295147}} demonstrate that GPs can still have superior expressive power and generalization if the kernels are dedicatedly designed. With the belief that deeper models generalize better than the shallower counterparts {{cite:709d965cfb0624a4b07437a97521f091ca8201d2}}, DGP models are expected to perform better in fitting and generalization than GP models do if the same kernel is used in both. However, such expectation may not be fully realized as the approximate inference may lose some power in DGP. For instance, the diminishing variance in the posterior over the latent function was reported in {{cite:248515e9bb4c3f90c094494bceaf10e112099b29}} regarding the variational inference for DGP {{cite:e6b7ce1c420eb55088639ad6f91781dcd386ab58}}. Here, with demonstration on extrapolating the real-world time series data with the conditional DGP, we shall show that the depth along with optimizing the hyperdata do enhance the expressive power and the generalization due to the multiple length scale and multiple frequencies character of the effective kernel. In addition, the moment matching method as an approximate inference for conditional DGP does not suffer from the posterior collapse. The simulation codes can be found in the github repository.
r
e11e4f84d2de6aea3bbec9aa0ea55541
As it was mentioned in Section REF , the AVE does not vanish for {{formula:ddc7e266-d471-437b-882b-fda4e5fd3419}} , as it is apparent from eq. (REF ). This means that the AVE does not need chiral imbalance to show up and persists for a perfectly chirally balanced system. We interpret this feature - at least in the form in eq. (REF ) - as an evidence that AVE is not related to the anomalous axial current divergence. As it was found by A. Vilenkin {{cite:889412720a93a3d5a351d476931b1140780844b5}}, {{cite:e0c322dcf7139035db99bc8ae4a525458b9df370}}, {{cite:f0528e6b7b2e250075e18066a28ebde0edffe0fd}} and lately highlighted in ref. {{cite:a93be5985ef6b546b2ebed6bb13be8ae56820c9b}}, an axial current proportional to vorticity arises because it is allowed by the symmetry of the density operator (this was also recognized in {{cite:64164a115b86858657b3e21c5d1a5c9591c95828}}) with rotation and, indeed, the very same expression (REF ) is found for free massless fermions, without coupling to either external or dynamical gauge fields which make up the anomalous divergence of the axial current. We understand that this statement goes against the conventional interpretation in literature, and yet some other authors have lately cast doubts about the anomalous origin of the AVE {{cite:2a909b4404459e077f327f7e2dc4582616d99322}}, {{cite:94f1d3e16f144c97fd57f5d6076635212a55a5dd}}. We hope that our viewpoint will contribute to clarify the point.
d
b771cbf581947007fbf891ef28b911ea
This supplementary material presents additional experimental results and visualizations of our method, which are not included in the main paper. Section  first describes additional experimental results on CIFAR10-C and CIFAR100-C datasets with different severity levels and the classification accuracy with 5 trials. Section  presents the t-SNE visualizations of our method, CAFA, and TENT {{cite:0510d74ffee8942752ddac1a96519869b0f63b74}}. Finally, Section  presents further implementation details.
d
45719097389665a9e87a2f460a0d943a
We have investigated a generic model of non-linearly evolving dynamical dark energy equation of state {{formula:ff8c1e10-7db1-4fe1-839b-53b8d384580f}} , in the light of the recent Planck, Pantheon, BAO data and recent measurements of {{formula:856567ae-3965-4885-adf9-ee04e0d0141a}} and {{formula:9b1bdcde-063c-4935-8cd8-51c45abd9521}} . We have studied the effect of such parameterization on the background and derived cosmological parameters. The results of our analysis is in accordance with the earlier studies with a linear evolution of {{formula:28f457d9-396e-40ad-9d35-5547b1b85406}} (CPL like) {{cite:d0185dddd4bb63bbf2c4d57bdedc30615a78cf18}}, {{cite:d712dde970fdac838e0f5895a2a426e26d52cd2e}}, {{cite:d90797f729229c9881b9c5302440b2504c1de7bc}}, {{cite:afc842c7681b05a39df7c736282382e773489558}} and a few other parameterization of dynamical dark energy {{cite:a85a2c6039354cb05428252a438836e39b728624}}, {{cite:0348d8664047506e9f1a0b8bc4a24560f6ba67fa}}, {{cite:70f1234b3263583bcfc52a3b5389f55049f2b5a2}}. We do not get any strong constraints on the two extra parameters {{formula:6eec0919-31a6-415c-8220-11f341e4036d}} and {{formula:24c5149b-b70c-47f9-9a64-809bd194bc55}} at {{formula:897c58c7-cba4-42c3-a8bf-627d0d119670}} level, constraints on {{formula:14536ebe-24a8-4a3e-898f-e3f614e9f220}} and {{formula:4a26be07-fdef-4439-8bf5-1bf380e22e03}} are in good agreement with the CPL parameterization. In fact this is in good agreement with the {{cite:a7cfeabdfa79fc1607737d9d3282a73543843813}} predictions. However, we do get slightly different and a more tightly constrained {{formula:4826d70a-3c7b-473a-ab75-4c1cfe0744f6}} when the model is tested against Planck and external data (Pantheon+BAO) put together. The added external prior on {{formula:dd531e7e-a0c3-47a8-8117-e7ca36d35fd4}} and {{formula:ec335b41-8130-40ff-8f57-7e7eb6a5a0e9}} makes the difference in CPL and 4pDE parameterization even broader. The 4pDE model can bring down the Hubble tension to {{formula:66921e90-bcf9-4465-9f62-9ef1277a3431}} level and the {{formula:b3a2935b-0854-4551-9e5f-55ed26792331}} tension to {{formula:03367911-8cf6-4064-bce1-0c66c8011e13}} level when tested against Planck, BAO and Pantheon supernovae data together. More importantly, we find that there is a negative correlation between parameter {{formula:5d31716c-057c-40b8-a2f1-3280dd428971}} and {{formula:9829018d-dbd7-4bbe-b8cc-8ab38e3c0970}} which is very interesting. However, both the 4pDE model and CPL model improves {{formula:3cdce092-50e9-4c4b-ac2c-ff5d2aba54a0}} for the Planck+Ext data set and the recent measurements of {{formula:de8e8669-5b25-4546-ac45-15c3310e870e}} and {{formula:ef881c40-960d-4dd1-b18d-2f3917232754}} in comparison to {{formula:ef1d8996-7843-48e2-8b58-8842494944ff}} CDM, this lowering of {{formula:02f0fc44-c9a3-4c35-a4c4-7aaec219a732}} is achieved at the expense of adding extra parameters. So if we follow {{formula:f8f0e55e-14fd-41d5-9507-8c59c33c019f}} AIC criteria like recently done by {{cite:c23dd6ad187e8a0a527003b9054be5bc75f83ae2}}, the level of success of these models degrades as none of the models has significantly improved {{formula:4d3d8b6e-c9f8-43b7-a07c-30107e7f9e60}} AIC value over {{formula:bd713eb7-1c28-4486-aaa4-de95da93db2a}} CDM model.
d
ba62f0cd2d155937d068de621b060164
It should be noted that many notes in PMC-Patients have token counts far exceeding BERT's 512 token limits and truncation is applied in our baselines, which suffers from inevitable information loss. Efficient transformers {{cite:3313315419b8215a7b0b978046c225a29bbbc026}}, represented by Big bird {{cite:68afdd94b804411fca55fa703195c67c4c990651}} and Longformer {{cite:943b7ba931ad6f8f5dcb2e86af4d191961c166ec}}, are potential solutions, and we leave that for future work. {{figure:d42666ce-3042-4c91-8e6e-5b0726c01d72}}
r
56aed857de4c24aba63fc6125688123c
The system of gas dynamics equations for INS in the Euler representation (e.g {{cite:fd6f1a2e1ea3e27f617d7add8dd78f5fd27cf306}}, {{cite:7dc0d184cb5d621ea4723d362fe5866cfcffe241}}) is: {{formula:1cd0b6e6-15fa-4bf8-bdb6-914474c6be1a}} {{formula:4abfb22c-66cb-41c4-9c76-ddd50453c9a5}} {{formula:63def4dc-c09e-43d1-8ae8-bc43bda8d9aa}}
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a6b50a199d10b7c2b39b8bad176a7a46
To illustrate our proposed method with a concrete example, let us assume that we chose MagFace {{cite:ef182a5c452928388d1e8b0f0524e6baf0b7f66f}} as the underlying unsupervised FIQA method and used the ResNet-100 {{cite:102713cb24a1a3bbc7a13646fe8b8e9fc5e5d842}} model trained with ArcFace loss {{cite:47b0e3c312a530e77c85ed6ea9b900fad9f1a82e}} as the face recognition model to extract the face embeddings. We further used ScoreCAM {{cite:a0239f26cf28416e2bac9b80b0ef28f2f4f13322}} as the approach for the activation mapping process. The activation mapping visualized the deepest convolution layer of the Res-Net100 and upsampled it to overlay to the input layer. The scaled version of the activation measures how the output changes to the face embedding. For each image, the activation mapping (AM) provided an output activation map with each pixel value noted as {{formula:9fa9de5d-d28e-4bf8-9ace-52039eb3f7f4}} of the size 112x112. However, this concept can be extended to any FIQA method and CNN-based FR model. More details about the exact models used in this work and the reason for this selection are provided later in Section .
m
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For the majority of our void galaxy spectra, the value of logO{{formula:8fd7bee7-7312-46fe-807b-43e92fac8028}} falls below 0.5. Therefore, one expects some corrections of t{{formula:e58a3381-df6d-4c72-b4a9-bcd544eb7f89}} calculated in papers by {{cite:d00e6e5b7e85212273639ac6db1a1d0a1eae3aac}}, {{cite:ed9ba17a5aff6ee7b55f4c7cacdc9ec46a164731}} and {{cite:d01bfb03f210a1115e1e2bc8796e51987f543e3a}} with the original se method, with a related small correction of {{formula:758acd55-d684-421e-b4ce-bb335c6677d1}} log(O/H). We employ this mse method and present in Tables B1–B7 the O/H estimates derived with this method, O/H(mse,c), for comparison derived with other methods.
m
373182a4803cd6c4a77c41c1ee095b00
Recent work has incorporated risk into the analysis, with different works working with different risk measures that satisfy various properties. In the existing literature, the more popular risk measures being considered are mean-variance {{cite:bd59180d0e86604109006ada21d4a697f187a3f0}}, {{cite:64427950862c094ef5e0b73d5049262f5ecc44b1}} and conditional value-at-risk (CVaR) {{cite:14e3d5e85ba5ca6162408430519a5020b85a161e}}, {{cite:eaee07117033de55f2054d91fe5c05489a07ff13}}, {{cite:7ab026aad7704305bb41088e936ed252245b5c88}}, {{cite:3d642b52532b9804a4ea656e3e3c78bc70ba0980}}. In particular, CVaR is a specification of a general class of risk functionals, called coherent risk functionals {{cite:c8832ea748d911dad4ce1fe0b5721abb0a826927}}. {{cite:d1089ffd848cfd1382cd66197904f7dd95dd34f8}} observed that when rewards are nonnegative, coherent risk functionals are subsumed in broader class of functionals called distortion risk fuctionals. Most common distortion risk functionals, such as the expected value and CVaR, satisfy the theoretically convenient property of continuity. However, not much work has been done to unify these various risk-averse algorithms to elucidate the common machinery that underlie them. In this paper, we provide one way to unify these risk-averse Thompson sampling algorithms, by considering continuous risk functionals, which we denote by {{formula:162d124b-435a-482b-ae02-0f91c108ea42}} . We design and analyse two Thompson sampling-based algorithms—{{formula:81842830-7495-444c-861e-71e1c8449f72}} -MTS and {{formula:0ab76edf-d78f-44de-9b2a-3b054e5efbf4}} -NPTS—to solve the respective modified MABs, achieving asymptotic optimality. Therefore, we unify much of the progress made in analysing Thompson sampling-based solutions to risk-averse MABs.
i
6fe4e11185b5b4eccf4db406608c14b0
There are a number of limitations to our work. As we have remarked throughout the paper, both inherent differences between the platforms and differences in data sampling and selection biases make direct and fair comparisons impossible in many cases. The content collected from the Twitter Decahose is biased toward active users due to being sampled on a per-tweet basis. The Facebook accounts provided by CrowdTangle are biased toward popular pages and public groups, and data availability is also based upon requests made by other researchers. The small set of keywords driving our data collection pipeline may have introduced additional biases in the analyses. This is an inevitable limitation of any collection system, including the Twitter COVID-19 stream (developer.twitter.com/en/docs/labs/covid19-stream/filtering-rules). The use of source-level rather than article-level labels for selecting low-credibility content is necessary {{cite:60079768ee5614a9a0b6bcb6ae1e1e6d94d35f4b}}, but not ideal; some links from low-credibility sources may point to credible information. In addition, the list of low-credibility sources was not specifically tailored to our subject of inquiry. Finally, we do not have access to many deleted Twitter and Facebook posts, which may lead to an underestimation of the Infodemic's prevalence. All of these limitations highlight the need for cross-platform, privacy-sensitive protocols for sharing data with researchers {{cite:0d87d29dc8654f033baefde043599bcf71cb9e4e}}.
d
60b55db83f8538aa1415b72170040251
We used the FedOT-GDA algorithm (Algorithm REF ), that is a distributed mini-batch stochastic GDA, for solving the regularized FedOT's min-max problem as formulated in Proposition REF . We used a batch-size of 20 for every user and tuned the minimization and maximization stepsize parameters {{formula:4807140a-1b06-4be9-833d-485a12362089}} while applying 10 maximization steps per minimization step. For the {{formula:8510863e-9991-41ab-8aa3-2020014fe641}} -regularization penalty, we tuned a coefficient of {{formula:f3722d98-5b36-4f0b-a3a1-ea98387262a2}} for the CIFAR-10 experiments and {{formula:dafecb0e-9b20-4ea0-8077-2d00ebf5cb80}} for the MNIST experiments. For baseline methods, we used the the following three methods: (1) standard FedAvg {{cite:dcf4443547bdf6a00824fe54fe55b992de9af228}}, (2) localized FedAvg (L-FedAvg) where each client personalizes the final shared model of FedAvg by locally updating it via 500 additional local iterations, (3) federated model interpolation (FedMI) {{cite:e4308a1654a00ebd95d18ef30a690e30262bf1ee}} where each client averages the global and its own local models, and (4) federated first-order model agnostic meta learning (Fed-FOMAML) {{cite:96103eb8c06ffc8d50c7c7d56339514c2d830766}} applying a first-order meta learning approach to update the local models. Note that our evaluation metric is the test accuracy averaged over the individual distributions of the {{formula:96c1049f-74d1-43dc-9426-91a11fbed225}} nodes.
r
9d464a9dac5446517906c00278c25789
Table REF lists the method comparison results. The ones labeled by “ours" were those pruned using the new pruning method proposed in this paper. Three other methods were compared: the feature reconstruction-based methods(ThiNet {{cite:1832618f49685ca2a06201aa9c7eddbf816b772c}}, NISP-50-B {{cite:b256afcb1376439e6577f3d913d1f7085e6e62ed}} and GAL-1{{cite:9b40f9cd55f52585996ee161c801e9db65b997e6}}), the Taylor-expansion-based method(Taylor-FO-BN{{cite:66fe463f3b93c665d56cb5ff574cc128078006c8}})and the information-theory-based method (HRank {{cite:21e00e2b1437d4ee3c62eba726ff258caad01d91}}). Using our hierarchical pruning method for a global variance contribution ratio of 0.99 (pruned_0.99, ours), we obtained a parameter compression rate of 52.76% with a Top-1 accuracy of 73.01% and a Top-5 accuracy of 91.11%. All other assessed methods yielded lower parameter compression rate but with lower Top-1 and Top-5 accuracy than our method although FLOPs were similar.
r
25696470e7772fef874c8b0ce6b0bf76
In {{cite:454ebe3732f65689b9433a966ba9b5aec820bdc8}}, Bowditch constructs the boundary of a relatively hyperbolic pair {{formula:66415242-0780-42d0-a7d6-47ce1f88f8cd}} and proves that it is compact and Hausdorff, provided that {{formula:28e5b991-938e-4575-a74b-6c996e84929b}} is countable. In Section , we show that the same elementary construction extends to the general case with no cardinality restrictions on {{formula:c67ab389-7446-4ab4-b172-1aa9dd251865}} . The resulting Bowditch boundary has a simple, concrete description and coincides with the canonical boundary introduced by Gerasimov in {{cite:053a52c84533154b05d01791b7c73298ccc7daf2}} as the abstract Cauchy–Samuel completion of a certain uniform space. A reader who is only interested in countable relatively hyperbolic groups may safely skip this section, whose only purpose is to extend the reach of this paper beyond countable groups.
m
bdfc7ac9d857a8379cde1392c0a430e9
Graph classification to distinguish the class labels of graphs in a dataset is an important task with practical applications in a large spectrum of fields (e.g., bioinformatics {{cite:bf14ed6ac44f43d19fa5e7a17ea556e386a4e2d4}}, social network analysis {{cite:695f2640398c33793754403d167e97e9b9f3644d}} and chemoinformatics {{cite:fc6939667e423216fea8adfd6bb43a4c4831eeac}}). In these areas, data can be usually represented as graphs with labels. For example, in bioinformatics, a protein molecule can be represented as a graph whose nodes corresponds to atoms, and edges signify there exits chemical bonds or not between atoms. The graphs are allocated with different labels based on having specific function or not. To make classification in this task, we usually make a common assumption that protein molecules with similar structure have similar functional properties.
i
136130925f0651b5037127af27aef005
Backpropagation, as described in the previous section, can provide us with the derivatives of the error surface. This can be used in a variety of ways to update the weights. What we just saw, in Equation REF , is known as gradient descent. One of the most commonly used optimisation methods is Stochastic Gradient Descent (SGD). In SGD, a minibatch of {{formula:590d8fa1-ea51-4f35-b9bb-04ac3a83da26}} samples is drawn from the training set, the gradient is calculated based on this batch, and the weights are then updated accordingly {{cite:1ec8abce230a1513fe8a8784764dc2a4cf2ae8ae}}. Other algorithms, such as AdaGrad {{cite:db0c818488f154548279bd7e95d818c8b8eb09eb}} and RMSProp {{cite:2bcc7a4fa25e4b78ca78bc599b992541090aa3f2}}, learn and adapt the learning rate ({{formula:1b3815a1-7901-463f-a151-1b5fa6c6eedb}} ) for each weight. Modifying the learning rate in this manner can both increase the rate at which the error decreases, and lead to lower overall errors. A recent and increasingly popular optimisation method is Adam, which is similar to RMSProp and yields better results on a many problems {{cite:e70e0c0e233c3f0ce6de1bda5965d79a43abd791}}. The choice of optimisation method is not all that straightforward, and no real consensus exists for how this should be done {{cite:3f8abaf9ce02bef199bddb1b9a559e88598d8336}}. Hence, commonly, trial-and-error is applied in order to make this choice, by experimentally investigating performance on a development set.
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05f57984738aea09e58477b576105b87
We change both selection and classification backbone architectures to ResNet-50 and pre-train them on ImageNet with MoCo-v2 {{cite:892ebae244ab7695367ab654e373157923fd8c8f}} for 800 epochs. We report the experiments in sec:imagenet with the new setting in tab:moco. This table shows that the superiority of {{formula:d52e6fa2-afeb-4b0e-add3-fc5efd2ee315}} -means sampling to other active learning methods in low budgets is not sensitive to the choice of architecture or SSL pre-training method.
m
d6fc598c7c3e711e244e918851298cea
In Eq.REF , {{formula:543664d5-6455-49bc-8d2e-c1ad410c82f3}} , q, E, V, and {{formula:f2d420bf-fb0b-4481-a461-95222ec97e8a}} refer to the reduced Planck constant, elementary charge of electron, energy, potential, and Fermi distribution function of leads, respectively. Near the equilibrium condition, by shedding the light on the channel, some electrons are excited to higher energy levels and their energy increases by {{formula:e8f5d9af-c4c3-4f08-895a-af35bbcb9ec6}} where {{formula:b612ef87-6896-498c-a552-2ce87a896edc}} is the frequency of the incident light. After a while, they come back to lower energy levels due to losing the same energy. In consequence, we are calculating the effect of the incident light on the quantum conductance of a two levels system {{cite:4becde873d5c824a7937ef2dfe0b809886fb61c8}} in which the energy of its electrons is equal to {{formula:b262ef41-ab6c-4d8e-8280-fff5e4e7be2d}} . Using Fermi’s golden rule {{cite:f9f59d26b6665bebc4d87863dd38aa08413e094c}}, one can calculate the electron-photon coupling matrix and consequently the self-energy of incident light to implement the influence of it on the system. This could be done by adding the mentioned self-energy to the Green’s function of the electrons similar to the effect of leads and their self energies (Appendix ). Althuogh the detailed information about incident light self-energy calculations exists in Appendix B, a brief explanation is provided in the continuation of this paragraph. In the first step, the electron and hole correlation functions and the initial value of carrier’s density are calculated by using the Green’s function of the channel and self-energies of leads without shedding the light (zero self-energy of the photon). By means of the coupling matrix and correlation functions, one can calculate the initial value of photon self-energy which is used for evaluating the new amount of the Green’s function of the channel and the self-energy of the photon. Using Poisson’s equation, the loop is repeated until the convergence is achieved i.e., it is a self-consistent method (Appendix ) in accordance with Fig.REF .
m
105f0d58eed8e2402a5c98944039d3d4
Limitations – COMET works better if there is at least one constant of motion in the system. If there is no constant of motion, then COMET works similarly like the neural ODE {{cite:9732df8086c12edcce0edacd53d8b719aa7ad4cf}}. Although we presented a way to find out the number of constants of motion in section , it still requires multiple training processes and manual insight.
d
5c320bac900d440a9dd6ae7efbcaca7f
cf. (REF ). Based on the KKT conditions {{cite:c0cb44e42c6b5600ca820a64acc131c736137dfc}}, it has the solution: {{formula:802dbb22-6d79-4ba4-824c-8493e75b303a}}
m
a9f91d2181035ed3f43ac9c43b9834be
Our method is distinct from existing works ({{cite:102c72c88d3975e3433acd10665dd28e03a71629}}, {{cite:669e8064b44922a3d8c29b738e9b45e4cba41beb}}, {{cite:3dfaf8d0b00e8e4f7be013255144056d47e6a285}}, {{cite:00a7da2f89a25a48dc8d09eb703933b9e5007db8}}) that formulate CRFs inference as Recurrent Neural Networks for end-to-end segmentation, mainly from two aspects: (i) our graph is over two volumes, a target scan and an atlas, to enable the label propagation for anatomical consistency of the labeling, while theirs are within the target image for smooth predictions; (ii) they mostly employ graphs of full connectivity for discrimination, which is computational costly for 3D data and unreasonable for medical scans. We have performed experiments on two brain benchmarks (MICCAI and IBSRv2) with three ConvNets of different architectures as backbone. Results show our method significantly increases the accuracy (increasing Dice Score of up to 4.38%) by reducing anatomical inconsistencies in predictions. Meanwhile, our method boosts the robustness of ConvNets, verified by testing on scans with unforeseen pathologies (reducing Local Dice Decay to up to 0.46{{formula:1a79a786-b729-4bca-8125-c5b24e5fca9e}} ), and by cross-dataset evaluation with scans of different distributions (reducing Dice Score changes to up to 0.40{{formula:5b14ef8d-29a3-471a-a177-741343de760f}} ).
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b2713d4e01b62a47e84df363e3a5853f
As a traditional vector meson of {{formula:5ddd44c0-ed77-4489-8d4c-84f932c8a3aa}} system, {{formula:f3ef9a76-f7b0-4bc6-87d3-374dab95117e}} is not only a bridge to explore the QCD from light to heavy quarks {{cite:7f0b931565e1898ed3e46cd8562b7486be97b7d2}}, but also its photoproduction process is suitable for studying the mass radius and mechanical properties of the proton. As high-energy experiments progress, some experimental data of {{formula:381f08e9-57cb-409e-b6cb-1e5f0c7026f0}} photoproduction near-threshold have been accumulated in recent years by CLAS, SLAC, FERMLAB, etc. {{cite:727ae58d0c90951ebdbed6ed6c2eac5f5ff780fe}}, {{cite:7b016217b0da3c301691652095654930d18741d7}}, {{cite:0ec410ceaa9a18b2e6242a4419d5534e9a16b70d}}, {{cite:1420e44888cf4b6297ffe175fe497bad12c2a55a}}, {{cite:398fc0be226cb61ed27900591a31ebab11fd30ab}}, {{cite:7980d59c7323eef6fc012037cafe90d725731b11}}, {{cite:54a01f0f545c4e67f3472485a2c6c52bd374b159}}, {{cite:0b6839c39d8cd51b7ac4e4282318f301f319bb15}}, which provide the necessary foundation for our research. In this paper, the two gluon exchange model {{cite:d4a97cec558294eeb251c39de6a1a520aadb94fb}}, {{cite:b28eba60f811ec586079aef9e07c870bac103c31}}, {{cite:b977b4bc7fd44c716a17d4b74fa4e905d9c3c66e}} is established based on the existing experiment data of {{formula:391131ae-eb53-4745-872b-ba36339e21bb}} photoproduction, and the pomeron model developed by Larget {{cite:19cec6e8f3dfbea377a249eaf584bc6c35298e20}} is also introduced. Since this pomeron model contains almost no free parameters and is in good agreement with the previous experiments, it can be used to compare and verify the validity of the two gluon exchange model. Based on the cross sections of {{formula:e2d9e77e-a0cb-4d89-b417-eb697f5bb0b8}} photoproduction predicted by the both models, the mass radius {{formula:4e512503-73aa-4677-85ef-ac605f279f3c}} can be derived by GFF {{cite:fac0f27eebae8eb6fd0f7250a8de5c5325f80476}}, {{cite:5ce9aac6efc246858317404f3bdfef8b611d8f6e}}, {{cite:c8049ab8444fb36264fde0a3d68b9e38c848e0d1}}, {{cite:187aceb3fd1f779fb4bf13cc6ba0b62d4ba3c57d}}, {{cite:84fff995147ae1a8f02f0d7af20d8fdcb9ba5bb3}}, and proton mechanical properties including pressure and shear force distributions will be analyzed. Moreover, the results of this paper can provide theoretical reference for further study of the proton structure with the Electron-Ion Collider (EIC) facilities {{cite:837206fb2fbf0d40ce0618b6bfcc1fecad10d8e1}}, {{cite:e97d55e75291bf87f5108475bf5985958b05b0a3}}.
i
d5f8a296413c89f5289852d0a685ecf0
In this work, we have proposed a CAM network, MESH, that exhibits a memory continuum, and can be used as a high capacity pattern labeller for recognition/familiarity detection, and locality sensitive hashing. While the convergence time of the Hopfield network scales as {{formula:cbaccdef-053a-44cf-906c-c54238a45a88}} {{cite:68e24a373b0fc721586828e155b9f1eb5d464455}}, {{cite:d26694e8854d044371901dbec5dbe9808dc8e02f}}, MESH converges in a single step through a {{formula:8b0f33bd-dda3-41d4-a158-c08e2c2d888b}} nonlinearity, or within {{formula:2c6ba9ec-7b13-400f-a4ac-289a042cccda}} time when a {{formula:85f6d51b-c3ba-4dc2-9101-33276f4a74f6}} -winners-take-all attractor is used. Several neural networks use a key-value mechanism to store and read memories {{cite:52e01829d8712266fa075edfddd7783cdd75ff50}}, {{cite:5409e19258161b2dbd60ec63c8b9dfb542fb1a80}}, {{cite:de623d8dcb41e205b850e626d635daf51c503387}}, {{cite:f400d0d8e58273998c2aa95c00cada681e3ea9ce}}, {{cite:74ceb53d0ac7c68b75595416b1a2a41d98ebf365}}, {{cite:3668a27c3a5bbc70a646e5c791d442b23938944b}}. MESH provides a neurally plausible architecture for implementing them through a factorized key-value structure provided by the Label and Feature layers.
d
6c583b61b30f309a616b874806224661
Random (Rand): Random allocation of token importance. Attention ({{formula:d6d1499d-e512-41ee-86cf-5cbae2e43299}} ): Token importance corresponding to normalized attention scores {{cite:9018a11210797e1fb8722a9f227fd55ec81045b1}}. Scaled Attention ({{formula:2ff8207e-7e55-4386-a047-565005edd16f}} ): Scales the attention scores {{formula:50b4d49d-62fd-4f6b-9650-018877b10ad3}} with their corresponding gradients {{formula:3290cde6-3921-4af2-a7d3-24a2efe15ce5}} {{cite:67b60e78d33ff1c3c2768739f76c923fffb78401}} . InputXGrad ({{formula:c1c3f7cc-c9b8-4edf-add9-18d326f9571b}} ): Attributes input importance by multiplying the gradient of the input by the input with respect to the predicted class, where {{formula:3bcc1faf-42a8-4e3d-a4c8-76eec89ab4cb}} {{cite:4eb9bf6b829daff1e7183d677cb2732c89381408}}, {{cite:a96a22693fb54f2229473011f4804343a45a2de9}} . Integrated Gradients ({{formula:15816b07-ef8e-479a-a3c3-b8c2cbf4f33a}} ): Ranking words by computing the integral of the gradients taken along a straight path from a baseline input (zero embedding vector) to the original input {{cite:0431c032a5d4d6152606ff27792484491b8b5875}}. DeepLift: Ranking words according to the difference between the activation of each neuron to a reference activation {{cite:781f1454a4407bddb0be4038b3c019c22d6c679a}}. LIME: Ranking words by learning an interpretable model locally around the prediction {{cite:9ce906b3a666077c37ed5f2a1edb3c21a926ec62}}.
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fb6775be47b39e158f08265b5aa3c79a
Compact objects present a tantalizing opportunity to study dark matter candidates. Their strong gravitational fields present a unique environment, and their properties are coming under increased scrutiny thanks to gravitational wave (GW) and X-ray observations. Most dark matter candidates consider one weakly self-interacting species due to simplicity {{cite:70956264633fff3b9bde890b897e00c6b935c717}}, {{cite:d4e8155009bc8e3d080ae7a2751a0b1bc4424579}}. One of the consequences of this assumption is that neutron stars (NSs) can then contain dark matter only through direct (gravitational) capture or through non-gravitational interaction channels, leading to admixed stars (i.e. those with a mixture of standard model (SM) matter and dark matter) {{cite:0187eced42792d6eaf11ca16bb2fbb8eeedd9c93}}, {{cite:c2f1ee17b2a0c3191b8397889a754f6aba70f12b}}, {{cite:3e56a0817d534add88baf8dd6a1f7b09694c0e41}}, {{cite:7df73696a58f1bf8d5cafbeea5861a4491879870}}, {{cite:8f7ef3ef6f15bc6f551648ca0b30d23a48ac5670}}, {{cite:ee3f90dc74a965a4178dd01e6ffae16526a52910}}, {{cite:5bce80f700c05dc4c09971c9e857c0b167df3143}}, {{cite:e246bdce8f9412b118af9600f141756d7e607b60}}, {{cite:9d8c8c006a7d178736d24b7014c02b67f0f0494d}}. Admixed NSs can have a small dark matter core {{cite:e246bdce8f9412b118af9600f141756d7e607b60}}, or a dark matter halo that would not affect the visible radius {{cite:9d8c8c006a7d178736d24b7014c02b67f0f0494d}}; sometimes, such stars can be composed almost entirely of dark matter, leading to extremely tiny dark compact objects (with masses of {{formula:8ba511de-6170-46f1-86c6-2bbf274ff8e5}} ){{cite:883270eba3eeae6e7e257a1b93e441416f1a8c01}}. Alternatively, some studies have looked into NSs composed of hidden sector nucleons from a dark-QCD sector {{cite:df5bcf621028669ebcc1513e155c425904d00329}}, fundamental asymmetric dark matter fermions {{cite:bc89488bb217d706460faf705910c5a466ffe3d3}}, {{cite:8634b5bfcc0a47e4dd0f801cd2dc30ab18e25df3}}, {{cite:c8652b22cb9055b8ec93e68ce10b5b91370afec6}}, {{cite:e175fb929bef21b90b943ed9d567368639e49bc4}}, {{cite:4b1f1d2f16597cf951c7284324ce2a6fd31e0333}}, {{cite:762267d9711eb99547c056b5c05b04db18024ee3}}, {{cite:e246bdce8f9412b118af9600f141756d7e607b60}}, {{cite:568638587428a9b8d4030a161b374f61a86767a7}}, {{cite:ef2531b99f71c3846247b86cc8377a4b73f8029b}}, {{cite:f3bbc3a1da2f24e84712d42999aa91de69c1dd17}}, or asymmetric bosons {{cite:e5d4986e9a6cf68ef95258d1548b1780b561b08f}}, {{cite:f7689d0e31d1e340f334e4969b8b378d43cb8b43}}. These studies generally consider simplified interactions of only 1 or 2 particle species. An extensive review of dark matter capture within NSs can be found in {{cite:c325a94e02da29a8a7a03b7327ceaf3c49e75812}}.
i
99c8079d01fe459550065be818a7fd98
Could this be an observational artifact caused by changes in the Thomson-scattering weighting functions? For this to be the case, it would be necessary that the Thomson weighting functions become narrower (in angle as seen from the Sun) as the closest approach of the line of sight to the Sun moves further from the Sun. In fact the reverse is the case as the electron density falls off faster than {{formula:036cd817-7adb-4665-b520-6e9c919a6900}} close to the Sun (e.g. {{cite:a66b1d89154d8fadc3d69c0d15e63f04197a6a18}}). In addition, the MLSO data (heights below 2.35{{formula:44aa93da-f09a-4ffe-a9b4-d0e9cf289680}} ) use polarised light which has a much narrower weighting function than unpolarised (e.g. {{cite:d6c640f2555506ad4533e4e8d128c695415be403}}). The emission-line weighting is generally narrower than the Thomson function at the same distance since the dependence of the emission is approximately proportional to {{formula:695cf45a-47ce-4ef0-8532-30d642d3f75e}} and peaks at a temperature of about {{formula:533cb847-8782-4bca-9cdf-8606b89e0d3e}} K ({{cite:bf71ab79959388b1798618d66a58900e56473150}}; {{cite:95afa39c46f04065ddc0541b7af24021a485e4f6}}). We have verified this by some simple simulations of radial streamers. These show that such streamers can never appear at a lower projected latitude than their footpoint, and that except at very high footpoint latitudes (above about 60{{formula:6e19489f-afa1-48c5-85b9-27b7020b097f}} ) they predominantly appear close to the footpoint latitude. If (as seems probable) we are looking at a band of activity reaching up to a particular latitude, then a wider scattering function will increase the sensitivity of the observations to structures well-away from the sky plane. Since a radial streamer away from the sky plane will have an apparent latitude greater than its true latitude this would tend to make that activity appear to extend closer to the poles, which is the reverse of the trend that we see, thus confirming that it cannot be an artifact of the different observing techniques.
d
2d7f16d84b5518d17a26826230356ce0
Very recently, the ZSL based SBIR systems are developed mainly in conjunction with the deep generative models {{cite:b7716d1969227f5227da820ac1e1532191c60c0a}}, {{cite:e58a94b80f620886c0e95b362aea3bc0b6278cbd}}. In this technique, given a sketch sample, the authors try to learn the corresponding class RGB image by generating pseudo samples corresponding to the unseen class prototypes. This requires access to unseen class samples during the training time. This fundamentally violates the protocol of zero-shot learning. They pose the ZSL-SBIR problem as a standard supervised learning problem of deploying the notion of adversarial learning to align the cross-modal visual space to the semantic space. Also, adversarial training can be unstable if the min-max problem is not intuitively designed. The pseudo unseen sample generation technique may fail to generate unseen samples which exactly overlap with the original unseen data in some feature space. On the other hand, we are keener on making the shared feature space discriminative, learning relevant image features given the sketch data, and avoiding domain dependence of the shared space. We bridge the domain gap by imposing semantic consistency by preserving the topology of the semantic labels in the network. If such a space can be realized during training, we can expect the unseen test classes also to follow the same and yield excellent results upon deployment in the testing phase.
i
d229a6113dc21eb43dcaee3c7456a9f0
In addition to extensive experiments, we also analyzed our method and other automated augmentation methods using the theoretical framework proposed by Chen et al. {{cite:e8c81f06f6d77742154ffbf7e38e384cfd667502}}. Using that framework, we show why uniform sampling is actually expected to achieve good results given an approximately invariant augmentation space. Besides being efficient and effective, UA can be easily implemented and applied to different models and tasks. One can view the design of UA as an instance of Occam’s Razor principle, i.e., one where the simplest solution is preferred.
i
f2aede2d9de4c2f126070c68429c9245
Hereafter, we compare the results of the proposed approach with 5 popular semantic segmentation models which proved to be effective on a wide variety of segmentation tasks across different domains, namely the original version of DeepLabV3 {{cite:c28007cc0d0bb9c5152c3635c058dc73fea9bcf6}}, its improvement, represented by DeepLabV3+  {{cite:1c000154a20a97e884e1fa588b0fd51a5a2c57e1}}, FCN {{cite:51de2e22ac2333c7ab704cbf28b153089f88049b}}, Lite Reduced Atrous Spatial Pyramid Pooling (LRASPP) {{cite:33e269b3742bf280f94a475f3f23b442ead87a68}} and Pyramid Scene Parsing Network (PSPNet) {{cite:30279df93c1858c53cdbac8a6ea75c97506975f7}}. Furthermore, we compare our model with the current state-of-the-art model for layout analysis of ancient documents, which we will refer to as MLA {{cite:78074f924024baee0179af601a352f61d217f933}}. All the models, excluding MLA for which we gathered the results from the respective paper, have been personally tested by us keeping the training and evaluation settings as consistent as possible. {{figure:ab10fdd3-e84e-43a3-9a00-377104ebd228}}
r
fa4b9547915507f4b793b818eeca26bf
Definition 4 {{cite:d47d704da2619ba4916ec3f3c952dbf0e2af10e8}} Let {{formula:ad83d92c-8a05-435d-9619-cbc007450ce9}} be a sector of complex numbers. A closed densely defined linear operator {{formula:c6a008a2-79b8-41fe-a6e1-02619386953a}} is called a sectorial operator if there exists a constant {{formula:caa3812a-6a2e-4392-96d4-0f6e5c979e1c}} such that {{formula:1948fed5-a54b-42ec-a14e-4c455037d9ff}} for all {{formula:049e903b-fc80-4a58-ba38-052f0283d009}} .
r
5d9271d2866b95ebbab5065ff299df79
We note that recently several works have come out regarding a SUSY explanation of the Fermilab muon {{formula:942afa15-b650-4117-b8d6-59fcdfced55f}}  {{cite:081515def0991f90cce777ae21edfffb0b0ee153}}, {{cite:34ab735b34c57a6f67387089d4412d6fde250f57}}, {{cite:3189465143eb773ca04c9771f8d78fa7b8f24647}}, {{cite:734ee56fe1b8920f669904555595a755efd33b8c}}, {{cite:df3495097b20feebd0e3916a97b363e465936bc9}}, {{cite:c35dd19c8dccf28fb6ca3b0352f83dc697c03d68}}, {{cite:522af8d300777d86dbf98f718f347e3ded9ee6ad}}, {{cite:fe88b44efdbc137fb5bdab668c223ff5ef6de974}}, {{cite:193c68ea12aef4a2ce446437cdb0dbfa651e38cc}}, {{cite:2570e68ddef743d2d18376da0eff54e5e24219a5}}, {{cite:a86bbafc2c82408730ff14c779048862832d1f33}}, {{cite:439cea153fce965f40c5257137d1a61688b2b74e}}, {{cite:ac74249e12b1937950408a734702bea2360aeab3}}, {{cite:7ace2cb56bda66a8b2850c943782301f92e48dea}}, {{cite:019a36f33a1e016214f98bd382c5f5159dbdbfd7}}.
r
481997af31326db07b188ce5f3358399
It was pointed out in Ref. cft1 that the operation of the evolution operator {{formula:45b0030b-e6db-4fd0-ba9d-b53392ff2085}} on any primary operator of the CFT can be understood in terms of a Möbius transformation of its coordinates and is therefore given by Eq. REF . This is further discussed in App. . In this section, we shall use this result to study the properties of the driven CFT with a cylindrical geometry which corresponds to periodic boundary condition of a driven 1D chain of length {{formula:8667ab74-9b81-4ca6-82c7-86aa48d4d4c6}} . In our setup, the coordinate of the cylinder is given by {{formula:a2a0442a-8232-42f8-91db-80720365aa21}} , where {{formula:deea7801-30ff-420b-adc0-192a7720361f}} is the spatial coordinate and {{formula:b3d180fb-258b-43dd-8f44-7d0112391414}} is the Euclidean time; we use {{formula:cf1cc3c2-ceb3-4e68-9e9f-6982c99816be}} for mapping such a cylinder to the complex plane. Thus for any primary operator {{formula:7c7fbb64-6135-4d6a-8767-84fd1f2df763}} on the cylinder, we can write {{cite:2e0f45da6354238107689728b5be005dd527fa55}}, {{cite:31354c2da4000ad865544371e564ed503b939517}} {{formula:bf91fb2d-3030-4bc1-9ad0-54d488ee4a9e}}
r
9f76b4f9bebdbd83a0f7e7537005425e
Lindsey's method (LM) {{cite:9ce7c8e9d74801c89a02dee280ffc3d12ad81bb0}} recasts density estimation as a regression problem. {{cite:81c6eebd6fafab3d8a63c445104fbe59da1fe3ff}} describes it as follows. Suppose a random sample {{formula:e4c1679a-9641-451e-afe4-12e2f30cc762}} from a density {{formula:291c7dd0-5f5e-438d-bd90-f21927ced256}} on [a,b] is available. Divide the interval [a,b] into {{formula:44791b8a-81e0-42f8-bbbb-01a5ebebc5e1}} equal width bins and denote by {{formula:29c355f4-e4d0-44cb-abb6-a0029030a27c}} and {{formula:ec180d65-6c50-42d1-9a13-bc8121ed9e3a}} the number of observations and the abscissa of the center of the {{formula:65b47cdc-940f-49ed-84cf-ecf327fc6f05}} th bin, respectively. Let {{formula:7d9ff4c7-d442-4d5b-bfee-d7ca5be8905b}} , then {{formula:c7fe43f0-6ff9-4810-9330-efa51768f571}}
m
bf873d0699d72a7a6ea63e83d619cac0
Experimental realization of these new quasi-periodic patterns can be also examined in various systems that are candidate of high-dimensional quantum simulation such as the Floquet lattice with multiple frequency driving systems, optical lattice and four-dimensional time crystals{{cite:4e53a542f2beb13d10b70ad165690a1c976af371}}, {{cite:b6794fc966cfb132b504aec6441b7c4854608616}}, {{cite:b35c8e2d872f9ea7d3c9ffb66bf2183b64828ea5}}, {{cite:3d081ca3e796b4ab969fbe2f2faed316046ad2fa}}, {{cite:8711fff564fb47719c74ba4386493e51bdf2b18a}}, {{cite:961c1032709a4ffcd786f68561e6a6ec90a594fb}}, {{cite:d8767000d43599cca58bc65bfa29c16fecedeefd}}, {{cite:d4bb2589c161aacc097c5267484dd4e0c772702f}}, {{cite:233f0c6567ab77de0ba10cdd5460b0a2b70ace96}}, {{cite:9e1d24683270b7dd46a2e7b89fa95d7de1bd953a}}, {{cite:3d62e46979f732270e2046fccf7b196e23a79a4d}}, {{cite:30d05eb49a56710a2da66e6dadca4ca7d530bc88}}, {{cite:4893a809ae27a219d7ceb58eda190fa6feae7229}}, {{cite:9777563c4480063349827d44a04108b54173045a}}. In addition, our study is also applicable to other higher-order symmetric quasi-periodic systems such as decagonal or dodecagonal quasicrystals in two-dimension, icosahedral quasicrystals in three-dimension and more general quasicrystals originated from the root lattices of the Lie groups{{cite:e157ea63bb47b815644f7dab286ddff6d0bb370b}}, {{cite:570b3196b1e516cf9cdc5cf4e1451a980e3d937d}}, {{cite:3e64f280081a88ddea3bd4ce4942665afc56a753}}, {{cite:c0a9d5d90eeeed3a12092da520cb15c7c78f5806}}, {{cite:dfdc2b9c218f1c1be9526e2a13576bfad2d8a914}}, {{cite:50a4c61e51a45a938ac86019bef05ad47f340f88}}. With the realization of new quasicrystals, one can further demonstrate physical phenomena originated from the high-dimensional degree of freedom. Thus, the characteristic symmetries of quasicrystalline patterns could be controlled via special operations of high-dimensional lattice. Along with the discovery of new quasicrystals, one could also find exotic quantum phenomenon that is uniquely present in those quasicrystals and we leave it as an interesting future workJunmo Jeon and SungBin Lee, In preparation.
d
21ed5b3e26ad0190ad8b38f9fe7aa3e1
As we noted in the introduction, DIS scattering in holographic QCD at moderate values of partonic-x involves hadronic and not partonic constituents {{cite:d6a8e5f58079fcc27a196461b5716723a4388104}}. Indeed, in the large {{formula:b17dcd18-91da-4c44-916f-146c81e085f7}} limit, the leading single trace twist contributions acquire large anomalous dimensions and are suppressed. The dominant contributions stem from double-trace operators with mesonic quantum numbers. Another way to see this is to note that the large gauge coupling at the low renormalization point, causes the color charges to undergo a rapid depletion into a cascade of even weaker charges, making them visible to hard probes only through double trace operators.
r
12f0ce5b5693597739cb256fc42b44ff
A model with SSB, via an explicit potential, usually includes nonlinearities otherwise a nontrivial vacuum cannot occur. This can lead to nonlinear constraints that may cause undesirable physical implications. A theory for a physical system must have a consistent mathematical and causal structure. It also should satisfy basic criteria such as having non-tachyonic propagating modes carrying positive energy. Moreover, it is said that the model possesses a well-posed Cauchy problem if its evolution is uniquely determined by smooth initial data satisfying the constraints, and/or if, under slightly initial data changes, the evolution varies continuously and respects the causal spacetime structure. On this matter, the Cauchy-Kovalevskaya theorem ensures that, in globally hyperbolic spacetimes, any second order, linear, diagonal, hyperbolic (LDSH) system of differential equations has a well posed Cauchy problem {{cite:0a445ac98f653730860dad79e948c5f4b468acef}}. However, when the corresponding equations are not an LDSH system of differential equations, there is no a general method to determine if the theory has a well-posed Cauchy problem or not. Hence, one has to prove each physical property, as causality or positive definite energies, independently. In general, for nonlinear theories the Cauchy-Kovalevskaya theorem does not apply and difficulties may arise. In particular, for theories with nonlinear constraints a chain of such constraints could “bifurcate” for certain combinations of the variables (or field configurations, in field theories), and consequently, the number and/or type of constraints would change on the phase space {{cite:7b25457659b6d852c7a9382c241f9a84a546b522}}.
i
359e952a0ed33beee78dc9bfb40b76e4
Initialization. The SDF weights {{formula:2a802e8a-e740-49eb-bec2-cfdd5c1e120c}} are initialized using the method of {{cite:64127435f1b37b9f85539945fd27db946aeb7805}} such that the initial shape is roughly a sphere. The diffuse albedo {{formula:7a0736b5-c1d8-42ec-a805-b9c8939d7ecd}} is initialized such that predicted albedo is {{formula:daa15758-3708-49fd-b0b4-ac761796cc22}} 0.5 at all locations inside the object bounding box. For the specular BRDF, the initial lobe sharpness {{formula:e72ae368-73a2-43d1-93ab-23ed3e0b2166}} is randomly drawn from {{formula:870292a3-a96a-49a9-8551-ce6e079bfc69}} , while the initial specular albedo {{formula:ab60aaea-4445-46ae-8a45-d50d2027e38b}} is randomly drawn from {{formula:9ea2a83b-9a00-49e0-b386-2c959795d9dc}} . For the environment map, the lobes are initialized to distribute uniformly on the unit sphere using a spherical Fibonacci lattice {{cite:ecf391ba0f8bf57a5f40c3edf45cc63a24536109}}, with monochrome colors; we also scale the randomly initialized lobes' amplitude so that the initial rendered pixel intensity output by our pipeline is {{formula:9f63b162-3c36-4875-9f9c-5c192aa52471}} 0.5. In addition, since different captures can vary significantly in exposure, we scale all input images of an object with the same constant such that the median intensity of all scaled images is 0.5. We empirically find that if the initial environment map is too bright or too dark, the diffuse albedo MLP sometimes gets stuck, predicting all zeros or ones during training. Our proposed initialization addresses this issue.
m
4f53d02353e4793c40e611d6910900ce
Werner states as special mixed states can be geometrically described as a curve of states in density operator space, which is from a fully separable mixed state to an entangled pure state {{cite:8f27d139007d00ccfb21f1da97c3b21ee9c1865a}}. There always exists a critical point separating fully separable states and entangled states on the curve. These critical points generally have different mixing parameters {{formula:359795f7-8d60-44b4-a26f-906d22147126}} that depend on the given pure states. The relative critical visibility as the ratio of quantum bound and classical bound of Bell inequalities characterizes the delectability of these inequalities. Although all pure states admit a universal violation {{cite:4632fb4e02a9b59682c6e6f3b2fe017a7ca2cc82}}, homogeneous Bell inequalities can only provide bounded violations that are incompatible with infinitely small critical parameter {{formula:99af6f52-ae4d-451d-8ec9-3b883f7e2fe1}} in terms of the full separability. We conjecture that this incompatibility holds for general linear Bell inequalities even though there are unbounded violations {{cite:c5fcdc85ed5a158413cc519e23cb480423cb3922}}. The possible reason is that almost all critical points require exponential violations {{cite:954169d20097431ef04227b67ee622f5d5db60a5}} (Appendices E, F) going beyond polynomial violations {{cite:c5fcdc85ed5a158413cc519e23cb480423cb3922}}. Unfortunately, our algorithmic proof (Appendix F) can only provide evidences for small {{formula:3eb4ee79-dd3d-4dc5-adc8-5ccdd862d24c}} due to high computational complexity. It is an open problem to find new methods for estimating unbounded violations. We further conjecture similar results for multipartite high-dimensional states.
d
7ce658060eb8fe548ee9883ae4d68dfa
This conclusion motivates astronomers to search for the binary companions of nearby SNe. Currently, there are only four core-collapse SNe with direct companion detections, i.e. the Type IIb SN 1993J {{cite:adff480a25240da0b90b6045259efa4542ceb4fd}}, {{cite:21d1bb633dbdfb4e2962713e0111a30b14da977c}}, SN 2001ig {{cite:6665411836fd101dbc6d1aaffd47adbc0bdaae36}} and SN 2011dh {{cite:951af74e4cdfcf5ac9df1a37c1eb2088184ee56b}}, {{cite:7379d2f866ab1e21518693b9a06306bcf0c8470a}}, {{cite:ebe1df2f8d26e23e748bdee5fbb93d5fe7915320}}, and the Type Ibn SN 2006jc {{cite:1e24e862527aadc4756ea58d497120c9cc1fb378}}, {{cite:1de798c0503e327859d8e3221b728a0228c90272}}. The detected companions can place tight constraints on the initial properties and the pre-SN evolution of the SN progenitor systems. For example, the companion of SN 1993J observationally confirmed an interacting binary progenitor model for this Type IIb SN {{cite:adff480a25240da0b90b6045259efa4542ceb4fd}}, which was theoretically proposed soon after its discovery {{cite:00a2b3a47805ed5718716b20863238470fa30105}}, {{cite:2a1ce8e8190ab03b41945529e780bb48e9cbe210}}. {{cite:1de798c0503e327859d8e3221b728a0228c90272}} derived an upper age limit for SN 2006jc's companion, which favours a moderately massive binary progenitor system and argues against the prevailing theory of very massive WR progenitors for Type Ibn SNe. For Type Ib/c SNe, however, there have been no companion detections reported yet.
i
da660e99603e17f6efc45c9902c7dabe
However, we get such a quantum cosmological picture within the scheme of a quantum {{formula:904c6ffd-0687-4d0e-855e-3db79d4f3912}} extension of gravity as viewed in the Jordan frame {{cite:cde384151ce1e6be2d50bbf8d52083afda245b43}}, {{cite:a1b706b5fc7e0d49232f323482371f1724118545}}. This choice is well-motivated by the idea that the gravitational Lagrangian can deviate from the Einstein-Hilbert one when the curvature scale of the space-time is sufficiently high, like near the Big-Bang or the Big-Bounce {{cite:5791d641061f7e50c4c068af491078ab226aa891}}, {{cite:e2e0e117031575221bacc1a7a6207c58bf6dae2f}}.
i
ba2d4b780383f813cd5527739176f04f
We recommend empirical researchers to examine the covariate imbalance using both formal and informal diagnostics, and when possible, incorporate the quality of statistical matching into their outcome analysis. For instance, one way to do this is to perform a randomization inference under a biased randomization scheme using Rosenbaum's {{formula:c121a538-b6de-47e1-842a-1a460dc76d13}} sensitivity analysis ({{cite:13eb979f5568f57d511d39a52e9b1ae1f827b794}}, {{cite:cc9c60e6b30dde630258946fd4a548627a4e6d78}}) with the parameter {{formula:123b5212-acc8-4bcd-b8e7-52d2d3ed5049}} set to the magnitude of the residual sensitivity value, i.e., {{formula:15f2954a-b55d-4471-ab6b-82e94ec8cdc4}} . Other strategies to formally reflect the study design quality in the downstream outcome analysis are worth exploring.
d
c8c2211f9dc8557b88c80c86d53b9042
where {{formula:f17a7e87-e6ac-4e4a-85a8-e58a631e5511}} . Then, after generating multiple bootstrap samples, the user will reject the null hypothesis if the test statistic (REF ) falls outside a certain percentile of the empirical histogram of the bootstrap samples, otherwise the null hypothesis is not rejected. Under the assumptions outlined above to ensure that KSD is positive when {{formula:2c5baeaf-33a9-4c7f-9a0f-bf9449781eac}} , the limiting distributions imply that the test is consistent in the sense that when {{formula:959d10b4-d7e6-4fea-b3b0-391e0aa0a01d}} the power converges to one in the limit of more data {{cite:ef5a7049dfbd48d6ec55561a201c67e114f8e36c}}.
m
bc95d3a0bd18787b02d2964c24aa7e32
The focus of this study will be on incorporating this process into a new global analysis, while accounting for the uncertainty of the data-driven theory, to determine the nuclear gluon PDF with greater accuracy than previously possible. A precise knowledge of the nuclear PDFs is important for the following reasons: Firstly, they provide a description of the hadronic or nuclear structure in terms of quark and gluon degrees of freedom. In the context of the standard pQCD formalism the PDFs are universal and therefore required to make predictions for a wide range of collider observables. Finally, they provide a starting point for comparisons with microscopic models predicting the nuclear modifications (at the twist-2 level) in different {{formula:a0d6600f-726d-4df0-a913-4d5dbb5268d9}} regions. This includes microscopic models for nuclear effects on PDFs in the shadowing region {{cite:e4652829c0e10b3a1c5b7c0340b17b8a19fad39b}}, {{cite:70ecd2caa82e7184d46b11158bb128fc27c00b80}}, {{cite:134c43f341c06a3b4261886bc64839bdc616d0ae}}, {{cite:7a25087aa45d81ea26bdbd5642a102683e3f51e0}}, the antishadowing region {{cite:f49932293d0b3dc7928e7cb76b1348fce2e44fc7}}, {{cite:663d45203dd42c621f2d4c37a95b4ff218c139f7}}, {{cite:7a25087aa45d81ea26bdbd5642a102683e3f51e0}}, or the EMC effect {{cite:92f588a89f29a48257d4211ac64eb8ac9c93e25e}}, {{cite:67804d1ea28669f862502c26837416803e5dbc34}}, {{cite:624bf19d578c5e6cabe4a844a253466b0d86c9a1}}, {{cite:edbbd914c145a30ac43762e8138c418679997c1a}}, {{cite:54726d20dc5743d2335c620234c16ee5d9c8ffa9}}, {{cite:7a25087aa45d81ea26bdbd5642a102683e3f51e0}}. At small-{{formula:d039ba3a-b614-4a8e-97d6-3bc649936505}} and moderately hard scales, the density of gluons becomes very large such that the assumptions underlying collinear factorization are expected to break down. This kinematic region is described by the theory of Color Glass Condensates {{cite:8e2e460a1791a0ac9422fcec6f3dab50decd71ad}}, {{cite:8542f8aa785730798828e75df36a9d4c564d77f5}} and there are also promising unified approaches which interpolate between the CGC at small {{formula:effb927f-fda8-46e3-97d0-8b6431eb1fb2}} and collinear factorization at large {{formula:296cbad0-7b28-4e91-bb2b-19f31bab1dd7}} , see, e.g. Ref. {{cite:b839c34cd4e50be63a47ebb8749b8ccf9c4d64b1}} and references therein. Nevertheless, it is fair to say that for now there is no unambiguous microscopic picture of the inner workings of heavier nuclei.
i
f5f9f9dd1d5457f39b4702965f2cf03c
To acquire a more complete understanding of the phases and transitions in the NRKHM, we present the DOSs [Eq. ()], the averaged AGRs [Eq. (REF )], the minimum of IPRs [Eq. (REF )] and the measure of critical mobility edge phase {{formula:8f26a587-b364-4389-a38d-593eba4cee1a}} [Eq. (REF )] versus the amount of hopping asymmetry {{formula:6956b800-2019-4382-8492-c86935f421cc}} and the onsite potential {{formula:aa47369c-4741-4cb7-a8bc-182bb4356220}} in Fig. REF . The consistency of the results among the four panels of Fig. REF clearly suggests the presence of an extended phase (with {{formula:2a135b78-365b-4936-a9c5-6258e3af7f7b}} , {{formula:74cefc4d-0c79-4cdb-bdea-e56c249286cb}} , {{formula:1ce33a99-bb15-4565-a83c-05cf32c52443}} , and {{formula:fb649101-4350-4be3-8bda-1965228ad85e}} ), a localized phase (with {{formula:514d2095-2555-4337-be10-c0c07a9ae499}} , {{formula:9370c095-6143-42a9-b5c6-4f74c202f043}} , {{formula:9bfbebe9-414a-424c-88de-8234a548442b}} , and {{formula:5f3fbd60-d2f1-4776-8f44-f1a166e37f41}} ) and a critical mobility edge phase (with {{formula:c25a885a-17f1-4f09-a8af-9931e04b941f}} , {{formula:d9bb5438-f9c8-4efd-9afc-6ce9f5bac344}} , {{formula:c14dd0e5-1811-4834-8610-bc72e9e86b6b}} , and {{formula:a5beb344-12fc-4a0b-a852-cca2362f855e}} finite) in the NRKHM. When the non-Hermitian parameter {{formula:2078fc82-39e0-4529-b204-25d2a2e59361}} is small, the change of the quasiperiodic potential amplitude {{formula:8bda628c-6bab-4b4f-911c-eac45782e2b3}} can only cause a transition of the system from a complex-spectrum extended phase to a real-spectrum localized phase, which is similar to what happens in the non-driven NRHM {{cite:d0d32460e51a0d59d2264dc596c69652f432f343}}, {{cite:65c39890219f452494a90cb8f02c69953e391e80}}. When the hopping asymmetry {{formula:91d119d8-43a8-4131-8831-486959ee599d}} is large enough, non-Hermitian effects dominant. In this region, we only find the transition from a complex-spectrum extended phase to a mixed-spectrum critical phase in Fig. REF . This observation suggests that real-quasienergy extended states could persist in the NRKHM over a broad range of quasiperiodic potential amplitude {{formula:e83a6e80-59e6-4407-801d-bdd089bcbec9}} at strong non-Hermiticity. In the intermediate range of {{formula:8be58939-d6e4-4d2c-a4a1-8a177ee91f3c}} , however, we find reentrant spectral and localization transitions between real-spectrum localized and mixed-spectrum critical phases with the increase of {{formula:4fb75196-894f-4c95-9606-4c80fa8a9d1b}} . This observation demonstrates unambiguously that the rich phase and transition patterns in the NRKHM are indeed originated from the interplay among three nontrivial effects when they are comparable, i.e., the non-Hermiticity, Floquet driving and spatial quasiperiodicity. The original phase diagram of the NRHM {{cite:d0d32460e51a0d59d2264dc596c69652f432f343}}, {{cite:65c39890219f452494a90cb8f02c69953e391e80}} gets most strongly modified when both the hopping nonreciprocity and the driving field reach sufficient strengths. {{figure:727f6f2e-08b9-4995-8ca3-b194ec0d42cd}}
r
8747bbcebeea02955577288d7205bfaa
Modular invariance is an promising framework to address the flavor puzzle of the standard model. In recent years, much effort has gone into the study of lepton models based on inhomogeneous and homogeneous finite modular groups. In the present work, we have performed a systematical analysis of the possible lepton and quark models with {{formula:fdaccacb-d3ef-4b7b-853c-192ca3b9abe1}} modular symmetry. Aiming at the minimal and predictive models, we impose the gCP symmetry so that all coupling constants are constrained to be real in our working basis and the vacuum expectation of the modulus is the unique source of modular and CP symmetry breaking. In the known {{formula:11a49353-13e4-4cde-9ed4-673700c97504}} modular symmetry models {{cite:6e7103655830669b076ee2b426513c1ee1846664}}, {{cite:79d02647f302df60f3bc136664ea96235ba6a9f3}}, {{cite:b74090568bdb5716c69918ad1c7622d30e882c97}}, {{cite:87b35edfc3cfde80d04b770dcec4315935e3b964}}, {{cite:74c262ca3c65835bbd5d1c09e0677bc5e0e7d7d9}}, {{cite:ec7f5e8b100b70d6f9d831501c87a8c0fa90dfcb}}, {{cite:8413ca7cf8d7472491ac517c9185a77ee94afb39}}, {{cite:1a9ee349125b43fbe114dd327870fda4b84d73e8}}, {{cite:5efb29c98e87360241a76cd67c5c9102a4f5593c}}, {{cite:1fc1e528aa2917cac20c9d73d2456f121f7250f5}}, usually the three generations of left-handed lepton fields and right-handed charged lepton are assumed to transform as triplet and singlet under {{formula:c4749664-3a14-468b-a369-91a0f0fd0859}} . Besides the singlet representations {{formula:5aaefe96-522e-4b65-be63-906c31cfbb1c}} , {{formula:e979638e-2e13-44e5-9318-28da0659219f}} and triplet representations {{formula:9d08b05a-f09a-4ab5-88a9-d84017fdce82}} and {{formula:2a589329-3cc2-4354-a602-ae0c7df0363d}} , the {{formula:22d7b08e-a557-442c-99a2-a9b9010f0265}} group has a doublet irreducible representation {{formula:a8f7ecaf-5f47-4292-b135-40d6430ab880}} . The presence of doublet representation not only introduces new features in the modular invariant lepton models, but also provides a new expedient to describe the quark sector. We give the most general analytical expressions of the modular invariant Yukawa superpotential of charged fermions and the Majorana mass terms of right-handed neutrinos. We have analyzed both scenarios that neutrinos are Majorana particles and Dirac particles. Under the assumption of Majorana neutrinos, the light neutrino masses are generated by the type I seesaw mechanism, and the conventional seesaw models with three right-handed neutrinos and the minimal seesaw models with two right-handed neutrinos are analyzed.
d
9dfc81ff282ec6bcc9f9724f331a7c24
are given in terms of Mittag-Leffler (M-L) functions {{cite:d6e0ddff7877519342a4d86fae1054012a31c1b1}}, {{cite:afd0aa47e00891e98c5dd15f2f2f92af0e39e88c}} {{formula:ece4e7cf-0268-47ad-bfca-0bc5eba1b348}} . M-L functions may be thought of a generalized exponentials that are defined by the series expansion {{formula:ab7b9ddb-baf1-46fe-966c-a87b86fe252d}}
i
36db096132711485f3957a0bd408703f
In another hand, the ESTC algorithm can only achieve optimal regret bound in data poor regime and becomes suboptimal in the data rich regime. It is interesting to have an algorithm to achieve optimal regrets in “best of two worlds". Information-direct sampling {{cite:0d9c1059cdb4f4a1dc33a142ef8d7cec88dd31c7}} might be a good candidate since it delicately balances the trade-off between information and regret which is necessary in the sparse linear bandits.
d
057b6e9ce455a223cb47d06e3bbd2831
Historically, there are some asymptotic analysis methods that can be used to derive the macroscopic governing equation (REF ) from the MDF-LBM {{cite:621cdb97d847ad79f4b7ad249e3cb9975a4aa493}}, including the Chapman-Enskog analysis {{cite:47b5b56e50d741e0cb92ce906886b7fb1e74b282}}, {{cite:c0c578503a6e4c73cf2265b8205bc50cdf216316}}, Maxwell iteration method {{cite:509fa873b620932541c1d821e01efdbeb85aeb78}}, direct Taylor expansion method {{cite:d16049dc7bfd5abf8e7751a4de2bd976a10d82b9}}, recurrence equations method {{cite:ee7676b47c7b09dee25eb83a882a48f74349df25}}. However, it has been shown that at the second order of expansion parameters, these four analysis methods can give the same macroscopic equations {{cite:621cdb97d847ad79f4b7ad249e3cb9975a4aa493}}. For this reason, we only consider the direct Taylor expansion (DTE) method for its simplicity, and additionally, compared to the commonly used Chapman-Enskog analysis, this method only includes a single expansion parameter {{formula:1c6549b6-6b04-443f-b1df-42bc4c8968a6}} .
m
a06bb669be405e506ef9ce2ebf6bc814
A model of the mental lexicon also requires representations for words' meanings. Word meanings are likewise coded numerically, making use of high-dimensional distributed representations, the individual dimensions of which do not necessarily have a straightforward interpretation. Importantly, vectors which are more similar to each other are also closer in meaning. Many different kinds of semantic vectors have been used to represent meaning in DLMs. A comparison of simulated vectors with vectors generated using approaches from NLP, such as Word2Vec {{cite:acd826d995aed4a828ecaeb16b573cb9b42e89d8}}, can be found in {{cite:94123b9602bcff471c123a329afe87693ee14bd2}}. In the present work, we explored various sets of vectors created using Word2Vec {{cite:acd826d995aed4a828ecaeb16b573cb9b42e89d8}} and GloVe {{cite:1c1069b6b02d0b9495ba83ead029f29cca0f7553}}. We obtained the best model fit for Subject 1 using Grounded GloVe vectors {{cite:4697b66029a4f2e7745a2229a147a4dad8d71bdf}}. These are created by aligning existing GloVe vectors with information from images, without letting the vectors deviate far from their original text embeddings. In this way, the vectors absorb some of the information available in images, but do not lose abstract information which is only available in text. The set of vectors found to perform best on various benchmark tests in {{cite:4697b66029a4f2e7745a2229a147a4dad8d71bdf}} have a dimensionality of 1024, which we accordingly used in our simulations.
i
fd583a102e98e7aea8d9bb61a9bdbca3
In this section, we numerically demonstrate the robustness of our algorithm in terms of both maximizing robust reward value function and satisfying constraints under model uncertainty. We compare our RPD algorithm with the heuristic algorithms in {{cite:df9dfba1d7d47df69fd60b8cca39ed617bf31020}}, {{cite:a8149fca14db199abc9d979506993ca0cfd36b8c}} and the vanilla non-robust primal-dual method. Based on the idea of "robust policy evaluation" + "non-robust policy improvement" in {{cite:df9dfba1d7d47df69fd60b8cca39ed617bf31020}}, {{cite:a8149fca14db199abc9d979506993ca0cfd36b8c}}, we combine the robust TD algorithm REF with non-robust vanilla policy gradient method {{cite:25b534e72e4b59f5276a6ec217269b84021dd7d2}}, which we refer to as the heuristic primal-dual algorithm. Several environments, including Garnet {{cite:cc88ef0a13a58627727c9a58e3f810c1308b70c8}}, {{formula:86bf5b26-8609-4fb1-90b8-0014952e4c77}} Frozen-Lake and Taxi environments from OpenAI {{cite:0c6f20f1e5bfd097f3a2c1bf9b23d3f4cafa7add}}, are investigated.
r
7a28c1509c1ab75cb27fd2fc961cc81d
In this section we present an example of the proposed correction. We focus on count data with low counts since this is usually a challenging case as well as low dimension random effects like the second order random walk model. Throughout we use MCMC as the gold standard and compare VBC to the Laplace method and INLA ({{cite:dccc249040ca8bfdc3ab3909a3724d01ec16e096}}) in terms of computational efficiency and accuracy.
r
4804ed955d9ba19b28b6280bc85854cd
One of the next steps would be to explore if QAOA can be valuable in applications that require BLLS as a subroutine, such as NBMF {{cite:f6a7437c6173bdf4f408b9d88713ff9338045ca3}}. Another step can be to try the BLLS problem on other types of quantum computers {{cite:01ff2973ec627189768452b670be5b23a1a43e40}}, {{cite:23f12cddf712f6260be99c60e227455204bb91cb}}, {{cite:7d531a65242c290e360ae6af68353eef0f0c7223}}, {{cite:135186271c92ca24a1a25b1fcadf59a3ecc588f5}}, {{cite:7af0e75d53946e2f9b35c48cb9428a41142006a9}} to see how different hardware implementations fare. Finally, from a practical standpoint, it may also be beneficial to apply a modified QAOA-like ansatz based on just nearest-neighbor connected CNOT gates, along with a larger number of parameters {{cite:226c9923195954c69f1cd5102121b97b635f1889}}, {{cite:4f23a29797e7dfea8c876e7880f13ea002aa49d6}}, or apply a SWAP-network QAOA approach {{cite:8b7202357768f056ed00b5c1c2275d493379529b}}. This may potentially lead to faster convergence and better qpu performance for architectures with limited connectivity.
d
8b86d42eccd1e514fdb0d53ff8b8a119
Qualitative Results on Car and Church categories. To show the generalization ability of our proposed method, we performed image editing on two additional datasets of cars and churches. For cars, we performed three edits: pose-change, background-change and background removal as shown in top three rows in Fig. REF . For churches, we performed day-to-night editing which is shown in the bottom row in Fig. REF . We use ten curated image pairs (See pairs in supplementary material) and pre-trained StyleGAN encoder models for cars and churches provided by {{cite:f068285706f302b9271844d4834871226a47ec7c}}. For cars, our method preserves all the fine details such as the orientation of wheel-rim, color, head and tail lights in the pose and background change tasks for cars. Similarly, it preserves the structure for day-night editing for churches. The wheel rim has changed for the background removal edit in cars, but all other fine details are unchanged. These results substantiate that our approach works effectively for other classes.
m
72d4ea4501dda657e210736084c1939e
{{cite:38cc7810baa3fd4a0de8cd23369f0c654bfb00e6}} did not consider the case of {{formula:e456d98e-5d5f-42b2-b617-b2b27b4bb460}} , but its framework can actually be applied to CFT{{formula:0db724aa-0827-4e22-bbc6-b9a049612f4a}} . In the case {{formula:43096ad9-52ff-4cbf-ad38-cff5def74dad}} , one can immediately see that all the lowest-twist multi-stress-tensors have twist zero due to {{formula:ef96676c-9f2b-46fd-891d-495f0998975e}} factor, as the result, there are no poles in {{formula:a39e7aa7-33c3-4052-a239-a7421526ef14}} . This is true, in {{formula:8b97b231-1f23-4806-80c3-5f706422f4b1}} , there is no mixing happen to multi-stress-tensor. In fact, the enhanced conformal symmetry, i.e. the Virasoro symmetry, allows one to gather all lowest-twist multi-stress-tensors together to find the vacuum Virasoro conformal block {{cite:43bc2928830de3e9fe2c1800949f0f15a68abc98}}, and moreover, there are no higher twist multi-stress-tensors.
d
5f7e3cd3de5251093c88dd463da163a6
A second theme addresses versions of the Frank-and-Wolfe theorem where the class of quadratic functions is further restricted. One may for instance ask for sets {{formula:4e07e3f7-e22a-4645-ae6c-2dc5643cad04}} on which convex or quasi-convex quadratics attain their finite infima. It turns out that this class has a complete characterization as those sets which have no flat asymptotes in the sense of Klee. As a consequence we obtain a version of the Frank-and-Wolfe theorem which extends a result of Rockafellar {{cite:0614c55e8a05ccf9a87c532c7b46a0a1912ad8f7}} and Belousov and Klatte {{cite:b851622dea213b9760638207da3ebeba970d2f5e}} on convex polynomials.
i
de92f45397fb5d4d911cb4f751cc8a99
In this section, we compare our results with state-of-the-art methods on CUHK03 and Market1501 datasets. Notice that we do not use any additional modules (e.g., IBN-Net) or post-processing methods (e.g., Re-Rank {{cite:74a6e2b2681b5dada8436246c0338a1895480e46}}).We just simply apply UP-ReID pre-trained vanilla ResNet50 on MGN. As shown in Table REF , MGN equipped with UP-ReID ResNet50 outperforms all compared methods on both datasets. {{table:97ac7144-acfc-4155-8592-4f5db65ce590}}
m
c046ec0241c70496d9186c0984192a20
As mentioned in Section 5.5 (Tables 5,6 and Figure 7) of the main paper, we apply D&D, D&D++ and all other de-biasing baselines on the Resnet-50 version of Arcface {{cite:01828282bc02d283e6da4e3221ef6da1b01562fd}} to evaluate their generalizability. The gender bias analysis and skintone bias analysis for all the methods are provided in Tables REF and REF , respectively. In Figure REF , we provide the gender-wise and skintone-wise ROCs in IJB-C for ArcFace and its debiasing counterparts. The overall verification ROCs (using all the pairs defined in the IJB-C 1:1 verification protocol {{cite:642faad7afaa5dbe08a57f4beabfd2e0148a7981}}) are presented in Figure REF . We also provide qualitative results in Fig. REF to show that D&D++ helps the network attend to similar spatial regions for both categories of the binary attribute under consideration. {{figure:d301032a-6962-45f0-9efa-59e3daabfea4}}
r
b31ee80b5907c9bef908d044d6639f33
A common assumption in the imaging literature, validated empirically by {{cite:27118de94c0cb994f6d865661a9b9c83a16eb9f1}}, is that distributions of natural images live on low dimensional manifolds. Understanding whether these distributions are composed of separated modes or not remains, to the best of our knowledge, an open problem. To that extent, the fact that unsupervised push-forward generative models perform well on datasets such as CelebA {{cite:74b689b9de323eb6375af43b872ba9e705253c3f}} could possibly be, in regard of our work, an indicator that the data distributions of those datasets are unimodal, or at least not composed of well separated modes.
d
efd3a92c3aa324bbce25ae2881e0be05
Data Augmentation (Fig. REF , {{formula:c8eadb87-5c14-4455-9f49-f3cb8c23e8f5}}{{formula:07d1249f-29bb-4594-8b1e-b5c7a23228c6}} ). When augmenting input scenes, we first translate them to the origin by subtracting the centroid from all point positions. By doing so, we make sure that the two scenes are overlapping in the following mixing stage. We randomly flip the point cloud in both horizontal directions, randomly rotate the scene along the up-right axis and along the other axis by Uniform{{formula:d66a0fc8-a864-4c90-b68f-7c85fb05593d}} . We also apply random sub-sampling, elastic distortion {{cite:faa152dffdc38458ed5f75f044c5bf1751a1b66a}}, {{cite:b2e12ea053ea8d3221962bc2a7ad532eae2c0a55}} and randomly scale the scene by Uniform{{formula:5b7b6ee1-b273-4d43-8772-6d740d164f08}} . When the input features include color, we additionally apply random brightness and contrast augmentation as well as color-jitter.
m
50ed25ed3027591a8d8685223c9e1d6e
One of the most fascinating features of quantum mechanics is that the vacuum is filled with virtual particles. In extreme physical conditions these particles can be promoted to real at the expense of a high energy field. For example, Hawking radiation is predicted to be emitted from outside the event horizon of a black hole {{cite:70a5309144cd151ec1cd90ed75e3d639bb0b8e5c}}, {{cite:d86a7ad859d06541b733e4c58d24c6f38cd1612a}}, {{cite:abd9f89cec77b23101d46c75711f602db2b471d1}}, {{cite:15ae8a817ef311d2e9181d00d875313874110733}}. This phenomenon can be intuitively understood by considering that the Hamiltonian describing a field inside and outside the horizon has an interaction contribution containing only counter-rotating terms. These terms generate an entangled vacuum between the field inside and outside the horizon. Then, the virtual particles outside the horizon can be promoted to real at the expense of the gravitational field.
i
758017b6ca1ef788f0bf492589a0980d
In this paper, we aim at bridging this gap and designing model families with high accuracy and inference speed, by taking into consideration hardware architecture details of TPUs and GPUs for both NAS and model scaling. We first analyze DC accelerators to find performance bottlenecks. Our analysis reveals the root cause of the recent observed FLOPs-latency nonpropotionality {{cite:77a417251d864d9a3b791b305e703189feabe9e3}}. We discover that SOTA CNNs suffer from low operational intensity and parallelism, which causes low computation rate (, FLOPs/sec or Ops/secWhen operations are done in different data types such as bfloat16 {{cite:a5c0289d228d49cdf5e7a5f3b83b42a9a2ce5668}}, float16 {{cite:8bbd8988dcb44200c73651aabdfdbd33d8e9c094}}, and tf32 {{cite:60e7f1ef3dae212848cf9d6ac9dbdaad8fb67c0c}}, the computation rate is usually denoted as OPS, , OPs/Second. Hereafter in this paper, we use FLOPs/sec and Ops/sec interchangeably unless noted otherwise.) and sub-optimal inference latency and throughput on TPU/GPU accelerators. With these insights, we augment state-of-the-art (SOTA) NAS with DC accelerator optimized search space to improve CNN model operational intensity and efficiency. Concretely, we create a new search space with accelerator-friendly operations including space-to-depth, space-to-batch, fused convolution structures, and block-wise searchable activation as shown in Figure REF . We propose latency-aware compound scaling (LACS) that uses a multi-objective of both accuracy and inference speed to search for scaling factors to generate a model family. LACS is the first compound scaling method with a multi-objective including both latency and accuracy.
i
e5607b68d6c4ad90416cbdf606712423
Very recently, the use of energy-efficient spiking neural networks (SNNs) for radar processing has grown to become an emerging topic in radar sensing and is currently being investigated by many teams {{cite:aa250063a623c70ce4f9053ad63d4225c977fd4b}}, {{cite:c7caa81c64b2ae218204d4af1feaa0217a820be2}}, {{cite:6f28ec95055c37527ddf8fc311f522dd67ed1c3a}}, {{cite:b83e86b71a7218c525d2a1b2d3e458d7e8cec7f3}}. Algorithm-wise, SNNs differ from DNNs as they communicate inter-neural information asynchronously, using binary spikes that are only emitted when the neuron membrane potential reaches a specific threshold. In contrast to DNNs, SNNs do not require expensive multiply-accumulate operations at the input of each neuron, but make use of inexpensive add operations only. Hardware-wise, SNNs can be integrated near the radar sensor (see Fig. REF ) as sub-threshold analog circuits, reaching more than 5 orders of magnitude lower power consumption compared to embedded GPUs {{cite:a1c64131af6b12414a6f7e79ca09e2e7c2c4da3f}}, {{cite:d5c31dac26e87fd9e36db4b17d783e349fdf16c1}}, {{cite:6a564ebebd6879a15def5aba7a40b053408a707a}}.
i
ad7e9a3626707c781762427a0b48fb41
The response scaling function has also been shown to dictate the response time not just for the mean of the current but the pulsatile components as well. This has an important consequence in that for any given network of compliant vessels there is a set timescale over which any section of the network will be able to respond to changes in any other section. Specifically, the time for any general wavefront to traverse a path {{formula:cadce7dc-8785-4f9f-8a4b-9c634cfec381}} is simply given by {{formula:d7276786-088f-4796-aaae-8ed90e1c651a}} , but if the path is too long relative to the values of {{formula:dfbf41fe-fd2d-434f-8f66-a3e8016473e1}} found along that path then the resulting wavefront will be substantially decayed and the time required to see a significant change in the current or pressure will be increased above the value {{formula:ff30dcd6-426d-470f-83e1-a27e4dcad33f}} . Thus, the timescale {{formula:00caa5c0-86f6-4b38-a52f-d29dc697e4cb}} sets a limit on how quickly mechanical information in the form of fluid wavefronts can be transmitted along that path. In order for fluid pressure and flow to respond more quickly, external information transmission is necessary. In biological contexts, this can be achieved through electrical signals in the nervous system, and the values of {{formula:35daba99-9525-4064-a177-d5d83d35c30b}} and {{formula:2242cdf1-dc3e-410d-be3d-fbdeb66a685f}} along certain paths may dictate where in the body such electrical information transmission is most necessary to maintain proper blood flow in response to sudden changes such as shifts in gravity from different body positions. The transmission of mechanical information in biological networks has some conceptual similarity to the propagation of the effects of a link failure in power grids {{cite:966fcd2cc46fcf6f776e8a13675d3767649cfe79}}, {{cite:f3a7a52c0af08c9be26462234f93664702fdda38}} - a concrete investigation of the analogies could help understand more subtle aspects of the effects of topology on the response of vascular networks to mechanical perturbations.
d
d5010bc188ed246902a1077ac3fa14ba
By using a physical observable like {{formula:21ab5816-dee5-4ddb-921b-29422aa39ffe}} , the leading singular terms {{formula:912b33eb-30ab-413e-ae2b-20d6723b8f78}} can be computed using a factorization theorem for the cross section {{cite:e4272c1b40f12c4fd488620c485b51dfd7317b8c}}, {{cite:1bf6c4f2f051f5bc107c5a71c945e7cf2d1a394d}} derived in SCET {{cite:da2fe7bc6c3872f06a99bcfbe8f485f5c1ece695}}, {{cite:198a98bd9d784c490fe6e914d2898f09bfad39ca}}, {{cite:ccac079473e06da5fca56736794860022a9f2f62}}, {{cite:dfb8cd28d686dd4bc2067195589e12c497dc2a5d}}, {{cite:b9db8b5a644a2d7bcc56dc1682764be3581d8d2c}}, in terms of universal jet, soft, and beam functions describing the soft and collinear limits of QCD. This provides explicit analytic control over the infrared divergent contributions. The required ingredients to obtain {{formula:d500bcce-187b-4e6e-958f-fa3428803a9c}} to NNLO are the NNLO jet {{cite:b727f82e6808cde5a54360b39285dc32cefec6e7}}, {{cite:d8bc442602376fdc1a22c6e772ca36b0b733d544}} and beam {{cite:74fe5eb77b6ac6d14b1cb0b99aef24c707044909}}, {{cite:8cd513db81ee50a30ac68cc268332e8deef6781e}} functions, which are fully known, as well as the soft function which is fully known to NNLO for two external partons {{cite:578edceed9204b1b4b34790e05cfe58ecfdf6183}}, {{cite:de147c21a9ed144c4589a0128cf23b1df33794f7}}, {{cite:9d97ef5c1f834870eb3d745c82fe2a925beaa1ae}}, {{cite:360eb798d31979e521f4b9a18df10dbbb770faff}}. The soft function for arbitrary {{formula:76ed9e67-e09e-4272-9fb7-405350deb538}} is currently known to NLO {{cite:063d2b6a3fea14a5711bcb03dc85afef0e8c62a6}}. The soft function for three external partons, as relevant for color singlet plus jet production at the LHC, was computed numerically at NNLO in Ref. {{cite:e1d134aa7c8c7f294c32ed68c2a3c53e049858b5}} and for a massive third parton in Ref. {{cite:ea1ad5385afa0535f5ffe1dc90eda6191f6850ba}}. {{figure:2c606d13-596a-44da-a5df-dfd679f5f29c}}
i
86b7d4068337bb2f7ca379a9cbaaf1b3
Many other ideas follow from a better understanding of computation in general, and how neurons might actually be engaged in non-digital computation, such as analog computation. Some have claimed that computation requires software, or the ability to be programmed {{cite:c2428fcaeb04d0cc2a1d3c7f10e2ca2ecc8914e5}}; others have claimed that computation requires universality of some type {{cite:0c7f55c2bbb13cac4f5494d4b6b6cb469a3d0fff}}. But analog computation, for example, is different in both of these respects, and yet still counts as computation. Moreover, analog computation may not even admit of a distinction between what {{cite:87b954070ac8b4b0b090fdcccea4bd733f66ae45}} called the algorithmic/representational level and the implementational level {{cite:30dd181bca6aa84a183cac6c1a75397f08ab078a}}. We may have taken what is true only of digital computation, or only of computation based on the implementation of Turing Machines (and the like), to be true of all computation. And while it would be a mistake to advocate for a return to analog computation in general, we should attend to all computational types when it comes to thinking about how natural systems might compute.
d
735e200e8c99b4b46837d6a50bf52911
Sections §REF , §REF and §REF discuss LAB areas, influence of the parametes used, and bias factor of LABs. Other uncertainties include assumption that particles inside a halo are spherically symmetrically distributed, lack of radiative transfer calculation {{cite:601596272ffc3163092c44532714d941438208ee}}, and lack of influence of other sources of energy (such as AGN and starburst supernovae). LAB source of energy is discussed in section §REF .
d
e95790f7cbeb8305950544204fb2774e
The usage of transfer learning for skin lesion classification in this work was additionally motivated by recent skin cancer classification study {{cite:40010fc9f9938687cce98e91284bce246c734154}}. It was performed by retraining the weights of the last three layers, where our version has seven neurons in its output layer. For training purposes, we used colour normalized augmented training dataset. We utilize stochastic gradient descent (SGD) for optimization, with a momentum factor of 0.9, and {{formula:6ceb872f-6010-4b43-b619-b6de8cf91d11}} regularization level of {{formula:0ef3d1eb-8fa3-4c19-bc68-fea22f5227c1}} . The learning rate of 0.0001 was used in a mini-batch scheme of 8 images and employing 50 epochs for retraining. Our solution was implemented using Matlab R2018a.
m
fbb7002fa0067d07f5de03a148c2a79f
The two following sections are heavily inspired from the recent {{cite:ece4c5da784dac816dc5f3d0e7674f66ac2e5909}}, and should be considered as a necessary reminder in view of extending our time-frequency ({{formula:b305f365-ec06-4301-b0a4-93aa292db4b6}} ) approach to the time-space-frequency-wavevector {{formula:afbe1d22-68b2-48b5-857d-a98901a53264}} . In Section is presented the integral quantization under its general form. In Sections and we give an outline of the Gabor quantization and its generalisations for the simplest case of the time-frequency phase space {{formula:f38ef462-d6a7-4731-a416-62d055787455}} . In Section we proceed with the analysis of the procedure in terms of observational and probabilistic aspects. In Section we extend this material to the eight-dimensional case for which the symmetry group is {{formula:4304cd21-c837-46bd-a0c0-b9f25cf01842}} . However, for a sake of simplicity, we restrict our procedure to the Gabor quantization based on the choice of probe functions {{formula:748375eb-8957-44b6-93d1-da4b6675da92}} . In Section , motivated by the 1935 Einstein-Rosen paper {{cite:b341bc8f3852be72d55be64c7625a8506fed1c49}} the Gabor quantization is applied to the most elementary (and singular!) metric field of general relativity, namely the uniformly accelerated reference system. We show how the regularising constant (introduced by hand by the authors) naturally emerges from our procedure. In Section we also consider another historical metric, the Schwarzschild solution, and show how the Gabor quantization and its phase space portraits lead to appealing regularisations, at the price of breaking the rotational symmetry. With Section we end this article by sketching some interesting perspectives.
i
a407280db8339a623494cd395e5d90d4
Finally, the proof of our main lower bound, presented in Section , relies on a combination of some delicate exact computations and multiple applications of the matrix Chernoff and Bernstein inequalities {{cite:fa9868aeb0c0766b43a4e83c6982b1cf985dc519}}. Technical difficulties aside, the main challenge in proving our lower bound is constructing the example distribution used to establish that constrained least squares is suboptimal. In addition to the restrictions imposed by the boundedness constraints, we discuss other distributional assumptions sufficient to ensure that constrained least squares matches the rate (REF ) (see Section REF ), thus making our main lower bound impossible. The intuition behind our construction is rooted in the form taken by our upper bounds. In particular, we construct a distribution tailored to make the localized multiplier process ill-behaved by simultaneously violating moment equivalence assumptions on the noise and statistical leverage score distributions. See Section  for more details.
r
1c609c18a758cbec0953bf501f7e7185
In the past few years, several work have attempted to establish that PG and SPG converge to a global optimal point for various classes of policies {{cite:81b79b8e37bf4ecd191f2c60465b2f011179a400}}, {{cite:0bedd38e65e0fa75f15797b85baeee2ec2ecf173}}. For instance, for Fisher non-degenerate policies, Liu et al. {{cite:8a006d097508ee8846774d3f9d33907ec84c155e}} proposed a variance reduced SPG method that converges to a global optimal point with sample complexity of {{formula:b501099c-9c5a-4a8b-bd80-70bb4758b7e3}} . By considering a momentum term, Ding et al. {{cite:6b158c5a9b42bd66aafb8be096a2ab25f04f24e3}} showed that the sample complexities of SPG for the soft-max policy and Fisher-non-degenerate policies are in the order of {{formula:2449fa16-fb1a-48b2-a80d-e313785320ce}} and {{formula:525fc6c0-b07e-4d1d-9bf0-98fc472171ee}} , respectively. In the case of weak gradient dominant functions with {{formula:d82a75dd-8cb3-4dc6-ae7a-a0097944a091}} (See Assumption REF ), Yuan et al. {{cite:6710c572e2ebc84c26cd8ac3eaf1e49debc898bf}} showed that the sample complexity of SPG is bounded by {{formula:7a53c08f-d837-4c71-8db0-321dd2a4f83a}} .
d
72571add75aaf537de75519f50fd8a32
For our simulations, the carrier frequency is set to 73 GHz and the mmW bandwidth is 1 GHz. In this case, the value of the wavelength lambda of the carrier frequency is {{formula:32248ff8-e776-4282-b81a-6f31e38af7b9}} mm. The number of transmit antennas at the mmW AP and receive antennas at the UE are set to 128 and 64, respectively. The duration of each time slot is 1 millisecond which is consistent the mmW channel coherence time in typical indoor environments {{cite:550eb380feb5185898685b5169fc181603aa77c4}}. The transmission power of the mmW AP is 46 dBm and the power density of noise is -88 dBm. We assume that the mmW RIS assigns a square of {{formula:de4eecb1-f266-4315-bcf2-673d1dd4ff4e}} meta-surfaces to reflect the mmW signals. Each meta-surface shifts the phase of the mmW signals with a step of {{formula:4af2bad0-e78a-4b94-91b6-25f571544e68}} radians from the range {{formula:62a5bb67-4c8a-4907-8c49-7ad1f15fbd2b}} . In our simulation, we assume that one mmW AP and two mmW RISs are mounted on the walls of the room and controlled using our proposed framework to guarantee reliable transmission. To evaluated our proposed RNN-based control policies, we use two real-world and model-based datasets of the users' trajectories in an indoor environment. To generate model-based dataset, we consider a 35-sq. meter office environment with a static wall blockage at the center. In this regard, we have assumed a given probability distribution for the users' location in a room. This location probability distribution can be calculated using well-known indoor localization techniques such as the one in {{cite:e43281c738991746a5f214fc5d97cf54fdeeafed}}. For generating the data set of mobile users' trajectories, we use a modified random walk model. In this case, the direction of each user's next step is chosen based on the probability of user's presence at next step location. Fig. REF shows the probability distribution of the user's locations in the office, the location of the mmW RIS, and an illustrative example of a user trajectory. We further evaluate our proposed solution using real-world dataset. We use the OMNI1 dataset {{cite:0f47be96f36038ab63dde50dba9fc1776b0aa12b}}. This dataset includes trajectories of humans walking through a lab captured using an omni-directional camera. Natural trajectories collected over 24 hours on a single Saturday. This dataset contains 1600 trajectories during 56 time slots. For comparison purposes, we consider the optimal solution, as a benchmark in which the exact user's locations and optimal strategies for the reflector during the next future {{formula:e58c1d96-a233-440c-9af5-080d80f30f34}} -time slots are known.
r
150ac5ac91264f45e072d9c9c3027680
the local {{formula:cc7bfc54-96ca-4fc2-80b1-dd4b386c651b}} -regularity of solutions was completed under the assumption that {{formula:cc06dc62-2832-44d4-b2bc-3df212140916}} is continuous and bounded; see {{cite:8790ef9c850657c9d70ac55dc683e31f32e005bf}} for the degenerate case {{formula:afc7ebe6-15bc-4ba5-bf48-260bbc44a751}} and {{cite:59ce0c902f152f2d8215486cfa0ba42bcc352e9b}} for the singular case {{formula:4485eea2-1c46-4eda-9964-f493d21b1087}} . Additionally, several extra aspects of such equations have already been explored as well, such as existence and uniqueness of solutions {{cite:a4ae2c464010a446b4665e8b1af32873c0880c2e}}, {{cite:c59a991dbd649be13b1982be94da1c687c45f6dc}}, the comparison principles {{cite:4f5e08aaf459fb3a7994051a9785f04bd8d8ffce}}, {{cite:634132d7e225c79a586d4d5fb73967dd3b830251}}, Aleksandrov-Bakelman-Pucci type estimate {{cite:16d2261b68221233d6652247cd156f0f835c3ce8}}, parabolic Harnack's inequality {{cite:c0bc588bf7b954a7966c0dec4a6c46ea2f8daaf3}}. For the related regularity results in the elliptic context, we refer to {{cite:1ad1f36b5184ab0f8ce8f64c46a27c4a38a7d123}}, {{cite:5030debfaee9f3854e243f7bcad5e1499acec6c5}}, {{cite:d961fa3796abd9b12ea38d30ec4f9d14887d9dce}} and the references therein.
i
70c0277a1162223452c7a32da87ba55f
where {{formula:cf2ac7e0-dbf3-4f29-890b-fd05fda9c61f}} , {{formula:0d30be57-5e61-4c38-a94e-f76d12be231c}} , {{formula:3cae11e7-f2b9-4056-98d8-befce4ddc2a0}} is the spin-dimensionality. For the 3D-Heisenberg model, there is {{formula:b8461dd7-65f1-4705-9b4d-9b4cc31d0adb}} 3 and {{formula:4928cd4c-4253-4ab3-80d3-f6bcc9e8a1a2}} 3. It can be obtained that {{formula:58b47b06-dd7b-4757-95ca-03576eb35f83}} 1.932(6) for Cr{{formula:3a78c172-cf1a-4e5d-9939-e929014eb7d2}} NbS{{formula:2e7ba3e9-bd01-4e28-82d6-3f6602eae5c3}} , which indicates that the magnetic interaction decays on spatial distance as {{formula:1bdce14b-1fb5-4d58-8f98-d03206565cfd}} {{cite:3d79c4dd9ca9033b9586bb9888698899d75fa0dc}}, {{cite:f4b7bdc999b0218bcd87e6d0d265f1073ffaf6d2}}. It has been suggested that if {{formula:c27da57f-0322-4d39-a76a-8675363d0905}} decreases with distance {{formula:85145157-8e27-4f9b-9206-77642f80e4a0}} faster than {{formula:cd4bf3a0-5412-4fe1-815f-e7e945c2e1b0}} , the Heisenberg exponents are valid for a three-dimensional isotropic ferromagnet {{cite:3d79c4dd9ca9033b9586bb9888698899d75fa0dc}}. As we know, these critical exponents should follow the scaling equations. Defining the renormalized magnetization {{formula:59e2dc8b-a70e-4eb9-b4a0-ed6e03adb355}} ) and the renormalized field {{formula:6f06214b-d2ed-4601-88ca-ac172e1f406d}} , in the asymptotic critical region the scaling equations can be written as {{cite:3eeae180a30efe88d3ad24517a4a34962d1cd655}}: {{formula:6e0cf151-3375-44c5-97c0-4d606a50dee8}}
r
8bdc0d8e427db0286fe55c7c26e1594d
A widespread classification of quantum correlations termed as entanglement, EPR steering, and Bell nonlocality, from a quantum-information perspective was given by Wiseman et al. {{cite:3587a2e0784f75dce8d467f2a57b3d3a5cfa6c1b}}, {{cite:3907765dc94ed907d9b7e66b8a2c587e4116dc89}}, {{cite:629cb601c04518e0bf5b5daad26fdb976ee02af3}}. Adopting here this fruitful point of view, we extend the quantum-mechanical line of reasoning initiated by Reid for a two-mode state {{cite:d2b0fcd023edf7196caa1b71c71a62221d3d5509}} by applying it to the whole class of two-party {{formula:70fdec2a-8fc1-4602-af7f-fbbd5fbd0702}} -mode states. A parallel analysis of their entanglement and steering makes use of the same pair of nonlocal EPR-like observables introduced in Eq. (REF ). Essentially, we take two steps. First, we employ the theorem of Hofmann and Takeuchi {{cite:3e0196793e9dbfdcd430dc56f6c521e6ad954ad6}} to write the uncertainty relations with the sum of variances of the EPR-like observables (REF ) for separable states, Eq. (REF ), and, respectively, for unsteerable ones, Eqs. (REF ) and (REF ).
d
bca3d8e9e1e96bbdcae0a6f9f1a6e583
Applying Au's Mathematica package {{cite:032e5f6ad9d910dae7dbb44aa7b3044aecef895a}}, {{cite:e93b1387da44821385cbcd40227f75ef39d527ec}}, we can find many explicit evaluations of AMTVs and AMSVs. We listed some cases, please see Examples REF , REF and REF .
r
357f699346db30466cc31063b60b09d5
One can then show {{cite:40b06243ded569d803678f243d3f59c1b4038b19}}, {{cite:443e0e5f7d72a1cd5d572c648decb90951579f9c}} that for every {{formula:339b03cf-f70e-4052-bba3-7a214f11fdda}} : {{formula:b0583f15-61dc-47d0-b05d-fab7d6517299}} for some {{formula:5932db10-d44a-4088-90f5-94634a54d0e2}} . This number, denoted by {{formula:f0bafa1b-5294-44c0-bab4-c3e77cdd3f2b}} , characterizes the distribution, and is called its singular order at the {{formula:2245a20b-f8c3-4e02-a2a6-751a952d599b}} axis.
i
668de98c5d25b6912fb0c159ac533729
Kingma et. al {{cite:589d94b95d0c3d25a271e4379b33a0124bbf1935}} have first addressed the problem of semi-supervised classification using variational inference. Subsequent works {{cite:77414f2fd20a780754b0e4b1bcec3be13fe38189}}, {{cite:3423ba36b2f14f70e77b969ac2550c28075e47dc}} improve upon Kingma's work by introducing auxiliary variables, multiple layer of latent variables etc. Within traditional VAE setting concerning unsupervised density estimation, importance of increasing mutual information between input and latent representation {{formula:d8d1c99f-f052-4e30-863a-69e80dd932a7}} is studied in {{cite:8ebcadcc48881346a34038448d35190d62c1ba4f}}, {{cite:820247499ece5902bb944df1ae9dfa62e14a3a0e}}. However, within semi-supervised setting, the mutual information between input and class label {{formula:6bc265e4-4678-4583-9e24-7f034f9cd2c9}} remains to be investigated. In this paper, by decomposing the semi-supervised lower bound objective, we show that mutual information between input and output labels actually decreases during maximization of the unlabelled lower bound (ELBO) objective. This hampers good representation learning. A decreasing mutual information between class representations and inputs is detrimental to the classification objective as well. Also we observe, during maximization, entropy of the classifier increases, which is also harmful for our classification objective as this forces the classifier to deviate from the cluster assumption. To tackle these issues, we regularize the unlabelled lower bound objective so that the mutual information between {{formula:a2bc6ad9-8788-4d88-b44a-5df16f3132aa}} and {{formula:fe540f38-25eb-472e-addf-2cb3a6bd5fbb}} increases during optimization and also entropy of classifier gets reduced. Various experiments on a wide range of benchmark datasets and prevalent VAE architectures verify that our proposed method can improve the semi-supervised classification accuracy of these VAE models. Moreover, experiments on the datasets reveal that reconstruction and sample generation of VAEs do not deteriorate. That is, our proposed method helps to improve classification performance without sacrificing the generative power of VAEs.
i
dc4478c7bcb626ff0d0f3fb012c6827f
Nevertheless, the negative sampling techniques suffer from the following limitations. Firstly, they introduce additional computation and memory costs. In existing CF-based methods, the negative sampling algorithm should be carefully designed in order to not select the observed positive user-item pairs. Specifically, to sample one negative user-item pair for a specific user, the algorithm is required to check its conflicts with all the observed positive items interacted by this user. As a result, much computation is needed for users who have a large number of interactions. Secondly, even if non-conflicted negative samples are selected for a user, the samples may fall into the future positive items of the user. The reason is that the unobserved user-item pairs can be either true negative instances (i.e., the user is not interested in interacting with these items) or missing values (e.g., positive pairs in the test set) {{cite:31cf426377bd1be7645565b18c249952c35110af}}, {{cite:4e32625d1a2afb894ac2e38a17d986e90f8725ee}}. Although another line of work {{cite:e670873d16935ad85c0b7b45d9e3c5b7fc9a2c1b}}, {{cite:b4df98cbaac46137d8e00ddc9da690a60138caf4}}, {{cite:4c70499d67359f699883bd452540ce7741866dc4}} have get rid of negative sampling and take the full unobserved interactions as negative samples, they may still treat a future positive sample as negative.
i
a73fc92fe80399975236ffd36634ee35
The vast majority of extractive, non-neural summarization algorithms use four data-sets for performance evaluation, exhibiting an interesting pattern. Unsupervised summarization methods majorly evaluate performance on DUC data-sets ({{cite:8f694aa0c7f163c143b4f0e8309f2463d826336d}}, {{cite:f58faedce3c83ffa6a4b276013c878563a1e4354}}, {{cite:84acfb51a2fe51bb655932ffd6768ce611febcdd}} among other recent works), while deep neural summarization methods use CNN and DailyMail data-sets. However, some neural methods train on CNN and DailyMail data-sets and test performance on DUC2002 considering it as out-of-domain data-set ({{cite:f6877fd1b855fed2eb8dc312d214602db53d796b}}, {{cite:7b780ebcdd44f334f8495b0526beea4a1eb13f21}}, {{cite:bf46eed8c826027ef13ae680ed6582c1ea476d41}}, {{cite:23191b1c2efc483390b54171344a865d2cb6aba5}}, {{cite:a35e4e84310f05f5b7897da2a0017a591523dc53}}). Recently added NEWSROOM data-set {{cite:12c2cf657a4be9b1d7f82772a3de1ff2786d4540}} consisting of news articles and corresponding human written reference summaries are gradually gaining popularity among summarization research community.
d
42877be5be5663dbcedf47f324e77420
Since the other 3D editing methods apply to specific architectures or have their generator part, we pick 2D attribute manipulators that have been proven to work well on 2D generators as baselines. They can also be applied to latent spaces of 3D GANs. InterFaceGAN {{cite:abaa2e95e3ae882149ccec788ace6a1d12e23c79}} and StyleFlow {{cite:5d6c64c93358e31613971f9c53e7fe65a2c8e611}} are the closest competitors to our method and were originally proposed for image generators. Similarly to , InterFaceGAN leverages pre-trained attribute classifiers to find the corresponding linear edit directions in the latent space of trained generators. However, as mentioned, linear edits are sub-optimal in the periodic space determined by the SIREN {{cite:99ff1a661f5ab6d2f3bf336589646c0d01e18118}} activation functions used in and MVCGAN. On the other hand, StyleFlow uses the attribute information during the training of normalizing flows as conditions. For example, when editing the desired attribute on a face sample, the user can give the desired attribute as a condition. In our comparison, we also consider methods for unsupervised discovery of editing directions: SeFa {{cite:b0bf5e32260848c40b75db46b8176034f23a7aa2}} and LatentCLR {{cite:fbe3c79feb37da502f0378bde59f78cbb05abeb0}}. Both methods do not have assumptions about the characteristic of the generator to which they are applied. Therefore, they can be easily adapted to NeRF-based generators like or MVCGAN.
m
77d3521ccc9d43163298a0ce8b825779
In the same time, AI is often presented as a solution to environmental problems, often under the larger scope of IT for Green {{cite:826c9493acee0eb04455d96f547aeed60deb8c1e}}, {{cite:fefe831874ea5bfa04b4241a6d815f9fc92164ea}}. The negative environmental impacts are briefly evoked - and in particular rebound effects {{cite:826c9493acee0eb04455d96f547aeed60deb8c1e}} where unitary efficiency gains can lead to global GHG increase - but no quantification of all AI's environmental costs are proposed to close the loop between AI for Green and Green AI.
i
0118a62a2e02eef3a9a716fcbcaa1b09
While the simplicity of the purely topological measures we have considered are important as starting places for understanding MCMC for trees, extending this work to branch lengths via BHV space {{cite:f2af595b8a30c83bc0cbd4b2fa331572af8c396d}} is an interesting possibility. This would have the advantage of additionally assessing the mixing of the branch lengths, which are currently unaddressed by most phylogenetic workflows. By comparing purely topological and BHV-based measures, one could also understand how differences in branch lengths contribute to the tree-to-tree distances relative to the topological distances. It is possible that most of the distance comes from differences in branch lengths, and thus the BHV-based tree ESS measures miss key differences in topology. Alternately, BHV-based tree ESS measures could adequately capture both branch length and topological dynamics. It is also possible that these two regimes co-exist in different regions of parameter space. In either case, reducing the mixing of a very complex structure (a tree with branch lengths) to one or even two ESS measures would be a useful simplification. In BHV space, it may also be possible to extend the work in {{cite:ca962a8d3ff5ab950bdff04aba4fc7ef3bfce9e6}} on confidence sets for phylogenetic trees to better describe the uncertainty in summary trees.
d
4a2e58b71774909f9c0bcdac2fc5fb96
We operationalise `topic' as a community in a citation network of papers, i.e. as a cohesive subgraph that is well separated from the rest of the network {{cite:3ae25cb575ef75e5311fd7df2c4bc19cd8c1fccb}}. Hierarchical and poly-hierarchical organisation inevitably reduce cohesion because larger communities include boundaries between well separated sub-communities.
m
3068cc517312abf0007e43948a63b4f1
Reservoir computing is a neuromorphic inspired machine learning paradigm, which enables high-speed training of recurrent neural networks and is capable of solving highly complex time-dependent tasks. First proposed by Jaeger {{cite:f22f20d0b8310cb64b626f45243847ce1d34e340}} and inspired by the human brain {{cite:64037012688811231247c4f09144f5d4f541d4a4}}, it utilizes the inherent computational capabilities of dynamical systems. Very recently, the universal approximation property has also been shown for a wide range of reservoir computers, which solidifies the concept as a broadly applicable scheme {{cite:fd069b02dae8618edc52ddd74597174bd49c44e6}}. Bollt pointed out a connection between reservoir computers and VAR (vector autoregressive) and nonlinear VAR machines, which may be one of the reasons behind the surprising efficiency of reservoir computers for time-dependent tasks {{cite:797a0a60d890d186605e16614134ca8aac844bd2}}, {{cite:2ed8fc8ef27ddfb8f818970ab79aaca2d3fd7efc}}. Many different realizations {{cite:d196be33345522613867cc42dd2bc7e2d2363e63}}, {{cite:815cda5ca2920b23d8974fead07180712620f4d4}}, {{cite:39f54beab326b3d24694e75464bf39f5b6821e0f}}, {{cite:29aa68247f618c0941ba7e40368c50c48cad3f2c}}, {{cite:fc19dc04454ee9568d7d841cd1c2b871480a24b1}}, {{cite:0c6ff93c8736df99aea4c453ccfc5f3829b8dece}}, {{cite:1f84261c2a98ec684a547546275876940f287784}}, {{cite:2b08d4e946fc88e9198f4b044e2265ab7a7d4bc2}}, {{cite:e9f4f64dca807116ed55cb3f9828ab71dc91233e}}, {{cite:62a5456dc8ae9742b6d70ddd2348d89d7a38b571}}, {{cite:8888a00d03c3f26846efd60267418cb93c14a3f3}}, {{cite:d66493fcfb578acf834ddb3bebd1343ab7279b6d}}, {{cite:bb3b3abf6e420826845b947ec740567749d9c188}} have shown the relevance of reservoir computing to practical applications, while analytical and numerical analyses {{cite:3c2b30817eb52aefd4352ad18d9bea35e0e45add}}, {{cite:823ed95b7616d42b09f8b5101dc2d7e624448072}}, {{cite:f991bf73b853c108b6d0ee2d6d7463e0ed9dec19}}, {{cite:758884279bd4c925367d3d026fd5b8c4faffdaf8}} help in building understanding of its working principles and improve its performance. Motivated by fast inference and low energy consumption, optoelectronic and optical hardware implementations of reservoir computers are often realized {{cite:c099766f407fad82af71ce79ecc0eeb18bcdf7db}}, {{cite:0fd179c3c17cb1dbb5110ce9896e72c4787ce01b}}, {{cite:0340ec42c391997c8f64485c3feda4850908c224}}, {{cite:32044212673ad4fdd4290ad9192b87a64bcc57c6}}, {{cite:4e2e518ab2e9c886b485fb0ca26241ef1d7f2619}}, {{cite:66c587790e115ed748c5f070aa3f30255617e826}}, {{cite:293494f6f693467e7621174dacf9b573755b2f53}}, {{cite:34204a7e432c2ebeea66f69b4d4ff039d24bffb9}}, {{cite:5770bfb1251203e3d878802636d65fb5d92858be}}, {{cite:a45cc6a9a6c4c01e6053e9c1533041069b71d536}} indicating a high future potential of such processing unit.
i
c0b2970ff2a575c0af4e9e0db2ed6fff
Relation to the Inference Model in {{cite:ea579f4341b97458ff7047a95e54cf6097e600b0}}   The inference model proposed in our conference version paper {{cite:ea579f4341b97458ff7047a95e54cf6097e600b0}} is a simplified version of Eq. (REF ), where {{formula:4307f132-a72c-440f-ad4c-8f8a82514ab0}} s are set to 0 and linkage between adjacent regions in the same layer does not exist. It is written as {{formula:ff8c972a-5a68-4e08-a6d5-4c7e7b2a96bd}}
d
fa4545f8ea0d86152c4443f59a44f926
In order to prove it, it was useful to introduce a refined classification of MMG theories by means of type-a and type-b theories. In type-a theories gravitational waves have the usual dispersion relation, whereas in type-b theories the dispersion relation is modified. To our knowledge, the proof that cuscuton and VCDM do not have an Einstein frame constitutes the first proof of the existence of type-IIa theories. (On the other hand, examples of type-IIb theories have been known {{cite:efb83e64cc063d05323880491bdafbd54cda835a}}, {{cite:31945da9ee35fbe873d83d7af036b0e2fa9e07df}}, {{cite:4fa5cc1eea3e328e036bca684ab02ae06dc087a6}}.) This is very relevant as modified dispersion relations are constrained by observations {{cite:fa12082809e7d5da5147b5649908ccc4ebd88176}} For example, the graviton mass in MTMG {{cite:efb83e64cc063d05323880491bdafbd54cda835a}} and the coefficient of the {{formula:04c8a24f-5518-46b2-891e-901dc640ad6f}} term in 4DEGB {{cite:31945da9ee35fbe873d83d7af036b0e2fa9e07df}} and its generalization {{cite:4fa5cc1eea3e328e036bca684ab02ae06dc087a6}} are mildly constrained. On the other hand, the deviation of the coefficient of the {{formula:164ae68c-76bc-4a5c-bf1a-de8e88daee5a}} term from the squared speed of light is strongly constrained.. As a byproduct of our analysis, we have obtained the most generic type-Ia theory by considering conformal canonical transformation of the GR action, as far as spatially homogeneous solutions are concerned. Furthermore, dropping the requirement of having a conformal transformation, the analysis can be easily extended to obtain more general type-I theories.
d
4a93b430ae87640b8717f5aae2531f3e
Usually, the prior information consists of global quantities calculated from {{formula:55977158-a25b-4256-b7cb-e2a7b6651e63}} , i.e., from all the data set. For Poisson processes, only one quantity is necessary: the mean rate {{formula:caa2178b-29b5-4058-aa01-96fb51fa7665}} . Considering the conjugate prior of the Poisson distribution {{cite:736b0b37997943cede8dcd86bf436cf651a3551c}}, the prior results {{formula:c71efd8d-1ec1-43b0-9189-813894407c45}}
m
6de5767cdbf224bdec35a2e03ed595ff
Our approach utilizes a reference atomistic trajectory (or set of atomistic trajectories) for a molecule we intend to backmap. The trajectory contains {{formula:96a4fe54-82df-4eea-9ef6-0e2d2ae77875}} atoms and is composed of a collection of {{formula:0bf00e1a-2c15-422a-9e28-ea426fa69c64}} frames {{formula:e8436df5-1a11-415e-a7c7-dc1d489b08a3}} , where {{formula:bea3b06c-0434-42a3-a806-33e17a20d1e6}} are the atomistic coordinates for each frame. We assume there exists a coarse-graining function {{formula:4db743b3-abe9-41e8-965c-ba1d6ba746ee}} that maps all-atom coordinates to CG coordinates, such that {{formula:36d7365d-87b6-4b98-8ee3-6c8cb1094429}} , where {{formula:a966c815-ad10-40dd-a1f9-8529f7bd4213}} is the number CG beads such that {{formula:2e799aed-86c0-43f8-95e2-e65d61721476}} . This function is then applied frame-by-frame to the atomistic frames {{formula:59ccfbf0-ee83-4726-9822-8d258e54d157}} yielding the corresponding CG trajectory {{formula:5e3d5a06-ec54-49b1-8813-4007a08c7384}} . This pair of atomistic and CG trajectories {{formula:22bdcfee-1c50-474b-aeb4-05acc72a771f}} compose the data used to train our super-resolution model (Fig. REF a). From this data our model attempts to learn the conditional distribution {{formula:e6977444-bee0-417f-a55c-5ccb1b4c2ff2}} implicitly, such that we can reconstruct an atomisitic configuration given the CG structure {{formula:f0e20b66-4edb-4611-baf6-abeacc759175}} and a previous atomistic structure {{formula:9944c5dc-59a6-4a57-808a-6371b9b5ade7}} . Each training sample therefore consists of a sequential pair of atomistic configurations and the current CG configuration {{formula:d8492ddc-a4a4-49fe-9dbc-de5a33a23173}} . While increasing the number of previous frames to incorporate {{formula:32009bbf-b40f-45f2-94ca-ca7c7d6b5d7e}} is straight-forward, our experiments show that this simpler Markovian posture already yields accurate temporally coherent reconstructions that reproduce structural, thermodynamic and kinetic properties with remarkable accuracy. A complete PyTorch {{cite:1f335e6870cbb403868fd0810ff88a35341ed9a2}} implementation of our model with all associated analyses is publically available at DOI:10.18126/tf0h-w0jz {{cite:a0f0e331b5e0ed39a0ecb1eb3ba38bac05ba0015}}. {{figure:8821b884-e61d-42ab-9cd4-e067ffdf80d0}}
m
4da755f7ef5b794379de85026561679e
The PINN method, developed by {{cite:517c62c948f173b22ff14360e4d2604a6c7b0df5}} (first published in arxiv in 2017), addresses the forward deterministic PDE problem by constructing a NN approximator, parametrized by {{formula:2e392b65-deb3-4267-baaa-0092338212f2}} , for modeling the solution {{formula:94c66492-803d-4a7b-9d8d-949c32b31fc2}} . The approximator {{formula:c88e0f14-e792-4ab9-b198-68be6f9d9091}} is substituted into Eq. (REF ) via authomatic differentiation for producing {{formula:844e8212-6fd4-4bac-80a1-784408c8c567}} and {{formula:0e4af265-a8ca-4ccf-8fb8-b3b2597da02a}} . PINN modeling for forward problems is illustrated in Fig. REF . Further, the NN parameters {{formula:9facb20c-0225-4996-85ae-1f97be09e462}} are optimized for fitting the dataset {{formula:081fd9f5-9432-41e8-ac22-fe8ed4f1389c}} using the mean squared error (MSE) loss. For solving the mixed deterministic PDE problem, an additional NN can be constructed for modeling {{formula:2b0c7ed1-f716-4e81-9af8-f41afc748438}} . For notation simplicity, the parameters of both NNs are denoted by {{formula:69ef7fe6-d79b-4389-950d-5bf97462acdd}} . Finally, the optimization problem for obtaining {{formula:7e7db626-2232-44c2-800c-88d958a117ef}} in the mixed problem scenario with the dataset {{formula:3c93c093-def2-4046-9c07-2b2aa67a3fe6}} is cast as {{formula:a8d2fa26-9779-4b33-9dc8-2aa7118b5683}}
m
dfd5a7f0828c177d3f7770e717ed2d56