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The digamma functions appearing in the expressions are easily calculated using the formulas {{cite:01f520c49f2b0978ccd82e3072c4bfe2c5d66268}}: {{formula:76f44841-ec47-4953-8d13-a6e5fea7d954}}
r
b37e7f6bdd98420e5941381db7428156
In the recent years, pre-training of deep neural networks has emerged as an effective approach to overcome the problem of data scarcity {{cite:2da76d4742990e30b10d207438db4f9bea47e5e3}}. The key idea of such a technique, which is also called “transfer learning", is to learn general representations in a setup where substantial amounts of labeled or unlabeled data is available and to leverage the learned robust representations to improve performance on a downstream task for which the amount of data is limited.
m
5be087444ed503e2926d5827604e14fc
Baseline Methods. We study the effectiveness of our problem formulation by blackbenchmarking against two language-conditioned baselines: Image-BC and C2FARM-BC. blackImage-BC is an image-to-action agent similar to BC-Z {{cite:848b5cb8c85f5d3328e57b9ac19ab03130cbe753}}. Following BC-Z, blackwe use FiLM {{cite:3110825b143ba7fb2bccfa2d9fb8987d9e2f8683}} for conditioning with CLIP {{cite:60fff872b4f32bfd3fb2dad37af58ae8b133a377}} language features, but the vision encoders take in RGB-D images instead of just RGB. We also study both CNN and ViT vision encoders. C2FARM-BC is a 3D fully-convolutional network by James et al. {{cite:39ec3fb1ff6aca8c2c04ca1513929592e549b19a}} that has achieved state-of-the-art results on RLBench tasks. Similar to our agent, C2FARM-BC also detects actions in a voxelized space, however it uses a coarse-to-fine-grain scheme to detect actions at two-levels of voxelization: {{formula:07115152-9957-4cc8-a9b6-03c3caddd994}} voxels with a {{formula:648c5d54-507c-496f-a04d-1eabfea7747e}} m grid, and {{formula:cd63eb35-8b34-41aa-9d50-6a087bdb7b3f}} voxels with a {{formula:19a18c91-6892-4df5-b2e5-9859b6835303}} m grid after “zooming in” from the first level. Note that at the finest level, C2FARM-BC has a higher resolution ({{formula:9b431493-7ba5-45db-b68f-a5552aeba698}} cm) than PerAct (1cm). We use the same 3D ConvNet architecture as James et al. {{cite:39ec3fb1ff6aca8c2c04ca1513929592e549b19a}}, but instead of training it with RL, we do BC with cross-entropy loss (from Section REF ). blackWe also condition it with CLIP {{cite:60fff872b4f32bfd3fb2dad37af58ae8b133a377}} language features at the bottleneck like in LingUNets {{cite:250173143e36199d7634fa26c8d81bd5519061d1}}, {{cite:9720505366b4ae3725317153354d8fbe2bc39828}}. {{table:c4dc3a46-a91d-48bc-9ad2-af82a0500cc3}}
r
68930f45d169d3a91a1cfd8724c7bd36
During the last years, non-linear equations involving general integro-differential operators, especially, fractional Laplacian, have been studied by many authors. Caffarelli and Silvestre {{cite:d2c86ac8591252cb9e3087f97527466c91454323}} gave a formulation of the fractional Laplacian through Dirichlet-Neumann maps. Various regularity issues for fractional elliptic equations has been studied by Cabré and Sire {{cite:3879179e6e97b9b10f56e3971b2433f544424de8}}, Caffarelli and Silvestre {{cite:afc49f3dfb40efcb08a4e09ead1e42606cb17d16}}, Capella, Dávila, Dupaigne and Sire {{cite:8344dffe0bec30bdb91d555fabaee936f0f9a333}}, Ros-Oton and Serra {{cite:11282ccd84b7890ab9642cd226119d0a7c2dc311}} and Silvestre {{cite:2275bb2c7d411e538293afe0bb6b71b44a61a24e}}. Existence and related results were studied by Cabré and Tan {{cite:3e4cd24782dcbbf9c69f6e6bf33af56f787cd769}}, Dipierro, Palatucci and Valdinoci {{cite:b7b3081e86673fb1c85f39fe78382b17096763a0}}, Felmer, Quaas and Tan {{cite:ac5ab95a93940260837f40bc44254a35f4b951fd}}, and Servadei and Valdinoci {{cite:a671b47811108fd18f47ee4d546e82a26055222b}}. Great attention has also been devoted to symmetry results for equations involving the fractional Laplacian in {{formula:e8256478-8f7c-4a6b-83af-41324b6789b3}} , such as in the work by Li {{cite:5735a38f5167e6dcee1fe0092d4b8e2a0110afaf}} and Chen, Li and Ou {{cite:a9e9df47fe54f47a3f3c5e3006ad8e95764bab17}}, {{cite:62633122e449a913275c0cd222f33fc5357f087a}}, where the method of moving planes in integral form has been developed to treat various equations and systems, see also Ma and Chen {{cite:1ac8aa168b4706f17e0d3c6970043382e002e967}}. On the other hand, using the local formulation of Caffarelli and Silvestre, Cabré and Sire {{cite:caeaba6dae0638546bce9f772967d64bc698da39}} applied the sliding method to obtain symmetry results for nonlinear equations with fractional laplacian and Sire and Valdinoci {{cite:700b071e7de6154805123a74a91a724759b5e3ab}} studied symmetry properties for a boundary reaction problem via a geometric inequality. Finally, in {{cite:ac5ab95a93940260837f40bc44254a35f4b951fd}} the authors used the method of moving planes in integral form to prove symmetry results for {{formula:46dde628-9967-4a5f-9fbc-d8561b0a3125}}
i
9249cd57655c253aa413abade98aa7ed
The objective of self-supervised anatomical embedding (SAM) is to encode the semantic anatomical information of each pixel, so that similar body parts in different images can have similar embeddings. Inspired by previous works on contrastive learning {{cite:790869e5b4e4f850e0fdf823fd08576cceb518f8}}, {{cite:6ac8652f808a1f4fe6d1e5fc3f90fd1a4b3b9dfa}}, {{cite:de04894b335cf106d122f68b37725462cefae3f6}}, we propose a pixel-level contrastive learning framework as shown in Fig. REF . Essentially, we let the model compare every part of the image to discover distinctive patterns by itself. The proposed framework comprises the following steps: stochastic data augmentation for training patch generation, coarse-to-fine CNN for pixel-wise feature embedding, and positive & negative sample selection for contrastive loss computation. In this section, we elaborate our framework for 3D images such as CT. It is straightforward to adapt SAM to 2D images such as X-ray by changing the network from 3D to 2D.
m
56b2e7278e14836bebb6e006c2754595
In our model, if the receptive fields of two latent representations do not overlap, they are naturally disentangled. For high-level representations, we propose to utilize a sparse prior to encourage disentanglement. We find that if the dataset only contains a few high-level factors, such as the 3D Chair dataset {{cite:a2ee7bdfbdf80480ae30efe6d6f4c7798352b7ce}} shown in Appendix , it is hard to find explainable high-level disentangled representations, because of the redundant nature of the encoding in flow-based models. Incorporating information theoretic criteria to disentangle high-level representations in the redundant encoding procedure will be an interesting future direction.
d
20292401c63bee74ce8748a814b66dba
Short-term forecasting up to twelve hours in advance allows for predicting weather conditions with higher spatial and temporal precision than longer time ranges. This makes it possible for these forecasts to have substantial impact on society by helping with daily planning, energy management, transportation and the mitigation of extreme weather events, among others {{cite:eb371d2f0a8fa782761c038e9b5e5bd0805ac64e}}. Short-term forecasting is also a longstanding scientific challenge that combines our best understanding of the physics of the atmosphere with our most advanced computational capabilities. Current operational models for short-term forecasting are Numerical Weather Prediction (NWP) models that rely on physics-based simulations. The atmospheric simulations make use of supercomputers with heterogeneous hardware that run virtually continuously in data centers around the globe and update the forecasts based on the latest observations. The weather conditions that the models predict include hundreds of atmospheric and oceanic features. The forecasts usually have a frequency of one or more hours and a grid resolution of 3 km to 12 km. The accuracy of a physics-based forecast is tied to the grid resolution as more precise physics simulations require a finer representation of the state of the atmosphere. This relationship creates a computational bottleneck inherent to physics-based models that has proven challenging to overcome {{cite:a7edf03584b5f404755b9185cb33f154cfe53f85}}. Besides resolution, the accuracy of the forecasts also depends on how well the physical models used in NWP describe the atmosphere at the various relevant scales; improving these models is a substantial scientific challenge by itself {{cite:c0a116428f1ca587ef3289a97632f8d6d53d59b3}}.
i
d06ef93009b5e2a427e462456673432f
The topological diagrammatic representations and our results of branching fractions in the {{formula:05c5c8bf-4b6f-40a0-a140-1073c6d3685b}} and {{formula:540fa2e5-cde8-4ddf-86c6-4443c8a90a80}} decays are presented in Tables REF and REF for the {{formula:27ee2dba-f3e0-4a8e-a829-c63721451f8f}} and {{formula:bcdb2c07-e8fb-49a6-a841-e61f3dbaadc9}} decay modes, respectively. The predictions are given in the last columns, compared to the experimental data {{cite:859e643979feb5bd0d369a6755d02cdda0b9af29}}. The additional data and results in the global fitting are listed in Appendix. In order to obtain a reasonable error estimation, we consider the uncertainties of those universal parameters as well as the decay constants and form factors involved. The errors of decay constants of {{formula:76cdf1a5-72fa-4e96-9d7a-8498c10a7230}} , {{formula:138bc564-5694-45b7-b7a7-94c103c7acfe}} , {{formula:1fd4ea75-6491-403c-a23b-cce68c2c9789}} and {{formula:fb0f0d5e-a347-4309-9e30-b637fe8d0304}} are taken from PDG {{cite:859e643979feb5bd0d369a6755d02cdda0b9af29}}, those of {{formula:6ab2817e-7556-4afd-b66b-bdb2a8e31d7d}} and {{formula:b3b2955c-a8bb-46a7-820b-bdf92daea9ee}} are from {{cite:a63e5aaceecd40518d9a6ea8dbbaed60b2ceb94f}}, and those of vector mesons are from {{cite:17f1c446524f9b1eb3e59bafc112e37de09387bc}}. The form factors and their errors of {{formula:2c13f0ea-e5b6-4ec8-86f3-82b72dc11a34}} are taken from {{cite:f1510a4018e2c3fa84507c3dc5a7d0b3e513261b}}. The errors of all the other decay constants and form factors are taken as {{formula:92728b66-5476-4895-bc1c-24f0705a84c0}} of the center value due to the theoretical uncertainties. It can be found that our results are well consistent with the data within the uncertainties. Besides, the predictions on the branching fractions of {{formula:387fe5a5-092d-4ef6-9fdc-0915b60e89ef}} are to be tested by experiments.
r
c9afbdf1c147811d4a7031e7c30aa8d6
Arbitrary Face Editing. In real-world scenarios, a fine-grained and wider-range control for each attribute is very useful. Previous works such as RelGAN {{cite:793c37f522db2291433c1fa74e22c18d6a886808}} and InterFaceGAN {{cite:c516545025a5c390b982ab6c9f0d86c191f0afa2}} also provide continuous control for facial attribute editing. We perform attribute interpolation in the range of {{formula:efafb4d3-00fc-433c-9eb9-0c9b1b141183}} with an interval of {{formula:de0818c9-9df4-4ad0-ac9e-e1fb9ecbe2b0}} , where {{formula:b8739ed0-f7f7-4d8e-9cd4-6dc19e429b61}} and {{formula:7694d6a4-362d-4fba-bd37-26324d025649}} denote that the desired attributes are equal to the source and target attributes, respectively. We show the visualization results in Figure REF , which shows that our model generates smoother and higher-quality interpolation results compared to InterFaceGAN {{cite:c516545025a5c390b982ab6c9f0d86c191f0afa2}}. When {{formula:e974cb73-896e-47a3-aa44-a842fa0eb71e}} is larger than 1, interpolation results of RelGAN remain almost unchanged, while our method tends to strengthen the attribute of wearing eyeglasses. When {{formula:fac8bc8f-ee4f-48a6-8905-17b1785cc380}} is set to 2, the eyeglasses in the outputted face image of our method will be replaced by a pair of sunglasses. Both qualitative and quantitative results demonstrate that our method has a significantly stronger capability of implementing arbitrary face editing.
m
218e18ffc8ab3fe6d83cf9acc8d1bb83
For the ease of illustration, we consider the case of two non-overlapping subregions (see fig-domain-decomposition) in what follows, where the interface conditions are invariably of the Robin type {{cite:39b967cea59eb4c0ef82203e4522e23995acd5a6}}, {{cite:f21a7c2ed8ea745129a80222c27501b2406de4c3}}, {{cite:769f49b0034268f450f93790bf92fa9d04916982}}. Note that the detailed iterative process in terms of differential operators is presented in algorithm DDM-Solution-Exchange, which is not restated here for simplicity. It can be observed that the update of interface conditions only requires the Dirichlet data of local solutions, which seems simpler and more straightforward than those based on a direct flux exchange {{cite:39b967cea59eb4c0ef82203e4522e23995acd5a6}}, {{cite:f21a7c2ed8ea745129a80222c27501b2406de4c3}} when combining with the deep learning models.
m
cd4bfa9b3f677f16f1343cbe0f5bf57b
In order to validate the generalizability of the EL module, we apply it to deeper networks, such as ResNet50 {{cite:b610170c501930e633ed058210a481007f54f568}}, which are rarely reported in existing literature. The results in Table REF shows that EL-ResNet50 (65.6% top-1 accuracy) is superior to the Bi-Real-ResNet50 (62.7% top-1 accuracy) by a significant margin, proving that the EL module maintains strong performance even as the network grows deeper.
r
bb25de8624a2dae6c77a87808fd9655c
Let {{formula:beec9933-b683-4303-9cf3-305f000796e8}} be an eigenvector corresponding to {{formula:9b490ae5-9244-4547-a223-8ab006613991}} , i.e., {{formula:4b208bee-89ef-46b3-8303-ab44f0a1c2cd}} . By the celebrated Perron–Frobenius theorem (see {{cite:413d5844c6240e700e8bcce00f2e36221aee291c}} or {{cite:73c0ef0bb62e6e45805c4a1e8d6e72a7a07cd141}}), we may assume that {{formula:0363a9a8-fab9-460e-a7c9-cbb255284666}} for each {{formula:1c288c09-4bea-4d6a-94e3-a80254588142}} when {{formula:d8473029-f42b-499f-897f-2816cd20065b}} is connected. It is easy to see from the eigen-equation that for any {{formula:f30dc915-eb8e-4bb1-b785-cf082fcad97d}} , {{formula:615c292d-2bdb-48e0-8130-983a4503219e}}
r
c67030cf07d4da10b7034beeb3eb4f0a
Uncertainty Sampling: Least Confidence (LC) {{cite:adc33a0d5b94f220985007b8ee202ac27a78db2f}}, Max-Entropy (ME) {{cite:6f49abd39b0fe5620201130b9d4e0f0b499c3354}}, Min-Margin (MM) {{cite:11b5e2306234fa8160859644c07d4bf2e57fe8de}} & Deep Bayesian AL (DBAL) {{cite:f13b992ebe0a7dd8e7848aeff4f7c4e5e425ec7b}} Diversity Sampling: Coreset (greedy) {{cite:e4c13a420009dfd3ca0ac7176d238938b64762f4}} & Variational Adversarial AL (VAAL) {{cite:f8938e95ce8e83a7282d030bd8f9356759717112}} Query-by-Committee Sampling: Ensemble with Variation Ratio (ENS-varR) {{cite:3899fc0df1479f0cc49e3c7d33a9f0f925c1bc8f}} (3 ResNet18 models) & ensemble variants of Least Confidence (ENS-LC), Max-Entropy (ENS-ME) and Margin Sampling (ENS-MM)
m
c2e9460673856dff25fea6b36c7a9cda
Our experiment design is shown in Fig. REF including datasets (A and B), the methods development (C) and their assessment (D). We propose a single-pipeline multi-reconstruction approach as data augmentation for fetal brain MRI segmentation. To strengthen the generalization of our findings, we assess our multi-reconstruction approach with two different SR pipeline, namely NiftyMIC {{cite:9341fb358f0372e1356ec5700e18a52b1c73e021}} and MIALSRTK {{cite:d9af983fa3f021493b9f55099c47c64ba2a5b5b5}}. First, we assess our single-pipeline multi-reconstruction method in a pure data augmentation set up (Task 1, Section REF ). Second, we further evaluate our augmentation approach in an out-of-domain experiment (Task 2, Section REF ).
m
a81455d66b03c801eaa0f0a7dea789a1
(2). CSI: It is a recently proposed OOD detection technique {{cite:d898cb2bf0c5f4c883220ccfb5835b27a07649e2}} that is highly effective. It is based on data and class label augmentation and supervised contrastive learning {{cite:a7e1af3752e2f80b72e298b584bee3f5b6e9ddcf}}. Its rotation data augmentations create distributional shifted samples to act as negative data for the original samples for contrastive learning. The details of CSI is given in Appendix .
m
5aa6a3694507f9e35899cb6a459d3f14
In the SME EFT formalism {{cite:9b897ddd2229dbde9c3fdf1e559ee3484ad3552f}}, {{cite:922c4b5fa7c623d9f711b7ff7d9ba075e28e24cb}}, {{cite:6b4374af81c7209518d5451b1243208eec140ad3}}, if the apparent cutoff above {{formula:e259acd9-16be-4cb1-9177-041580f7b5d2}} PeV in the neutrino spectrum shown in Figure REF is caused by LIV, this would result from an EFT with either a dominant {{formula:6f933cb8-0146-4594-bc6f-e7a20fe8e073}} term with {{formula:5972c7be-937d-4549-889c-ac49bb5d5820}} , or by a dominant {{formula:547ebe6a-b563-4711-8c18-366b21d738ba}} term with {{formula:7e79ef27-3b16-4fda-a1d2-06f5c9000234}} GeV{{formula:b8248ac8-c7a8-47f8-9f19-cb947f4a2830}} (Refs. Kostelecky:2011gq,Stecker:2014oxa, see appendix B) The IceCube collaboration has looked for deviations in {{formula:30f9db7d-f377-4868-9562-d24634c343e2}} oscillations between horizontal and vertical muon fluxes of atmospheric origin in the detector {{cite:cb6c31d962e12d1e04d3bbb5f142c554ac9e5758}} (See Section 4). The horizontal path length is much shorter than the vertical path length and is used for normalization. They obtain constraints of order {{formula:1947b4a2-8952-4726-824e-3620a62c78c5}} GeV{{formula:3f5e2ad2-60bc-4e86-baeb-ed0edd5b5b21}} on the {{formula:1be12732-a566-4d7f-9dc9-b561eb1f7091}} operator involved. Such a cutoff would not occur if the dominant LIV term is a {{formula:8e06fb41-275b-4724-bf9e-fbe9d6d1593b}} -violating the {{formula:c2003375-d608-4983-8278-5c950db73200}} operator. Future detections of astrophysical neutrinos with energy above {{formula:5eed2ecb-37ef-41db-97c9-829c40a093e8}} 2 PeV would indicate that the above numbers should be considered to be upper limits on these parameters.
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c3485cc972d1e2e1fbb06d364e4db6a9
There are many potentially relevant sources of information beyond an agent's own experience, or that of other humans or agents. For example, it has been shown that YouTube videos are useful for learning to play the Atari game Montezuma's revenge {{cite:97aae43f95f5c9b275f99c1df1f1b62696af915d}}. Training an embedding network on sufficiently diverse data may enable retrieval of information from a wide range of contexts {{cite:0807a6a9a6c433cf345c4075343a7c10db7ca433}}, including third-person demonstrations, videos and perhaps even books.
d
1db3680a7bcc9cb905a0a917b59210fe
It is known that multiple instances in the single natural image possess the co-occurrence relationship, and usually have different semantic meanings. Therefore, the models should have the ability to distinguish the semantics of different instances. However, it is still challenging to discriminate different instances residing in the single natural image when no instance annotations are available. Several region-level based methods {{cite:90ef7ce033acd8c6641bd344951f642f8dcfc790}}, {{cite:0c60e9f2a25a80192b0128fa197eb89d26aff974}}, {{cite:53c89df80daa9323818b51d9c5a6b51f4570db0f}} propose to leverage multiple local regions to pre-train models using non-iconic dataset, and achieve the success of the specific downstream task. Nevertheless, these region-level based methods do not explicitly distinguish different instances in the scene. In addition, their results of linear evaluation are inferior to the baseline, , these methods can not obtain versatile visual representations. Moreover, natural images have prior that the scene and instances in the scene have the semantic affinity since these instances correlate with the scene. Current SSL methods are not aware of the prior and do not encode the semantic affinity. Because of the above problems, the application scenario of these methods is limited. It is essential to design an effective learning paradigm to obtain versatile visual representations.
i
d7f150160435f6f77fcc23499a9bcb28
Text image: Images containing text usually appear in images obtained by scanning a text. In recent years, with the expansion of the use of smart phones, scanning software has expanded {{cite:bd6172092011bce0ce05e26e15a0c84b59268e35}}. Various factors can affect the quality of the output image, such as hand shake when using scanning software by smart phone. The results for two text images such that blurred by kernel 01 and 04 in Levin dataset are shown in Fig.s REF -REF . The results of the proposed method are compared with {{cite:55f80e9b0417933e28a15f337271a68d77699980}}, {{cite:5a5e6d71225076093fb267c7dfa27a769b3294fe}}, {{cite:9d1cb0449c67b9052aea484f68091effc79bdad9}}, {{cite:3aaf68fcb9b885df845d7e5f64cd3365371414f1}}, {{cite:9d04de1dc85603faf01249912b6f2cf87669ceff}}. In Fig. REF , the results for MS-SSIM, IW-SSIM and F-SSIM are given. Also Fig. REF shows output deblurred images. The Fig. REF shows the close approximation of the PSF by the proposed algorithm. Also realistic blurred text image includes car license plate is restored by the proposed algorithm and compared by methods in {{cite:9d1cb0449c67b9052aea484f68091effc79bdad9}}, {{cite:9d04de1dc85603faf01249912b6f2cf87669ceff}}, {{cite:478f762ae7e8a632bac5c84a84f66fde884ab998}} in Fig REF . As can be seen from these figures, the proposed algorithm has a better output compared to the other methods. {{figure:23a28b1a-d13c-426d-b45d-a62303e07f48}}{{figure:f53d238f-406e-404f-9963-b796a99f80e8}}{{figure:88901aad-7b53-489f-9f1e-51fe8d45e8b0}}{{figure:30b04842-360d-453a-a624-20f49b1e7b71}}
r
9eb13010bc0edec039f3b03b13b79bb3
From reactions fueling cells in our bodies to internet links binding the World Wide Web into a small-world structure, networks are at the basis of many phenomena. Random Graph theory sets up a common toolbox studying networks independently of their context from a probabilistic point of view. The most basic random graph model was introduced by Erdős{{cite:3c5f137332767d6ed8b58f244e1bd436cf3c8598}}. This model refers to a set of vertices, where the probability of two vertices being connected is chosen in advance as the only model parameter. Vertices from such a graph satisfy a specific degree distribution, namely the Poisson distribution. Since Erdős' first results appeared, many models yielding other degree distributions followed (see for example {{cite:e655833aaed945c93057bc4be10286572dcd6b17}} and the citations therein). This exploration for new models was driven by both a theoretical desire and a practical necessity.
i
90f8cca71f2109057ff4b55b8b75179b
To calculate the anomaly score of a sample from the Softmax probabilities, Golan et al. (2018) {{cite:f4453f0bb11f90a1f3c7f27654601313351dbd9b}} combined the log-likelihood of the conditional probability of each of the applied transformations: {{formula:6a63a15d-93cd-4b18-abfe-ccad1918f5dc}}
m
5fe9c1c6e74fe49f44e6598292411ed6
Regarding the spontaneous microphase separated regime, this is notable especially because there is no term in the free energy density {{formula:325ab20d-d7ba-4c52-aa7d-b4bfea9f4ba9}} which explicitly favours demixing. In other words, in the absence of {{formula:a2464972-98ce-436f-985b-d2b25d63c11a}} the system would remain uniform. Phase separation arises due to the coupling between density and order, measured by the parameter {{formula:46c10306-3ad9-4f47-9bb1-d3af13701177}} . In this sense, phase separation is not driven by activity but rather thermodynamically, and indeed it can be explained with a theoretical discussion of the free energy in the passive limit (Fig. REF ). In simulations we observe a microphase separated pattern rather than macroscopic phase separation, as the active flow arrests coarsening, and controls the size of the steady-state domains observed at late times, similarly to the case of active model H {{cite:7b41e955e9b0876f187e3c86d39e156b20b2b519}}. While experimental realisation of active nematics have shown plenty of instances of active turbulence {{cite:151e4306985beee95cc498befabf073199067425}}, {{cite:812da1324d5985863d83b1b4ab6537c23a48d7a2}}, the spontaneous microphase separation regime appears to not have been found in the lab yet. Our model suggests that the most promising avenue to realise this regime experimentally is to control the density-order coupling {{formula:6483f5ac-bc55-49e5-bfff-b7cf1cc4b817}} . The latter may be estimated by monitoring how the isotropic-nematic transition point depends on the density of nematogenic particles (for instance, microtubules) in the passive limit of no activity.
d
a38585172548f73ef1de998a546fb019
It is difficult to obtain all the structural data from the above pool of published articles. It is rather practical to use chemical compositions as the direct descriptor. In the preceding studies, {{cite:200c5ea1a4d9ae94ca793301f684650deebc30ee}}, {{cite:038112fa81d29e31b94e4708a82d34969a6a84a1}}, {{cite:ba75f77aad6e1f1c8a553b089815f3f90f6f25fb}}, {{cite:5a0d45bd8f8eaac7f9aab85a110e21c60202c7c1}}, {{cite:89df20f16644add11df721f9a7b5a432ab927987}} it has been found that {{formula:6dfb2ea9-9416-4a60-b8cf-0c76e72bb563}} correlates well with (i) space group, {{cite:22501f1f83465ec4189c0cfab44e5d1c29795849}}, {{cite:883cc5c7435457853dcf8e9ba695c3590dedf8dd}} (ii) density of states (DOS) at the Fermi level, {{formula:e51780b7-e316-4ecc-af79-a52a27981455}} , as a measure of the applied pressure, {{cite:038112fa81d29e31b94e4708a82d34969a6a84a1}}, {{cite:ea9c217a9c3cfdf54df615e00b168f65fd2788ca}}, {{cite:ed78fab6d08294ea2155acb170986b7120d48169}}, {{cite:2d550c53d6f9c8f8e354eea2059f203c4c18ad75}}, {{cite:3e99e14e98267fdb750ccb8e6112da03bf2aeeb3}} as well as (iii) the chemical composition. {{cite:28f3bea67f11851d13e03a8a4c5c51aa167deabf}}, {{cite:ba75f77aad6e1f1c8a553b089815f3f90f6f25fb}} By the procedures explained below, we finally set up total 84 descriptors corresponding to the above three features: For (i) [space group], we took the number index for the space group (e.g., No.166 for {{formula:fae6df7c-f954-41ac-8fd6-41bbf02ab81e}} ) as the descriptor. For (ii) [pressure], we used the scheme taken in the preceding studies, {{cite:cc70c7b8c23265391535ab53512d20d736388909}}, {{cite:920d030aef8edb993ff3af7ae37ab69f6436f467}} where the descriptors were composed as weighted averages over the quantities for pristine materials composed of each of elements in a compound (averaging weight is based on the composition ratio). The quantities were evaluated for the structure of each pristine material taken from the Materials Project {{cite:07499167098b9c3c1fd683df0632404c5f2f750a}} by using VASP {{cite:660d46e4440f4f61205e3ad79dd17d135cd59cd9}}, {{cite:8f51b644776e5ac907b4886b79ee2405742a8245}}, {{cite:dbb3809bc62888e21daaa7db2b40fdbbf648d44c}}, {{cite:8d5325eda65e99f14075c3cf12ba5c09a6ef7fc4}} to get DOS at several values of pressure (detailed computational conditions were provided in S.I. (§REF ). For the weighted averaging, we took the same manner as in XenonPy. {{cite:0b6157d9742fa3df04f07b04a7503870955d3861}} The procedure provides total 56 descriptors for (ii) at this stage. For (iii) [chemical composition], we used a XenonPy utility {{cite:0b6157d9742fa3df04f07b04a7503870955d3861}} that generates many possible descriptors, from which we picked up 290 descriptors at the first stage.
m
eb2fd211984cc267919e2903bda970ad
Last but not the least, as a physical model at cluster scales, the {{formula:3dfc89b1-97f2-4f04-bebe-536f2a705e0b}} should be subject to more observational tests, just like the NFW profile of the dark matter {{cite:e552d46e19b09d23e157e3cf32ac947f8fd16948}}, {{cite:58397792d88e469d4a34ff41d46634bca26045cf}}. A new challenge is posed by the Abell 520 cluster {{cite:e790090899776a6fe084d5b8f0c66085b03c785b}}. A combined constraint on the model should be carried out. Relevant research are currently undertaken. We hope that it would help to constrain the form of {{formula:12657463-db3e-4281-b43d-5d80f4701f1c}} , which embodies the symmetry of Finsler spacetime.
d
ae600da969837b1a3267b602d701203b
Finally, we see similar ideas circulating in the neuroscience community. A recent neuroscience commentary, “What artificial neural networks can learn from animal brains” {{cite:572f0afd9c9a9a737cd6e4db897bde99155342c7}} provides a critique of how learning (and also meta-learning) is currently implemented in artificial neural networks. Zador {{cite:572f0afd9c9a9a737cd6e4db897bde99155342c7}} highlights the stark contrast with how biological learning happens in animals:
d
923435796067434909e7422b7d2f0f77
Effectiveness of tracker hijacking attack. Fig. REF shows the average number of frames that the AEs on object detection need to fool for a successful track hijacking over the 20 video clips in the evaluation. Although a configuration with {{formula:a9a080ce-6ab3-4208-aed3-b6e786ecd4b5}} and {{formula:0e513525-cf69-4b00-9f23-3fe84dbd0bbc}} is recommended when fps is 30 {{cite:2a055f145a6336d78773dad8fa8278906bcde662}}, we still test different reserved age ({{formula:d055d477-7479-4d28-adc1-b91a7cee8e6c}} ) and hit count ({{formula:e495afeb-7538-4220-b145-d21ce8ab032e}} ) combinations as real-world deployment are usually more conservative and use smaller {{formula:accd75fd-5052-46d4-8b11-d32e94be91a1}} and {{formula:52802004-4426-44c2-96f8-a1f17b0cdf0f}}  {{cite:e3160f82623afaf633cc719e6c17639545220e10}}, {{cite:4b6e4339836e37aee4fdf9a6b21e7a77095eff97}}. The results show that tracker hijacking attack only requires successful AEs on object detection in 2 to 3 consecutive frames on average to succeed despite the ({{formula:3eb3dd11-00de-4bbf-894e-4eb210369bd6}} , {{formula:ff8f2c33-7cb5-4748-825d-57cd217c8cb4}} ) configurations. We also find that even with a successful AE on only one frame, our attack still has 50% and 30% success rates when {{formula:7ce8277c-4313-4b49-837e-c044965f234a}} is {{formula:2e630cd9-d064-4663-9d28-4924eae765fe}} and {{formula:e52f03f5-0581-4dbe-9854-cd421f82a7a0}} respectively.
r
1a170f7ad550aefb46ea8fa02cb690a3
where {{formula:df4ad3a2-5563-4757-8435-32c7d9e3368f}} is the graph cut of a weighted graph with {{formula:f2d3ba0e-c31b-4777-8846-3b3696465d50}} vertices and the adjacency matrix {{formula:9ecc01fc-e4c6-4e46-aae2-1f5c923e1d8b}} . Hence, the balanced graph bisection problem {{formula:412000fe-2f04-490a-bfbe-bf72717d8eca}} , which is known to be NP-complete {{cite:7e08e3fa3e9ba0bce1e3f3526c7b649356e44d71}}, reduces to the ORSTP with a special vertex degree sequence.
m
785ba0ae292b3aedf86e5473e1298876
Today, a large number of text and written materials are present in English. However, with roughly around 6,500 languages in the worldhttps://blog.busuu.com/most-spoken-languages-in-the-world/ {{cite:a64edbb9178ce4b2d81c4ebe39774d2f052ae807}}, {{cite:c92e08d29155fe7fde78eed422ad332d839e9565}}, {{cite:c4bdc940b3c0a71311d894501ace4062fb286e73}}, every native monoglot should not be deprived of this knowledge and information. The manual translation is a tedious job involving much time and human resources, giving rise to Machine Translation (MT). Machine Translation involves the automated translation of text from one language to another by using various algorithms and resources to produce quality translation predictions {{cite:66d5aa5f97142c3f8905fac3a4c4aabd0c3fae45}}, {{cite:9703fb26c4e19451eb3750588a478642e3be4ba0}}, {{cite:88ed2b0f59e4ddad2164812803519d3eb44e9f56}}. Neural Machine Translation (NMT) brought about a great improvement in the field of MT by overcoming flaws of rule-based and statistical machine translation (SMT) {{cite:4d16b76597bcfc6019fe73e13827f01395d22dec}}, {{cite:311a61f988cea77723ce21b3c04853c9b6181582}}, {{cite:90d6a24c0159caa8e09a7982498c5779560c3215}}, {{cite:a5caf889dbb12bdc3750d018fd6476dd068f10ca}}, {{cite:11b37bf982e20036a8d60f8294678e78794b3c4f}}. NMT incorporates the training of neural networks on parallel corpora to predict the likeliness of a sequence of words. sequence-to-sequence neural models (seq2seq) {{cite:3ac14b44a38b51815ad15aef75e2afd6f429cdf2}}, {{cite:cf4a5a7d75ed3eab84b8491987b91b4e0070941e}} are the widely adopted as the standard approach by both industrial and research communities {{cite:560616a7d0eafbcd9748a13da066111d44b00df0}}, {{cite:96e5a1f2108caa6fe56a6e129942bcfcce72f2e3}}, {{cite:63dbaaae57cc0842407c4f53e7c60df49849b3b1}}.
i
26b17225436cc2856d3dbea88cd273ac
The Hamiltonian Eq. (REF ) [Eq.(1) in the main text] is essentially the same as that used in Ref. {{cite:c5152e5125d8b482173dc14d789f6c5a4cb251ab}}, {{cite:836e604ab210138eea65c904a9ceec0af111e6c9}}, {{cite:1f2fed818937ced879770dce57371a8327d99e4a}}, {{cite:430009c2aa0cd3e7381f22a12a0b4a1075a5b394}} resulting from the phenomenological Raman interaction. The only difference is the term proportional to {{formula:2fa704fd-83c8-47df-9a0a-62cb6931963d}} which makes the above Hamiltonian positive definite. The Raman interaction, proposed to study spin-phonon interactions (SPI) based on quantum theory and fundamental symmetries {{cite:a879757f5cefc0fb5e73e823ae3741277172273a}}, {{cite:a0e8ec21d5783abcf6f91ce4f911d64706a9e343}}, {{cite:b99d6d97709e241892525cb7aae9cd0d0375ba6e}}, can be expressed as {{formula:a1c20bb9-fa36-47f3-b669-11c3abb721fe}}
d
0296c776e2093e67ecf5049f87f624bc
which can be checked by plotting the autocorrelation function in lin-log scale as shown in Fig. REF . Here, {{formula:7b24f17c-5997-4b0d-9dc4-82470c0774c2}} is the exponential correlation time. The correlation time gets higher with increasing {{formula:26f67423-4fbc-4e43-8a57-6bef37c49c6c}} . The curves show that there is a clear critical slowing down in the system at the critical competition parameter. An alternative way to provide insight about characteristics of simulations is to calculate integrated correlation time, {{formula:59e07839-ddcb-4e43-a4f2-a4f2c43baa73}} , defined in Eq. REF . Lattice size dependence of {{formula:15274733-b506-460a-b381-b49f2b2fc4ab}} is depicted in Fig. REF . The correlation time is expected to obey  {{cite:5e9ca48bf9cc86284402082835b77dbdaa1a514a}} {{formula:b64be436-8ba2-447e-be20-7ca98c3af5c7}}
r
87d03c36678cf20b98f464cc7e371b6f
To further improve the recall, one possible direction is to learn a joint model for detection, tracking, and prediction. The intuition is that, future predictions can be used to infer the subject's location during tracking, whereas accurate tracking results can improve the prediction accuracy. Recently, several work proposed to perform such joint inference on point cloud data {{cite:b39ecfbc15a0c1d3f859ae0ee4569acba0646626}}, {{cite:76e392043ae1aea30c9f722036b0903239c7db02}}, {{cite:56fdfd6d21fb535b7d8d1fe255691b6665edd342}}, {{cite:c6991986088c42e596edb33b8808c2add04d0410}}, {{cite:fe9c5c443980833af40d34761657afc814559139}}, {{cite:e7cfd7a772a0839e823ca422589b2803d9def398}}, {{cite:c26e87baf519926175895418c7b3623e04cd5547}}. However, one challenge in applying similar ideas to datasets like SDD is that state-of-the-art data-driven detectors {{cite:fca5c80277bc3e7413f7a69f4e70d4c4c8dc30e8}} failed to detect small objects in bird's-eye view. In this work, we resort to a motion-based detector instead. It is interesting to develop a model that leverages the motion cues in videos for joint detection, tracking, and prediction.
d
b372fb50ae6d4e5b33b05e5de3893f4c
Although attribution methods have become an active and important area of research, their general applicability and usefulness have been scrutinised and criticised. For instance, Rudin {{cite:ad85a47942528c7ccb4fbf200b9e4d17d9fbcc9a}} argues that explanation and, in particular, attribution methods cannot be completely faithful w.r.t. the original black box model and that attributions often do not provide sufficient information about how the model actually works, they rather tell us where the model looks. Kumar et al. {{cite:c1c39d9eaab30539a0107a631608c179c62084cd}} criticise Shapley-value-based explanations, such as described in {{cite:7ada4801ca775943f515f11ad1bbe0823094bd28}}, {{cite:89a9a6a825be6ec7fc8d3b9d3fa25dcbc328e1f8}}, {{cite:37447985b29b72001c0b9b1909993c373bb6cc9b}}, for their reliance on the additivity axiom {{cite:5311096384ed67913d627643e466174b8cde7577}} and lack of human-groundedness and contrastiveness.
m
3bb2c3ef68d6ea675d15d2f0a8e188d1
Theorem REF and REF apply directly to models of random maps when all faces have the same degree to deduce the following corollary which extends the aforementioned results of Le Gall {{cite:776bc19f1b2d8c8530abaa9c90787aa76f34bcf2}} and Bettinelli & Miermont {{cite:e62db669ddf12b30d02c7ecc81d174e79c090927}} when the sequence {{formula:2ee98b1d-8495-4831-994d-3412b421f640}} is constant.
r
05ede55fa80ab3e8af62a0f2decab7ef
Table REF reports the evaluation metrics of different normalization layers on the Split CIFAR-100 and Split Mini IMN benchmarks. We consider the averaged accuracy at the end of training ACC({{formula:a77780bb-9ab4-40c9-aef8-ecc01850f197}} )  {{cite:f4dcc3eb7b395f828433e1c652b8393e4f47c1fc}}, forgetting measure FM({{formula:8f6d55cb-8322-4336-a934-7e3dfd8c71b5}} )  {{cite:ad29eb552b24b8d2abeec26cc5f66ad21c4b7355}}, and learning accuracy LA({{formula:9dfceb18-5670-4e5c-819e-0e08bcad9d7f}} ) {{cite:2689a4ee87a96d6afc3a2747e8cf3fd83ba84e06}}, details are provided in Appendix . Clearly, IN does not perform well because it is not designed for image recognition problems. Compared to adaptive normalization methods such as GN and SN, BN suffers from more catastrophic forgetting (higher FM({{formula:303feabb-9565-49f6-998f-df0739aa8d7e}} ) ) but at the same time can transfer knowledge better across tasks (higher LA({{formula:5ec6daab-4f1a-4f15-9351-8ea088fb42e9}} ) ). Moreover, BRN performs worse than BN since it does not address the biased estimate of the global moments, which makes normalizing with the global moments during training ineffective. Overall, the results show that although traditional adaptive methods such as GN and SN do not suffer from the cross-task normalization effect and enjoy lower FM({{formula:925610f8-b893-4fe1-9c00-74896e0bd792}} ) values, they lack the ability to facilitate knowledge transfer across tasks, which results in lower LA({{formula:9de27a02-1427-48a5-955b-b5ad8d2068f2}} ) . Moreover, BN can facilitate knowledge sharing across tasks, but it suffers more from forgetting because of the cross-task normalization effect. Across all benchmarks, our CN comes out as a clear winner by achieving the best overall performance (ACC({{formula:89d0f056-cd55-408a-b9b0-001db05befda}} ) ). This result shows that CN can strike a great balance between reducing catastrophic forgetting and facilitating knowledge transfer to improve continual learning. {{table:c8eec614-a805-4443-948e-a86fa7353832}}
r
f66384542191efdbbfe6bd0952a04749
Let {{formula:832ced75-320e-4633-9975-f2112db06da3}} be constructed as in Definition REF . We may write {{formula:ee2c49f4-9b9f-4952-8603-c5560f237ccc}} , by symmetry and independence of {{formula:8df8a57e-f3bc-4f8b-87fd-598f95348239}} and {{formula:650a4824-2283-4763-b71b-b1a157458077}} (c.f. {{cite:2bf586ca0536b005436d48bf992ee8ee869c1feb}}). Then by convexity, we have {{formula:a0914a25-bd12-4538-bb82-6cb0ab2a7a41}}
m
bba8b516630a3825971baf9525212df2
Beyond first-order methods, the most developed methods are maybe second-order methods, among which the closest to our setting are cubic-regularized Newton methods originating from {{cite:61e8574e3e4c3d9965e5c97dd0f9d078f22d39ff}}. This line of works includes the development of accelerated methods {{cite:1652cb318fe8b4d23948b9c32f7fc38a11282e8f}}, {{cite:f0cba26bd1640dff18efde77a2d4263c61e2e5f2}}, {{cite:afb92c2a1577dad539368ec1c82f350057b74818}}, extensions of trust region methods {{cite:fb6f3bae9ddb8586a9dafef92277362240fba790}}, {{cite:8dc545cb966301e24187454e1d974ca432a8f2c7}}, {{cite:e294799a920456de915d748487d9e47273159ec4}}, {{cite:2a9668a55852bb39280438f0570ede99b0196d91}}, {{cite:19a5644ef5440e99f9f52301fafa6e7347a2f4d6}}, methods with inexact evaluations of gradients and Hessians {{cite:b85c17d3c409cc6719cf4b6faf826a82aba74af7}}, {{cite:131ca13499f20df2a6943e56216b7684877ef638}}, {{cite:d655f682836338322233070ef1b10d96fdb6a283}}, {{cite:1f55fe256f55c5a8491e828019db0faf48f503b1}} with application to stochastic optimization in the online and offline settings. Stochastic second-order methods for convex optimization {{cite:bd9896ffbd116c610176b4b471438bd75a41d3d4}}, {{cite:a7dae9394e6ca2991fc9632428632e4709a4dc0c}}, {{cite:9f4add0312621977b1616bac4de6b3dabb52d07c}} and non-convex optimization {{cite:b27cdde90a2825815a8bfe7d16c34240656235d9}}, {{cite:cc908a172285a3fdfe6f91d3ae26479ed214de47}}, {{cite:6e1a5d8c7abb3a58337d300a1590a6d178720ed0}}, {{cite:ab0584b4c81535389a36f2a5537fc1e8ae3cc619}} have been extensively studied in the recent literature. The difference with our setting is that these works consider a particular case of {{formula:d3429d7d-ef16-425e-bb95-a038351fdd85}} .
m
4452f3bc8f408530d87f284fcc9c2815
Since the aforementioned problems are intractable, relaxations of these problems have been considered. The problem of computing chordal completion that are inclusion-wise minimal, has been intensively studied, either to find an optimal tree decomposition with an exponential time algorithm or to find one tree decomposition in polynomial time. Over the past decades, numerous polynomial algorithms have been provided to compute one minimal chordal completion {{cite:a0a6b6b13e6d0114937df88bb218f61568e4545b}}, {{cite:bf0e9fd653ccc0209dde5d12cd3c4ca217380fe9}}, {{cite:26781b441adae51369a23901dc4e2ab1923af0b6}}, {{cite:771d49fc310c38e7fc0c47cce2e89d4520257f56}}, {{cite:98534d3d06759ebc06f931ce8067bb6f5a4cc624}}, {{cite:afe980a427caee109975717a6f82ec58a67b6842}}, {{cite:1e6b3df33cbf65b25a81d60b8760b11b0c833e5c}}.
i
121d45036d84296287821ec942610d0b
With the rapid development of the World Wide Web, most of the human activities are migrated to the Internet, such as game {{cite:826ea83411af48f51bd796e1f865703a25fe3c26}} and social {{cite:fccc536f00815f4b10ae2e4b216d2711ca4ae757}}. Online service providers often develop efficient toolboxes to improve our online experience by analyzing our activities. A popular practice is recommender systems {{cite:4a2cc3087e6bb89bd3d0979523ecd6e1fb047553}}, which analyze user behavior like viewing and purchasing, and then recommend the items to users so as to fit the obtained profiles of the individual users. Apart from the need of items, we naturally desire to make friends because friendship constitutes a critical part of humanity. In recent years, the development of recommendation systems is mostly concentrated in user-item setting {{cite:3e3a4afa6ca8ba20a7a449de21cdbf76ec508216}}, however, recommending strangers to make friends is also a desirable feature in many applications like players in games and dating applications. How can we suggest new friends to users in an online setting when their interactions are sparse, mostly unavailable in reality? In this work, we focus on online games and refer to this setting as friend suggestion {{cite:4f4173d0f7ca73cd6b0a6639b1e4c615c715ff93}}. {{figure:f15b39e6-1fb3-42b5-a9e8-768de672856a}}
i
0eaa337c4e631c4c82e2f6eda5d61af0
These errors are intrinsic to the data and current mapping algorithms. As seen in Table REF when using three different popular Burrows-Wheeler mapping programs for Illumina data on sets of simulated chicken read data{{cite:d83a70372c7a9640501a2a9044ac6e227655d485}}, {{cite:744814896a7600a214cf2daf5ceaf502ec7adfb5}}, {{cite:5357fd6adfe145d432474b473fd153e2902a962b}}, the results are nearly identical. These results confirm that alternative splice variants cause high/nearly constant false positive rates while incomplete reference transcriptomes decrease the true positive rate.
r
668cfddf611c6ecac334b159b41e67f4
The authors made use of the fastText C++ library (with default hyper-parameters, except where mentioned) by {{cite:5d2cd79d3b2637307154769ed4a974ad31590688}} to generate 8 word2vec models and 8 subword models from each corpus, based on the optimal hyper-parameter combinations demonstrated by {{cite:6a7fdfc2d49f69c2ec477c1dc0baeeac52865e38}}. Each model was intrinsically evaluated using the new Swedish analogy test set by {{cite:36e6db5abd6b9e97da85e1f29cddf7f2a0b59a80}} in a Python-gensim program {{cite:b85a373b7f5588c1880c89e4148dccbb43843a04}}. The hyper-parameters tuned are window size (4 & 8), neural network architecture (skipgram & continuous bag of words(CBoW)) and loss (heirarchical softmax and negative sampling). The subword models used lower & upper character n-gram values of 3 & 6, respectively.
m
07e1787feadca667b5c9364e14fe7c22
G+0.693 is known to be one of the most chemically-rich interstellar sources in our Galaxy {{cite:42675d632264eab9cf447af19c3a6cf153606c4b}}, {{cite:40efa402531affd063678e487741985e0bf96c8e}}, {{cite:dabd6ecd94b1d20128c47cd29c45992a056445b4}}, despite the fact it does not show any sign of high-mass star-formation activity {{cite:3a6ad9be1d8bed371c58daec6afe818328f94127}}. The chemistry of this cloud is characterized by the presence of low-velocity shocks {{cite:1f8a6a1bc6254ecbdaf2d2363413a0b9fc72c81c}}, which sputter the molecular content of the icy mantles of dust grains into the gas phase {{cite:7baf5be934c6b038bceb59b696755a6f4e8a9f20}}. The H{{formula:e17d0965-d4c9-48c1-9cba-5e9da865214d}} gas densities in G+0.693 are of the order of a few 10{{formula:89205cf8-b9fc-4a59-8c57-253b30e45d5d}}{{formula:0858ff2c-c0de-4e9f-98af-32d535d60925}} cm{{formula:8bf8b2a6-0d49-40ab-b51b-449fa6f5357a}} {{cite:3a6ad9be1d8bed371c58daec6afe818328f94127}} and the gas kinetic temperatures range from 70 to 150{{formula:7269442a-737b-4211-b647-233431efe6c6}} K, as measured using CH{{formula:1aa0720e-b55c-426a-ab7f-ec7d6a24626f}} CN {{cite:dabd6ecd94b1d20128c47cd29c45992a056445b4}}. Due to the low H{{formula:20142040-01e2-472d-b97c-3db0087ef687}} gas densities, the molecular line emission from high dipole moment molecules such as complex organics is sub-thermally excited, and their excitation temperature lies below 20{{formula:8d57f759-260f-4248-89d7-056424b6a792}} K {{cite:42675d632264eab9cf447af19c3a6cf153606c4b}}, {{cite:dabd6ecd94b1d20128c47cd29c45992a056445b4}}. This represents an advantage for the search of new molecular species since the millimeter spectra observed toward this source present rather low levels of line blending and line confusion. As a result, G+0.693 has yielded several first detections of new molecular species in the ISM including Z-cyanomethanimine {{cite:6434af8993af2c1e9c0d14907b3aacc51f1012b4}}, hydroxylamine {{cite:1ca39bfe0ed750871794d6f152e6f3ca7703c316}}, ethanolamine {{cite:7835141be9cacc34581307c8db8c28d41c35036c}}, cyanomydil radical {{cite:baa758cbd848c1dabf92b8c4be50c4629392dc69}}, mono-thioformic acid {{cite:8cf0ef0090916836452aa7eca0f24c0662228019}}, ethyl isocyanate {{cite:92928365567c4b72bf81d0c2af6c45f937ef3da6}} and PO{{formula:322a3ec7-8b77-46ec-b8d0-8af8551f01d2}} {{cite:6419f7df08ee951ba955c476b660894073021be0}}. Urea, an important prebiotic molecule {{cite:9ec56280e04d480d0cbb6453356dab8790cfb5e0}}, {{cite:5d98e901f0a963c08fa4655591621c77506ac2ac}}, has also been detected toward this cloud {{cite:598b76352fc8e429c2945172f4fee779f8117d9e}}.
i
a0d038abd7373bf480c42bddcd990e01
The number {{formula:dcc61581-d94c-49f7-b9dc-a461ea126d1c}} is the number of eigenpoints of a general tensor in {{formula:80ac4b82-9ead-4958-b45a-bdb7ca8a908a}} , as proven in {{cite:c58286be2f267608432002181ca35fd8c9541a64}}.
r
6e471cf237c8b59f7f618cfc20964acc
Lundberg and Lee {{cite:7ada4801ca775943f515f11ad1bbe0823094bd28}} propose a model-agnostic kernel approximation of Shapley regression values described above. They also demonstrate that both LIME {{cite:37447985b29b72001c0b9b1909993c373bb6cc9b}} and DeepLIFT {{cite:89a9a6a825be6ec7fc8d3b9d3fa25dcbc328e1f8}} are special cases of the SHAP framework that resort to model-specific approximations of Equation REF .
m
5239336e14b52ed85518be3dee803608
The fact that the condition {{formula:9cd8a84f-dc7f-473e-9ee2-5dbd5e5b3b39}} holds for curves with involution is known. In the CKP theory {{cite:31edd2b5219aace10e1f2e9744ad9e1f3b1fc0db}}, {{cite:288913801967f6b6e1adc3ceac9f9d851d959374}} equation (REF ) plays the same role as equation (REF ) in the KP theory. Namely, both equations define the first flows of the corresponding hierarchies (see details in {{cite:ac840d51bfce0e4b322a68e196d48492f6b4ed10}}).
i
a3e6f2c4fb7182296f93cf7181cb2c4a
Change in the polarization of laser field also affects the dynamic phase of electrons undergoing intra-band motion, ultimately affecting the excitation rate during multi–photon absorption. For example, circularly polarized lasers are also important as an ultrafast laser waveguides{{cite:9c724244b847cee88f4cce0affdada38a52b1963}}, and in controlling laser–induced nonastructure {{cite:f0d38ef9922493fa02cfdee590b76a535dd5e3c9}}. M. Kozák et. al. have reported that the ellipticity of the laser polarization decreases the excitation rate in diamond {{cite:cb8955d441fe9668c9214af57084a39bdad782d0}}. On the other hand, V. V. Temnov et. al. have reported that the electron excitation rate induced by a circularly polarized laser is twice that induced by a linearly polarized laser at the same laser irradiance in fused silica and sapphire {{cite:62f6610b45b65e2d17765947f10b9708f993b9f0}}. We have to study the laser-matter interaction with elliptically polarized laser in order to understand the above two conflicting experiments.
i
e4e37d0b5b53cd4c15af4f5a77b171ce
To verify the effectiveness of our proposed model, we conduct our experiments on three publicly available datasets for NER. These are CoNLL 2003 {{cite:60a9af5f62f33c44ffc433597a3d4fe3c241614f}}, CoNLL++ {{cite:3684e63a8140d011f5f0577216807b633b7e2c7f}} and OntoNotes v5 {{cite:86716a1574c3f6f26c06d2aca84efe3ca54c7c00}}. Experimental results show that the global embeddings generated for every word using KARL, when used for feature augmentation, can result in significant performance gains of over 0.35-0.5 F1 on all the three NER datasets. Also, to validate the model's generalizability and applicability in a real-world setting, we generate the model's prediction on random texts taken from the web. Results suggest that incorporating world knowledge enables the model to make accurate predictions for every entity in the sentence.
i
da2128ec96cdf94f14019613815a2224
To validate our study, we have compared our results with others in Fig. REF . It shows the dependence of {{formula:c2fae165-91d8-40c4-ae85-000ebc123159}} on system temperature for a fixed system size at zero chemical potential ({{formula:ecae0157-b207-451a-b1cb-418edd2a6a44}} GeV). The AdS/CFT lower limit to {{formula:11f5ea1b-66a4-4c9a-b60e-0a174196be0d}} (also known as KSS limit), which is {{formula:d02224e8-d431-41c9-bdf4-5a90a099200d}}  {{cite:bb36518a3b4a948e16ecc9a1ce758bbc014a6695}}, is also shown in the figure. It is observed that the {{formula:d029cb3d-6b8f-4640-bf76-5d174f97c899}} in the given temperature range of the hadronic phase, shows a near perfect fluid behavior towards higher temperature. Our study is in good agreement with the values of {{formula:14126146-ceba-436a-baf6-df5774fdab8f}} obtained by Gorenstein et al., where the authors considered EVHRG within relativistic molecular kinetic theory {{cite:079fd3c9afd6a0820f6d6335158d75aad315de67}}. We have also compared our {{formula:3b6cf775-8d7b-4273-ab91-67ba23eca413}} values with the results obtained from Chapman-Enskog theory, relativistic mean-field HRG and EVHRG formalism with Hagedorn spectrum {{cite:d8e29ead5efe77b8f580b776a5629d0bd0bd8da1}}, {{cite:85c02186b52d8fe6884fa39369a768b621a7cf77}}, {{cite:14262438b524a27170775df69952657d66757bd1}}. {{figure:08be5a74-3220-4dd6-9e47-a0edfad103de}}
r
d4ec6628e8571fd156460360b2d5fe4d
Convolutional neural networks (CNNs) have achieved state-of-the-art results on real-world applications such as image classification {{cite:7cdfe60c5732e5c8465ebc25a1b19a3b187a1926}} and object detection {{cite:3d7f0ce1f61d88087d294b0e5ed54d665f0f63ee}}, with the best results obtained with large models and sufficient computation resources. Concurrent to these progresses, the deployment of CNNs on mobile devices for consumer applications is gaining more and more attention, due to the widespread commercial value and the exciting prospect.
i
400615ba09834279dd2b7f424b0fb30d
For the existence of polynomial solutions of Heun equation, one of the parameters {{formula:eb8ebae8-e018-40ab-ac0e-90cda96e1ceb}} or {{formula:7ac2560d-0adb-4fdd-abfd-4d0e880ed40d}} must be chosen conveniently. For instance, for the class VIII Heun polynomial these parameters are chosen to be {{formula:e2f18e39-954b-45a6-9df9-87491ce2bffc}} and {{formula:8b3c7fed-30a0-456b-9976-74f6ea6c68af}} {{cite:10674d66d78c8b53f1a035687b40ba41794bfcaf}}. In the solution which is obtained by extended NU method, the parameters {{formula:da8673a2-71c4-4c9b-b31f-b94d1870d5b2}} and {{formula:834e4387-ed11-4a7a-82e2-e21b0af80acf}} can be determined exactly. Also the accessory parameter {{formula:cab4ea59-5c43-48eb-9349-0fa429568334}} is specified exactly up to a constant of integration.
m
d3de5b2bc9fca3e0937e323488340f88
Moreover, we test state-of-the-art deep clustering methods that learn deep representations and cluster assignments jointly. It has been studied extensively in recent years {{cite:8d2fe2da5846e7e6d53e091d2ba6917bf3e529ac}}, {{cite:db3471b62019661c9740359da4b453e06ad3659e}}, {{cite:63cae24c0880056a821276075095c8d7c5d8287a}}, {{cite:044c6073dd3e97ea710bf92ee08eec9659735ad5}}, {{cite:d73251348631ce73f77e639c87375fd425bc6df6}}, {{cite:366d872f9e732e9844b1ba452b34087e5946a7a6}} and demonstrated a strong performance over shallow counterparts in clustering object-centered images. We test a few methods, including IIC {{cite:044c6073dd3e97ea710bf92ee08eec9659735ad5}}, GATCluster {{cite:366d872f9e732e9844b1ba452b34087e5946a7a6}}, and SCAN {{cite:d73251348631ce73f77e639c87375fd425bc6df6}}. Since we have a few images per category, methods like SCAN that require a self-supervised pretraining may be suboptimal. In that case, we use the ImageNet pretrained model instead of the self-supervised pretraining. Implementation details are in the Appendix REF .
m
4ad5681687508fb3bd5ee971d0baf7ef
Since {{formula:f71dd79a-6d9a-44e1-95c8-932606ed3c59}} is {{formula:e37dc2d7-41ce-4bd4-bde6-21e075a78e62}} -convex for supports, Theorem REF (a) implies that {{formula:2de04d7d-6ba1-4b9d-88c3-af4532bfcf7c}} satisfies the minimum principle in {{formula:30acc5d3-adff-4a24-9e8f-61b7e9e2ce59}} for every {{formula:eb958bca-134f-40c3-bc41-771d8f8eca8e}} . Hence, by the hypothesis on the geometry of {{formula:b9464fce-7528-4472-87f3-b4948087a3e7}} and {{formula:57337f85-59d4-43f9-983a-31039986e10d}} and Lemma REF , {{formula:40d34c6d-8f62-4783-9f6a-a3e9a48b428d}} satisfies the minimum principle in {{formula:eff564e1-f9b6-45a1-be72-30ad52a48225}} for every {{formula:dfb21f57-e3c5-4abd-9df4-613859742ba7}} as well. Another application of Theorem REF (a) yields that {{formula:cddea934-3892-4ab9-bbed-012c6eb545f3}} is {{formula:6b6da00a-3d6b-4e70-8033-f74f5105bdc4}} -convex for supports. By Proposition REF , it suffices to show that for every {{formula:0ffa0d20-f295-47eb-9e82-d1702ab0b398}} with {{formula:931b1ef7-73e1-46bf-ad84-770a9d4cf9c3}} it holds that {{formula:44b1de6b-cca3-4b02-b9ea-64e0268cc69b}} . Set {{formula:fb998a22-7202-420f-8007-6e1f820a87c2}} . We claim that {{formula:24039de7-764f-420c-85f3-97b0a1876f14}} Once we have proved this, {{formula:2343e5d6-707c-44a3-937a-bff1243ec600}} (theorem of supports) implies that {{formula:33106062-6cf2-4757-916f-201965b78d69}} Set {{formula:56759220-3ab2-4f40-80d0-ff88583fe131}} and {{formula:cf26ae43-1dc6-46cb-9a26-0dc394855a32}} . Then, {{formula:e56058a9-7d75-4209-9101-97c7650987fa}} is contained in the union of the disjoint compact sets {{formula:c074ed83-2686-49c6-88c7-b91359ecbdb9}} and {{formula:039c9c9f-ca33-42e3-9398-65a5fd21d2d8}} . Hence, {{formula:3ed9cf33-203b-49c0-8fe5-be5d0d4c406d}} with {{formula:a44ce9a6-dbe3-478c-85f6-594294c3f2e9}} , and thus {{formula:4f2cd28a-d78f-4755-b50e-e3f3409583eb}} . The injectivity of {{formula:7ed9311a-c131-4552-b5b6-0dc6c892a1f7}} on {{formula:6e9490ba-a4b0-466a-9c40-71849f7d24e2}} yields that {{formula:4c69f06b-7d4e-47c7-877c-97e17a77d18b}} , whence {{formula:9eb9b72e-dbd5-4d2c-959d-db43dc2223c3}} . We now show the claim. Let {{formula:57844154-9163-405d-8bac-a29314e0ecee}} be such that {{formula:a0d6d8f5-1ef8-41f9-b54d-55ecd1a01d94}} . We need to show that {{formula:d73e4f9c-b2aa-4a18-9a9c-410968ee140f}} . We claim that there exists a continuous, piecewise affine curve {{formula:4e1de5e7-2cc6-4e4d-8644-5345c7377bea}} with {{formula:da106dfb-5892-4951-9f65-56e230800e31}} and {{formula:a002e0a9-2dbe-42bf-b923-0b3445bb8207}} . Let us assume, for the moment, that we have shown that such a curve {{formula:8f89dd98-29f7-47a8-aa49-4b5a3032230e}} exists. Since {{formula:c07bbb44-22dc-4d94-a110-69164f467f82}} , there exists {{formula:4342518b-d751-4987-baa7-1368235b2715}} such that {{formula:d8530c08-d7d5-4892-886b-70f53cbcbef6}} . Let {{formula:8298ec5f-3952-4a6f-8dc8-e0cfab020804}} be a partition of {{formula:9175d830-1583-48ac-a30a-94993c0f7541}} such that {{formula:1c44c8df-0054-48b9-8a72-cd66429048d1}} is affine in {{formula:6a1defb0-b4ce-4b71-ab79-b7f4d8fb346a}} for every {{formula:fa51622b-3edc-4a76-a423-b79cc15f74ea}} . Let {{formula:bd25b60a-5885-453a-83eb-4dc5c39b9573}} be such that {{formula:6f2fb0ad-48da-48fa-9d4b-ad133656612f}} and {{formula:f28a1000-f2af-4548-80aa-b67c4213cd5b}} . Consider the open convex sets {{formula:a9137e55-79ec-4a1f-8f9f-8ad80b7f2fbf}} and {{formula:6e0dc830-9d44-44a4-ab15-38afaaae735f}} ({{formula:83333657-12e7-4abc-94c0-d7c4a5544505}} is convex because {{formula:0e205228-0b39-4434-b161-910bc67d1b44}} is affine on {{formula:fd4f99d9-29ed-435f-8872-9023a1f50142}} ). Then, {{formula:abd08d7f-c168-48e8-b1bf-dfdf2a68b5f5}} vanishes in {{formula:547dfcad-e882-4ed2-906f-5ad085650f38}} and {{formula:e338b69b-f3a2-482f-936d-55380b742370}} vanishes in {{formula:fd1efe5f-6be1-4cbb-b3ff-ca55d2e95fe3}} . Note that every characteristic hyperplane for {{formula:dd481b31-01ee-41b2-9276-64cbad6f7341}} is of the form {{formula:4da70d8c-fd36-4acf-8238-7f025c64a73f}} , with {{formula:466f45d9-f376-47b3-ad8c-0bfcd1155d77}} and {{formula:b0c14a5f-8a64-4637-bf1d-7e36caff5056}} , Hence, each characteristic hyperplane that intersects {{formula:19151c7e-39a0-4022-b66e-6267438979c6}} already intersects {{formula:a4a5753d-0721-4504-bca5-50d99de39f50}} . It follows from {{cite:498fa95601d8a59ab6d1833e82adcb45e401b6a1}} that {{formula:47c79b4f-9662-4271-8354-3700163a380c}} vanishes in {{formula:feccbf9f-70a0-4aab-9127-9a00a9a62ef3}} . Iteration of this argument yields that {{formula:7fec9bec-56db-4660-8958-16d4d3385894}} vanishes in {{formula:8f110050-e461-4ad9-bc21-0fa1c1309d9e}} for every {{formula:1ecfad81-9546-4afd-ba7c-33f96a62a5e0}} . In particular, {{formula:cf8ed4f2-33ed-4a2f-a019-d9cc29f6c085}} vanishes on {{formula:fb5d6518-d39e-4784-83c1-ae0ac5f4b262}} and thus {{formula:50fab0e2-4da9-445d-acb5-662c575d16cd}} . We now show the existence of a curve {{formula:ce0d2fa1-57c4-4e08-a1cf-aecad68308da}} with the above properties. Let {{formula:526a82b9-1f60-4ba5-ab58-5078ef85635a}} be the connected component of {{formula:dfd50b60-b4d5-47a8-8013-1e7b65b55bda}} that contains {{formula:05a7d220-d06f-40f0-8132-0b3c5850b243}} . Then, {{formula:34a48545-fa39-4dfc-bf40-ca700f68799b}} is pathwise connected. If {{formula:2c0c8b26-dd14-4b8a-814d-c1851139cbad}} is unbounded, there is a continuous, piecewise affine curve {{formula:ffecafed-8635-468f-9884-fec7390cb93c}} with {{formula:f8722cd9-fc43-4498-98e0-8bfb2a88e154}} and {{formula:46b3cf29-a811-4968-ae1e-76cd7b52bd9f}} . In particular, {{formula:a2014646-e3ca-4a67-af01-a4e40218962d}} has the desired properties. If {{formula:3e2b5c79-f489-4e6b-be37-323da9463a06}} is bounded, as {{formula:0d50ceb2-8e64-412c-952d-d4d4313a5163}} is {{formula:db66e452-3e05-4c57-abd2-a12dd08eb1b5}} -convex for supports, {{cite:13861f865f5c78872f81061280c24c03f5ef4556}} and {{cite:1a8d245f73ba78ed18ffd78008c383a9a45ce42f}} (see also the proof of {{cite:7dfee61aab6362696af74ef697f4a2aa11591cb4}}) imply that there exists a continuous, piecewise affine curve {{formula:a98ab1f8-31aa-4dc4-9d26-40128658cfad}} with {{formula:2bea47cb-744e-4147-8042-09dab8628ef7}} and {{formula:8014b2e0-0c17-4f5b-b231-a77bf607632f}} . Note that {{formula:0458d749-035e-4410-8a04-d6795275816b}} . Since {{formula:449600b5-f2ce-4830-8d13-e2b877ed499b}} is bounded, we obtain that {{formula:4c66f225-3a31-4e7f-a0b9-5785d7d13cc8}} . Hence, there are {{formula:aa38b5ce-10c9-42df-a744-8b1f7ced39c9}} , {{formula:9e9a4bcf-b181-40fd-a919-74508a544868}} , and {{formula:42f6bf90-7ae0-4f8b-858b-58331d48d7d6}} such that {{formula:895c9df2-0598-469e-ac46-d021f26d4551}} and {{formula:b12c8af7-2484-428e-ac02-523a06a220c9}} . If {{formula:5bc7d1bf-cbcd-4e6d-a8de-009e451b6388}} , we consider the line {{formula:6ef776c6-9f96-491f-9347-952d5fa5e6a1}} with {{formula:3c05c0ab-2219-4f8c-ad21-a4c22c3f8f77}} and {{formula:c0124b33-17f9-4ae9-b389-c26c83ec0468}} . The concatenation of the curves {{formula:68b82e74-f1cd-41de-9ba9-de30b0dc0dfb}} and {{formula:8180db19-38fb-4762-8ae5-d4ccffade840}} defines a curve {{formula:c3b6d8e7-7084-4758-8845-a491137eb2cb}} with the desired properties. If {{formula:71f4a9c8-1da5-4281-af2b-b70b1e5ea5bc}} , we may assume that {{formula:b519f91b-1687-4565-8920-19bbd246fc15}} . Consider the line {{formula:a9103d5a-61b4-4064-ae70-0a648e06f346}} with {{formula:7244d1fb-09cb-4c61-ad52-8e95cdd15e4c}} and {{formula:a306888c-4c95-4141-bb26-135033fa9f5b}} . Let {{formula:ecfdd5d4-2ea4-4643-aa56-68e4e808a204}} and {{formula:e9ed73c9-4c85-4a9e-9ed3-ba5feae84ee9}} be the connected components of {{formula:30f84472-8f7e-4cf0-8a42-f4d0a1012684}} and {{formula:3ac764f6-584d-4655-8881-fba49b713378}} , respectively, that contain {{formula:35140653-5563-46dd-baa2-0a447257edec}} . Then, {{formula:4ec0393b-45e1-4f12-a802-59a1590b2c51}} and {{formula:4502180c-c8b2-4f52-94e4-b000f9305b37}} is pathwise connected. If {{formula:5dbed4bd-5f0b-4385-920b-a41db9999036}} is bounded, by the hypothesis on the geometry of {{formula:a7af6fcc-2e1b-4f73-95c9-f108b6d6b622}} and {{formula:85c08448-b813-4684-93a7-f8fb830f1343}} , {{formula:77faefaf-d1c5-4b1c-a640-e00cb2b27c16}} contains some {{formula:2e0ee72b-e76e-4499-9fd4-f24e709a5168}} . Hence, there exists a continuous, piecewise affine curve {{formula:63b18bcf-ca1f-4584-98a5-7e845a115451}} with {{formula:04dda4df-3f0f-4612-9b52-a792dfc554a6}} and {{formula:e7da70ca-6de7-4b65-9f85-d9404280fe75}} . The concatenation of the curves {{formula:1e71e69d-a110-43a7-a27c-c6bb818bfe4c}} , {{formula:92afda6e-d483-4452-842e-a3bf7632889d}} , and {{formula:4ad578b7-c3b9-4454-aa76-008004dcff27}} defines a curve {{formula:dfbec082-97ba-4922-a3b1-d0659354dac8}} with the desired properties. If {{formula:73a000ac-577f-4ea6-b804-df483dacad76}} is unbounded, there exists a continuous, piecewise affine curve {{formula:d8a6757c-467c-431d-9d0f-0e149c98aad9}} with {{formula:4cc63397-bf02-4e58-9c7e-ab5e51a2d20a}} and {{formula:b69a0c02-7c43-4057-9e0a-c694d3213c3c}} . If the range of {{formula:db68675f-3623-410c-b12d-fc3dc0013c75}} does not intersect {{formula:5a42f846-0d55-44b9-b2b6-e0e950ae62e2}} , the concatenation of the curves {{formula:2a4d919d-8dc7-4a87-a90d-1f935f065c2c}} , {{formula:9954414c-b9cc-413e-b2f2-ba42d4b9f18d}} , and {{formula:6720791a-7052-42f9-81c5-7f61e58d5924}} defines a curve {{formula:0e4555df-7ef0-430b-9434-02bb3339268a}} with the desired properties. If the range of {{formula:f248576c-dfe9-4931-8521-1f927f26ebc3}} intersects {{formula:60f798a4-c000-407b-ab17-bdc74f41e328}} , we consider {{formula:a75d84cc-23f4-44a0-955c-0e17948a24d4}} . By a suitable reparametrization of {{formula:f2b885aa-c1e0-41c3-ad05-265026965676}} , we obtain a continuously differentiable curve {{formula:eba3089d-169e-4ca0-9ac1-b4f9e2dd15be}} with {{formula:30d8fc41-133a-4367-859a-c9583bd43445}} and {{formula:d470217c-a7bf-499e-b80e-4c97b3dcbcfa}} . Again, the desired curve {{formula:f2f1c667-1543-4c29-99c6-446b16ac7b00}} is obtained by concatenating the curves {{formula:c5472ae1-1fe0-4ffe-8504-806f0a7adc8e}} , {{formula:eb5348e9-9369-49f3-94df-d1d9e5c61bc8}} , and {{formula:946eb539-bbb9-4850-a28a-e82da49e506c}} .
r
5eea0cee287a143be6e27cb0e58ecb5e
In order to study networked systems properties, it is possible to exploit a method allowing the creation of a random network by using a given degree sequence. To this end, one of the most common and used tool is the configuration model {{cite:a4dad8ee2321925714c65c66b60c06bcb1555778}}. This latter, defined as a generalised random network model whit a given degree sequence, is build up by means of a simple algorithm {{cite:ba6c928131a586727ed9b6488acdae88672041f8}}.
m
6de51a4b20cb209b8bd75a23fdf06318
The class is defined for each {{formula:e6dd65b2-902b-4264-b965-74dff94a7c30}} here we shall focus on the case where {{formula:167d33cf-c234-41e4-a5dd-9b18786d7c1a}} which may be generated by an {{formula:8cd504d2-8633-4786-9881-7fcf984f9556}} -stable subordinator in relation to the work {{cite:759d73a219457c510e936da3ec22713a6a41596b}}, {{cite:16c4ca67d0db72bf82d94c073bad4dd9a65d9c82}}, {{cite:13f1c54529ff47e98699cc6c824e0e5a9b7bd052}}, {{cite:1f662fc3cba9d4b5d6273892c98dffe16181d958}} on excursion lengths of Bessel processes. In particular, let {{formula:4c7c121f-3b7b-49bf-b47d-6fa9b33e1504}} denote a strong Markov process on {{formula:977fdacd-aad6-44aa-ae99-46a4145031ee}} whose normalized ranked lengths of excursions, {{formula:f3125a4a-9462-45d6-b78c-c431e7a05e3b}} follow a Poisson Dirichlet law with parameters {{formula:fd35e296-a501-4819-ba2d-f470fca5d52a}} , for {{formula:28b03d23-58aa-4f17-a693-fd67c943f563}} as discussed in Pitman and Yor {{cite:16c4ca67d0db72bf82d94c073bad4dd9a65d9c82}}. Denote this law as {{formula:ef96af15-0776-4614-a142-d9c0b658f24d}} on the space of mass partitions summing to one, {{formula:f8d81646-67eb-4497-87b3-65f51a80359f}} Let {{formula:036c6764-4680-4973-8311-9b995263ba4f}} denote its local time starting at {{formula:62803864-c49c-40c5-be2e-68b31a7b6235}} and let {{formula:8d3f1b37-d1f2-4592-9760-57840e9811ae}} , denote its inverse local time. In this case, {{formula:b760ae84-a818-4976-8b9d-5e0a4ce2e6ce}} is an {{formula:de7ec5bd-1f4c-4eb9-ae18-e11de40db927}} -stable subordinator. For each {{formula:ff4ddc47-2fbf-4109-8e03-094baf5f957b}} {{formula:261e5a35-123d-4b7a-ab69-fc1256b425f7}} where {{formula:11142570-18b3-407b-b84a-8578e31f0078}} is the inverse local time at 1 with density {{formula:ede3a01a-bf96-4787-8689-f2e9b5eac6fd}} and Laplace transform {{formula:7de6126b-6a7f-46a5-b2c0-c9acdc13a891}} Due to the scaling identity (see {{cite:a2deb1a05a8727803637d89ddbe84943e1a63fbf}}), {{formula:c902c60a-6c87-43b6-9118-05e064af73bc}}
i
8391cd30f48bd556de8d8aeed45fddd6
In {{cite:0d2ac08305a9478ebfcace0e38ccfedbe7c1bd52}}, the above bound was developed for the DA setting. We have adapted it to the DG setting by identifying “source” domains in DA with “seen” domains in DG and the “target” domain in DA with the “unseen” domain in DG. While the first two terms of (REF ) and (REF ) are quite similar, the main difference comes from the way that the third term is optimized in practice. The practical DA algorithm proposed in {{cite:0d2ac08305a9478ebfcace0e38ccfedbe7c1bd52}} ignores optimizing the third term {{formula:4d48a283-fb00-4ec9-bfd9-c724589a32bc}} of the upper bound in (REF ) since the second term of the infimum in (REF ) cannot be estimated during training. Moreover, the first term of the infimum in (REF ) is already captured in the first term of the upper bound in (REF ). In the DG setting too, since the unseen domain samples are not available during training, one usually optimizes the bound only over several seen domains as in {{cite:bc9161452b22fcbbfbf21775a9ec999ee410ce10}}, {{cite:ba2080dda7793ab633f16a5658aa7363cfa83c07}}, {{cite:6e72ecf9ada1fb9312986f745b027a5b6590e77c}}. In contrast, the third term in (REF ) measures the mismatch of optimal classifiers between domains and, therefore, can be practically optimized via designing a representation function {{formula:d5b5b25a-c198-4f08-b042-cbadcafe2307}} followed by a classifier {{formula:161bf21e-9580-4fbf-9bb1-6d7fe0f0c836}} that is optimal for all (seen) domains. As will be shown later, finding an optimal classifier over all domains encourages the use of concept-alignment algorithms. Indeed, designing a classifier that is optimal over all domains is the principle behind the recently proposed IRM algorithm {{cite:063aea776f3093a029aed156c4563e4db2657423}}.
r
7c11320e2523bb45c205dfdcfb7808d9
ii) to observe resonance {{formula:de1e7303-b1b9-4065-a5af-b14e7f3c2bcb}} in {{formula:79266f90-59ae-418a-ba10-5642f4525fa6}} {{cite:7b388abdf1f3c6dc577fbfcc8ee29644326c2be1}}. In {{cite:be3dc9b7f0bc2103f39041a1dc54724c4f5580e6}} the data fitting indicates that the enhancement is a S-wave Breit-Wigner resonance {{formula:854f68d7-e0df-4efa-ae51-62a15c06a83f}} {{cite:febcfc3c3048fecded35aadaca35c9a63a4a6df6}}. It has been estimated that the decay branching fraction {{formula:16ba8cff-2222-45e2-a489-a722f024f72d}} {{cite:a098253dbc62e0cdecc4c713d3edfeb32191a7a9}}. The decay mode of {{formula:e21092c3-1486-4a1e-9d33-7b52374a3805}} is due to the tail effect of enhancement resonance of {{formula:bcebca04-b9c7-43f2-a759-1c3ac42b0d5a}} near the threshold of process {{formula:14ece297-f3ba-4802-a179-d69befeb2e59}} , therefore the fact of {{formula:c2591346-12ba-4fa5-a9e1-8fa4c3924bde}} means the coupling between {{formula:dfcc9ada-61c0-4cba-a90e-27c0c68241c0}} and {{formula:c8e425c6-6da6-45f6-9a42-5251f71b359a}} is very very strong. The most natural interpretation to this fact is that {{formula:e08b8480-bbb7-4a82-acdb-3a34212c9838}} is simply a bound state of {{formula:711c4922-0409-4f47-b564-ab48fe95ac9f}} . Namely, {{formula:81b0e67b-7e9b-477f-a45e-69fd58213d9f}} is a {{formula:4101a2cc-d4e0-4331-b244-5f7a740d4f73}} -baryonium molecular state {{cite:9ef7836aa640b2cbe7649bb4f7534237f4a751ce}}, {{cite:82cd86c770b9258a4b9da094204f03acdc1dd198}}. In another hand, the major decay mode for {{formula:6fedeeb4-c12f-4731-9395-9b6d8d41047d}} is {{formula:f90b7680-ecbc-4700-a7ec-821a98a6ab24}} observed by BES {{cite:7b388abdf1f3c6dc577fbfcc8ee29644326c2be1}}. It indicates that {{formula:cd794a4d-d269-4ede-a6ce-29311fd7b777}} is a molecular exciting state of meson {{formula:10a60ae3-7e2c-463b-a727-1015e093174c}} {{cite:82cd86c770b9258a4b9da094204f03acdc1dd198}}. Consequently, the quark component of {{formula:1859faab-cdb9-413c-a8d6-2780bc2f8022}} should be same as {{formula:63359782-192f-499c-9c60-544cd2f3d48f}} , i.e., {{formula:8762ef9c-af1d-436a-89f8-da04d2ae2021}} would be a {{formula:4d2af743-276c-4ca6-852f-9988a1a12cda}} -baryonium meson, or a meson with large weight baryonium component. BES observations {{cite:be3dc9b7f0bc2103f39041a1dc54724c4f5580e6}}, {{cite:7b388abdf1f3c6dc577fbfcc8ee29644326c2be1}} provide evidence to this multiquark picture for {{formula:0e45b8b1-1209-46e6-a9ae-174a6b71654f}} meson.
d
5393ac52c9780ddc6a3c099bf723d106
Future Link Prediction: We report the tranductive test AP scores for future link prediction in Table REF . Unlike previous work which focuses on {{formula:31d42dbb-b629-43be-8c05-1f23a60e8b23}} , we evaluate all models under {{formula:0709738b-ea0a-418f-8bd4-4d2023f9818a}} to test their medium- and longer-term forecasting capabilities. Unsurprisingly, all methods degrade as {{formula:e7f12e2f-0d9f-48c4-a518-4edd8b0c4e1e}} increases. Our model significantly outperforms all sequential and message-passing baselines for {{formula:8aea1255-f661-420b-aaa7-1ed77bc4941e}} and is on par with SoTA (CaW) for {{formula:1a3c95d6-e513-4498-934f-8ee24a621a93}} . The gap is particularly large on the UCI and SocialEvol. datasets for {{formula:13cff786-33b9-4dc0-a765-dbf02f2c20b3}} , where DyG2Vec outperforms the second-best method (CaW) by over {{formula:fd16db4e-631f-4ac7-b0f5-ecc96499d754}} and {{formula:5635c80b-444b-4445-b204-3792a62e5719}} respectively. Interestingly, while SocialEvol. is the largest dataset with {{formula:94655eec-8857-405b-8339-1e35c80a759d}} edges, our model is able to achieve this performance while only using the last 1000 edges (See Table REF ) to predict any future edge. This further cements the findings by {{cite:8e9fbc65436c2d69e0ea47ac12c9cf23a4e1552a}} that capturing recent interactions may be more important for certain tasks. Our window-based framework offers a good trade-off between capturing recent interactions and recurrent patterns which both have a major influence on future interactions. Appendix REF contains results in the Inductive setting which show that DyG2Vec is competitive with CaW while using a small fraction of the computation (See Figure REF ). {{figure:08c2a778-7731-4262-93ac-0cc9d6bba8b0}}
r
81395294c5f47ae9341da2e9e8978512
Recent studies {{cite:7b7bbce3424d111bdcc1e3cad40a23c538110718}}, {{cite:01f6cd4d4da207b1bef1939575fe3222955eefdd}} have proven that despite different propagation processes of various GNNs, they usually can be fundamentally unified as an optimization objective containing a feature fitting term {{formula:037ab3f0-6e31-4fab-9435-cfb32bb54dea}} and a graph regularization term {{formula:3fb2ccf8-3ec5-4403-8bf5-a7dab6a723fd}} as follows: {{formula:7f117c1a-0a83-46b4-b91a-914fa281f017}}
i
1c50a1eab6e8de0aea3e5694ebc0ec24
For resource unconstrained PDA, LoCO-PDA is compared against ETN {{cite:4b0496cc928fc3256c05161a06207d5b6d1d61f2}}, IWAN {{cite:f7531315c5a198edd095aa04881237f1b069c744}} and PADA {{cite:439155183a4f446343ce907c8d0b4c6a456c4886}}.
m
af6c8aeb6c04cdee0a63197956ff7b65
Recently, we can easily obtain high-frequency data such as stock price data and life-log data (blood pressure and EEG, etc.) thanks to the development of measuring devices, and statistical inference for stochastic differential equations based on high-frequency data has been developed. For parametric estimation of diffusion processes based on high-frequency data, see for example, Yoshida {{cite:c1325615fd1318056180f18468e929347b279039}}, Genon-Catalot and Jacod {{cite:d2d2533002e427c7ed15d9bef7a3eb9f17cf6e02}}, Kessler {{cite:d8125e43582d1295357bc21924dff3c3028ada93}}, Uchida and Yoshida {{cite:541fe5a117d7e3fd33ec8bcb0e712bc7ccd0af3f}} and references therein. In financial econometrics, the factor model for high-frequency data has been extensively researched. In this field, parameters and the number of factors are estimated by using principal component analysis for high-frequency data (Aït-Sahalia and Xiu {{cite:718a94832d667f883f3e90d4ad5246a3cf6e3322}}) when the factor is latent; see, e.g., Aït-Sahalia and Xiu {{cite:32e55dbf5449853b7b3f9d9095a25e3ffb945b2f}}. However, these studies are based on high dimensionality. For a low-dimensional model, the estimator does not have consistency; see Bai {{cite:90a2a16429cbb63bc47b835d0e8e1bb28e2ec6ef}}. On the other hand, Kusano and Uchida {{cite:adc1c407792b0d0670bbf988732fb8bb259ee58f}} proposed classical factor analysis for diffusion processes. Their method works well for a low-dimensional model. However, to the best of our knowledge, there have been few studies of SEM for high-frequency data. Oud and Jansen {{cite:11cb897f1ec4ee41e486009ed0595cd17d14889e}} and Driver et.al. {{cite:894307adeeb6d5ad3197247618e451cfc59dfdc2}} considered SEM for stochastic differential equations. Note that their model differs from the model in this paper. In the field of causal inference, Hansen and Sokol {{cite:43f2693704a83f7d6528f81b70e7db0f5f07cdf7}} studied SEM for stochastic differential equations. However, their model is the path analysis model, so that their method cannot describe the relationships between latent variables. Note that these studies do not assume that the data is sampled at high-frequency. On the other hand, we propose SEM for diffusion processes based on high-frequency data.
i
7d3229bab14db834c960a69a98c50b63
General relativity is the most successful theory of gravity, which could explain a variety of observations, including the bending of light, perihelion shift of Mercury and the recent detection of the gravitational waves. Despite this great success, there remain some issues with the general relativity which are not yet resolved {{cite:8029038b586d0842c0d63efb455bf60fc1df8d55}}, {{cite:7f0047a1bfc22ba6eca817bb4520ad92c747c4d5}}, {{cite:ed99bc652ddb33e7411ed874392852b543f1fc8b}}, {{cite:aa90599d3c10568a7f57a2a46f1dfd4c767e2e2e}}. One of the important issues is the presence of singularities {{cite:8029038b586d0842c0d63efb455bf60fc1df8d55}}, {{cite:ed99bc652ddb33e7411ed874392852b543f1fc8b}}. It is generally believed that this issue could be resolved by formulating a quantum theory of gravity. But, Since general relativity and quantum mechanics are different at the fundamental level, formulation of a quantum general relativity is a difficult task {{cite:aa90599d3c10568a7f57a2a46f1dfd4c767e2e2e}}. Meanwhile, the deep connection between gravitational dynamics and thermodynamics motivates the emergent interpretation of gravity. Such a connection was realized after the discovery of black hole thermodynamics by Bekenstein and Hawking {{cite:aa2936fd343eb891c3d7264e4e51a30241afec48}}, {{cite:5930c00e94e6ff45b4270640a73482e42b284e86}}, {{cite:4ee4105e608dd37171c7c64cf848f8ba1384673e}}, {{cite:432eb99d0ca8674584a8ad2b2f398fde8a7d0236}}, {{cite:3b2ddb6631f0898a29e80ecbcca5f69ec39c11ba}}, {{cite:42c6b64fed60a99525c8faacfc11da38aea68641}}. A significant step in this field was put forward by Jacobson {{cite:28e5792301ec366d7ed6fc8910a611d9d566e43f}}. He obtained Einstein's field equations from the fundamental Clausius relation on a local Rindler causal horizon. Following this, various schemes for relating gravity and thermodynamics were discussed in a variety of gravity theories {{cite:e570f6872d4da2bc241fab6a0ab0c242ba6b0b2b}}, {{cite:fb40ded8cd02634d5eee2f4f8b4e396a85fcdb70}}, {{cite:bf51b1a9913845efd4062a2e6f8973ee92017642}}, {{cite:ee444616c607599ff9fd056931e4bb0d9b77fa21}}. This connection of gravity with thermodynamics, motivates to consider gravity as the thermodynamics of spacetime. But thermodynamics, is an emergent phenomenon, which deals with the connection of macroscopic variables like, pressure, temperature, volume, etc., which doesn't have any existence in the microscopic world. This in turn implies that, gravity also could be an emergent phenomenon.
i
5fb5224ef58dcd0ac95971695b7ae35f
This performance difference suggested the possibility of a combined, fused classifier of our proposed relational classifier and the more common CNN based low-level feature work of  {{cite:07ae01524cce46846388400f5d26db80bae09247}}. We combine our model with the predictions from the baseline CNN, the pre-threshold probability of the baseline model is summed with ours before selecting the overall highest. The Combined approach improves on the current state the art {{cite:d17acc15b745f4c4cc3c3e9cb33ff4c25197a452}}, by 2% across the 1600 videos. Similarly, when comparing the performance of the fused model and the current sota {{cite:d17acc15b745f4c4cc3c3e9cb33ff4c25197a452}}, there are significant differences across categories, for example, for actions 14, 72 and 74. This demonstrates a substantial difference in the type of relationship that the approach can capture with the human-like approach. {{figure:7b905de7-85cb-42d3-8cec-7937a80958c8}}{{figure:bc569dee-c3ff-4320-8fa5-369ecb8b1fef}}{{figure:52ed83ac-9c13-4f5d-9942-d561293ec052}}
r
dbd7142c3cdad1c52df1a75de5a772e6
Our results may depend on the model setup, in which new blood vessels are created as endothelial tip cells move from left to right. In the future, we may explore the use of extended persistence {{cite:f19e97181b1d189a18aa6faeaa084cfead1b5c6f}} and/or PH transform {{cite:df310d088b240f555ee46a78722e23535b58d828}}, which allow consideration of multiple different directions in the topological analysis. If the vessel network grows radially, for example, then radial filtrations may be more informative than the LTR filtration {{cite:c48972659afa3d7d7a5c5161f8b0c42481173a88}}, {{cite:b6267ddf7162eafeb4dabb15d7388b800d85cbab}}. Classically in PH, topological features of short persistence are topological noise, yet there is growing evidence that these short features can provide information about geometry and curvature {{cite:1fde2654071028f722854cadc4780d9e3a720942}}, {{cite:b6267ddf7162eafeb4dabb15d7388b800d85cbab}}, {{cite:f93c9f5f3e5a543d917136b9f35df3612e1b8054}}, {{cite:9e7a4b62fbbf93aa7426e6658ed1803ba1b43116}}, {{cite:991dc4c912cc547176279131a21d41db28dd42c5}}, {{cite:d753690f95bb658816c8afc19b7f49eb14095f6b}}, {{cite:56cc7b46581faef6828bfc6ed38ee9f0af536755}}, {{cite:d2237fa1c2359f0968ffd4d7d04a2a090b3bdcb1}}. Our results using persistence images with unit weightings, rather than ramped weightings, also suggest that short persistence features may be informative for distinguishing vessel morphologies. The spatial resolution of the output binary images that we used for our analyses was the same as that used to generate the simulations, enabling us to distinguish the presence and absence of individual endothelial cells. In future work, we will consider finer and coarser binary images to investigate how the performance of the methods depends on their spatial resolution.
d
f9e6e2ef8946ba84f20b8750b9ea4296
Fine-tuning is the dominant technique for using pre-trained vision models to perform downstream tasks, which has contributed towards significant advances in a wide variety of computer vision problems {{cite:7b85e0aee43d97c8b17c57e0fcb7db199fefcd3a}}, {{cite:6f3b89cae56a8deb1c9e47d939ec87ba7dd0b0d1}}, {{cite:7c3f9212985aa91dafc709738aab77a1c43f2e1b}}, {{cite:87c84b8a29b0bf653fef919e09e99ced8080acd6}}, {{cite:ba8784459750b8b3a8cd9cba254cfcf9b75f9a7d}}, {{cite:5ad60854725155869a2d4b0d719ee2a629c25aef}}. Its standard practice is first to pre-train a general-purpose model on a large-scale dataset (e.g., ImageNet {{cite:4c6b233942b21669614649f5db4b05b3c7d4f606}}), then fine-tune the entire pre-trained model on downstream tasks. Although the achievements in the literature are brilliant, the fine-tuned model is still quite intractable to handle practical downstream vision applications for two main reasons. First, it requires updating and storing all model parameters separately for each downstream task, which is prohibitively expensive for the current ever-increasing vision model capacity. Second, its effectiveness heavily relies on high-quality downstream data, however, realistic data encountered in practical scenarios probably contains various negative distractors. In Figure REF , we provide an empirical study of fine-tuning along with other popular tuning strategies. Though achieving decent accuracy on CIFAR-100 {{cite:bbf14a2a13ee6114a48b072a1b7e466f6349dee9}}, fine-tuning encounters devastating damages on various pre-trained vision models under distribution perturbations, e.g., more than 12% validation accuracy drop on long-tailed CIFAR-100 {{cite:a92ae0736fea59cd008ca6abf2523745dfe883ff}} with imbalanced ratio 100 over their performances on the original CIFAR-100.
i
a2159ecaeb01c9851bf25b269a493a05
Second, it is expected the topological phase transition is second order {{cite:b973b14934d7180dd60bbb8398d3412e85591b0f}}, {{cite:f7bd2d27828ef38fa5260cfea328115c89b9a0d6}}, {{cite:ea9293b47c6eb99ee4db46a1814dfaeb1e05fe75}}, {{cite:231b640253b202ae40c1bb9799b7cc74509f6e8a}}, {{cite:d630faf9c7262e52e93d1f2be37f77f7b69e9628}}, {{cite:58c1a174d38c3c18f1d36bfa7a8ef282ee857d53}}, {{cite:5891b2b1546a42d86da23221ea8f690b875126b3}} if the number of the CS brane is {{formula:8b5c63f5-643d-4afd-8970-db4394d84fdb}} . This can be achieved by taking into account the backreaction of CS branes. However the number of CS brane is given by {{formula:bc90ba7d-e88d-4094-a969-543789d0fa85}} which relates to the boundary value of {{formula:21b6a25b-255f-49f0-82d8-67af9c956eee}} in our current setup. So the bulk dynamic could not involve the backreaction of CS branes in this work. The valid way to include the backreaction of CS brane is to solve the IIB supergravity action with a fluctuation of {{formula:72593185-ae61-4926-abba-ee8c05746c9c}} sourced by the CS branes then the next-to-the-leading-order contribution in the large-{{formula:42bfc6ab-d80c-4e8b-991a-eff88e28c268}} limit to the vacuum structure would be able to analyze in this sense. However, we would like to leave this for the future study.
d
f24847671bffc3e4162943fe38ee4a31
An important test for theories of star formation is that the successful theory needs to reproduce the fraction of binaries in dependency of the mass of the primary stars. Most observations have shown that the fraction of binaries decreases as the mass of the primary star decreases. This appears to be in contradiction to the constancy of the fraction of binaries near 100 percent for all primary-star masses at birth, which is assumed here. The observed correlation however arises naturally from this constancy through dynamical processing, as has been shown explicitly in previous work (figure 7 in {{cite:12e03e453ab90c8de39a1759b515b86b3c22e062}}; figure 6 in {{cite:860e44a173b262e88f9ae644735cc7c6b4ba10d4}}; and as a basis of prediction in figure 3 in {{cite:43a9c6bb09933ab71cd27ba67f327963dc5d1183}}).
i
f7bbd3b14cab17a26a88b6bd55e441fd
Hate speech {{cite:e4fb9ca19140d8c453763182019ce01ae563610f}}, offensive language {{cite:73aa876371c886fb474c9004e0b9d81f5ba52198}}, {{cite:6d24a5e7ef041ec8b73ad2596fb5de1046e38fb2}}, abusive language {{cite:e55d764ee358cfeaf13029d3e5990a6f3d742c08}}, propaganda {{cite:de96e8aacb31694e0702aec76fcb5284d4f121a9}}, cyberbullying {{cite:9e8c42f7eee850c994bc0af9c315ce7a3e132b8a}}, cyber-aggression {{cite:33be21affb99382679cc88e583c82663770def3d}}, and other kinds of harmful content {{cite:3e25b2ef1a55c58f48882487499156b4fa6f2d75}}Disclaimer: This paper contains content that may be disturbing to some readers. have become prominent online. Such content can target users, communities (e.g., minority groups), individuals, and companies. Social media have defined various categories of harmful content that they do not allow on their platforms {{cite:739bd16f17d59bcbc56468733239c3e46b869135}}, {{cite:7b1bb5d9547c54d5765d37fe08d78bddb19958bb}}, and various categorizations of such content have also come from the research community {{cite:7c20447e40d76e452955b7338346f0ce2c6e4c68}}, {{cite:e65a2848700b6bfbe9c8e6d927412730318ee797}}.
i
a612a6963b16990e58228b5297638b53
We conducted extensive experiments on CIFAR10, Speech Commands {{cite:2f2fbb866cf7db5b4d4f37d49795fe280939f62f}} and FEMNIST {{cite:8d1e4c9dbe8adc66af7e471a99d51f8b573df360}} datasets. The CIFAR10 experiments follow the same experimental protocol as for baselines experiments. The three local sparsification strategies are compared with various mask ratio {{formula:f587b2be-ab13-4b0f-89e8-1c789bfea7ad}} and to vanilla SWAT without ZeroFL. Similarly to results obtained in Section REF , sparse training performs better with exponential learning rate decay. Hence, all setups are investigated with this scheduler. Table REF reports the test accuracies achieved as well as the gain in communication cost when applying ZeroFL. {{table:fe2693fa-c1d5-47ec-a59d-f39b6b937440}}
r
b30d4b46e6ba53e5c5a28d8aefbca67d
Next we will explore the relative contribution of low- and high-frequency phonons to the heat released into the system through the contact region. In Fig. REF we plot the phonon spectra {{formula:c084a7f4-9068-44da-b120-bbb13dc3174c}} of the interface oscillators at the left and right sides of the contact for both the adiabatic driving limit, {{formula:d40e856d-5b63-421e-915a-40d34264974f}} , and in the thermal resonance regime, {{formula:f4f8bd36-f3a8-41e0-9ca9-14b878f923c3}} , which corresponds to the maximum heat flux {{formula:f1e9a9d5-a72d-45f0-a120-4efc173d65b3}} of Fig. REF . It is evident that the spectra in the latter regime have almost twice the spectral power as those in the former, which results in a larger overlap in the low-frequency range of the thermal resonance regime depicted in Fig. REF (b). The energy transport into the reservoirs goes through the phonon channels determined by the imposed thermal bias since the structure, unlike the magnitude, of the spectra remains largely unchanged. The results in our Fig. REF can be understood if we recall that there is a critical temperature {{formula:0a07a239-35a1-429b-bcb7-b6c65657ff4c}} above which the kinetic energy is large enough to overcome the on-site potential barrier, hence the contribution of the on-site potential can be neglected. {{cite:1966ea435611fc385f52c07c0f77d574e434faeb}}. In our particular case we have {{formula:5c12eb9d-f767-4525-8af9-4b35d238d864}} for {{formula:ca910efb-7929-4d58-ba15-db03b20b3e8d}} and {{formula:2260fad5-d0b6-47fa-bc72-ace46e1da21c}} for {{formula:dcb0da55-85e6-4852-881e-b8812e4be2b3}} . Thus both sides of the system are in a temperature regime, well above their respective {{formula:e42048f1-a63e-4234-b166-fde0cc3c468f}} values, wherein they behave as harmonic lattices with a phonon band of {{formula:6459df58-a2a4-4581-bb30-e7080d2481b3}} composed mainly of noninteracting phonons which gives {{formula:55bddc33-4d5c-4bec-8ef3-aa9cb5685529}} for the left oscillator and {{formula:19aff044-ce18-4ff1-a694-d75a303b20f1}} for the right one {{cite:1966ea435611fc385f52c07c0f77d574e434faeb}}. In the weak-coupling limit ({{formula:3d13c7c1-592b-428e-925e-effb6f2867c3}} ) thermal resonance can occur only for frequency values in the overlapping region of these phonon bands, which implies that {{formula:c0d91ea7-634a-4a08-b8e4-c01dd34ec4fd}} ; our result {{formula:709270c5-0b5c-42c4-ab51-33a26cb79b3e}} is in good agreement with the above estimate. Therefore, the net energy flow from the external source into the thermal reservoirs is accomplished by the external driving due to its interaction with —and ensuing alteration of— the phonon bands activated by the thermal bias imposed at the boundaries. {{figure:0162b10a-4747-45b9-8599-339c98e0e90f}}
r
fa476af4ca5484b66e781996beae7a75
Several directions have been taken to understand these phenomena. The interest in the stability of SGD is one such direction{{cite:1cb95d4f6671046914cd3c80b93baab9e0bff9d6}} {{cite:b32444282e462a346976462b5720956be3ce61d0}}. Others have proven that gradient descent can find the global minima of the loss functions in over-parameterized deep neural networks {{cite:e629e089142cf9545e08303f0bb4603a23c23719}} {{cite:094c4219b1b5a4c14c2105b8e5b8ee00efe76e82}}.
i
7e1dcc15f8667527ea248b0d37130025
We see that our approach provides competitive performance, both at 100 % of the labels, as well as there is only a small drop when reducing supervision by factor 20{{formula:c2f99fd1-9900-44b8-9340-a97780d12146}} . Our mAP at 100 % of the labels is better than both variants (with and without color) of 3DSIS {{cite:74962f2eb1f3b5fa9d5097a68ab78a568913f06b}} from 2018 and similar to MTML {{cite:6eda903423ca9b30f1e3d8e2af24302af2638520}} from 2019. VoteNet {{cite:a629b409ce78f3e4621d23f7c745fcc579143920}} and 3D-BoNet {{cite:a503ad485dbc9bff5122f8d266c9ea56aca5d58b}} are highly specialized architectures from 2019 that have a higher mAP. We have included BoxNet from {{cite:a629b409ce78f3e4621d23f7c745fcc579143920}}, an ablation they include as a vanilla 3D detection approach that is similar to what we work with. We achieve similar even slightly better performance, yet at 5 % of the supervision. In some categories, our approach wins over all approaches. We conclude that a simple backbone architecture we use is no contribution and cannot win over specialized ones, but that it also is competitive to the state-of-the-art. We should note here, as we do not carry out Semantic instance segmentation in our network, we did not test on the official test ScanNet benchmark test set. Instead, we reserve 20% of the labeled training scenes for testing.
r
711a07ce7275f46e31e04d3b60635194
The argument by Misner, Thorne, and Wheeler {{cite:4ee4f13e3af8d0161a5ef7503ac267e029e7f895}} begins with what the authors stress is a definition {{formula:00ee1b02-6961-4dd6-96b7-7d1fabc7f59b}}
d
d1d0caced36e5f49733e439a8fe853a5
The variation of the in-plane London penetration depth, {{formula:113aa005-19b8-451f-b742-fe9bf544dfef}} , was measured using a sensitive self-oscillating tunnel-diode resonator (TDR) described in detail elsewhere {{cite:eaa999c610a743af2e9c0f8709ec681730c84a65}}, {{cite:f24888a90d5f324de056d0fd4be258bb4cd7f852}}, {{cite:22c3f8d71f46bb361afe01f489b8a55f84ea59ad}}, {{cite:21215025f97f2414030d6f45d0bdc9ada77f6ac7}}. In brief, the TDR circuit resonates at approximately 14 MHz, and the frequency shift, which is proportional to the sample magnetic susceptibility, is measured with precision better than one part per billion (ppb). The coefficient of proportionality that includes the demagnetization correction is measured directly by pulling the sample out of the resonator at base temperature {{cite:21215025f97f2414030d6f45d0bdc9ada77f6ac7}}. This technique was developed specifically to detect minute changes in the London penetration depth and is now considered one of the sensitive tools for studying the anisotropy of the superconducting order parameter {{cite:586bbe8c736f39ea7352ddbea76fa423899aff33}}, {{cite:21bdfdad444278976076ba1d422838696c90554e}}, {{cite:461bbeb9769a1150f0cb9c98a99b881b35c42d51}}. We use this technique to determine the superconducting gap structure, as well as to show that we do not induce magnetic states with disorder, and that our crystals are very homogeneous.
m
13c64d6d0b11df0946210d5c46ea7db7
Generative latent variable models have great utility in scientific and clinical trial analysis to improve hypothesis generation and experimental design {{cite:b9bdab54613f6f6093251828191f5b589dea0e29}}, {{cite:aae054476c6f2ebfcc7571c64e7521a07dcda82b}}. This scientific and clinical utility often depends on two goals, obtaining an accurate representation of the data and ensuring that the latent representation is predictive of an auxiliary task. A commonly used inference method, the SVAE, has been previously used to achieve both of these objectives. However, this objective function induces a previously-undetected bias in the encoder that hinders scientific utility. We have shown, both on synthetic and real data, that the theoretical bias in SVAEs corresponds to a detrimental impact on learned representations in practice. To address this, we developed a novel inference technique that allows for supervision of an auxiliary task while maintaining a generative representation. We demonstrate empirically that our novel inference technique achieves both scientific objectives without bias, and demonstrated the efficacy of the proposed methodology in relevant neuroscience applications. Furthermore, we have provided two relevant extensions to our methods that address critical needs in the neuroscience community.
d
16c44d48858859dee7a14f0086effce5
These are all the minimizers of the Sobolev inequality, up to scaling. There are many interests regarding to the stability of (REF ). From the perspective of discrepancy in the Sobolev inequality, {{cite:1e59a8f02a3bffe5ad225c0c0dca278f620aeeed}} gave a quantitative estimate near the minimizers, that is {{formula:5dfe6adb-0f64-419e-afc2-59cd72779721}}
r
febf6a559c1a2f6ee149e921b4cac797
With Figure REF , we have demonstrated the overall superiority of our proposals with respect to a common penalty framework in group-wise recovering of sparse precision matrices. Nevertheless, when it comes to performing the analysis a single value of {{formula:cf3d5c3c-7a97-4ac4-8e49-f075afd80aae}} must be chosen. Providing a solution on how to select the common penalty term goes beyond the scope of the present manuscript, and we therefore rely on previous results {{cite:aa11f13dbd75978704056617db803c85f54b3b5f}}, {{cite:b0508ac4c219ce313ad9fb82d9e0f76bae60085e}}, which propose to select {{formula:acc94a4a-25ef-47d4-82fa-45212998d016}} by maximizing a modified version of the Bayesian Information Criterion (BIC): {{formula:c5b00f87-2aeb-4655-994a-88503e39fe82}}
r
98ddbbf62b1ebc24aafeca4b0d67e15d
Overview. The architecture of MVSFormer is overviewed in Fig. REF , as the seminal MVS pipeline in {{cite:f8399a656085914c5fda56484e39bb92b4e436d4}}. Given a group of {{formula:1a38f012-0311-4e77-bf2c-0ffa5b86493e}} images with different views which contain reference image {{formula:ca905d3f-6030-4a02-a0ac-25ef98a1cd41}} and source images {{formula:74a7aab9-0d3d-49b3-ac4f-934ace421a92}} , as well as the their camera intrinsics and extrinsics, MVSFormer learns feature representation in feature extraction (Sec. REF ), enhanced by the plain ViT– DINO {{cite:17d85d8eff01272bd820504317b1ac9d3d9deb42}} (Fig. REF (a)) or the hierarchical ViT– Twins {{cite:5e7f7bbfbbe6c3188a4194126f73d35f68bbac20}} (Fig. REF (b)) with several novel training strategies (Sec. REF ). Then the multi-stage cost volume formulation and regularization are presented to compute the probabilities of coarse-to-fine depth hypotheses (Sec. REF ). Finally, cross-entropy loss is employed to optimize the MVSFormer, while the inference is made on depth expectation (Sec. REF ). {{figure:36172b56-3401-4f30-a4a7-05b3b6c5270a}}
m
c587c1b46f39aa600748a68e3c3abab6
We remark that in the convex setting, theoretical guarantees for large-scale second-order algorithms have been established (e.g.,{{cite:dacc682bdc01e38f568f38a4e969fcc3e2384558}}, {{cite:9b45ea59c27a021db978a920a89f9d73e12c454e}}, {{cite:ee3046b3763edef0600f0891eb952541fbb6a42f}}, {{cite:3d893fb0bac53f4b63d14a078ab2746335aa994d}}), but such rigorous analysis in non-convex setting was only recently proposed ({{cite:86975ed719b93149fcacca3f5880c39d1c930860}}, {{cite:92f437e69e698fee1f06b4c1dff4d96fd0d93a43}}). Our algorithm bears some similarities to the NewtonSketch algorithm of {{cite:9b45ea59c27a021db978a920a89f9d73e12c454e}}, which also incorporates sketching into second order Newton methods. A key difference, however, is that the algorithm of {{cite:9b45ea59c27a021db978a920a89f9d73e12c454e}} works only for convex problems, and requires access to {{formula:ed7928f3-29b3-4acb-982c-6e2baf2c6cab}} (i.e., the square-root of the Hessian). Most importantly, though, {{cite:9b45ea59c27a021db978a920a89f9d73e12c454e}} use the standard (black-box) Sketch-and-Solve paradigm to reduce the computational cost, while this approach incurs large computation overhead in our non-convex setting. By contrast, we use sketching as a subroutine for fast preconditioning. As a by-product, in Section we show how to apply our techniques to give a substantial improvement over {{cite:9b45ea59c27a021db978a920a89f9d73e12c454e}} in the convex setting.
m
a02ee001b74848ee2c5bfa4777a9e1f4
blueExisting work in control systems engineering typically restricts perturbations to a subset of nodes, typically the control nodes of a network {{cite:97999d3b7cc13c8f2cc7702648bd43b04a4bc8b7}}, {{cite:093195f0805dcf8f3f889e32889a3f177ea09775}} or nodes that translate biologically, e.g., pirin and WNT5A driven induction of an invasive phenotype in melanoma cells {{cite:5280013d4e9a64813a77defe7fa4b6cb4887d4e5}}, {{cite:e323742947c5ade35200e36b866fd0825acec024}}, {{cite:52f9a7d104bda60368705b9ad79beefec711db37}}. The general case where perturbations are considered on the full set of nodes is less studied, with the exception of {{cite:b870ea828ae00d3d2cfc79d21ad5d58255fbce1a}}, even though it is relevant in contexts where control nodes are not available, or computationally intractable to obtain. Further, motivated by the biological properties found in various target states, different approaches perturb individual nodes' states in a PBN in order to either drive it to some attractor within a finite number of steps (horizon), or change the network's long-run behaviour by affecting its steady-state distribution (by increasing the mass probability of the target states).
i
de96d60968cc07ac7cbf8a7c4deaffc5
Overlap-aware resegmentation. While our segmentation model was found to be useful for both voice activity detection and overlapped speech detection, post-processing the output of existing speaker diarization pipelines is where it really shines. Table REF summarizes the resegmentation experiments performed on top of three of them, ranked from worst to best baseline performance: pyannote 1.1 pretrained pipelines {{cite:7c25fd730a6dc28cd2fd554b31da9669f965effd}}, dihard3 official baseline {{cite:6fd567aa4c83d9fc372a30c0a16426ea09e7f81b}}, and BUT's VBx approach {{cite:d7829abbc1098180ce1e23aeec4a1b553559f344}}. The (admittedly wrong) criterion used for selecting those baselines was their ease of use and reproducibility. Because results reported in {{cite:d7829abbc1098180ce1e23aeec4a1b553559f344}} for VBx baseline rely on oracle voice activity detection and the shared code base does not provide an official voice activity detection implementation, we used our own (marked as Ours in Table REF ) and applied VBx on top of it. Our proposed resegmentation approach consistently improves the output of all baselines on all datasets. Relative diarization error rate improvement over the best baseline (VBx) reaches 18% on AMI, 17% on DIHARD, and 16% on VoxConverse.
r
bbd2f8cd05dda75e24397ec535a89019
In general, we observe that the framework is sensitive to hyper-parameter changes, and that the various settings of each block affect each other, thus requiring extensive experimentation for appropriate tuning. From Secs. REF and REF we observe that overlapping patches when drawing positives is detrimental, and lightly adding natural backgrounds is beneficial. This could indicate that the original positive examples sometimes share time-frequency patterns that could be used to lower the loss of Eq. REF , but that hinder the learning of useful representations. These undesired patterns are denoted as shortcuts in computer vision {{cite:b09f0eee4063164b4ffa91ce22b4726079bf1f2b}}. Examples of shortcuts in audio self-supervised learning include e.g., recording gear, room acoustics or background noise. FSDnoisy18k is based on Freesound audio, which in turn is composed of audio contributed by users. Clips coming from the same user are likely to share some of these patterns, which has been shown to have an impact in supervised sound event tagging {{cite:67c6d828f08d326755772f09748826fd23542034}}. We hypothesize that this could be a source of shortcuts in our setting, which is being mitigated by stochastic sampling of positive patches and mix-back. We intend to further investigate this in future work. Finally, previous works report advantages of using larger batch sizes as a way to provide more negative examples, which facilitates convergence (e.g., sizes up to 8k are used in {{cite:4121bc61c7068d3138a6e9aad2ec46770c3be6c1}}). Our compute resources do not support such large sizes, hence all our experiments are conducted with a batch size of 128 (commonly used for supervised learning). It is conceivable that using larger batches yields even better results than those reported here.
d
49c9419ad1eb9511a26da5358166c964
If one wishes to treat general functions {{formula:b009ce46-9ea1-41a8-9a20-6b4c2cfc4d5d}} in the Sobolev space {{formula:a710db34-af84-495f-9758-329ca51e9d48}} , it is necessary to restrict the dimension of the ambient space to {{formula:6b490ecd-12d3-4c52-bc2a-0d5b324c2a51}} , since the norm on the left-hand side of (REF ) will be infinite for any continuous function with {{formula:86490a84-8f45-4b8c-84b2-b76c2a22d781}} when {{formula:bfc7a413-0bfc-4e2d-b042-8c200b4c7298}} . Rellich {{cite:21b1a2c6c92f2a3485bbd87deec3411cdb1b2fb9}}, {{cite:1a498688510c628c8ce124ffcd35bd3b62c8ef32}} proved that (REF ) holds for any {{formula:ad546af9-57b1-4954-be11-f0971baac035}} when {{formula:22e59297-39af-4e61-a0c7-7bc35339a39e}} , and when {{formula:2bcdf584-65bc-44eb-9f85-11ccd506869a}} , in order for the inequality to hold, we must additionally assume {{formula:913d47d1-19a6-49fc-8328-d55ca2dab3f5}}
i
080476237b7ce7fb7792f926e327573c
In this paper, we propose to apply Bayesian methods based on GP to the inverse problems with sptiotemporal data to account for the space-time inter-dependence. This leads to fitting the whole trajectories of the observed data, rather than their statistical summaries, with elaborated models. More specifically, we use the STGP model {{cite:37668b3bbfe93fd0b8060b00a68a07e8e62a78e8}} to fit the observed multivariate time series in comparison with the static or the time-averaged (for summarized data) models. Theoretically, we justify why the STGP model should be preferred to by investigating their Fisher information, which can be used as a measurement of convexity: STGP renders a more convex likelihood than the other two models and leads to an easier learning of the parameters. We also demonstrate in numerical experiments (Section ) that the STGP model yields parameter estimates closer to the truth with smaller observation window required, and also provides more reasonable UQ results. Note this implies faster convergence (future work) by the STGP model, which is computationally important because complex ODE/PDE systems are usually expensive to solve.
i
6a82b176e2267a8c5921bbdeb2b20efa
A further contribution of the paper concerns the evaluation of VaR and ES in the context of portfolio optimization (see, e.g, {{cite:6c43627975c2f287d7316563e05472154fac6f95}} and {{cite:c97af569e38f472f42fef960be3fea31745c230e}}). blackIn recent years, the MAL density has attracted wide attention in the literature for its flexibility in modeling financial data ({{cite:693db03c13edce1a45a78a47b425d2a9e76949a4}}, {{cite:e1633fdf552f6a7f12b17c8e858902d6849643ab}} and {{cite:405fe63cbe6919abad9a80f18c1e65968e4c44f3}}) and for its interesting properties that can be exploited to derive optimal portfolio allocations (see {{cite:174bfd464ab6332286d2ac287c3fe560ee6d5e46}} and {{cite:496147af80e2ae9496d550dbc366a73a89b92e08}}). blackIn the classic Mean-Variance (MV) methodology of {{cite:012a0008d12b157f7ef1acba7f05b8c8e68a2c8b}}, portfolio risk is measured using the standard deviation of the portfolio. However, the MV approach is reasonably applicable only in cases where either returns follow a Gaussian distribution or the investors utility function is quadratic. Given the empirical evidence showing that market participants have a preference for positive skewness and they are more concerned about the downside risk (see {{cite:fce63423c7eb54bbebc92aa7373585742c755a47}} and {{cite:acd4e3ab8505c0bb786789ca8ce9d99235b142c7}} among others), the MAL distribution blackcould represents a more effective tool to select optimal portfolio allocations in the case of risk-averse agents. blackTherefore, in this paper we exploit the MAL properties to incorporate skewness directly into the portfolio optimization method and to identify the optimal allocation weights. We then compute the corresponding portfolio VaR and ES as a function of the multivariate structure of the data. We prove how this result follows directly from blackthe fact that any linear combination of the MAL components is still AL distributed, with location, skew and scale parameters that are functions of the MAL parameters and the portfolio weights. Therefore, once we obtain the Maximum Likelihood (ML) estimates of the MAL parameters from the proposed dynamic quantile regression model, we fix a desired level of risk for any target portfolio and search for the optimal allocation weights according to the adopted strategy.
i
8ab69e180a99d1dcff90a68da8746193
Approaching clinical presence as a multi-task problem can be understood as an embedding regularisation {{cite:b7fcbe0103c51846dd2066511b9e1fb363ef7b27}} which results in a more clinically relevant representation for survival prediction. However, despite multi-task improvements observed in the literature, theoretical foundations are still lacking {{cite:a86cfc5254d41d14b539cae3403858e52e2edd93}}. Another limitation of this work is the lack of consideration of potential competing risks, but also the assumption of independence between patients: in the medical context, and even more particularly in the ICU setting, prioritisation is key in the delivery of care. When considering clinical presence, the assumption of independence might consequently be questioned and calls for future work. While we propose a set of experiments to study robustness in the MIMIC III dataset, this focuses on one hospital, external validation would allow the quantification of the methodology's robustness under different shifts. Lastly, our modelling highlighted the importance of modelling clinical presence in the context of laboratory tests. Studying the relation between adding new covariates and the change in predictive performance would indicate potential correlation between covariates and medical behaviour.
d
5d6de84689f471889da2f1c36fa8729d
Existing work on explaining GNN predictions can be categorized mainly in two directions: 1) factual reasoning {{cite:1a7e601718092d900b0a5415429f6ba5d70566f7}}, {{cite:2fbfe15ebab8ef336ebb3612d2161f4064bf93ca}}, {{cite:c21954a357ce98c8eb9cec6adcd983cba24723eb}}, {{cite:994e55cd76dbcb3dddefeee25db0967c68a519b7}}, and 2) counterfactual reasoning {{cite:839ed59e8a448e27905ca23968960c51d4460d9f}}, {{cite:cd8179c5d4bb9eaf67bc3ee63bd6f5442f9740ff}}, {{cite:1204cc007bdc678b1c47104dff8090479bd5db74}}, {{cite:340a3f5d55262161939c43a54a89c00de2b526f7}}. Generally speaking, the methods in the first category aim to find an important subgraph that correlates most with the underlying GNN prediction. In contrast, the methods with counterfactual reasoning attempt to identify the smallest amount of perturbation on the input graph that changes the GNN’s prediction, for example, removal/addition of edges or nodes.
i
a947f861e38fd796a594b5dc58ecbc67
Probabilistic models allow us to make quantitative inferences about the behaviour of complex systems, and are an important tool to guide their use and design. When such models are learnt from data, exposed to potential distribution shifts or are partially unknown, it is important to be able to verify the robustness of inferences on the model to these uncertainties. This is particularly relevant for decision functions taking action in the model, where much work has gone into verifying worst-case behaviour when exposed to various disturbances or changes in the environment (distribution shifts). Causal Bayesian networks (BNs) {{cite:e39dd923a9202ee231937736d444531cf01b487b}} are compelling models for this purpose, since one can perform causal interventions on them, giving rise to families of distributions that share a common structure. However, performing useful inference on BNs is often intractable, and one way to address this is to compile them into more tractable representations such as arithmetic circuits {{cite:b2cfda1c0abd60224689fb28ec5545321934ac5b}}. Recent work has shown that such compilation methods can also efficiently compute bounds on a decision function's robustness to causal interventions {{cite:a7049730de382b8a109c25fa077a624f8edc97a6}}. A limiting factor on the applicability of these methods is the need to have an exact model, where all non-intervened parameters are known precisely. This is difficult to achieve when learning parameters from data, since most settings will only allow reliable determination up to some error bound {{formula:9606d90b-aa14-4d84-af04-42024fa745c5}} .
i
9d1fc544797dea02f66666ff9b71ad88
We have introduced an approach for learning conditional radiance fields from a collection of 3D objects. Furthermore, we have shown how to perform intuitive editing operations using our learned disentangled representation. One limitation of our method is the interactivity of shape editing. Currently, it takes over a minute for a user to get feedback on their shape edit. The bulk of the editing operation computation is spent on rendering views, rather than editing itself. We are optimistic that NeRF rendering time improvements will help {{cite:d47673568949f505595d260a7002ce5dfbcba259}}, {{cite:1c15a93e9a4a9ca0d01e1a22f21b846517414868}}. Another limitation is our method fails to reconstruct novel object instances that are very different from other class instances. Despite these limitations, our approach opens up new avenues for exploring other advanced editing operations, such as relighting and changing an object's physical properties for animation.
d
84f637a3a29028b843683b0587c53fab
For the pre-training task selection problem, a probably exciting direction would be to design pre-training tasks for a specific downstream task automatically, just as what Neural Architecture Search {{cite:555edf6794b7506180482603d1a66f333cc2cf7f}} does for neural network architecture.
d
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We compare BMCoGAN with recent state-of-the-art methods on generalized zero-shot learning, and the results are shown in Table REF . The results of LATEM {{cite:b65984cadc626af1d534c5ef0e62564aa5b092f5}}, DEM {{cite:a30d9af7f1966d4ffbf00617b9df241ba153ff95}}, and SGMAL {{cite:76f06917be1a8f647554a69f9b726c4166e283d5}} are adopted from SGMAL {{cite:76f06917be1a8f647554a69f9b726c4166e283d5}} and the results of other compared methods are obtained from their corresponding published articles. For a fair comparison, we compare the performance with only inductive methods, which do not use unseen images during training. The results with 400 synthesized features per class are shown in Table REF . Though we present results from embedding learning and feature synthesizing methods in Table REF , for comparison, our main focus is on the bidirectional methods. We perform GZSL tasks with the proposed BMCoGAN using both 1-NN and softmax classifier. The Harmonic mean (REF ) is the main indicator of how well a GZSL method performs.
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The method consists of a few steps. Firstly, a fast enough process to construct the data sets with which train, validate and test the NN is needed. In this work we train the NN with a set of 2PCF mock measurements obtained from log-normal catalogues. The construction of these input data sets is described in detail in Section . Specifically, we create several sets of mock BOSS-like catalogues assuming as values for the cosmological parameters the ones inferred from the Planck Cosmic Microwave Background observations, except for {{formula:01c3a0ba-bd16-4bfb-9098-2a07149dff11}} , that assumes different values in different mock catalogues, and {{formula:288ecedb-b6f8-4601-9df4-d49553f6e4f3}} that has been changed every time in order to have {{formula:f1a6ac5e-484e-4f95-8f9b-271fa8bd620b}} , where {{formula:73cf3aad-57d3-4319-9247-794cfac47400}} and {{formula:006478c9-8153-4301-b098-891983a785fa}} are the dark energy and the radiation density parameters, respectively. Specifically, we fix the main parameters of the {{formula:833abf89-c4b9-4367-af6f-45bda9cb989e}} -cold dark matter ({{formula:fdda6c71-5283-4383-af3c-769ba4e30d3c}} CDM) model to the following values: {{formula:fb382987-46b5-45f1-a460-8f57a77bc82b}} , {{formula:c500c09e-d579-4e34-9eb5-1c6f97dfe930}} , {{formula:242b2234-9f40-4c78-9ddc-dadf05b76601}} , {{formula:8046f371-ce15-41c6-be53-65e4d29ed69f}} , {{formula:46a2d77d-33e0-4500-a467-d82ac14b446b}} , and {{formula:0a1ccbf1-b909-48fe-a9e5-adbc09c6859d}} {{cite:0529804eced4ed15b88ed36b05710f5852ee8ec8}}. Here {{formula:b196d777-3340-4571-a3d8-3e459ff84ec4}} indicates one hundredth of the Hubble constant, {{formula:c754a3a1-6ca5-4c54-90da-3ea6ea0fb519}} . The data sets with which train, validate and test the NN thus consist of different sets of 2PCF monopole measures, labelled by the value of {{formula:02e16fdf-cff8-4719-b9e7-bc735754c102}} assumed to construct them.
m
b45bc413121b06e850d5f1fff265d621
Recently, several methods based on data-augmentation have been proposed and proven to perform well on a large spectrum of SSL tasks. The idea is to have a model resilient to strong data-augmentation of the input by predicting pseudo-labels for unlabelled data using a augmented version of the input {{cite:91cb3c6085626d0083f52bf901c7f9d540130c08}}, {{cite:d160fc51f4e2e224aec7a1de4f28606f485f9471}}, {{cite:42af5a4300993463b8dd756800dec79163dbbab2}}, {{cite:a81db849fa5635d7192d96e1919d96b4a53e7199}}, {{cite:950f5658326d5414bbe4812e5abccd870fb589e5}}. These method rely both on the cluster assumption and the smoothness assumption and are at the border between entropy-based and consistency-based methods. See Appendix .
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0a67e25ddec07bf8c61212c9a85cd9c9
Our preliminary experiments and analysis show that summarizing legal contracts in plain English is challenging, and point to the potential usefulness of a simplification or style transfer system in the summarization pipeline. Yet this is challenging. First, there may be a substantial domain gap between legal documents and texts that existing simplification systems are trained on (e.g., Wikipedia, news). Second, popular supervised approaches such as treating sentence simplification as monolingual machine translation {{cite:e0f5440a7e17794a05dba543b00899b71ebfd175}}, {{cite:90d14117d156de69ac3cad588cee3b9c8491eeda}}, {{cite:1d048cf61b912a15ab6147cdc34cf430af14c0e7}}, {{cite:a4690e67e81976d99ef3a802e9e9ba84e393b5e1}}, {{cite:b5f06a0f3ea8099dd7e0104b47a1ee9ee780d052}} would be difficult to apply due to the lack of sentence-aligned parallel corpora. Possible directions include unsupervised lexical simplification utilizing distributed representations of words {{cite:45889ce80d443d2bc7b5a9d2c1a468ef69edb3e5}}, {{cite:2ead8a4a80422b52830d963709a70c2d8d9259c0}}, unsupervised sentence simplification using rich semantic structure  {{cite:92ea80e6d03d33c7f3d6266da3afc1d09bb76cf5}}, or unsupervised style transfer techniques {{cite:9c3cca7af269ac50fcbeec673d5d28cabf1e353d}}, {{cite:8f10fdbdb2f3046a5272e2e303d9fa1d194ccd4c}}, {{cite:95b01b858d23b86f1572e5e2d4632fc68c810a35}}. However, there is not currently a dataset in this domain large enough for unsupervised methods, nor corpora unaligned but comparable in semantics across legal and plain English, which we see as a call for future research.
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9f7a92abfb547d6b1b4a814027d97285
(3) Branching ratio for the {{formula:35bc3a06-a94c-43ef-9bf5-10f60c546ff8}} {{formula:c4ab40ac-a28d-4b5d-b4ff-e340e1d531aa}} {{formula:bdf136b5-309e-4ed2-972d-7498acad4f0c}} decay is a few times of {{formula:ea753af4-32da-4c7a-ac90-e6559647d1ad}} . So the nonleptonic {{formula:abe4131a-6be6-49d0-981e-a2245b357734}} {{formula:fb3f5d10-9700-4a23-b3a8-430429da9129}} {{formula:0687e0ee-ca0f-417e-9364-b3e60d7a401e}} weak decays could be sought for with some priority at the running LHC and the forthcoming SuperKEKB. For example, the production cross section of {{formula:052de530-2258-4ef8-a7b5-8bc227f03373}} in p-Pb collision can reach up to a few {{formula:561d6a38-fa42-4896-acb5-87b049079ad8}} with the LHCb {{cite:361348627d97cb4e40c6c2a74dc5768a81f8c998}} and ALICE {{cite:f3118fc130f594d435bf0ae79d513951e09c328e}} detectors at LHC. Over {{formula:077bdbdb-733b-4103-9aa5-0a87478c9d63}} {{formula:028c2696-da97-4237-88ed-3a05ddd99ba8}} particles per 100 {{formula:02f7425a-d7cd-474a-bab7-1fd2bc92d72e}} data collected at LHCb and ALICE are in principle available, which corresponds to a few tens of {{formula:01192eb7-50d6-4a79-9901-fd8679413b3f}} {{formula:037c6c60-a8f2-4d5b-aa95-f7913403fb93}} {{formula:deab2d5b-9e7a-4c1f-b362-1e8e18684688}} events.
r
8c8eaaf70c366dba1f40c6cd4e841017
Flickr30K Entities. Table REF also reports the performance of our TransVG on the Flickr30K Entities test set. On this dataset, our TransVG achieves 79.10% top-1 accuracy with a ResNet-101 backbone network, surpassing the recently proposed Similarity Net {{cite:b508ab11f80790ccbcf76e6bf77a5c5eee2f37fe}}, CITE {{cite:a32d6804983655bad4f40efe9b32c6ee59671609}}, DDPN {{cite:9c5917c9ac252a61f7a2ac2dd638ba2b970c2902}}, ZSGNet {{cite:ceef37475f9ab2d1784e1ac274976f4a4d139deb}}, FAOA {{cite:56a66d326c978d003561bfa82b5bc803248e2809}}, and ReSC-Large {{cite:fe5db91d9389eb4f382b65ff57271ab4717bd05d}} by a remarkable margin (i.e., 5.80% absolute improvement over the previous state-of-the-art record). {{table:0af79384-3620-4fc4-aeac-5dcc37a2f377}}
m
34d867de84aedea1d3e5b4c304dda901
For every {{formula:2254d87c-9219-4821-bf66-3813c6cc524d}} , the {{formula:ee967f6a-3e43-45ac-9c69-d408ac15bfcc}} -Weisfeiler-Leman algorithm is a generalization of the naïve colour refinement, giving an approximation of the {{formula:3c1621b7-73ef-41f3-ac8c-8caf0ad3e03f}} -orbit partition. For a graph with vertex set {{formula:6c218dd7-f371-4435-9ce1-40b81b14609c}} , each of these algorithms outputs in time {{formula:9289d3ea-28f8-4a7b-b1fd-9ba6c9302d5e}} a canonical labelled partition of {{formula:b9abf2b9-bc50-4ff2-b3a6-946b17905612}} satisfying a stability condition and respecting local isomorphism. Informally, they can be seen as forming a family of algorithms, each defining a notion of equivalence on both graphs and tuples of vertices of graphs. A result by Cai, Fürer and Immerman {{cite:1f24e25fb927b46768985cce4ccaca8d13b4eb2e}} shows how to construct graphs {{formula:65264a1a-ee4c-48c9-886c-74b6f0763494}} of size {{formula:957b491d-82e2-4f86-9a28-6b59c2795eab}} for which the {{formula:7207473a-22c7-4989-aa04-670603cecd50}} -Weisfeiler-Leman algorithm fails to produce the {{formula:359ce22b-cad8-4ada-bda4-6b39939102b2}} -orbit partition. In the same paper, it is shown that the equivalence classes of the output partition of the {{formula:596853f1-0809-406b-908b-9c960befd77e}} -Weisfeiler-Leman algorithm coincide with the equivalence classes of {{formula:4be074a0-8a8a-4d28-9896-b653361d6d9a}} -tuples of vertices distinguished by counting logic formulae with at most {{formula:17bec19e-98db-4f18-93b3-850a17dc1171}} variables. Thus, one deduces from the tight connection made by Immerman and Lander (see Theorem 2.3 in {{cite:29bedfe18dd962cdde64f5d2d36dd730c57a172b}}), that the equivalence notions defined by the Weisfeiler-Leman family of algorithms delimit the expressive power of fixed point logic with counting (FPC). Intuitively, one such limitation is the expressibility of solvability of systems of linear equations over finite fields, since the above mentioned constructions by Cai, Fürer and Immerman are essentially graph encodings of systems of linear equations over {{formula:2b4fc417-d5ff-4349-aa1e-9a282c0eba4b}} {{cite:c0326736b23e4533077f9d790bd202460e306aeb}}. This has therefore prompted research into families of algorithms graded by the natural numbers, whose notion of equivalence on tuples of vertices of graphs is conceptually a linear algebraic invariance over some field {{formula:e03ce95e-bd73-457b-b033-ee92dc638b0c}} . One such family is that of the invertible map tests over {{formula:c1fe7a10-52a0-4ee1-b33d-d1bf7e7c537d}} , first defined in {{cite:44820fa343407ae452bf92ac42a384846a0cdffd}}. For any graph, the {{formula:fc45c5d3-0c3a-401e-869f-116e9f657d5e}} algorithm of this family also produces a canonical labelled partition of {{formula:3ee37df9-d6a9-4229-a66c-e8f0d9146790}} -tuples of its vertices, satisfying a stability condition and respecting local isomorphism, thus giving another notion of equivalence on both graphs and {{formula:7aead0c2-a231-48e1-bae1-3605a570fefb}} -tuples of vertices thereof. Furthermore, such equivalences delimit the expressive power of the extension of fixed-point logic with quantifiers over linear algebraic operators as shown in {{cite:a27871b03ecb3cbd05f09431be5b75b3103068f9}}.
i
da0e323576d812f842305972e6d26c9b
As depicted in Figure REF , a more complete comparison between DeepHMap and DeepHMap++ is given. For all eight sequences from the Occluded LineMOD dataset {{cite:ff89a59e1a5ff1855d37f1f33af77feea69f4ced}}, DeepHMap++ steadily achieves better results than DeepHMap under different pixel thresholds. With the 2D reprojection error metric, a smaller pixel threshold means more accurate estimation. It is not unusual to find that the boosting of DeepHMap++ is more obvious under a low-threshold phase that ranges from {{formula:b868cedc-5965-48ea-8b86-249c21c9a582}} to {{formula:78dcd3bb-c1b9-4e23-bf23-7a86213dd0bb}} . This is because, when a test scene corresponds to a larger pixel threshold, it means that the estimated pose deviates significantly from the ground truth. Dealing with such challenging scenes is very difficult for both projection grouping module and correspondence evaluation module. Thus, the improvement of DeepHMap++ becomes limited when pixel threshold reaches a high level that is bigger than {{formula:4392c7ec-9b5a-4d07-bf8b-8381da5b4855}} . {{figure:4c0a5e6f-da81-40ed-acbc-15096e32e780}}{{table:ac7a2ca5-354d-4422-bded-0e7ad7ffab44}}
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3b9b32acf608fc46535d49488494bd29
We use AI Fairness 360, a package for the discovery and mitigation of bias in machine learning models. The protected attribute in our dataset is gender, while the favourable class is “man”. We employ two classification algorithms implemented in ScikitLearn {{cite:a565572abf3eb9fa6c54de3f6c95c97b586899d9}}: logistic regression and random forest blackWe consider these models because they are simple, widely available and widely used within and beyond the clinical field.. For logistic regression, we use the “liblinear” solver. For the random forest classifier, we use 500 estimators, with min_samples_leaf equal to 25.
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59124113cdf1355682d00eeee6fbe6a8
The MW-Net Learning algorithm can then be summarized in Algorithm REF , and Fig. REF illustrates its main implementation process (steps 5-7). All computations of gradients can be efficiently implemented by automatic differentiation techniques and generalized to any deep learning architectures of classifier network. The algorithm can be easily implemented using popular deep learning frameworks like PyTorch {{cite:f118f213584d0e0351cc6011281743a9c803c5e2}}. It is easy to see that both the classifier network and the MW-Net gradually ameliorate their parameters during the learning process based on their values calculated in the last step, and the weights can thus be updated in a stable manner, as clearly shown in Fig. REF .
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7ca718da0fe32863791714199cb748bf
Perhaps closest to our work is Bacry et al.'s {{cite:e01c897073f5df3077f152203b54685a0d3f62f5}} study of mean field inference of Hawkes process values. In particular, those authors inspected the effect of varying the decay parameter across a range of values: With increasing decay, fitted self- and cross-excitations decrease while baseline intensity increases. We go beyond their study by deepening our understanding of the (noisy) properties of the Hawkes log-likelihood as a function of the decay. Methodologically, our Bayesian approach relates to Hosseini et al.'s {{cite:6c606260668d4cdd289c08a789ad3ed4556627b9}}. Those authors infer the decay parameter by assuming a Gamma prior and computing the mean of samples from the posterior (as part of a larger inference problem). In our work, we instead focus on the Bayesian approach as a means to quantify estimation uncertainty. Further, as our Bayesian changepoint model captures breaks in stationarity, we simplify previous work {{cite:00a2e2ca87c0d0b8aaa017d9fc54d7e1e8dd9c74}}, {{cite:174802c334c1d9aed729ac848b8de487f78f22e6}} which relies on additional assumptions, such as estimating stationarity via the time series of event counts. Finally, our work complements recent efforts {{cite:826d655ec77d81aa9b8d39c3edc2c9fadea16482}} to learn Hawkes processes from small data.
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ff412ec4b60f538a3952c24b36d2eda0
Efforts in making legacy models couplable, either for MOSSCO or similar frameworks, however, leads to additional benefits besides the immediate applicability in an integrated context. Couplability strictly demands for communication of sufficient metadata, which stimulates the quality and quantity of documentation and of scientific and technical reproducibility of legacy models. Indeed, transparency has been greatly increased by wrapping legacy models in the MOSSO context. All participating components performed introspection and leveraging of a collection of metadata at assembly time of the coupled application and during output. Transparency is expected to be continuously increasing by new coupling demands and more generous metadata provisioning from wrapped science models. MOSSCO is moving towards adopting the Common Information Model (CIM) that is also required by Climate Model Intercomparison Project (CMIP) participating coupled models {{cite:7e7c14e6d6b6385df12af1ed8260eaa09ceb4eb9}}.
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305783a839e8e1767825adcf419bf5f5