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Rule Size. Holding the graph size and rewiring probability steady at 3000 and 0.0% respectively, we vary the maximum rule size from 2 to 8. Size-2 rules correspond to edges; size-3 rules can be one of the 5 directed 3-node graphlets. There are 34 different size-4 directed graphlets, and this number increases dramatically as the maximum allowed rule size increases {{cite:6cab326b6c0ebbc41712da1c6b7b85daf0bf0ca3}}, {{cite:a92fdd119978383f02bca8687588d1b7ddcfbe7a}}. This increase in expressibility is certain to cause an increase in runtime. The results shown in Fig. REF (center) illustrates that the compression rate increases dramatically as the rule size increases (higher is better).
r
0f8878efd7e51ec058a817d31de5b185
is regularly varying of the index {{formula:cf381d6b-89dc-4998-a629-cd45226d47ce}} as {{formula:6482ca11-8eed-49ab-97e1-4de494406869}} (see {{cite:652e8982e461f120e19fff4bf0e431a09c013f56}}). Now the statement of the lemma follows from the properties of regularly varying functions with a positive index.
r
c862b58a91266f001437017381d41902
Let {{formula:3dca0d5d-fb48-4c01-8bdd-e4e68a95ae1c}} and {{formula:a0ceb65d-415c-44bc-ad00-a2a3e7896bd3}} denote respectively the orthogonal projections on {{formula:6509cba4-af83-4b9d-b6fd-b85c6c9bf46c}} and {{formula:73000470-5dfe-468e-abd5-5511db074088}} In what follows, we assume that (REF ) holds. Let {{formula:591c72cb-735d-4fda-9817-6ddd0140a708}} (that {{formula:a04bf748-750d-49eb-aa57-04b12230a73f}} follows from Lemma 2.1 of {{cite:6294aaeb99ba2b8d279d7491e75cb5fa5b3c3f28}}) and define for {{formula:9beb8eda-5ca9-4d77-a292-5c508beaa886}} {{formula:69acea19-469f-477b-a296-094a5253112e}} {{formula:39d5624c-ab89-493c-8b5f-5f6aaf05ffae}} {{formula:62a78d15-6d95-4611-958a-683036d1c892}}
r
3876134c326db24f67cb2c3034bbb2cb
Reduction of Unimodal Biases (*RUBi)  {{cite:04a4c232797eabd0f9f37bb56c39a9fbf2e00f42}} multiplies the outputs from {{formula:c6787bf0-e9b2-4ba2-9c9f-073f599924a9}} with sigmoided outputs from {{formula:65e7687b-907c-4da5-9bbf-041983055c43}} , thereby assigning higher loss weights to samples that cannot be predicted through biases alone. RUBi was the previous state-of-the-art on VQA-CP {{cite:2043296acbe33c2c3f9caae7b793000ea710a42d}}, a testbed for measuring robustness to biases in VQA. For the bimodal problem of VQA, the original implementation focused on linguistic biases, training {{formula:9e604262-0d96-4ee9-a011-f2cf119f12b2}} on question features only. For our studies, we instead train {{formula:6d8cbec7-47e4-40a5-8b6d-a716cac55827}} on {{formula:2a48ea8e-2364-43ad-9a1a-cf2f837f7c76}} directly, to control the type of biases captured by {{formula:372e667a-6796-48ae-ad0a-8770df3ab949}} . We assess RUBi {{cite:04a4c232797eabd0f9f37bb56c39a9fbf2e00f42}} over others since it performed better in the preliminary studies.
m
009507f0e1d57d2b101669091c2c04f7
For the case of {{formula:a367f3a6-cb04-47ce-9d28-ae59e3b77659}} , one can gauge the 1-form {{formula:80be42f0-ec07-4d09-9e97-33c60d1dfc9f}} symmetry of {{formula:b534b8d5-5463-4c36-ab09-44ab50299602}} , which gives the Arf-Brown-Kervaire (ABK) invariant based on the quadratic refinement {{formula:6fbe3dd0-a2e9-4b0a-8c6c-232f637d9248}} of {{formula:4ad35195-e47e-4473-a770-23df016aee1b}} . The resulting theory turns out to generate the {{formula:d3eb3ae3-c812-4b7c-b1a2-06dce3e31b0f}} classification of the exotic invertible topological phase {{cite:05a060d53cfc7ccfeffdb52426b5f25111a237f2}}. This generalizes the {{formula:767b7dac-a0d5-42f1-ae72-b35c894bf93d}} classification of the (1+1)d pin{{formula:d7774b85-9a19-4fc3-8924-f4b935df269f}} invertible topological phases that corresponds to the (1+1)d topological superconductor proposed by Fidkowski and Kitaev {{cite:26ad540b5154fbc9db0257a38fffc87a7d2efa8b}}.
r
591e79c70d52b1ef378e96ca0d8e1d6a
All of the samples from KDEF are reserved for investigating the learning behaviour when a different data distribution is used for re-training the proposed approach with unlabelled facial expressions. This experiment better represents realistic HRI scenarios, where a network is trained in advance using a public dataset and deployed in a real robot. Afterwards, the network should be able to improve facial expression recognition from facial expressions captured in different conditions, such as camera resolution, background, and so forth. Finally, the faces from both of the datasets are cropped by the Viola and Jones's algorithm for face detection {{cite:db4a3f6c45e112999c97031528788b853f42679c}}, and re-scaled to 96 by 96 pixels.
m
3149deffafdf7ed464d69e624ff7a2aa
This perspective brings into view two further desiderata for any benchmark meta-RL task distribution. First, the ground-truth parameterization of the distribution should ideally be accessible. This allows agent performance to be compared directly against an optimal baseline, which is precisely a Bayesian learner, sometimes referred to as an `ideal observer' {{cite:5a9c40569664e24a8aeb7ab0fefd0f643e468331}}, {{cite:b2f34eb2403e94488c18e4304cc19a42196fe243}}. Second, the structure of the task distribution should be interesting, in that it displays properties comparable to those involved in many challenging real-world tasks. Intuitively, in the limit, interesting structure should feature compositionality, causal relationships, and opportunities for conceptual abstraction {{cite:d65b0d98442930cb0583bb8fc8c61737bc5d905a}}, and result in tasks whose diagnosis and solutions require strategic sequencing of actions. {{figure:2799178d-abfe-48b9-a412-2e141ddf78b5}}
i
434faaec681a7665da6556a89fe6e763
Extension to GZSL Setting: ZSL methods are biased to assign high prediction scores towards seen classes while performing GZSL task. Due to this reason, conventional ZSL methods fail to achieve good performance in GZSL. Our proposed method solves this problem by adapting seen-unseen class diversity in a novel manner. Unlike {{cite:19ab23948fa3de6d77e7619b37be634498a3839d}}, {{cite:c0755c014c8191be612d21f048ed008b4f9af11c}}, our adaptation technique does not take any extra supervision from training/validation image data. We show that class semantic information can be used to adapt seen-unseen diversity.
d
e74050e3c85f6bdc96fcea89d98575c1
Locomotion models {{cite:f1bb0ae9584dbd8f5fd499da553252c8e5f7ed96}}, {{cite:fa6f1280b198cbadc5608c8e141d2bc3543ce47f}}, {{cite:05c395615fef5902d8d1abf865a7c0c45030ccc6}} work well for unidirectional flows because they are mostly validated against empirical data {{cite:ffdfeb3a21ff30918087f23058853652ed679538}}. They can provide helpful insights and make crowd gatherings safer. But often locomotion models fail for setups that seem only slightly different. For instance, when a first aid-attendant needs to forge a path through a dense crowd to reach an injured person. When reenacting such a real-world situation in current simulation tools, agents often get stuck and end up in a deadlock situation because there is no real interaction between agents, compare Fig. REF . {{figure:a66d662c-22ba-4081-9831-b9b312aa4a53}}
i
8d30889d3e4a7c61526aacf1c3be45c9
The output of the encoder that parametrizes {{formula:1efd716a-bebd-4edc-ab41-a9ef55a30cc5}} yields the representation. Regularization serves to control the information flow through the bottleneck induced by the encoder, while different regularizers primarily vary in the notion of disentanglement that they induce. {{formula:10b886a9-4bbb-4e9d-acce-0ccb50747b04}} -VAE restricts the capacity of the information bottleneck by penalizing the KL-divergence, using {{formula:57203d86-0c73-45bb-a656-0d04e26d3f9f}} with {{formula:b0e0780c-9be2-48d0-bd6a-17e5a4335677}} , and {{formula:158754f1-2b99-48ad-af57-94b487418e20}} ; FactorVAE penalizes the Total Correlation {{cite:66009724a22ddee1f20c7d909931b3924ea5e800}} of the latent variables via adversarial training, using {{formula:2089834c-df83-43eb-9ca4-d010e110ff3e}} and {{formula:7a005341-327b-44fa-b3cf-25d1acfe8587}} with {{formula:53dbad32-1a44-4163-9742-dfbae96e71b1}} ; {{formula:2ca6fe0b-8637-4761-9998-5718529eef1c}} -TCVAE also penalizes the Total Correlation but estimates its value via a biased Monte Carlo estimator; and finally DIP-VAE penalizes a mismatch in moments between the aggregated posterior and a factorized prior, using {{formula:842b4c12-4b41-4b48-8d70-ba129af6628e}} and {{formula:18b3e626-9991-45d4-8b4c-d9ac73cc21f8}} with {{formula:bd0fe257-6e3c-4f51-9c38-cb226a517b42}} .
m
64f535bf0884fd3f0905adcc6721613a
Let us start by briefly reminding the tensor product construction. Concretely, this can be given the form of Lemma 11.17 from {{cite:7795e29ddfdbbb37fd885c39ef511b0168ad6e3e}}. We haveOur signature convention is opposite to that in {{cite:7795e29ddfdbbb37fd885c39ef511b0168ad6e3e}}, which explains the flipping of {{formula:5ea63518-59ee-45c2-b46a-74150dc4cb89}} as compared to this reference. {{formula:6bd14870-f443-4785-aed9-a5fbf0eef0ff}}
i
f4296dedc6239985286cd53a39c51680
Right for the Right Reasons (RRR) {{cite:6f4639de8a648983a6a99e3d68b9fb6a34a06935}} pushes the saliency gradients of the summed log probabilities of the {{formula:f92e4776-7b77-4657-9b5f-362ed3e5e838}} output classes to zero in regions outside of the ground-truth segmentation map by minimizing: {{formula:ac70b866-3562-40a0-adda-7713aea865da}}
m
513899be8d5496c1c22aa04b7763ea3b
We present a full characterization of the mechanical, thermal and electrical properties of two open-source, fully 3D printed, quasi-direct drive actuators. With our thermal solution, actuator mechanical torque capabilities were comparable to metallic actuators currently used for small quadrupedal robots, but with a significantly lower inertia {{cite:bba27a29c2f1ec1ae6e8e4c7a8650559a04302b1}}, {{cite:5a7eecce48415942e5a9190cf918398c55ac5929}}. Life-cycle testing of the 7.5:1 planetary transmission prototype for 420,000 strides (57 hrs) revealed little increase in wear and backlash—after a minor drop in the first 10 hrs, efficiency rebounded to original levels. This pattern suggests a relatively quick rise in friction until saturation, until a slower break-in process became apparent; nylon gears exhibit a similar process {{cite:b48d30aeb4d2eb00fbb0265ff106be0a99133df0}}.
d
1226f7a770596a24324beeacce81a37d
It is of arguably fundamental interest to know whether PREs exist in 100% of cases where, according to our heuristic, there are more parameters than constraints. If this were true then there would be only a quadratic difference between the classical and (minimal) quantum ensemble size, despite the fact that there are infinitely many possible pure states for any finite {{formula:fcb73f4a-f823-431d-a6c6-3eb235bf69be}} that the system could explore. In fact, this would be the case even under the weaker condition that, for any {{formula:9342ee55-cc22-452b-8fae-7a8256ce9f20}} , there always exists a PRE for {{formula:52933592-ceb0-49bc-9bce-3788cdfc3772}} greater than {{formula:ee63263f-0dc2-4f6a-bb7b-f473b6556947}} by a term {{formula:c03c5da4-f11d-436a-a9fe-04ac1f9aac79}} (it could be 1, but not necessarily so small). The quadratic difference, if it is universal, would presumably directly relate to the difference between a quantum density matrix, with {{formula:4f657218-d51a-4b5c-8e17-bd34f436d9fa}} parameters, and a classical probability distribution, with {{formula:72a0340a-8a66-4cff-a981-a7ca7af9662e}} parameters, as arises from fundamental considerations of the difference between quantum and classical {{cite:b6d6a0dccddd6e36b4591a7834eeed11ad2885cf}}.
d
8f63bad77ddee95a1b18130fb9daa7cc
The study of effective potentials plays an important role in quantum field theory as a powerful tool to solve several problems. The effective potential is a function whose minimum, if it exists, describes the vacuum state of the theory. As it is well known, the effective potential can be expanded in power series of {{formula:92580524-4171-4547-a6d6-9c79d6eaf63a}} , that is, in the form of the loop expansion, so that we can obtain higher-order quantum corrections without losing the information about its classical aspects {{cite:965d2d61a81044e167cf06051a81a992fdb065d0}}. Such method was proved to be especially useful for the study of vacuum stability and searches for spontaneous symmetry breaking {{cite:965d2d61a81044e167cf06051a81a992fdb065d0}}, {{cite:439d12ee0b0bc58f1b8271d22685931a6c0fedaa}}, {{cite:be511aae37e8d27cc242a573adc6ffffeb8e96b1}}. Jona-Lasinio in Ref. {{cite:439d12ee0b0bc58f1b8271d22685931a6c0fedaa}}, for instance, applied the effective potential method to understand spontaneous symmetry breaking, and Coleman and Weinberg in Ref. {{cite:965d2d61a81044e167cf06051a81a992fdb065d0}} analyzed spontaneous symmetry breaking taking into consideration radiative corrections, i.e. they studied the dynamical symmetry breaking. In addition, Huang et al. considered the effective potential for a {{formula:2caab408-f66f-4741-9e7e-474dc38a6651}} theory using a {{formula:4c96b550-996e-4b04-a3e5-98863db006e7}} lattice {{cite:be511aae37e8d27cc242a573adc6ffffeb8e96b1}}. Higher-order corrections were investigated in a curved spacetime by Odintsov in {{cite:a46b53de5ad37c38864cdcd43dbbfff5b0a43be2}} and vacuum stability issues for a nontrivial spacetime curvature – by Einhorn et al. in Ref. {{cite:a826fa4466f045156ed33a25e31b382777bb91ca}}, with focus on non-convex behavior for radiative corrections. The role of effective potentials was also studied in supersymmetric field theories with use of the superfield approach (see for a review  {{cite:e3b9fa17c102b090fda0181e2de3160a2201eefd}} and references therein).
i
821c72929244181a60c18b5e062a4464
It is challenging to fully understand this complexity in star formation. However, during the post-gas-expulsion phase, if a star cluster was still bound, the stellar dynamics would re-virialise the cluster and would result in a roughly spherical stellar system as observed today. In this work, we strengthen that the massive OB stars can also significantly influence the long-term dynamical evolution of the post-gas-expulsion star clusters. The wind mass loss of OB stars after gas expulsion continues to reduce the gravitational potential of the star cluster. Meanwhile, the death of OB stars can leave compact objects like black holes (BHs). By being much more massive than stars, they are the most likely candidates to end up in dynamically formed binaries. The interaction between these binaries and surrounding stars is a heating mechanism that influences the long-term evolution of the system {{cite:5fadef52a128affc212de2750f807413879b7dd0}}, {{cite:6071792b29e1bf681c5e3e42dbd006885d4c85a3}}, {{cite:5464d38a215f6f8e1ca6f5eb2b1bcb293665dd1f}}, {{cite:0b39b992802d0326e74e54e869f5349a270065ae}}.
i
a9cf17a711d7cf12f364a34a9bbed2be
When compared to the tightly related work {{cite:30b8705bc41ff23bfef9f6733855911b622b5db4}}, {{cite:79ceb6c61eacee0fa289d864e1267ce6144bc215}}, {{cite:98809ea0ddd9351687b3cadddd7c843966cb1a8f}}, {{cite:6ef101192bcdaaca8143f2e1d0b1d8d3ed68b26e}}, {{cite:bf454f42d9fb084ea5b9c58e125662840e3d06fa}}, {{cite:55d516c8e82b1e799243a1543199ef27a17a5c08}}, {{cite:826bdc9fbed07ca61c0ee1b7c92342041fa75344}}, this paper provides some slightly stronger convergence results under weaker conditions. The detailed discussions and comparisons with these works are shown as follows and presented in Tables REF and REF . {{table:3464f553-8d81-4cfd-a3f9-547985a1f7f2}}{{table:c1aa7ca6-acfa-4da0-8a2e-90af7ccc707c}}
d
99742c60962090ff2e6c4ee1369cf1dd
We explore the scenario of {{cite:c031214a8323c8fb7904c16ca3c453080136c5c8}} and {{cite:b088677d3f6d557d07612762d23ed51cb1340aee}}, where multiple, equal-mass planets on circular orbits span a region interior to the disc, and clear that region of debris (the black circles on Fig. REF show such planets for {{formula:e55af60e-479e-4cf3-bb1a-9b4173ad7e77}} as an example). The planet orbits are assumed to be spaced such that each adjacent pair of orbits are separated by {{formula:95977f1a-eae9-4077-a35b-38b1c099e26a}} mutual Hill radii, where {{formula:7166fe0d-2c2c-40c2-8ed9-48e1e4793ff3}} is a constant and the mutual Hill radius is {{formula:ee2638e9-3781-4ddc-a19a-9ac3437f97f3}}
m
6a7bb8c193fe48bb0c557605c9d74622
The limitations of existing augmentation strategies for GCL inspire us to look back to the characteristics of the GNN encoder itself. In Figure REF we visualize the raw node features and the embedding of the randomly initialized untrained SGC {{cite:3cba7bdaabb1bf3bc55923bdbff924f5428fc4ea}} activation layer. It can be observed that without the help of trained model parameters, a more discriminative graph representation carrying semantics information can be obtained by neighbor information aggregation alone. Thus, we argue that a better contrastive scheme should be tailored to the characteristics of GNNs (e.g., neighborhood aggregation).
i
e7968d0eacdbf1d698de5714900ab5b9
Data Availability. The dataset studied is bottlenecked by time and space due to the limited data availability. The census data below annual granularity and for other cities has been challenging to find. Also, the dataset only covers three years, limiting our analysis to the period from 2011 to 2013. The geography and time in our study are discretised by neighbourhood and year respectively, which might be too broad. It is worthwhile to employ causal modelling like Granger Causality {{cite:4d3c48c8b8dfd3d17dfc4c747aac05e56fb30852}} to leverage spatiotemporal properties of LBSNs and study this effect at a more fine-grained level {{cite:28fd467f4d113f95528c026cf1a7a15dba9f934a}}, {{cite:39875d24cc92544662e2510c26aeb762e14f5b43}}.
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b93e7280f172ed1d98b255198902e7e3
We show the general performance results of all quantification algorithms over all data sets in Figure REF and Table REF . The letter-value plots in Figures REF ) and REF ) represent the respective distributions of absolute error (AE) and normalized Kullback-Leibler divergence (NKLD) scores resulting from all experiments. Colors in the plot indicate algorithm categories, i.e., count adaptation-based algorithms are shown in blue, distribution matching methods in orange, and adaptations of traditional classification algorithms are shown in green. The plots in REF ) and REF ) depict the average performance ranks of all algorithms per data set along with the critical differences between average ranks which indicate whether or not the difference in average ranks is statistically significant according to the Nemenyi post-hoc test {{cite:8226073f511a437dd6a6ad739483be25d619712a}}. Here, horizontal bars show which average rankings do not differ to a degree that is statistically significant. Tables REF ) and REF ) complement these plots by providing the average absolute errors (AE) and normalized Kullback-Leibler divergences (NKLD) for all scenarios per algorithm and data set. Based on these averages, the rankings for the plots REF ) and REF ) have been compiled. Further, a total average error score over all data sets is provided.
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6ac9eacf160225a6d433be93b4826514
{{cite:f215da7b07ec921af3097f4543878a208576291e}} corrected the raw SDSS-DR7 spectra for the foreground extinction considering the dust maps from {{cite:2779af5687cb52d24e1205d928afa838bbe358a5}} and were then converted into the observer restframe. Next, the spectra were fitted with FADO in the wavelength range between 3400 and 8900 Å with a base library from {{cite:ad34a5ee974f46615d560304ee108c5937834aa6}} composed of 150 simple stellar populations (SSPs), containing 25 ages (between 1 Myr and 15 Gyr) and six metallicities (1/200, 1/50, 1/5, 2/5, 1, and 2.5 Z{{formula:d97006f7-7742-4978-827b-7e1c68d00023}} ). A {{cite:a75a0e52848352051fe173a29ab192de84df545b}} IMF was considered to match the base library, Padova 1994 evolutionary tracks {{cite:e03b431c3070b66ef4c3f33f3d6ec76f3f4f93c1}}, {{cite:2213ca01e4e6780e89315c2092f13e87a6017572}}, {{cite:a96c90087e728b451d558127e1a7b1af7f87ba7c}}, {{cite:ee6bd2b19e29d7233370630558a80f2ac03a4e55}}, {{cite:720036b30706e3d2b0781b2eef8818de72dab0d0}}, and the {{cite:fbeeb9cf7335e55fd149b82b1b5052f7b01eaa55}} extinction law.
m
f5d6e34417a3871198428bed3b71e655
One of the most drastic conclusions from the framework of Cauchy Slice Holography is the fact that, given a holographic theory {{formula:0e917888-8f16-45aa-bfcd-727e951db81a}} , the quantum gravity theory thus defined has a unique allowed state satisfying the constraints.Ignoring for now the issue of the normalization factor raised by equation (REF ). This is a consequence of the slice {{formula:7815334c-349d-433b-a45c-4c701ede0ba0}} on which we are defining the state having no boundary. Had it had a boundary we would have had freedom in specifying the boundary conditions to the holographic partition function. We have no such freedom on closed slices. This point was emphasized in Section REF . The very deep and interesting question remains of how to do quantum mechanics when the observer is part of the quantum system. In particular, how are we to obtain a notion of Gibbons-Hawking entropy in the semiclassical limit for an observer constrained to the static patch of an emergent dS spacetime? This seems to require the emergence of a finite-dimensional “Hilbert space"The use of scare quotes is to remind the reader that the work of {{cite:bbc1413c60f7ab2620dff6edb69a77655bdaabfa}} suggests that one should instead think in terms of the algebra of observables restricted to the static patch. They argue that it is a von Neumann algebra of Type {{formula:9996d63c-db59-4af1-9eb7-241a161707e3}} which means it does not have a faithful irreducible representation in a Hilbert space. Yet a von Neumann entropy can be defined. associated to a subregion from the one-dimensional Hilbert space associated to the full closed slice. This is not the usual pattern we see in entangled composite systems. We leave the difficult problem of obtaining this directly from the unique quantum state (REF ) (potentially with matter included) as an open question. However, we believe that our framework can give a new avenue to explore this problem by focusing attention on the field theory. It would be very interesting to understand how Cauchy Slice Holography is consistent with the edge mode story in gravity {{cite:16ed8ccea4c0cc4400c6c9c813165bac34c403a5}}. From the perspective of the field theory, if we make a cut on the {{formula:bcc0696c-edd6-4208-b433-03afdfbf23fa}} , there is a Hilbert space living there, which may somehow be related to the codimension-2 boundary degrees of freedom of the bulk theory.
d
2f8ef4b79751af7fcf98354c5c805154
Redundancy in ViT representations Unlike all other models that were considered, representations from early layers of ViT had a rapid eigenspectrum decay with {{formula:ac604f4c-b519-499b-b05f-22201257a552}} (see fig:accalphaarch). The transformer architecture has a notable difference by design, i.e. early layers possess global receptive field context via self-attention on patch embeddings. Raghu et al. found that early ViT layers incorporate both local and global information {{cite:f6c83e8e4ba58dd25c549246e38c32de3908f63f}}. Based on these insights, one intuitive interpretation of our results is that the representations have a low effective rank, and encode redundant information relevant across multiple scales.
d
8b82e14621ae96da776e172d729a29f1
Figure REF shows the Stokes {{formula:baf6628a-26c7-4d40-a57e-2d75f6938e98}} dust emission at 3 mm from our observations. The dust emission morphology is consistent with previous observations. The red line segments are the observed polarization direction, which we will refer to as polarization angle “vectors”, although they are not true vectors as they have no unique direction. Table REF lists the measured values for total intensity and polarized intensity, as well as the beam size. We also list the 3{{formula:08de048c-179a-4125-9241-b81d17a81f21}} upper limit for the two polarization non-detections. The integrated Stokes {{formula:9f8507ae-8533-4cea-b647-a9e4fa92c49c}} fluxes of DG Tau, Haro 6-13, and MWC 480 are {{formula:75fdd163-002f-4b06-be22-02b1f89067af}} 30% lower than those reported by {{cite:5aceeecb9ffd3497d75a575019281f8f43c792d7}} at 2.7 mm using the Plateau de Bure interferometer. The Haro 6-13 flux at 3 mm is consistent with {{cite:04298b7f845c672ddcf3f67d3cb74d06f589891f}} at a level of 10%. The integrated Stokes {{formula:f285d196-f447-43e7-a7f8-1d7f01dbc30e}} flux of DL Tau is 20% higher than that reported in {{cite:5aceeecb9ffd3497d75a575019281f8f43c792d7}}, but it is within 5% of the 2.7 mm flux reported in {{cite:04298b7f845c672ddcf3f67d3cb74d06f589891f}}. V892 Tau's Stokes {{formula:2e2a777a-bf61-4c82-baa7-8720bd7d3c45}} flux is 20% lower than that reported in {{cite:97acf98c7b939f64f24522a01f556cdefdb0dcf9}} at 2.9 mm. We attribute this variance as likely due to typical absolute amplitude calibration uncertainties with incomplete u,v coverage in the previous observations. {{figure:0cc22bed-a2bb-4fb2-96b1-690fc7a2d9c7}}{{table:ec2363e9-c9ef-440b-b38e-bab081ae7665}}
r
0b90ef9881bac23ab24a584c5f0cf816
When the output normalization is {{formula:25dd1f15-84e6-4615-ad78-aebf84d2a6ba}} -norm instead of BN. Experiments in [fig:identity-init-performance]Figure fig:identity-init-performance seem to suggest that there is still a gap between using {{formula:5bbaa08d-ee48-439e-9b84-2bb8965b6958}} -norm and BN as output normalization methods. In this case, the acceleration effect may not happen in exactly the same way as in the BN case, but we believe they share the same underlying mechanism and can be proven in theory. The mystery of the projection head. As our experiments in [wrap-fig:1]Figure wrap-fig:1 showed, the outputs of the projection head in the symmetric case (without the prediction head) suffer an extremely strong correlation even with batch normalization used. However, the impact on the base encoder is milder and thus the network can avoid complete collapse, shown in [wrap-fig:1]Figure wrap-fig:1 and [fig:identity-init-performance]Figure fig:identity-init-performance. It is mysterious how the projection head works in non-contrastive learning, and also how it compares to the case of contrastive learning, which has been studied by {{cite:8bb55a97ca88ad0556911d2cc8721198f518e41e}}, {{cite:534cb25e03617686959ed7532e70e3f7b809679f}}. Learning non-linearly features. For the simplicity of analysis, we have assumed the features in the data set are linear. It is of interest to study whether neural networks trained by non-contrastive self-supervised learning can learn non-linear representations better than traditional learning methods such as linear regression or kernel methods, as there has been a series of papers {{cite:70a5ac3ccbe1c015ccf43b1ab3b6aa999e7331eb}}, {{cite:f4759024cee74fb047f8dbf952c4d9ee2f01b3e0}}, {{cite:19eda972251d1a8e55f638d56d99bdcfde49866f}}, {{cite:412738d7571c079b301aa27cab2982ce26b58585}}, {{cite:02c19d1a2a548d01a6cc01a0b30415c6f193df19}} trying to understand it in the supervised setting.
d
72f3507e4519e8f5c23439d45d9cf530
In the following subsection we evaluate the support recovery capabilities of RLS in different settings. We compare the performance of RLS to several strong baselines, such as: the LASSO {{cite:9117164e42a2f80c39fcbb7883a8404590978504}}, IRL1 {{cite:5869ce1a1c6a32909cb545781656437a9e7f3b91}}, TL {{cite:8d0e49c1b96c2f3b08ec5e066255f1166dfdafee}}, OMP {{cite:f9ebfded6b65c76dbbe525b7c461d544dfe8c0ae}}, ISD {{cite:2a9e76956d16ef14fc7348b5e8d7e79dbcbcc613}} and RAWLS {{cite:4ba83b82cafc59a55a7c1ac2a1769a666fd33bcc}}. We apply RLS with {{formula:f9a33c6f-f02d-43f3-8954-f25118495a72}} which was shown stable across different settings (as demonstrated in Fig. REF smaller values of {{formula:43d8441c-e442-4f51-b712-370b4c6cef20}} may also work in practice). We evaluate performance in terms of the empirical probability for perfect support recovery. This probability is estimated as the portion of simulations which obtained perfect support recovery out of 200 runs. Perfect support recovery is counted only if {{formula:ac515d49-d84e-4e6d-b89c-349af07b3bf5}} , where {{formula:9b42f7c6-89a6-4964-9a62-87e2cc00da7d}} . {{figure:12924636-322a-4d69-8e61-aa5f0ccbf771}}
r
7c3ac7865bf0261119301453f451677c
A Lax pair for the Maxwell–Bloch system was first found in {{cite:5278c2a1bd1f0b5c8f4053a2ffa3d63cf7bb0023}} by using results of {{cite:2d5b3670af3063a07e88a9abe233d7f7db6d2e87}}, {{cite:53827562701ef5b8ebbdc63e6108fc1615ae5a6a}}, {{cite:5b026aa74500379ed3a154dce134058c3e324392}}, {{cite:319426c763d9d23e45188823fd0364420d859eb1}} (see also {{cite:4f8162936d33ad0e7e7baff2f5591164a7065284}}, {{cite:637906a8b510b1476c4446b52a9f632431d4c249}}). It was shown that (REF )–() are the compatibility condition of an overdetermined linear system, known as the Ablowitz–Kaup–Newell–Segur (AKNS) equations {{formula:b769b581-0de8-4a90-9c9b-8b01321ea2e8}}
i
821a2760238e29e524d5ce834cc4b96a
Complexity Analysis. The proposed self-balanced multi-aspect re-ranking algorithm iteratively selects items from candidates according to the similarity with selected items. Formally, it has comparable complexity with vanilla MMR {{cite:184397fdb1055d418567452735f9f4bd97ff590e}} where the time complexity can be roughly estimated as {{formula:4dcbfa36-2f94-403d-a1fc-8700edec7edf}} and space complexity is {{formula:264d7ba2-25ae-4dcd-b248-b2bdbb34dbfa}} where {{formula:399ce481-d285-4aae-ba70-e542323cf344}} is the number of candidate items and {{formula:871b8bdb-bffe-4c34-b15f-2362c1e3cbca}} is the number of recommended items. The additional costs are mainly attributed to the involving of the disentangled representations. To further reduce the costs, we can offline compute the embedding similarity (e.g., using an efficient vector recall algorithm MIPS {{cite:71e652f72f6eb98caf0d6cc29add5f2a7841afcd}}) and store the top similar embeddings via ID-based index. In this way, the time and space complexity can be reduced to {{formula:e70353c7-2d2a-4989-9103-5d9159781c55}} and {{formula:2d6a18d2-5614-4737-b9dd-bd4ac42bf4ca}} respectively. To sum up, our framework has comparable complexity with those lightweight diversity re-ranking algorithms (e.g., Fast-DPP {{cite:a27b0bef1b16c3cd911de1f13670a10f864e3709}} and SSD {{cite:13c7f9089c48fa3dbbfc86425990fcf399d9ab61}}) when {{formula:757e5f9b-03ba-4ea5-a1b6-26a73b571d04}} .
d
25fb7925227b3bc24382554433aa935e
Topology plays an important role in various physical systems in different areas of physics, such as gravitational physics, condensed matter physics and cosmology. The presence of topological defects changes the geometrical property of space-time. These defects had formed during a phase transition in the early universe through a spontaneous symmetry-breaking mechanism Refs. {{cite:0f890e945e5ba1f6db466714d0d3592acecbf93b}}. Topological defects are classified into Cosmic strings {{cite:3eec2bc04172b2d31716700aac8844c753c07e4f}}, Domain walls {{cite:6178315686616da76f02dd1d5a3622e4705326bc}}, and Global monopole {{cite:aee92e76a8f360d1d3a5962626b9721dda5c726b}} (see also, Ref. {{cite:bbec784c477634eda53000c14a2bb4b90700a15b}} for detailed discussions). In condensed matter physics, the topological defect by vortices in superconductor or super-fluid and domain walls in magnetic materials {{cite:720c1445e55b45905c749292c240c18db0e29693}}, soliton in {{formula:3b240f5e-d701-4c7f-a304-edd2eeb64df9}} polymers {{cite:b84e5ffc46744a67aca4b261aad09ebb43f4f027}}, and dislocations or disclinations in solids or liquid crystals {{cite:a76324a733eb31898aa2f5d3ca228e0e0f0ca484}}. Topology change of a medium introduced by a linear defect, such as disclination, dislocation or dispiration in an elastic media produces some effects on the physical properties of the medium {{cite:981fbea2126f4ec8673bea9b5f03a4b13eba4eb2}}.
i
ad013ddd9a249203cc58f88c63377510
We fabricate a depressed-cladding optical waveguide and on-chip electrodes in a {{formula:332c5631-f355-4e01-80f2-45a556f7256a}} : {{formula:3a07e57b-5434-45e3-8ee6-557dbdafd835}} crystal. On-demand storage of polarization qubits with a bandwidth of 10 MHz is achieved by implementing SMAFC protocol using site-2 {{formula:28890635-e45c-43d9-94bc-5771f43e5d7b}} ions. The fidelity of the storage process reaches {{formula:28e7b9e0-e47a-4448-a369-5abf996b9fa1}} , which is approximately the same as that achieved with the bulk material {{cite:9b35a33c0f60d2c29df5dc6457b431f475869a9b}} but provides the additional capability of on-demand retrieval.
d
f723e5e21d78b9665c07ed768489c481
For a topological space {{formula:778763bc-a2e4-459b-bea4-bbe7d94a4e60}} with a fixed-point-free involution {{formula:3375975b-2c02-468f-9715-ceee82f83ef0}} , we say that {{formula:6b51028b-bdbd-4e09-b020-d79a77058b6c}} is a BU triple if for every continuous map {{formula:baf679bf-fea1-4183-8359-b47179fecbfb}} there exists {{formula:a84cd215-715a-44d3-8173-31ba13e1a6f6}} such that {{formula:19c216b4-2933-4559-9586-46fc00fb052b}} . The index of a free {{formula:b16ee302-7020-4213-bb3b-261c0c42d5b4}} -space {{formula:50212d07-3351-4725-96af-9621fa448e30}} is the smallest number {{formula:547944eb-4661-4198-bc82-3a05c1ef10f7}} such that there is a {{formula:501c39f3-5bc9-48ba-8140-c543d9dfefa1}} -equivariant map from {{formula:4abf5d30-a504-4f4e-a11f-3f7d028e86f3}} to {{formula:fdcd039e-b718-4e7d-88cd-8d140693c10b}} . In {{cite:3f79873c1b02ab80c35b8c77184484f440dbcfb1}}, the authors used the index and the Stiefel-Whitney height (see coind) to find BU triples. There is also the dual notion of coindex of a free {{formula:6b49fa5f-bcf1-4a42-a2ec-b31227175a58}} -space. A {{formula:998c0ee6-5ccd-4564-858f-6686298912f9}} -space is called tidy if all these three numerical parameters coincide otherwise it is called non-tidy. Many authors have considered the problem of finding free {{formula:740c9b83-11d0-40ae-bd80-d58379cc730e}} -spaces that are tidy. For more discussion about index, coindex and tidy spaces, the reader is referred to the book of Matoušek {{cite:d2b8bcc258ce4155a14ccb4b01ef74b01f97409c}} and Csorba's thesis {{cite:252b703088e8c333556abe4dd49a36968c9ec2ff}}.
i
f43ce92402ffb67a003d6f2170842620
Comparing the results of the low energy spectrum of SU(3) Yang-Mills Quantum Mechanics with those obtained in Lattice QCD using asymetric lattices, eg. by Morningstar and Peardon {{cite:136b70498375988b31779c26b23d600df843f6f6}} and Chen et al. {{cite:60b6ceed17bc35161b1f67f548f7f83fa6261f1c}}, using dimensionless results obtained by dividing by the lowest (spin-0) mass, show reasonable overall agreement for the {{formula:369bef4d-03cb-4ce3-ab7c-ddc02434a93e}} , {{formula:473ef294-f56f-4405-9b82-e2543ea29aa0}} , and {{formula:cefdbc1b-fe1e-4eae-b95e-84bfbdcaefe7}} glueball states considered by them. Their {{formula:660314b1-6478-4219-aa42-f5bfd601f370}} results , however, are much higher in energy then those of Yang-Mills Quantum Mechanics.
r
e3e860f3b20532fa6d45164490a6effc
In our analysis we compare a number of detectors: Xception {{cite:89f0a290a82e809098708af4acac94276de6a4cd}}, SRNet {{cite:851e9037b30dee37b7357d9a7a2012af950b41d8}}, Spec {{cite:8e97bf1cb004d875e18ba17c2563939e8659f110}}, M-Gb {{cite:3fb5add6e3bfb0f23dfa6189d4d2a822edff5f1d}}, Co-Net {{cite:4fc262b3f90136b64c79e4748cde300e20f17670}}, Wang2020 {{cite:766666918f5a5d94f8810e8e6c569c1f68c31835}}, PatchForensics {{cite:8306ab9beb25af113dc4345e2b9a46084d0b7782}}. Their main features are summarized in Table REF . Together with methods specifically proposed for GAN image detection, and already described in Section 2, we also include SRNet, originally proposed for steganalysis. Indeed, steganalysis and image forensics pursue very similar goals, and successful methods transfer well from one domain to the other {{cite:c8b9c67d8bd6143b0f5a21accf51f4f913b2622f}}. In particular, we find SRNet worth studying because, to preserve features related to noise residual, it performs no down-sampling in the first layers of the network, a solution of potential interest for GAN detection.
r
c0388eaadd515bc8611a6d4f606be52c
We compare NCAs against Compositional Pattern-Producing Networks (CPPNs, {{cite:8473888604a94139443fec34676f309dc3bcc93f}}), which can generate spatial artifacts such as images {{cite:f2bf6d1ff88112574b35632ad410384534db3843}} by taking coordinate-pairs as input and outputting the multi-channel value at the corresponding pixel. CPPNs have previously been used to generate parts of game levels {{cite:1704dde9e057499c6683ae18c3ddda4cd6c4fe67}}, and can naturally encode spatial patterns such as symmetry. We train CPPNs via MAP-Elites with the variation operations from the NEAT algorithm {{cite:f5d3f08e3e9db4e0ad8bf5768e00ff4e0c5e43d4}}. MAP-Elites maintains an archive of diverse generators and mutates their architectures in search of new elites. We choose MAP-Elites over CMA-ME, since CMA-ME only works on fixed-length real-value vector representations and cannot easily be extended to augment network topology.
m
6bffbb4a586dc8fb8012b5253cd19b18
where the left-hand side of eqaution (REF ) does not depend on the control laws {{formula:87d7d1a9-4959-432f-81fd-0141997237dc}} . Hence, one can find the optimal solution of Problem REF via the dynamic programming principle {{cite:09ffb280c4944ea6ee36063e68420c4af7b5c02c}}, and this leads to the Bellman equation (REF ). {{formula:45cbd8ab-23b1-430a-8252-9177139f70c2}} According to Theorem , the optimal strategy does not depend on the history of infected users and infectious process, i.e., it is sufficient to know the current values in order to optimally control the network. The cardinality of the space of the Bellman equation (REF ), i.e. {{formula:079d29f9-f44d-463c-ac82-2c06b89c0fdf}} , is linear in the number of users {{formula:eee74173-94d2-4c1c-8935-99e58726304b}} .
r
eeda1eddd99466d1ca8978a4799a5601
A non-zero quark mass is essential to correctly reproduce phenomenology in the low-energy sector of QCD. Therefore, our modified SS model can be the starting point of a more quantitative version of the phenomenology initiated in {{cite:9bb2df1885041917b27c522767801e8e692f6fb3}}. For this purpose, our treatment needs to be extended to the non-abelian case, which should be a straightforward exercise. The correct tachyon brane-antibrane action for curved directions transverse to the branes is not known. It is important to have such an action since this would extend the applicability of the present treatment to such interesting cases as e.g. the antipodal configuration of the flavour brane system and its connection with massless quarks. Another direction in which the present ideas can be extended is to discuss this model at finite temperature and describe the chiral symmetry restoration transition and study the phase diagram in some detail. The connection of chiral symmetry breaking with tachyon condensation seems fascinating and a deeper understanding would be useful. Finally, baryons have been discussed in the SS model. It turns out that they have a very small size. This may change in the presence of the tachyon. This is because in the presence of the tachyon, the flavour energy momentum tensor is concentrated away from the infrared region where the branes meet. In other words, there is a new scale provided by the quark mass. It would be very interesting to investigate whether this effect makes any difference to the baryon size.
d
01dccb95d85b947fbf13ad1fe9f4dbf2
We should note here that a few features in the red part of the spectrum are not reproduced. In particular, emissions near 8100, 9000 and 9500 Å are weak or absent in our synthetic spectra. The emission near 8100 Å may have contributions from [Fe i], but the relative expected line strengths do not match the observed profile, and other [Fe i] lines are not seen. Our synthetic spectrum shows a weak feature, which is caused almost entirely by [Fe ii] lines. If a weak underlying continuum was removed from the data the discrepancy would not be as large. Another possibility is poorly known atomic data for these lines. This may also affect the emission near 9000 Å, which our spectra only partially reproduce, while we have no suitable candidate for the emission near 9500 Å. The emissions near 9000 and 9500 Å were also seen in SNe 1991bg and 1999by, while the one near 8100 Å was not {{cite:3fea1d8448f267dc3575fc06c2635518f14e343a}}.
d
b6cf0a153d7e5143ecd625c446adb909
Motivated by the novel method of Albouy and Kaloshin for celestial mechanics {{cite:6d405c7841e081397b0ab46135a6015e2d5bd648}}, the first author introduced a system of equations (REF ), whose solution set contains relative equilibria and collapse configurations. The system would admit a continuum of complex solutions if there are infinitely many relative equilibria and collapse configurations. Then the finiteness of all stationary configurations for the 4-vortex problem is established by analysis of the singularities of the system {{cite:e438b503e92625a70e203a7287abc70498cad56f}}.
i
7fcbde149d9960692b0a499f902591fb
Motivated by those problems, a lot of new physics possibilities have been proposed. The leptoquarks provide tree-level explanations of both {{formula:029974ba-6c24-4ce7-aeb0-d22d4bc5b45f}} and {{formula:b3622d18-580a-4c43-9fa7-62405c17d1c7}} anomalies. Various types of leptoquarks, scalar or vector, representations under the SM gauge group, {{formula:d6b5e106-ac12-4756-9393-8201d1f9778d}} , are discussed in e.g. Refs. {{cite:40ea3b6639fd1d10e0d7d1721c0893f56f0606f2}}, {{cite:4131ff04ed6be5141772afbae33bf2d77574b21f}}, {{cite:e7a943aa1b9b662f3cb79022a3b6c3b513bd9363}}, {{cite:7dafe0f0a566b422309ec845182c6c06329d14d3}}, {{cite:9d351c05a5a65879bd47290a44364ba8f639c18b}}, {{cite:8b6bc762ccc367c383db7d0391e046ed002e3960}}, {{cite:7eb79973ec6e32349f366b60272046d59056595e}}. It is shown that both of the anomalies can be explained by a vector leptoquark with {{formula:d9d30446-3242-4c10-9dd4-e5281fd6c9c5}} under {{formula:e2eb4fc3-6f31-417d-b64f-f5c4d4a35853}} , which is realized in extensions of the minimal PS model {{cite:75d47eaa8c00b805d3bde031d47d031351ba9c39}}, {{cite:49b7ca011474c20f723f7c3437a4bc88745d8d1a}}, {{cite:475656339bf5ad5e2e9d3bda2a8104df4e173e9e}}, {{cite:4e8205abadb16ec1b9817e4924c0a30ff683dd66}}, {{cite:def0b15f736bba029aea177dcb5c2312c4c456c8}}, {{cite:0d6bab556cdda0d1214e2e4ecc8996ebba790d56}}, {{cite:3c6f9361b132518922ce9ba8677c9dcee29dfa5b}}, {{cite:e0f6ab12530bf12b351becc590b78527bec5dc44}}, {{cite:304c27aad014198e24ed2f1cc7a2129fa0fbf358}}. Besides the leptoquarks, the {{formula:887a1bc9-7d12-4dd5-968b-26f246415d1a}} anomaly is explained by {{formula:837c8cbb-c6ed-474a-a08d-ce6c2bc76106}} boson at the tree-level {{cite:d0e5f0d71027f12c1ff4e14bd94edf3e54da67bd}}, {{cite:493ed70e802e205c9270dbf5174237d2f1598865}}, {{cite:483179e128497fda26a2feeed5812d72e62dff67}}, {{cite:6ced618eba2828cab4a9a8bd44577bd06a20b332}}, {{cite:e086e6fba2e5de8ab2a999b603873a7bebe9f09f}}, {{cite:ce675c65fd0c9d879fd78c23d3b0be980a783a70}}, {{cite:340cc9a3bdc24307a243c396d6bb2d3d4c41641e}} or a 1-loop box diagrams mediated by extra fermions {{cite:1944d3b964868286262b098612bc1ee930378b9f}}, {{cite:c94ebd253dbd0695da2a3dfab0d750b6eb286e06}}, {{cite:b6b93288c6e78e9f8b8281a9c2f9566b06698f8a}}, {{cite:0645108a3f814bd3a68932a2f74dfa5adf21da12}}, {{cite:18eb862c5850df6bc5f937de39eb318e9f847418}}, {{cite:b83a0c4c43240bfc678ef54eb36fe7b1bf3963fd}}, {{cite:ff24e183528f321e9ca92fd4699440f2902db1a6}}, {{cite:2a1987a63fa093bb129d9c0518bbcda96a535cbf}}, {{cite:439463d7acebed5480a9a87025a744e29499cfc1}}, {{cite:0dc5fbe80f0e426ea29dd8df3916b5b1c9bf5f06}}. However, the explanation of {{formula:cc59f4de-256c-4cea-bb6f-92d99d77f1a3}} anomaly with a charged Higgs boson {{cite:dc224a298c94568a099bf0537b0c3bcb427e584a}}, {{cite:9768048ac7e08974da8ab4a1c2f18227bc219441}}, {{cite:92296e191514f28572ee91d050f234dda30da763}}, {{cite:18453472e180d427ebff42f92accd37f96c742a8}}, {{cite:6de9ce74d20ad09cc2688e92ed76fe8a1ee5a06c}}, {{cite:1bccebbfc6b2e5c3105d0576e5805396f60beeb7}}, {{cite:d322be59efc7fec81283e924e61e9989e4e22bce}}, {{cite:ca6721f37668859988279515484478c09264f39d}} is constrained by the collider search{{cite:8ff46a206090789360bb061bcd3264f84124e8e5}} and {{formula:0e301d33-9d65-4ae0-bac7-2b212f48e286}} decay {{cite:ef0137e8a98d8286be1d24e81bfaf2a7a47dd1a1}}, {{cite:d19ac5d4a75a9a647ff42f068bfbce66efef0be4}}.
i
9a5e2533e65ef6aa38441d04574d3247
We restricted our empirical studies to a conditioning set size of {{formula:ed420680-fc77-4c14-af71-f2394551e856}} , after finding limited advantage to larger {{formula:4f5ecffe-f4ce-4969-aa94-5be430472345}} . This echoes other GP-Vecchia works which have found success with small conditioning sets {{cite:1425f72d04716ca97a2e6fa9a10392d932d82880}}, {{cite:2251679c941023dcaa336aab45ef5eb8d6fc89bc}}, {{cite:b0e5f0cc044578b97e83256ea24bcc97960d339c}}, {{cite:3c8bd2fd6185c1dda5b1549f9219b297e7fa8320}}. Similarly, we entertained only two-layer DGPs. Our experience with three-layer DGPs – mainly involving surrogate modeling – is that one of the latent layers settles into a near identity mapping, resulting in a lot more computation for no additional gain. In some cases, the added flexibility of a three-layer DGP can lead to overfitting and adversely affect predictions/UQ {{cite:cbc5daf7319e5df259e6924c8dc1f5f721619733}}. Our test functions and real-data computer simulations may not be non-stationary enough to warrant two or more levels of latent warping.
d
890c2bcd32c0982a322002c3238fa9c2
Federated learning extends the traditional parameter server setting, where the data are located on different workers and information is aggregated at a central parameter server to coordinate the training. In the parameter server setting, many effective communication reduction techniques were proposed such as gradient compression {{cite:bdbe1a5bfdeb4f02ce48dfa5da48131d57e6f20d}}, {{cite:e34d99520c67cfed9f09f56d63c8904918029621}} and quantization {{cite:e7443545a473074669b4e51e7be963e08132d6ae}}, {{cite:a9d25d42aa0ceb71284ea623408124306b52a44a}}, {{cite:39303e735556ac87cbabc1226a29b2cd6f762190}} for distributed SGD. In federated learning, one can substantially reduce communication cost by avoiding frequent transmission between local workers and central server. The workers train and maintain their own models locally, and the central server aggregates and averages the model parameters of all workers periodically. After averaging, new model parameter is fed back to each local worker, which starts another round of “local training + global averaging”. Some of the aforementioned communication reduction techniques can also be incorporated into Federated Averaging to further reduce the communication cost {{cite:cef444afedb8df0390d21c51c128ea311c7dd7ac}}.
i
e6dda12b48b909cdc6e51649b6de7fa6
The results of comparison points other than MaskFusion and TEASER++* come from the literature {{cite:8befb2228b7cc623d66bbef18828e679d65ff6ea}}. The open-sourced codehttps://github.com/martinruenz/maskfusion of MaskFusion is used for evaluation, where the global SLAM module is disabled to avoid inferring object poses from the camera's estimated ego-motion. The dynamic object tracking module is kept to solely evaluate object pose tracking effectiveness. Its original segmentation module Mask-RCNN {{cite:a712d6a37868327578b296671d7be86d9148c496}} is fine-tuned on the real training data provided in the NOCS dataset for better performance while the synthetic data rendered using category-level 3D models are not used, as this method is also agnostic to any 3D models {{cite:10e8424da98c2b4874a5342f7a6cda1da66748bf}}. In addition to ICP reported in {{cite:8befb2228b7cc623d66bbef18828e679d65ff6ea}}, another state-of-art 3D registration approach {{cite:42ab29f4c23c1697a11849af5d11b75552f70d69}} is included for comparison and denoted as TEASER++*, which is robust to outlier correspondences and agnostic to 3D models. It takes as input the segmented point cloud and feature correspondences that are computed using the same modules proposed in BundleTrack. For BundleTrack, an initial mask {{formula:e78c3467-3fbf-4b80-961d-de5738d1e774}} is required as input to the framework and is provided via the aforementioned Mask-RCNN. During execution, BundleTrack does not require external mask input nor any form of re-initialization. As exhibited in Table , BundleTrack significantly outperforms the comparison points under all metrics and over all object categories, despite not accessing instance or category-level 3D models.
r
a5143e05f3565eb8071362d021504302
As the incorporation of higher-order curvature ingredients in the {{formula:5f77ea6d-234c-48c1-80be-896fcec0411e}} 's generic action as corrections appears to be a natural progression from {{formula:da3299e5-f55f-45c3-b80a-046a370b4fc7}} . Therefore, one can also construct the cosmological models in which the Gauss-Bonnet term {{formula:e82369df-afbe-48ff-a976-627f0c98722d}} or its generic function {{formula:bd2704c4-b3a2-4224-bbbb-52b47ee0d9b9}} , appear in the gravitational component of the GR's action. Such generalizations give rise to {{formula:6666c3ae-7fb8-4425-b100-b9844779e02e}} gravity models {{cite:27c3d5d5915974a433e06afdb6ad403b7e8ec912}}, {{cite:5260b4f20a175b7e9be2853326fa1888d824318d}}, {{cite:c645b3bd58d268bc39960aa1f201b2e23fca729b}}, where {{formula:75716260-d730-47c9-b086-7b4ffc7c0f63}} is a combination of quadratic-curvature terms, given by {{formula:51946a93-f7c2-47f2-b5de-da3c4b0a3b8e}} . Here {{formula:1085abeb-12bc-4f4d-8063-420365b348e6}} , {{formula:e5b811e7-d933-44ba-b277-5761b0c0f3ad}} denote the Ricci tensor and Riemann tensor, respectively.
i
661591f32d8d58cda3b313ab79286258
In Cooperative multiagent interactions, agents need to collaborate towards common goals, which introduces challenges associated with coordination, communication and teamwork modeling {{cite:af275c6d6a9d369ee97387d554a88301d541149e}}, {{cite:af048dd13527ae2a152fa3e4bc9d07afc927c1c0}}. Self-interested interactions, in contrast, require the design of indirect incentive schemes that motivate selfish agents to cooperate in a sustainable way {{cite:56300bc8bb593dd2801543adc9db865d8cdffb78}}, {{cite:af048dd13527ae2a152fa3e4bc9d07afc927c1c0}}. Cooperation is often framed as an altruistic act that requires an agent to pay a cost ({{formula:b0adf0d4-718d-44f6-8c67-e569727f0dd2}} ) in order to generate a benefit ({{formula:2eb72f1d-801d-49e6-b022-a8f0753d941b}} ) to another. Refusing to incur in such a cost is associated with an act of defection and results in no benefits generated. Whenever the benefit exceeds the cost ({{formula:b8e066d2-2cf1-491c-9646-08c8526c3bdb}} ) and plays occur simultaneously, agents face the Prisoner's Dilemma, a decision-making challenge that embodies a fundamental social dilemma within MAS {{cite:51c0e969ba959c8e359b3b7f866248542af877e9}}: rational agents pursuing their self-interests are expected to defect, while the optimal collective outcome requires cooperation. If defection is the likely decision of rational agents, however, how can we justify the ubiquity of cooperation in the real world? Evolutionary biology has pursued this fundamental question by searching for additional evolutionary mechanisms that might help to explain the emergence of cooperative behavior {{cite:e716837132e8c5f3e9ecc290a0810e318a925bad}}, {{cite:bc64d3f87b2365b3cb15eafe4e19c0046d2ecfa5}}. Some of these mechanisms allowed to develop solutions that found applications in computer science, such as informing about ways of incentivizing cooperation in p2p networks {{cite:6c8c6dc6143148e3693a780053983c5bcd50014e}}, {{cite:7d67f618df23cf392597ecc5fc340f510f617ac7}}, wireless sensor networks {{cite:bd5a991c7c7b318202af37a3c3ed749bcdb621d8}}, robotics {{cite:63d5ff9b7b9b3dd04977e20e069b7fa4802fda86}} or resource allocation and distributed work systems {{cite:3fc64064b2f6abb783206e604ee170f427ea223e}} – to name a few.
i
19cdb9f4972f444f63b3e2db2e114e73
In this paper, we investigate the holographic anomalous current at a finite temperature. For the external magnetic field {{formula:fcac5516-4bec-4a20-8396-be691170a765}} , we derive an exact expression of the holographic current. As for general background magnetic fields, we obtain perturbative and numerical results. It is remarkable that the temperature dependence of the holographic anomalous current is universal in the high temperature limit, which is independent of the choices of background magnetic fields. Similar to the case of free theories, the holographic anomalous current is still enhanced by the high temperature in dimensions higher than three. However, the temperature dependence is quite different from that of free theories. The reasons may lie in the fact that the holographic CFT is strongly coupled and there is non-zero resistance in the holographic model {{cite:382a9d69647dab3bc5d9a5e7359c13eccf3ef498}}. In this paper, we focus on the probe limit, where the background spacetime is given by the AdS-Schwarzschild black hole. It is interesting to study the back-reactions and the charged black holes to see if the universal temperature dependence of holographic currents still holds or not. It is also interesting to investigate the low temperature regions carefully. Finally, the temperature dependence of the anomalous Fermi condensation {{cite:2c97be67416549e15bda5d7b027f88e3aacf7f0b}}, {{cite:ad2f026f194c8c507481b5bcb4c9847890f0058c}} is also a problem worth exploring. We leave these problems to future work.
d
3e884dfd513d1b664f67bf41718b5417
For synthetic datasets, we vary the distributions of edge weights. We compare the performance of our proposed heuristic algorithm to that of the greedy heuristic under two models based on generating edge weights. First, we consider an adversarial model. Under this model, edge weights are generated according to {{cite:cfbf910c4002cab96191405e5ecce25ecd09f62b}} and as shown in Figure REF . We set {{formula:c039b538-ac5e-4e1c-bfe2-53b09cda435f}} with {{formula:a2118628-bc79-43c8-afd2-e3ec384b1c72}} being the number of clusters of nodes and the largest distance between adjacent nodes is set to {{formula:acdcf339-049e-44cc-8a1d-b294efea8836}} Under the adversarial model, the greedy heuristic finds a solution with cost {{formula:494af373-5316-42bc-a37e-5013d4c9de44}} times the optimum cost {{cite:cfbf910c4002cab96191405e5ecce25ecd09f62b}}. Next, we consider the Lomax distribution (a long tail distribution) {{cite:1ed154383b68938535f271f68cf331afe57ef07b}} for generating the weights since they are widely used in real-world applications {{cite:acf23293905c5f4c44e6d6f2a6752e03d1f5ebbf}}. We chose the Lomax distribution parameter from the set {{formula:3ae304e7-933e-4672-b320-827bfdb69729}} . The parameter settings are motivated by {{cite:acf23293905c5f4c44e6d6f2a6752e03d1f5ebbf}}, {{cite:453390e8ac7b2a0acca6dbd269bb66f13aaaf18b}}. We set the number of walks per node and length of each random walk to 20 for both deepWalk and node2vec. The embedding number of dimensions, return ({{formula:10b8670c-e1a3-4209-a64f-15f9b1e89ce1}} ) and in-out parameter ({{formula:54810919-8f94-44e2-9282-2ab4fba26bc7}} ) are set to {{formula:d8eb1d6a-ccb4-4a8f-820d-988a4f9c8694}} and {{formula:d7befee0-7e10-4a1b-9a91-231f200159a5}} respectively. The experiments are repeated 5 times for each parameter setting and the {{formula:4a894abd-e3fc-46ca-9452-c85955e42b31}} confidence interval plots are reported. If not mentioned, in our experiments, n = 100 and m = 4950 for non-bipartite graphs. We focus on MCM and BM algorithms in non-bipartite setting. We get similar results for bipartite graphs and hence omit them here.
r
c75ea661916eab4ba3ab07f04f796cfb
The capability of our procedure to precisely determine equilibrium systems corresponding to nonequilibrium pair statistics has important implications. First, our procedure provides an effective means to test the Zhang-Torquato conjecture for structures that span diverse hyperuniform and nonhyperuniform classes {{cite:c2732b4b39aead7e5c8bbf7df4979b941b45d242}}. Second, the dynamics leading to a nonequilibrium system that has the same pair statistics as one drawn from an equilibrium ensemble must be reflected in differences in their respective higher-order statistics. Thus, such differences in the higher-order statistics is expected to provide a measure of the degree to which a nonequilbrium system is out of equilibrium. Third, such investigations will enable one to probe systems with identical pair statistics but different higher-body statistics, which is expected to shed light on the well-known degeneracy problem of statistical mechanics {{cite:acc7421647a7c7b41c994bf90925fc5b4ce948c6}}, {{cite:1d80c3f92d67f70ae66df93be91856c678be4aa7}}, {{cite:0d87e241f1183694bd0e7c4a5e9fbcd787ee4cc7}}. Fourth, one could explore thermodynamic and dynamic properties of such effectively equivalent equilibrium systems, such as phase behaviors, excess entropies {{cite:6eec3fb37134a4e252e23acdf43722115dc4c130}}, {{cite:1b548f4d0d3cf1c1e142ba1cb7138a8eb44c5810}}, and inherent structures {{cite:d5dd988b680c77856eba61b855b5c30a1418e58d}}, which are outstanding problems for future research.
d
eee80316527670f9f4486b3b98cd31fa
{{cite:d0f4bb309453a7deef8a85b575a66b5f166f2aa1}} proposed the following weight update, {{formula:59a80345-ce0f-434b-ae55-68d5d9cb1bd5}}
m
f77dcd95b829907b13e9a2a14a23e92e
In this work, our goal is to develop efficient methods that can utilize decentralized navigation schemes {{cite:a8d8007a6e6c1434091328b62efc5ddf63ef931c}}, as they can handle dynamic obstacles and unknown environments. These decentralized methods can scale to a large number of agents without using a centralized controller and perform local navigation to compute collision-free trajectories. Furthermore, they can be used for robots with car-like or non-holonomic constraints {{cite:77f504be14e879efd4c6d6f16fc56da03d57cc9f}}, {{cite:70ccb06b0b4a99d1a53f96d40a30cfedf50ec463}}. Moreover, we would like to treat these two problems of task allocation and navigation as part of an overall coupled warehouse automation system {{cite:9113b33238e16ec13322a0c63f229675ec3a94be}} to improve the overall efficiency in terms of task completion time and navigation metrics.
i
21897247a6238314fae80fec31b6087c
Fig. REF shows the overall architecture of our X2Teeth. We define the input of X2Teeth as a 2D panoramic radiograph (Fig.REF (1)), and the output as a 3D occupancy grid (Fig.REF (5)) of multiple categories for indicating different teeth. Different from the existing single-shape estimations {{cite:67dc59b075ac0a1361fd76f8386634c30c14d48e}}, {{cite:6e230c4d7b0afaf594894980564338ae9f86e826}} that mostly employ a single encoder-decoder structure for mapping the input image to one reconstructed object, X2Teeth decomposes the task into object localization (Fig.REF (b)) and patch-wise single tooth reconstruction (Fig.REF (c)). As such, the reconstruction can be carried out at high resolutions for giving more 3D details under the computational constraint, since tensor dimensions within the network can be largely reduced compared to directly reconstructing the whole cavity volume. Moreover, both sub-tasks share a feature extraction subnet (Fig.REF (a)), and the whole model can be end-to-end optimized by employing a sampling-based training strategy for the optimal performance. With the derived teeth localization and tooth volumes, the final reconstruction of the cavity is derived by assembling different objects along the dental arch that is estimated via a {{formula:e747fc28-d069-4c85-b17e-bd42d27f0047}} function model.
m
69c16bbb8ce87478a89212139923b4db
In this paper, we propose an end-to-end framework to simultaneously synthesize face and body animation. Face animation adopts a learning-based method to generate lip movement and facial expression, which constructs a multi-pathway transformer network to jointly model the speech information as well as phoneme labels from textual scripts. Besides, we also adopt text analysis to extract semantic key words to perform expression fusion. In the branch of body animation synthesis, we adopt a motion graph-based retrieval method {{cite:ba6dd8e3f914e43148c6fbf4a109147365aa7f29}}, {{cite:5f716babfdbce3dd727ba3e223bacb71e0574aad}}, {{cite:e4e65d3f932ac0cec263b0b565fad66a9c7959fa}}. This effectively avoids average pose when synthesizing. In addition, we propose two synthesis rules to make the whole synthesis process fully controllable. First, special semantic text requires corresponding semantic motions. Second, the rhythm of non-semantic motion needs to be aligned with the phonetic rhythm. This not only ensures that the synthesized motions are highly speech-correlated, but also the semantic movement greatly enhances the expressiveness of the animation. Furthermore, our method can synthesize diverse movements under the rules, and the demonstration video is shown in https://youtu.be/MipiwU3Em_8. {{figure:83249df2-3c5d-4084-bb4a-aa8e6f65c3a5}}
i
1d072d976f50cbbb3a110ff4a8487167
LightGBM {{cite:9c04322dd16ec6c42453ec35f6f880697186135c}}: LightGBM is a gradient boosting framework that uses tree based learning algorithms. LightGBM is being widely-used in many winning solutions of machine learning competitionshttps://github.com/microsoft/LightGBM. MLP {{cite:1051d070e977a5790accf0f00250cb79c22c4c18}}: We use the base structure of our AITM framework as the single task model. It is a Multi-Layer Perceptron. ESMM {{cite:a1cc74616e064e2b17b5d2163d05c269673a4200}}, {{cite:9c7a301f09624755d8058a1dec82aafc45769424}}: The ESMM and {{formula:f859b0bd-8f56-40e1-9ba2-6570d78e7ca6}} with Probability-Transfer pattern are designed for solving the non-end-to-end post-click conversion rate via training on the entire space to relieve the sample selection bias problem. OMoE {{cite:ecfbcf9259dfacf5d5ce528d4ac9983747d6f5f8}}: The OMoE with Expert-Bottom pattern integrates experts via sharing one gate among all tasks. MMoE {{cite:ecfbcf9259dfacf5d5ce528d4ac9983747d6f5f8}}: The MMoE with Expert-Bottom pattern is designed to integrate experts via multiple gates in the Gate Control as shown in Figure REF (a). PLE {{cite:9ebdb2dad38825d22dc01d2bfe2aa6c8afa7847a}}: The Progressive Layered Extraction (PLE) with Expert-Bottom pattern separates task-shared experts and task-specific experts explicitly. This is the state-of-the-art method under different task correlations.
m
bd7be6c86f823cd8a1dbf8c3d8b558f8
In semidetached Algol, mass from the coldest (donor) star flows through the inner Lagrangian point onto the hotter (gainer) star forming a gas stream. If the gainer is large enough, the stream hits the star forming a hot shock region on its surface. If the gainer is small enough then the stream turns around the star hitting itself and eventually forming an accretion disk when spreading by the effect of the viscosity. This was investigated by {{cite:d48e21204935d9e5497298c8997ca84ee859754a}} who determined this gainer critical radius {{formula:11b9ceed-72a0-46da-b19c-c51eb9b31471}} as a function of the mass ratio. Actually, due to the finite width of the stream, a range of radii marks the transition boundary between impact systems and disk systems. On the other hand the disk, if formed, cannot extend beyond the region when the tidal forces impede its stability, this maximum radius {{formula:ca0c60e2-efa4-4005-bb6f-b2f80351a3bd}} is often also parameterized in terms of the system mass ratio.
d
535a80ba0078587ee91eb13e519d320f
where {{formula:8f1f3dd3-fb7c-4683-9f12-a57e87f80006}} is a relaxation parameter, and {{formula:682f4fac-8de1-4eb6-8e95-4cae0b0b6a9d}} where {{formula:7bb44f62-751d-420c-af49-75413703c5a4}} , and {{formula:b422fc28-0f23-4f04-bec6-380912c3a939}} are diagonal, strictly lower triangular, and strictly upper triangular matrices respectively. Here, {{formula:b13e20ca-4e2e-4ccc-8498-1152638a2e35}} and {{formula:ee3900ff-3bc8-4cb4-a9aa-f870850d0aef}} have zero diagonal elements, and the assumption that the diagonal elements of {{formula:f093007b-3944-4344-8da2-89dec38b97d7}} are nonzero ensures that {{formula:8b99b153-3568-4a49-a842-a86e069abfa6}} exists {{cite:cc83803044bb6a8f0f29683e53799d0e8655802a}}. The Gauss-Seidel iteration is a special case of the SOR where {{formula:972b4049-2eb7-439e-b783-ce0fc4d9078f}} .
m
dbc063d0a38a5d2422676aa297618df4
In this section, we first discuss the shortcomings of LIIF{{cite:1924daeed416ac3f86ccb7b025d1f3934a43ca59}}, propose the solution, and finally present the overall architecture of our model. As described in sec:preliminaries, LIIF{{cite:1924daeed416ac3f86ccb7b025d1f3934a43ca59}} samples only the center to render each pixel. Essentially, LIIF ignores the fact that an image pixel is actually the aggregation of the color in a small area, and considers the color value at the central point as the color of that pixel. Imagine that we have an HR image and a corresponding LR image down-sampled by 2, where pixels in the LR image are not necessarily the same as those at even positions in HR. Therefore the scaling factor or, in other words, the size of the target pixel is crucial in this task. And to address the problem, the original LIIF{{cite:1924daeed416ac3f86ccb7b025d1f3934a43ca59}} simply concatenates the pixel size and the central position of pixel area as input to the MLP, called cell decoding. But both our and LIIF's experiments reveal that this cell decoding strategy is not guaranteed to improve the quality of results. {{figure:8c03df6e-f2e2-4b64-8827-80e0baefa384}}
m
672a937a556d59d2ecd33f73414e3e4b
In this paper, we show that such a catastrophe never happens with the other major dictionary compressors, the Lempel-Ziv 77 compression family. The LZ77 compression {{cite:55e60a4cea220cfaf2bdde9d1797389734dc829b}} is the most important dictionary-based compressor both in theory and in practice, it can achieve {{formula:eeda1d50-f65f-41c8-88e4-cb75e8ba7ed2}} compression in the best case as opposed to the {{formula:4a393999-f4cd-4a3f-a15c-25a54cb05060}} compression by the LZ78 counterpart, and is a core of common lossless compression formats including gzip, zip, and png. In addition, its famous version called LZSS (Lempel-Ziv-Storer-Szymanski) {{cite:13fbf2dc5cfeb0dc00a89ec61c3c1fbd71cc29a7}}, has numerous applications in string processing, including finding repetitions {{cite:76a15a6b71d755833dbf9e729e8c33b4107194cd}}, {{cite:2a685edd73649e688f4eda60c5ca2a48b8a28457}}, {{cite:cffcd6f682a4c793586038c64a5932520acb27d4}}, {{cite:16dc907dfdaf44616905491216e8abd6d63818df}}, approximation of the smallest grammar-based compression {{cite:c67d33b4872976ff6891b9d86466c80e259e63a5}}, {{cite:f797305a210cada4ce2ab8f0549ddade6ae37a0b}}, and compressed self-indexing {{cite:86dbcbec2e6e562e7dc6db1f5dd0be1e83ac2120}}, {{cite:c2f212145c0b8b1b7f7bbeaf07a757d6b530d260}}, {{cite:b27b0d4638e6ffb3bd5051e4e98749cae5060280}}, just to mentioned a few.
i
398c2c85edb14ae4b93e641d8943fbcb
GerryFair algorithm is an in-processing method for mitigating bias in datasets which takes into account the individual level of unfairness. The dataset needs to be specially pre-processed in order to fit its requirements, in a similar manner with the optimized preprocessing method. It also has several hyper-parameters to be tuned before being able to perform a suitable job for the dataset.These parameters include the fairness target ({{formula:92a83b18-def1-4316-98f7-66dce40a2e56}} ), maximum number of iterations, the maximum L1-Norm to be used for dual variables and the learner to be used. The learner is required to be a regressor. Our typical logistic regression used as a classifier in the experiments is not supported by this method, therefore we tried the learners recommended by {{cite:543d6cef56d132c91294dc356c566f96b3185ac0}}. We found it quite difficult to tune the parameters in order to obtain a reasonable trade-off between fairness and balanced accuracy. The method tends to overfit when dealing with the german dataset because of its small size.
r
5ea7653746393301fe28cb1714c6e0a3
The so-called weak measurements, used in {{cite:fec102222f0d4c9ec480995629a1b54bca865be6}} -{{cite:094884a6b607054304bf0d85ee8961909c332134}},{{cite:99c91c08c18d57bf9ed555f934ed63f3ccbcdcee}}, quantify particular relations between Feynman's amplitudes {{cite:29c3ee18c7b84402f6390d1c14fec3292cf5727f}}, but provide no insight into the amplitudes' meaning or physical significance beyond what was said in {{cite:5af67cc0a6cc74b16590dcb09aaa343b233303ad}}. A quantum particle is not in two places at the same time - it is either in one place, or it is impossible to say where it is {{cite:fe8b9099c498075725c6402519d2317a98f458be}}. Similarly, using the weak values as the evidence of the particle's presence does not prove that photons can be found in a place they never entered {{cite:a9893e5454dd06832686db3036148ca4c123d80c}}, but only that two non-zero amplitudes may sum up to zero {{cite:531c7bcdd612fef4ed654b736d1f2aa65a2d5481}}.
d
6c6a00566a12442ffe0c5729e20a69b4
Furthermore, deep learning (DL) becomes a prominent tool in VS. Comparing to traditional machine learning (ML) algorithms{{cite:4c5947f0cba42a65acbb3e7fa5a333f604bb37b4}}, {{cite:482680d4a514b358803c77934390337e708fa0d9}}, such as neural network{{cite:8301f933c59723aa60fab0d2bf9b9054401d5372}}, support vector machine (SVM){{cite:193b4b3f9820e46870c213e344c84bb269a8dfd4}} and random forest (RF){{cite:9cf976b3067ec250b9bdbad9508f592a1b3183d1}}, deep learning models require minimum feature engineering. Ideally speaking, if enough data is provided, representations or features can be learned directly from dataset without any human design{{cite:4c9008c48fe4979327ea1547947ab131cedb899c}}, {{cite:e5e3e754ecc83f68e7d670ea2f5482451c9e80ea}}, {{cite:d1fad1dbb3fd6371a26efcebd4f0af9ce84aedbe}}. An early successful DL example is Quantitative Structure-Activity Relationship (QSAR) {{cite:3b9954b3ca8c9ce167828a06daea871724efa5a1}}, which operates over molecular fingerprints. Wallach et al.{{cite:d7a81015af463348240d8cae87d3e7fc6bb8ae7e}} find a way to apply 3D convolutional neural network (3D-CNN) to a protein-ligand complex which is represented on a 3D grid. Ragoza et al.{{cite:cef36b682a4add4d3cfc59ccb8c5c390e0a1c16b}} further extended it to include active and inactive binding poses classification. These 3D-CNN methods successfully outperform previous works and also improve the accuracy of predicting absolute binding affinities{{cite:f8380263cd03c4b3b101846910a94588adb52673}}, {{cite:9cf976b3067ec250b9bdbad9508f592a1b3183d1}}, {{cite:d02646949928aee94bca71b2b0157458ee366ff0}}.
i
f40ca8085a5218141b3d9084116807e0
When calculating SUSY indices, one generally use supersymmetry to argue that the index is invariant over the moduli. Then one may simply work in the weak coupling limit to obtain the index via a free theory computation. Such twisted indices have been looked at in the literature in various particular examples {{cite:b87bed6b0f190ae47f24452a8eba4abfd2d6b12f}}, {{cite:fd7cc99f708f7aa6aa710ccb5c8aef4f7ef335ec}}, {{cite:e34fdb9df4bb33e2f393f7e1a1f916b75f6d5dfb}}, {{cite:1ff13c3de7f8affe8f4ea967223a082f9a7db3eb}}, {{cite:8dc87619b8cb9cec5bd1070a8da3dafb9b3c5ca6}}, {{cite:175f7453d563f7ae90b00b71eedf7ca0fa215766}}, {{cite:b9e7805175d86e977af4fa393e0b1a8ba87b9bed}}. We highlight that a number of developments related to the application of Hilbert series and the Plethystic exponential in QFT appear within the context of the operator counting program in effective field theory, see in particular the technical and conceptual ideas appearing in the works {{cite:cae45e47d4516ae7fc58b17e529e1a28af26748b}}, {{cite:ecf6d175aa0385749889e7a16312101325d851fb}}, {{cite:5e724a27812a8e8396d449562114283ecabb200c}}, as well as several others {{cite:31e6109ff6031830d50661520ecc8c8545d94e0e}}, {{cite:438e69572a763ebb6e1e382fda888d4503356c0a}}, {{cite:0d189254ddf695aa9d12e1637a530c78847c942c}}, {{cite:0ba8ed64b51aaa5f34d1808aa2da051762a49790}}, {{cite:d9f14a39e7179be1aa6c02faebc8a9cadab86957}}, {{cite:597da3013858950895ca1949c1f74fe42fbf3a47}}, {{cite:ed66a5583c86bfbf5ee5f86ddf1d4fb45128a6d7}}.
r
b1353975efc93b3140e40e25a917f45e
The condition {{formula:8069bcef-77be-445d-b335-7fdbe9287535}} should be satisfied for the jitter radiation, and {{formula:b7cda5b5-2c30-4d62-8a5b-83582221c999}} is called as the wiggler number {{cite:93bf8335463e59df882980b93db7c07ef4463d6a}}. It indicates the deflection angle of the electrons in the random magnetic field compared to the beaming angle. If the deflection angle is smaller than the beaming angle, we have the condition {{formula:8995f4df-79e3-4cb9-9b96-78db75ae767b}} , and jitter radiation is valid {{cite:a044b76c4404fce5db9dfb94781852ade454886b}}. We then calculate the wiggler number as {{formula:4f17bbb1-ed6b-4641-bd62-0dfd45785dee}}
d
34f79455ae136d130fabd62d81798972
One of the fundamental problems in deep learning is to characterize generalization bounds of non-convex stochastic optimization in the empirical risk minimization (ERM) setting {{cite:11b7811941058c8878c0f1c18beff67ba2d697cf}}, {{cite:3ca5d8dd06cb02ade36056e5a85592c4b011920e}}, {{cite:7263b2f5545e2a2a45c4dacb64df4f0d90e5929e}}, {{cite:453fbb3f5c8ee6572dbba6191a29b850a0cbdef4}}. Some traditional approaches study the generalization bounds by measuring the complexity of the hypothesis space in a data-dependent manner (e.g., the VC dimension {{cite:6e2b6cdbd82462bb56e590a1ed90bfa98999ef4d}} and the Rademacher complexity {{cite:fe39788a448a6e7d9acf64c00e49bb4419e63d88}}). Nevertheless, directly adopting these complexity measures often fail to characterize the generalization ability of various learning algorithms for training deep neural networks (DNNs), in which the algorithm explores the hypothesis space in an algorithm-dependent manner {{cite:ba3b8031b30d3895aa07f9b9cc01956083dad0bf}}, {{cite:11b7811941058c8878c0f1c18beff67ba2d697cf}}. Prior works have shown various empirical evidence from the observation that the hyper-parameters of stochastic gradient methods could significantly affect the generalization ability of the learned DNN models {{cite:11b7811941058c8878c0f1c18beff67ba2d697cf}}, {{cite:60fc7eb7567e620846b62e96e2fd69ed4200ab2e}}. For example, the large batch size training often fails to generalize to the test dataset well while the small batch size could introduce more stochastic noise as an implicit regularizer, which further improves the generalization ability of the learned DNN models {{cite:60fc7eb7567e620846b62e96e2fd69ed4200ab2e}}.
i
fee7e76c97184908f4c668ca02c40dbc
d) The approach of Ref. {{cite:e662682e45ba00181fb60b93579a6bad94b469a1}} is of a strong coupling type and therefore {{formula:4fe46e42-ae68-4793-879d-e6d74bae7347}} is a good quantum number, which is not the case in the present paper. Indeed, we use the laboratory frame and the meaning of the quantum number {{formula:5ea0b534-6f44-4abc-9e13-e210e2fb1343}} is given by the fact that the {{formula:5a33af04-cb02-41b0-b09b-0a5f27096620}} -component of the spherical function prevails over the components with {{formula:9782e3bf-3cc5-4d71-a940-fa9f97ca323c}} .
r
aea745a57efd169ae967e34643e030d9
We consider here a rigorous procedure of the application of Friedrichs and Krein-von Neumann extensions to the abstract settings of Section REF . Let a dissipative extension {{formula:b0b168d2-792e-43c7-a7e7-e55c507bf641}} of the abstract symmetric Maxwell operator {{formula:c7ec41ac-a12f-40e8-a7e8-443e89c7f320}} be defined via the condition {{formula:c555fe04-e95b-4450-815c-7430096b41e8}} with a nonnegative impedance-type operator {{formula:dd7c309a-6329-47dd-b644-83de0de2e6a1}} , i.e., {{formula:99a49737-50d8-403f-adef-77dd75e0c2ac}} . Let {{formula:26bf29dd-8dcd-4f21-be19-83418bd81d1a}} be a certain fixed linear homeomorphism from {{formula:865b678e-2d0d-4454-8b15-f1752619551c}} to {{formula:1e9a30c6-98fb-4305-878b-c4d779efce67}} (for Maxwell operators we use {{formula:749c2ce9-36dc-484e-8db1-76b120f68d90}} ). Then {{formula:66a48c6b-4b8d-4f38-a6ea-bffed1df2cd1}} is a nonnegative operator (possibly nondensely defined) in the pivot space {{formula:833a0be3-cba9-4fbc-947b-e0e00461a756}} . Its graph {{formula:6bc558f7-27c8-46e0-aa3b-9dea56b6d05b}} is a nonnegative linear relation in {{formula:5cfc81b3-4491-48c4-a843-8ee6d027a481}} . The class of selfadjoint nonnegative linear relations in {{formula:05e0dcca-13df-4edd-b761-551836864113}} that are extensions of {{formula:dcdc3411-e7d1-4648-9186-5de98691befb}} can be described as a closed interval w.r.t. the partial ordering associated with corresponding quadratic forms {{cite:59de2adb2249b69e8d6ae93ff3c5518264614a06}}, {{cite:b0b2c06c0bfd90b2f06e7b0984856feb9a98a2f0}}, {{cite:6595e86e2056f93bf8703ed630bfd8ace1c4c14c}}. The Friedrichs extension {{formula:13a69a41-a425-4a59-b748-eabe2080ca0d}} and the Krein-von Neumann extension {{formula:6139e6f5-b512-4288-b8c6-eeb2e728b252}} of {{formula:b9ed8f97-c588-4816-ab7a-537a88098f2c}} {{cite:0597632161ff0fa62a8e6015d9521d68368c9fa2}} are the greatest and, resp., the smallest elements of this interval. So {{formula:ccbdf999-8b95-47ce-8bc4-e2474c654cac}} are nonnegative selfadjoint linear relations in {{formula:41085210-de35-402b-94d2-a2a6af540413}} . Then {{formula:db29c50a-4b2f-4248-baa6-58962a16477e}} are m-dissipative linear relations in {{formula:73e2691d-de2d-4a00-a28a-062b7c6edb3a}} containing {{formula:a91e79dc-6424-4396-9593-ca7ebbda313c}} , see Remark REF .
d
36edb341388b9d8a98c97a2287b557b5
We now show that {{formula:315d635d-5b0c-4899-ad35-463bc4c207b3}} in probability with respect to the density {{formula:ce7663cd-4167-4a83-829f-de9b3260359d}} . (REF )-(REF ) easily implies that {{formula:7f4a2254-47ec-42df-9286-e5d04ac6de83}} for the weak convergence of probability measures. Similarly to the proof of {{cite:ff99abd185da4e08092d4310d7e719d5ef499136}}, this convergence implies the convergence of transport plans, meaning for all continuous bounded function {{formula:13a6d17b-35d4-48eb-8a76-3453898ab372}} we have the convergence {{formula:574bdca6-4af2-4fb7-a391-6b9c85521cfe}}
r
692e6c642111541f01f0401f0e276fac
If many super-Earths can in principle be magma ocean worlds, they may host consequentially large volatile reservoirs in their interiors. So far, these deep mantle reservoirs are not taken into account when inferring volatile (or water) budgets from planetary data. Previous studies have published inferred surface water contents {{cite:7a192280e257ad6cf7678d50cc1e4f9860b88aad}}, {{cite:ba1d88530a63fbb08f4ae1dce68efe7e065d0eac}}, {{cite:92703a47330003d19d6263f7ce9412607c724539}}, {{cite:1dac55c8682a212d0d8eaf273e23e81649bc2bd4}}, {{cite:36e52e2886607f802f9d92213d590f6da37d6fa4}}, {{cite:6dc2a0d3f1e8dc20f0215c2ef433fa744b387758}}, {{cite:90722959c1a75aea141a2a30c3379154d98a8562}}, {{cite:339ed9f6d4714f6dbf9e9da0c18d0c10b4eef288}} or are limited by only accounting for surface water reservoirs when modelling interiors {{cite:da9f9fa4c293b0c456d7298d19d7d609293cf082}}, {{cite:86e8bfad46223111ca8c2a6eda6542b7eb7cb3f6}}, {{cite:baf01a852c9fc644c23fb1d88c1fa8dc06f328e7}}, {{cite:dce738a818157e65973d11d842505a4cb70a3adb}}. Our study highlights that there is a clear difference in bulk water contents versus surface water content. Taking magma ocean reservoirs into account can increase water budget estimates by one order of magnitude for a given radius or it can reduce calculated planetary radii by up to 16%. This is equivalent to a change in planetary density of 75%. Clearly, there is a need to reinvestigate possible water budgets for the populations of observed super-Earths and sub-Neptunes.
d
9b1ad90b0d36e38922dccee057d11985
Though the realization of the Kitaev model in real materials is still challenging, it's possible to be realized in a cold-atom system {{cite:9175d897947753a23587035e2a6af66a864ed1e8}}. At the same time, the fast development on single-site microscopy in optical lattices makes it promising to achieve and manipulate the Majorana zero mode we discussed in this work, especially through the locally polarized spin in the Kitaev model. In such case, a braiding procedure of Majorana zero modes may be performed according to the scheme discussed in a p-wave superconductor in Ref {{cite:74b8aaf6c12b8981593cba7737f14f6b14f14706}}.
d
bb21962909527bc5388d4375b0544cb7
Comparing the behaviour of fast endosomes (MSDs, VACFs and propagators) to the behaviour of the entire ensemble, we find that they are most consistent with FBM models {{cite:0b9d254f33583ca75ecf309116be6b92687bf457}}. Therefore, we conclude that fast endosomes follow heterogeneous FBM {{cite:0b9d254f33583ca75ecf309116be6b92687bf457}}. The ergodicity (Figure REF A) and the VACF (Figure REF A) suggest that slow endosomes are also described by the hFBM or heterogeneous generalized fractional Langevin equation motion. For slow endosomes, crowding and obstruction effects could also lead to sub-diffusive behaviour {{cite:092e012117454941f63fad6a63be42bebb88d1ad}}, {{cite:02f2c4d2922c7614b12c9431fb67417d0ce38108}}. It is known that obstructed diffusion has many similarities with fBm such as stationarity of the increments and the equivalence of the time and ensemble MSDs {{cite:2cd8bd8476e35ce37f4052519028ffb7f60a78cf}}, {{cite:3d2927cec8a712fa535c3be6086fa8e0121a529b}}. The propagators provide a clear way to distinguish obstructed diffusion from fBm. Therefore, we calculated propagators of experimental slow endosomes and compare it with analytical prediction for the propagator of obstructed diffusion and prediction of heterogeneous fBM. The results shown in Fig. (REF ) indicate that slow endosomes follow hfBm at longer time scales while on smaller scales obstructed diffusion likely contributes to their sub-diffusive behaviour as well. Crowding effects remain as a possible source of anomalous diffusion of slow endosomes. Recently, numerical simulations of lipids in crowded conditions of the membrane was shown to be multifractal and anomalous. The dynamics was no longer described by the mechanism consistent with the fractional Langevin equation, or by any single known mechanism. Instead, the motion was found to be non-Gaussian and heterogeneous, yet maintains its ergodic properties {{cite:9165bd8c7a21563c21d3569870ee0655716d8d52}} which is similar to what we observed for experimental trajectories of slow endosomes.
d
f4f370a62a4704b25cc3ab63899cb4b4
In the plasma physics community, particle-in-cell (PIC) schemes have been widely used for the simulation of kinetic plasmas since their inception {{cite:effa0fea170f8d39bee7e5ff39c772f6d6eafb95}}, {{cite:d51e706fb2a98d8becfb3409df08793a97359fbd}}, {{cite:041cb59bbbabf4edb3a58d3ffd2e11e914d61598}}. The attractive features of PIC schemes include simplicity, ease of parallelization and robustness for a wide variety of physical scenarios {{cite:844ed9ba5418a54f9baf15d14ff853eeaffe5997}}. Because of their flexibility and versatility, PIC schemes are employed in many production level plasma simulation and particle accelerator codes such as TRISTAN-MP {{cite:440f12acfe8740743533c690bfb3fe299ea771bf}}, {{cite:9816048f3e4fb3d045ac3bd8254e70d666483e47}}, ORB5 {{cite:6e8bd457d68a88a7e5b516fda054cc4a2a1de18c}}, XGC {{cite:6859de1d14cf21b46d5eeea672c2337cb0e7eb34}}, OSIRIS {{cite:e5ba6832a54da67ff9b982bb425bd618e1c0aabf}}, IMPACT-T {{cite:3898447f86e2e5f1d6d505951c53d6f10dcf1fe8}}, OPAL {{cite:c7b65d171e6f0ef2e4b2b5d0a540ab8ad604d36d}} and Warp-X {{cite:934753a3a47697c6b8de2e4e685c844f18561c55}}, to name a few.
i
3223014ebe94a72bcf24fb3fe183b024
Regression tree {{cite:c8607db26ca2bcd6de72332efb2a3e462384f86b}} is the basic building block, for classification, regression, and ranking tasks. The idea of trees is to recursively divide the data points on an axis-aligned fashion based on some “gain” criterion, and report the average (or weighed average) responses of the data points in the final (sub-divided) regions as the prediction values. The sub-divided regions can be organized/viewed as a tree, with the leaf nodes corresponding to the final sub-divided regions. {{figure:f1d14364-34a8-4b9a-9190-6084fc180f02}}
m
42e48bcf881049369573c63fef10e64c
Lemma 18 (Tail bound of sub-Gaussian variable {{cite:9136671d0b712488abe2bb8f512bf917d188cf24}}) Let {{formula:a421614a-c2ee-46e4-ae54-007522d82a7b}} be a sub-Gaussian random variable with mean {{formula:1ec1fe17-9f42-4190-9d4a-fcebe7939e95}} and sub-Gaussian parameter {{formula:317f1d10-c8ab-4048-9770-809d0495854b}} . Then, for any {{formula:9079463a-5833-4d6f-b503-df70f4f10cb7}} , we have, with probability at least {{formula:032aca0e-d79a-4d16-877b-e58cc3743742}} , that {{formula:4fd455fd-793b-4d9c-8ccc-d0b11003fd52}} .
r
3b80596b2e2dba2726c9c1d387f83206
In parallel to these empirical evaluations, several works have proposed that explanations should fulfill a certain number of `axioms' or `unit tests' {{cite:c0bdbd74c5cec89500d4e393d1e104784580f471}}, {{cite:20747ed26ca9215feebcf916d311234fc7a06a0e}}, {{cite:206b6de7aecacccea285797a1d6f04cf543c4822}}, {{cite:d7c047cd33499a85aca51ac76daf4f68254c87df}}, which need to hold universally for a method to be considered good or valid. We place our focus on the model-randomization-based sanity checks {{cite:d7c047cd33499a85aca51ac76daf4f68254c87df}}, which state that the explanation should be sensitive to a random permutation of parameters at one or more layers in the network. Specifically, the authors proposed to apply measures such as ssim {{cite:54b26104b7bae32a12ba684a0596a210e6d5ebcc}} between attribution maps obtained from the original model and a derived model for which the top-layers are randomized. The idea is to require that methods used to compute attribution maps should exhibit a large change when the neural network model — i.e., its defining/learned parameter set — is randomized from the top. The authors of {{cite:d7c047cd33499a85aca51ac76daf4f68254c87df}}, {{cite:e2ae85d1938f8f8d015d96293f25c1f3a26d7c8d}} suggested to discard attribution map methods which perform poorly under this test — i.e., have a high ssim measure between attributions obtained with the original and the randomized model — under the assumption that those XAI methods are not affected by the model's learned parameters.
i
1f4c97695ca8448e8a440497174bc3d5
If scaled by the rotational constants, the spin-rotation interaction constants determined for HC{{formula:1ce7c998-0a15-4450-b3e3-5a4f9e5ac39f}} HCN are similar to those for the CH{{formula:714ef522-e751-4c7e-a33c-5e3e8b679c93}} C{{formula:83b1d502-a384-4db1-8ea7-4480078454f7}} N isomer, as shown in Table REF .The {{formula:bfefedb2-6bef-4f11-9866-7e5e810fe18a}} , {{formula:a29a1990-9735-4617-a369-cd57887ce136}} , and {{formula:cb1d575b-74e3-415a-adaa-15f3caaf70e0}} constants for CH{{formula:de76d77b-bc67-415b-a110-65f834b6276a}} C{{formula:41215672-61ce-4fd6-84d3-ef9664e6d42e}} N are 288000, 2195.08395, and 2177.77590 MHz, respectively {{cite:9db1e62d02a91a9576f398b94bfc07c691b58a6e}}. This implies that the two radicals have a nearly equal-energy excited states, {{formula:bd6b02c2-4565-497c-bd42-8c7c78701314}} in the case of CH{{formula:9fe327c7-8aff-4e4b-aca9-4fec8d431dec}} C{{formula:76c06dd6-2f88-48c8-8b70-ce9c8b6b77e1}} N and {{formula:e14b6d20-41b6-40dc-b76b-a678beafd223}} for HC{{formula:fb12b4d7-6a2e-4894-bfe7-3bfc38fa603e}} HCN, which contribute mainly to the spin-rotation interaction constants in the ground state through the spin-orbit coupling. The Fermi coupling constants give direct information of the unpaired electron density on the nuclei. The {{formula:0887215f-79b4-401a-96a8-4219810d0ff9}}{{formula:e21011b0-f4e1-48e8-9035-964b8532dc55}} and {{formula:b87705b6-5830-4bb6-aa6b-e986de71a322}}{{formula:e809ace7-6fd1-4060-8ab2-e917c82484f3}} have negative values due to the spin-polarization in the C-H bonds. The difference in the absolute values between {{formula:2d333bec-80e7-4173-be80-867bc01d91dc}}{{formula:7df2545c-7826-410a-81c3-e90d9128b223}} and {{formula:2eda3bd2-4983-447e-9d8e-4aec4095b245}}{{formula:7c1dfbf7-099a-4ae5-b704-5752b3304333}} indicate that the unpaired electron density in C{{formula:cb51c1a2-94d6-4312-b210-fd8fe4ea7958}} is lower than that in C{{formula:0fa663f2-b0c2-4e13-84f9-ba6ffd503184}} . This is consistent with the predictions of the molecular structure and the unpaired electron orbital depicted in Figure REF .
d
0be669dfcc0da9474bf82aa4f916f2a7
The maximum rotation gain in reflection is larger than that obtained in transmission. This apparent advantage is perhaps illusory: the strongest rotation gains occur together with the smallest efficiencies. In this regime, the rotation angle {{formula:46e5e0a7-c906-4710-b63b-4cbc872240c4}} is large because {{formula:3b9e2e14-5fc3-484c-a459-666cc94a05a8}} is small, due to the destructive interference upon reflection from a cavity near critical coupling. Such “dark fringe” interferometric techniques can be advantageous, especially in high-power interferometry, when the detectors' optimal power levels are below the input power {{cite:95d8a6d402833a3c98dce56db20dcb6124eae26d}}. In probing atomic systems, however, the input power is limited by saturation of the atomic medium {{cite:33a6da9024d6e07270cfb0b5dca2a86d4f0dde7c}}, {{cite:5d84f64b586dd9f6bca6a035167eb9d1184a8513}}, {{cite:3584a980f3116742affc88767f8efd4e92e7d1ee}}, leading to power levels that are easily detected with typical photodetectors. In this scenario, there is no advantage to reducing {{formula:36043751-1b30-4ae4-9492-8eb74f7b05ed}} .
r
5414b56fcb60662acdcdb0838787cd54
Electron localization function (ELF) of MSi{{formula:e9d54ea6-5d75-4184-af83-33c9a6e19c7e}} Z{{formula:94eb4fab-4015-406a-aece-3c9650bf11e4}} is considered, as shown in Fig. S9. The maximum ELF value between the two atoms of each bond is above 0.85, indicating interstitial strong localization of electrons and thus a covalent-like nature of these bonds. Considering the polarization effect of group-IVB and -VIB transition metal atoms on phononic nature and further thermal transport properties, we also calculate Born effective charges and dielectric constant, listed in Table S2. Phonon dispersion and harmonic ({{formula:0580dad1-7152-4d63-bbf4-bcbae4e7eace}} ) interatomic force constants (IFCs) are calculated via finite displacement method within PHONOPY package {{cite:d34a82f3a02185c6bc6c9fcacfc27d7e507fbd08}}. The comparison of phonon dispersion of MoSi{{formula:73abcf6d-b2f3-4ddb-9ef7-50c08503a97f}} N{{formula:3cff4f96-1a9b-48ff-bb05-a41df759f1b6}} with or without polarization is shown in Fig. S10. It is worth noting that, the high-frequency optical branches show obvious splitting near {{formula:1f28a8a1-c889-4c65-9ed7-08893f82c65e}} point which indicates the strong polarization phenomenon. Thus, Born effective charges and dielectric constant should be considered in calculations of phonon dispersion and thermal conductivity. The supercell of 5 {{formula:e2f8e7d7-9ee2-45e8-b7ea-478160015bdd}}  5 {{formula:f742a10c-0f71-4f6c-b61c-a223ab0dd5b7}}  1 and {{formula:091d7ae2-e7f7-4d79-962b-92899e28ddce}} -mesh of 5 {{formula:ed205dd0-1e8d-4ee1-a52b-7fc126d02384}}  5 {{formula:61bd9b27-aff2-40c9-b532-df97f1738797}}  1 are adopted. The anharmonic ({{formula:8e9faa80-99ad-4148-987a-f06cee5e5942}} ) IFCs are obtained by the same supercell and k-mesh. Then, {{formula:9cb377a9-4869-4daa-a8fc-f1864bab2159}} and phonon scattering mechanism are obtained by solving phonon Boltzmann transport equation (BTE) {{cite:d3885897423398a5fc73a0c19b92d3abd4b77181}}, {{cite:afb935861430e0f31a68ab4a84d221b48e4023b0}}. The calculating process is performed by ShengBTE package with a {{formula:638fc7db-bc40-436e-85af-ab40ba88adce}} -mesh of 81 {{formula:7c5cdeba-207b-4c49-862b-20168302eadd}}  81 {{formula:064d8265-1317-4675-aaeb-ea3f9b678e11}}  1 and a cutoff distance of 0.5 nm. The convergence of {{formula:c3a6ae44-ae60-4349-988f-75f3b4612840}} against {{formula:4205897b-1b14-44fa-a7c9-ffedf3543974}} -mesh is tested from 61 {{formula:ce89ba88-f402-4ce0-a43a-a0f262c044c7}}  61 {{formula:1ce0f76c-a6fc-46b6-badc-7640996bacdb}}  1 to 101 {{formula:1d834e38-746a-490f-9dc4-170757e7a860}}  101 {{formula:7dbec2a7-f2e8-4437-a158-fbe4d6284875}}  1 as shown in Figure S11.
m
c76308e6a088912d7d582b9f1b059f58
Learning to rank is widely used in online web search and recommender systems which selects a small group of items to present in a limited number of positions after a user starts a search session {{cite:4af335584af0ff50ae40bb69cd0fab41e2a31e31}}. Online learning to rank (OLTR) is to learn the best ranking policy through user interactions and aims to maximize user satisfaction, e.g. the number of user clicks, during the learning period. To understand the click signals received from users on given ranked lists of items, many click models are introduced and studied {{cite:fef39729d6baccb36ccb2c1b6ae7425d3b946c68}}. One of the most popular click models adopted in the industry is the position-based model (PBM) {{cite:c5ca782c99b25e05808fa10be715f138eef5b667}} due to its simplicity and effectiveness to characterize the click rate as a product of item attractiveness and position bias. PBM is studied in OLTR setting with theoretical analysis on regret {{cite:40ba9a3e212aabd030682d99ac063bacc9ebe515}}, {{cite:64a61c76f4ebef710dbfdca74ffd9689197eb51c}}, which is in expectation the difference of the received clicks from the clicks of the best policy. Some other works in OLTR study the cascade model {{cite:ffb897429c2e7b6a97ae87f14a45dbfc5b5d5aca}}, {{cite:8e5ec1aba870955643f3666eba1a8fc0d8d4a87d}}, {{cite:3e55f69429da05a880fdf2f33b1c3cd5c56e6b58}} and general click model {{cite:bfa7dde00f05f19695ef080152128730ddcf66ca}}, {{cite:170e4aa5d73ca582da8ec8e3daa98166c2630eff}}, {{cite:246caf466ea8b4c47886ca01465d93fbd16c84bf}}.
i
eb43a83827c40e25452c575cdc0fd81c
The present study carries out molecular dynamics simulations of granular materials using the free and open source software LIGGGHTS {{cite:6c64800d6250df08f317317b10ea7b56f6137bf4}} which is an extension for granular matter of the the well-known LAMMPS {{cite:b598b12796ae34e9a6cf90bffccd19383f7e66eb}} package. The advantage of this choice (apart of being open and free) is that LIGGGHTS has many interaction potentials already built-in, including the most common for granular matter. Besides, it is efficiently implemented and parallelized for fast simulations.
m
4080d061c27c583fd37493c28fe4e008
Our work also have following limitations. First, as COVID-19 is caused by a novel virus and only traced recently, we only have a sample size of 152. A larger dataset could potential improve our model performance. Secondly, we don't apply some other trending time series prediction model such as deep transformers {{cite:81beb4582acaff9334191d331fbecb05e7cd36b4}}, which has shown great success in influenza prediction {{cite:d42d3e76c2c508d6df908f5d8ebdb0628f96d77c}}. Finally, we don't try other configurations such as 2 week time lag, the monthly hospitalization change and so on. In the future study, we will keep monitoring this global pandemic and update as well as upgrade our model to achieve better hospitalization change prediction.
d
2b4dd241dff6afb901c83b96d80e12a4
      We have shown the consistency between pole-skipping points and QNMs for Unruh's acoustic black hole. Now we further conjecture that QNMs are consistent with the pole-skipping phenomenon in all cases of acoustic black holes. The analytic WKB approximations for QNMs are given as {{cite:180f21615d2980f757a173420447292827333ba9}}, {{cite:34d0f3a5d51181f58f92d7180dfc5f0432fde883}}, {{cite:12307d0ece869d548b1d01b6a057cdd5697e439f}} {{formula:a9bb12d4-105a-4992-83e1-a606cb48fea5}}
d
d1efc92324d365963ac3dea58e33029c
The recent Early Data Release 3 {{cite:e52e7f01719e19857311e01bbb4299461b5bf7de}}, {{cite:28c0e7c8a20d191ff83e3902c018f07ba9396c01}}, {{cite:162831c736f81d704e177ff509a528ec504b46bd}} from the Gaia mission {{cite:1b132859d07cfba2118ae9b087b349925487baef}} opens a new chapter in the measurement of parallaxes, placing the precise and accurate determination of the distances to nearby Galactic globular clusters within reach. None may be more prized than that of {{formula:71aeba7b-3138-4967-98fc-20e4199f23f9}}  Cen, the most massive cluster in the Galaxy at a distance of {{formula:e213feee-c9e5-4381-aa33-4c0563d68430}} 5 kpc; a precise determination of its distance will characterize the luminosity of a broad sample of stellar types. A precise distance to {{formula:560569e8-7062-4814-a0ab-7f865f77b379}}  Cen will also provide a geometric calibration of the Tip of the Red Giant Branch (TRGB) feature, which in a cluster of this mass can be measured directly {{cite:70ce485a1b3a44e190a33a531dcc0d6f8010f7ca}} without the need for extrapolations or comparisons with other stellar features {{cite:f279805518280f2332c2f88769fcc55ac13dc936}}. The calibration of the TRGB is especially timely because it is a powerful primary distance indicator for evolved stellar populations that can be used to reach the hosts of Type Ia Supernovae (SNe Ia) and help determine the Hubble constant {{cite:38eb449437f1b1638b9c6e89dc1f6b22998210c2}}, {{cite:25f0edd47e6ec6108bef7874bc69427615682598}}, {{cite:f58f9e7dac54d81dcab7329414e4bf8b93a1381e}}, {{cite:5a2bf38f81c3c87b6e4c0ce1b49d1d6aeb9e7f0c}}, {{cite:6795ed697ce7cc3d2219fa61b1701a0a545dbea5}}; for a review, see {{cite:c9c9e4b335f757b057a87038eab7ba510f11b44d}}.
i
9f549a11f211db8d410757725149a049
We use the standard identity expressing sums of powers in terms of Bernoulli numbers (see, e.g., {{cite:228bf2039508369bb03ab514fef779e5354709a8}}): {{formula:e7479d82-71b6-4999-bac2-3010d3bfb2fe}}
r
3ace038e7a84457b42e12cb4ba1ba0d7
Once the temperature of the universe cools sufficiently, the twin electrons and the twin hydrogen and helium nuclei combine into neutral twin atoms, again mimicking recombination in the SM sector. At this point, twin BAO ends and the twin atoms begin to fall into the gravitational wells already seeded by any non-interacting cold dark matter. Prior studies have made semi-analytic estimates showing that the size of the suppression in the matter power spectrum at small scales depends on the abundance of twin baryonic matter, while the scale at which the oscillations stop depends on the time of twin recombination {{cite:af0b799e7e395006373e19cb3ff433dd3c8f7909}}. Such estimates provide a crucial first test of the MTH cosmology, but are not precise enough to make true comparisons to the high precision data on the CMB from Planck and on the matter power spectrum from, e.g., the KV450 catalogue {{cite:df5f33eb8d4e8c105e9f279c64027d14e7eb8bf0}}. Nor do they allow us to predict with any confidence the ability of future surveys, such as Euclid {{cite:d24b23741e9ce9e1cd5e85fc0a6ee5f0cc98cb54}} or CMB Stage 4 (CMB-S4) {{cite:8f6261da6da2ee0da0fb13925752fb2ecc232444}}, to constrain the parameter space of the MTH model. Given the increasing accuracy of the datasets available, such comparisons are only possible when calculating the full evolution of the universe within the MTH paradigm.
i
3da37ef9aa425d52f49a1c68a5d47cc3
We compare our method with other state-of-art SISR methods including EDSR {{cite:66bd3ab09b2252d4bf2dee38d6fbe7dd74c339c5}}, ESRGAN {{cite:ade288ce2aef240b8179ffbb13dfb71a94bf8d83}}, SRResCGAN {{cite:94b9be2d6c1b4786897e6837a52e3c9992a06f58}}, and SRResCycGAN {{cite:48976b371d27082e7cd25489509c63799ae35ad7}}. We compare the SR results with one deep feed-forward residual network (i.e. EDSR) and other three GAN-based approaches (i.e. ESRGAN, SRResCGAN, SRResCycGAN). Although there are existing SR methods {{cite:5113418591f3c3322b6237803bd90ba69f71f7fd}}, {{cite:40c5c3403541f6c6955628355d845691abef5673}}, and {{cite:d43dc87cfb0960859607749e4e0ec59f2ae3fc1c}} by handling multiple degradation settings, but they are the non-blind SR techniques with deep feed-forward networks, while our proposed method is a blind SR GAN-based approach. So, the comparison with {{cite:5113418591f3c3322b6237803bd90ba69f71f7fd}}, {{cite:40c5c3403541f6c6955628355d845691abef5673}}, and {{cite:d43dc87cfb0960859607749e4e0ec59f2ae3fc1c}} methods is not fair. We run all the original source codes and trained models by the default parameters settings for the comparison. The competing methods are trained for just one degradation setting and tested on the different ones. Unlike them, the proposed approach can be trained with multiple degradations instead of single degradation.
m
2df4f6908e50cadfe3b39f31a6644c30
In our approach, we study the effectiveness of self-supervision as an auxiliary task for fine-grained image classification. We follow the concepts from {{cite:ce30302ddade746a9e983a6f734b64eb70c1fdff}} and build a parallel network design for applying self-supervision to the CUB classification task. The original images are passed to ResNet-50 backbone followed by a classification head to calculate the class probability scores. The supervised cross entropy (CE) loss is calculated using these class probabilities. Alongside, the images are transformed to generate self-supervised labels for the SSL pretext task and are passed to the same ResNet-50 encoder. The SSL loss is calculated using the auto-generated labels and added to the supervised loss to compute the total loss. The complete pipeline is shown in Figure. REF .
m
075110837a3a8e49ca41e0b4d3b3c28b
DNS results. The objective evaluation of our SE systems trained with different losses using the DNS {{formula:53ff13d2-f51c-4211-8906-b43ceb87bda5}} and {{formula:65a79fb2-dcc8-4fe6-a8e2-080120fd3a58}} test set is summarized in Table 2. Even with a large amount of training data, our GRU(TFE+STME) loss function outperformed both the GRU(TFE) baseline and the provided challenge baseline {{cite:dd7c202e03af2a42971c2e4a111f1793d66c4a90}} in all the objective metrics. Most notably, there is a significant improvement in PESQ which results in our system having a similar PESQ to the top system in the official DNS challenge {{cite:15af18b7bf0529df7f48bd6c0f6d538e11e7822a}}. We also evaluated the benefits of the stme loss by itself, GRU(STME). Curiously, training with only our the stme loss provides a higher PESQ but much lower SI-SDR compared to training with only the TFE loss. Nevertheless, optimizing the combination of both losses during training caused both the PESQ and SI-SDR scores to increase compared to training on each loss individually. This confirms our belief that the medium-time stme loss is complemented by the short-time tfe loss. As in the VBD experiments, the use of automatically-learned Gabor-based STRF kernels provides a greater increase of PESQ scores compared to the use of randomly-selected Gabor-based STRF kernels. {{figure:58a931c4-254c-4e72-80ea-89fa28b7ec67}}
r
5a6f0ffcd5954aef0e6ee7fbf279134e
We follow standard procedure in attempting to measure the importance of neglected higher order terms by measuring the renormalization scale dependence of various observables {{cite:5606ef84807b867f537d58ac7ea676aba346dec4}}. In doing so one needs to make a somewhat arbitrary choice of what range of values for the renormalization scale one should use in the loop calculation. However, even the generous range for the scale parameter considered in {{cite:ab4175db6519012fc03d73486918ed248830563e}} can have the next to leading order predictions not enveloped within the uncertainty bands of the leading order prediction. Our analysis should therefore give a meaningful idea of the calculation's convergence.
m
9d09e7c84b4c4eb3df29268348736037
You Only Propagate Once (YOPO) {{cite:f55f4119514720aa22784debdf6e60e00b432ccf}}: They show that PGD updates are coupled with the first layer of DNN, so they restrict the adversary updates to the first layer, hence, reducing the computational cost.
m
d2c02c6f67a877a316b9c8cd1f38072a
Pursuit-evasion games have seen a wide range of perspectives {{cite:5c71c4484e7dba4937dfe366eb5da50f5ad14042}}, {{cite:799d89781022a79dbc9f7953bc6099deed3f9508}}, surveys {{cite:34355957f50d674a970357798122e9be26e276ad}}, {{cite:445cf470c7f98bcf7199a5f1c18f5d8cfc4e1523}}, and applications such as search and rescue {{cite:f1b57b62b68cbc59760fd00e3ee611b50a7b00d2}} and environmental monitoring {{cite:0fefe52a192847b425fc27767fb14c323244358d}}. Problems with multiple agents are complex due to their high dimensional state-space {{cite:4154781c6cf2c7258a7725aa0c9b4be049f0e28f}}. We investigate a variant of the pursuit-evasion game first introduced as the target-guarding problem where the pursuer/defender tries to prevent the evader/intruder from reaching the target {{cite:6185c3c4e5c53d8ee81bf3a004d695a8548ef21a}}, {{cite:f2a6b804802fa32f324c074ea470d892770e1f21}}. A large body of the work on this problem {{cite:6ce74c3cdddfdd40e042e4fb928f2e1afa3b6f81}}, {{cite:59002b93d882f4ac87fa73ac79d5f0c36046f85b}}, {{cite:2cf84f689eba925a4c0f76a2345b02e7e66a1f5e}} studies how multiple defenders decompose the problem into smaller games {{cite:7f74762991107f196f042872146f61cff87b4042}}, {{cite:94de0d0dc0bbd74d53fac3d28e1544752dd75b28}}, or reduce the defense strategy to an assignment problem {{cite:739e77b09094074439df54e5e78ffec00f0db439}}.
d
5ffba94ff94e16ea3f16a21dfe3a5a9e
Machine learning has begun to have impact on various facets of medical signals and image analysis {{cite:17a132d85ca5fe154de03c7252db3f38eef52e09}}, {{cite:21eed1749bbd26699dd9acbbfe78b745616e7e30}}. Computational means for lung sounds analysis have been the subject of various studies using machine learning {{cite:be4618febd3442d2906417e654d90fbf14bd36cc}} and other related approaches {{cite:e562fb78dc9b06f6ddb64341024b7d34b6df58f3}}, aiming at detecting respiratory pathologies.
i
5aec126ddec86706fb3cd3959e52ddfe
He et al. paper states it very clearly that networks with rectifier nonlinearities are easier to train than networks with sigmoidal activation functions {{cite:3eaf0f7879f4a72c3ca726aa79c651aca2c1e8a5}}. This statement is also supported by papers like Krizhevsky et al. , Glorot et al. {{cite:97c8c30f5c5e2e6f29891c10ab7518d7f3ddca2b}} {{cite:b5bf1cb8ef81b0bdb65a9df371234cf5308df036}}. This is why He et al. completely ignores the sigmoidal activation functions and focuses on rectifier nonlinearities only and also produces a generalized form of rectifier nonlinearities PReLU.
d
0a0c5580843041f9f528f09cb15a4ea8
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type {{cite:184657f99356283226a71222b0f394acfc68cfa1}}, {{cite:a1ad32fd8ae1a12492474dfeae5ae1809962c484}} and Hamiltonian operators in the formal variational calculus {{cite:456e106fd18b2d946fc6a3012bc9ee01a8a42bab}}, {{cite:ff7332ee9a2efae73ffb2b5e5763904e92d9162b}}. The theoretical study of Novikov algebras was started by Zel¡¯manov and Tikhov {{cite:3a27ff15610835d98bc792dadc105e5317fab31e}} and Filipov {{cite:9a7b9783597d8f97c31734f807c1604c15d32812}}. But the term ¡°Novikov algebra¡± was first used by Osborn {{cite:839c659c2e3e54d16e478d831ad77b3c23998fea}}. The left multiplication operators of a Novikov algebra form a Lie algebra. Thus, it is effective to relate the study of Novikov algebras to the theory of Lie algebras {{cite:a7917fffeb6f4a3246c96753e5e83aa3cf978993}}. Novikov algebras are a special class of left-symmetric algebras (or under other names such as pre-Lie algebras, quasi-associative algebras and Vinberg algebras), arising from the study of affine manifolds, affine structures and convex homogeneous cones {{cite:7b79ef44a2ebf31afaca331c5dd3af2ca953e466}}. Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics, such as infinite-dimensional Lie algebras {{cite:184657f99356283226a71222b0f394acfc68cfa1}}, classical and quantum Yang-Baxter equation, quantum field theory and so on.
i
4f589d8716ad1d0d9a7ed0608e81cfa5
The considerable interest in studying the dynamics of disordered BEC driven out-of-equilibrium by slow (adiabatic) or sudden (quenched) changes to system parameters such as the scattering length has been boosted by remarkable advances in the tunability of ultracold atomic gases {{cite:292dee45cedaaf214f622261f6a98f1c17d22e6d}}, {{cite:7b8593598672e66e52fd709e07023cbf45d4c211}}, {{cite:7114ab6672dc04eb76c37eb4fd46df5988799a2d}}, {{cite:d8f9553d905812ebe9e33a9f84d181cdac807e17}}, {{cite:7b61f14ba68e5e09592020000186dee7f2249c52}}. Non-equilibrium evolution of BEC offers the unique opportunity to explore strongly correlated systems and transport in realistic physical systems. Chen et al. {{cite:bd15b0129911ec60fe370e0d627ec2f9406a60cd}} have shown that for a weakly non-equilibrium disordered Bose gas under a quantum quench in the interaction, the disorder can substantially destroy superfluidity more than the condensate leading to the so-called dynamical Bose glass. Moreover, it has been revealed that externally controlled spatiotemporal periodic drive constitutes an excellent platform for creating novel nonequilibrium states of quantum matter {{cite:7037d90d9faf41bfcd25ea73452ae3159d256cbd}}, {{cite:4d2252e01a556e1b812974048771f7aaf805292b}}, {{cite:fcfbe74c29c0e90c21e8902e26f6ef35ef591844}}. Recent study demonstrates that the condensate deformation is a signature of the non-equilibrium feature of steady states of a Bose gas in a temporally controlled weak disorder {{cite:f0f2c66d5d3be061c4e8ca4797062d7d4fd6a37c}}. Quite recently, experimental realization of ultracold bosonic gases in dynamic disorder with controlled correlation time have been reported in Ref.{{cite:54d073769295a8fe2b18d82f795a2195183635b7}}, where the microscopic origin of friction and dissipation has been well illustrated. There has been also an extensive amount of work addressing dynamics of bosons in disordered optical lattices (see e.g. {{cite:7b8593598672e66e52fd709e07023cbf45d4c211}}, {{cite:00650c3c8b3e03f15fb2bb4058778eb9ee4378cc}}, {{cite:d79a4145c26452d45bb80b1cf8c61f1bb7113056}}, {{cite:4318f960b1c7a5909bb859e195c56514950f6109}}, {{cite:708a50e081de68c346649c7e5c08856ad11b28a8}}, {{cite:7c7ef0a1f8e0775180d34c1859f58b10f8d2c4c6}}, {{cite:fd6486a3ca74e01df5e5ef3a6f4856ccb7999f87}}, {{cite:bbf21f7ed2fa3a2ec9526ea8088e8d2a350f4a97}}).
i
5128c340857fa73476d8fefedec5105d
for samples {{formula:a13d0cb7-29ad-4f54-a0a7-b04802ab9354}} . The data are assumed to be centered so the intercept can be ignored. The spike and slab model {{cite:cfe173cc7e0df581633e79098ad5693598498555}}, among the most popular Bayesian variable selection methods, imposes the following prior on each coefficient {{formula:cf2811ee-c41e-41ac-8fc0-0ef9c836a024}} : {{formula:109c4f8d-1d6f-4b13-be5f-64e41c393b1a}}
m
31ed2a59dcb295a3599c50a4579098ad
Different language metrics like Bleu_n {{formula:53ac287a-2c7f-4bdf-a6d5-bc6844cc1b8d}} , METEOR, ROUGE_L, CIDEr-D and SPICE are provided as these are standardized in the community and are used for performance evaluation and comparison of our model. However, each reflect very limited perspective of the generated captions and hence Figure REF provided a qualitative comparison of the generated captions for our new architecture. Table REF provided a comparative study of our models with some of the existing state-of-the-art works in the image captioning domain using image features and also with others like Attribute-Attention {{cite:6aaf635468dc66640dc858dfb89427fdfbb33f81}}, RCNN {{cite:5257deb40e870a5424d1a77aa20904d578a07233}}, {{cite:f360bbe702bdb5a8e8fcfbc8ea2a8fa67dd42343}}, where {{cite:f360bbe702bdb5a8e8fcfbc8ea2a8fa67dd42343}} used advanced features for their work and yet our work is comparable. The main functional characteristics of our work is the tensor product based positional aware representation, which embed the structural characteristics of objects and interactions in a graph. Generated/trained structural features undergo approximation and then compose new representation through different circumstances of weights, where the weights never been able to represent the whole dataset with different characteristics. Most of our new architectures performed very well and either outperformed or at least same with the existing architectures, which do not have concrete reasoning behind their working principles. With the introduction of semantics, our TP{{formula:6795c367-4f7c-4c28-a6bf-a933f550cb07}} R-sTDBU architecture performed much better than the existing works and performed better than the TP{{formula:71380dac-b05d-4601-ac34-6cf94c7df6ad}} R-TDBU architecture, establishing the fact that they generate better strategy for caption generation. However, the TP{{formula:42f9bb2e-98e4-4131-ba73-3b6296d12c51}} features and the Scene-Graph feature generator was trained with images which are not correlated to MSCOCO dataset and the accuracy of detection is around {{formula:d4345822-803f-4710-ba36-a9b484a8fd6f}} 28%. Also, the average number of Scene-Graph features detected is 8-9 on average and maximum at 15, which is way less than {{cite:f360bbe702bdb5a8e8fcfbc8ea2a8fa67dd42343}}, where they extracted 36 regional features and did not disclose the principle of selection of these regional features. Hence, in comparison to {{cite:f360bbe702bdb5a8e8fcfbc8ea2a8fa67dd42343}}, which achieved 36.2% BLEU_4, our TP{{formula:8c4b1d17-b0fb-4270-8764-06c29217062a}} R-sTDBU architecture achieved 34.9% BLEU_4 and is still comparable because of the fact that the Scene-Graph generator model {{cite:7adffe6fe81af559764820541053f947d604fea6}} was totally trained with a different data. Though statistical metrics provide many qualitative insights of the generated languages, they hardly reflected any language attribute quality related to meaning, grammar, correct part-of-speech etc. These can only be evaluated through reading and hence we provided comparison in terms of diversity and descriptive attributes in Figure REF . {{figure:3c57a718-19e2-42c3-b715-0a1c76ed2d2a}}
r
4ee177fece1a806c47595950799d6056
Land cover (LC) maps play an important role in many applications such as precision agriculture, urban mapping, and environmental monitoring among others {{cite:3964e4ccd0d5b172bba35e8408441d6231c82fd1}}. Earth observations provide valuable data at global scale that can be used to build applications for LC mapping. Recently, with the advancements in machine learning (ML) techniques, several studies have been carried out to develop ML-based LC classification models {{cite:84db9f65c4a2a097a4d11d75e3516b0f076bfae8}}, {{cite:d749604c88e136cd122700b5b025560a940fc408}}, {{cite:85b8d4f1551e722a261e4fe9f54f8e0e2e51c9ec}}, {{cite:0d52032ae68a2fbc2cc5758b17bd7a3f3da7d374}}. However, the remaining challenge is lack of high-quality open-access training data that represents the geographical diversity of LC classes at global scale {{cite:ce30b6fa58782175ce2898183612837410b78de0}}, {{cite:d09ce665f59a9f635afc47b87272827ac2f7fbfc}}. Such a training dataset can open the value of open satellite imagery (such as Landsat and Sentinel missions) for regional and global monitoring with enhanced accuracy.
i
24e84c0bf2aa56830771b233536d5a31
Many surveys of methanol masers have been carried out in last four decades. The surveys of class II methanol masers (mainly at 6.7 GHz transition) have detected nearly 900 sources to date {{cite:2db1e52412adbedec7e262720f8903be0ddbca57}}, {{cite:f32004493bfe55e8072079a325fd8a7fecdec298}}, {{cite:1ddb47c4d09ccadb6e70e0fda72ac7c24f3146e3}}, {{cite:de392af7aeb2a83e181e5db07abcd46648d8742f}}, {{cite:4df86e7c194b611963ef035d9c38af6161438857}}, {{cite:9bdf9bdcb570f2c057932754487476cb4f0bcc6d}}, {{cite:0e323bb3b393390e702d9fe9ac59224d7d49f51e}}, {{cite:fd7a959299e7024dde9775ea3335a7cafa66e3a5}}, {{cite:f1fb14003dca76ab905fa6023001acce9fa49361}}, {{cite:07eac3a2b006bbee62fcad5c647c8fcf2dd5df18}}. While studies and surveys of class I methanol masers are rare compared to class II methanol masers surveys. There are only a few single-dish surveys {{cite:34c359fa93f17ee67e45375cc9e9a9d953014de5}}, {{cite:0315c14eba32696ea2f205308f1fa944c36ad3ba}}, {{cite:38a36d531c2f049826d58065c06abd4a7eac7629}}, {{cite:b52de71df4b687eec5c4576e240facad12978d57}} as well as interferometric searches {{cite:c5f5328181a398a4758d7d5ca052a929f1b09112}}, {{cite:4df86e7c194b611963ef035d9c38af6161438857}}. However class I masers have recently become the focus of more intensive research {{cite:5a1fc7933f63b639e24544f22031c3036ba9e0d7}}, {{cite:2ddd97f66d38d8724fac1f9f3750c7ed5aeb13e9}}, {{cite:9cd8eb330141555e87cf7b0b2e1dc5934839e8ff}}, {{cite:85f1c4bff60a66f0b0e2d3fe3ee9299d2f92ed06}}, {{cite:38111dfc0fb95a5f1dbc0f0bc669958b35955cae}}, {{cite:100a991622a520c7c238d2dd184c1a7e5f39af99}}, {{cite:7c1591a566d7acba3d945c864075268937e58591}}, {{cite:4ee55b5251a99ade17c680fe88b009d308a2d87b}}, {{cite:037367828d7f18e3bf8e6f22add7f712ae18e77a}}, {{cite:1083100e257e2458f99f75595bfc93c264ac6420}}, {{cite:e1a2f85e6cfb82beacb64a8e82cc68319830f325}}, {{cite:ee1839ca1c129dfb3a0a7c617bf3bed7ccd0e7a8}}. Some surveys have been carried out at the rare maser transitions, e.g., at 9.9 GHz by {{cite:38111dfc0fb95a5f1dbc0f0bc669958b35955cae}} and 23.4 GHz by {{cite:7c1591a566d7acba3d945c864075268937e58591}}. To date altogether {{formula:2cf291e5-bcdb-4d31-8a81-c1723729071d}} 300 class I methanol maser sources have been detected in our Galaxy {{cite:037367828d7f18e3bf8e6f22add7f712ae18e77a}}, {{cite:1083100e257e2458f99f75595bfc93c264ac6420}}.
i
a7514c4e81ffd0dce8391d8a0da8a845
The above formulations assign similar embeddings to nodes with similar neighborhoods with similar attributes, even if they are distant in the network. However, embeddings need to account for the node's position in the network in many settings. Applications like routing, which involves the number of hops/distance between nodes for the end objective, are examples of this requirement. Specifically, the node's position in the network should also be a factor in the learned embeddings. PGNN {{cite:fe9e9a368f3114f934090c51dc5a6776c5a23d49}} proposed a concept of anchor nodes to learn position-aware node embeddings. Assuming K anchor nodes as {{formula:ef865820-9a79-49da-a16c-bc8af51cc843}} and distances of node {{formula:917c04dd-969d-434d-8a8f-dc760d2043b7}} from these nodes respectively as {{formula:9d047ef9-d125-4138-9034-b6591260d7bd}} then a node {{formula:79bd91e0-eea6-41ae-9dd9-d51203b07e7b}} can be represented using a position encoded vector {{formula:68ad142d-dc69-4b12-ae44-d8daf745b31d}} of size K. More anchor nodes can provide better location estimates in different network regions. PGNN generalizes the concept of an anchor node with an anchor set, which contains a set of nodes. Node {{formula:d1c4eff6-7a76-44bc-a7b0-8af9556992e4}} 's distance from an anchor set is the minimum of distances from all nodes in the anchor set. We denote {{formula:41054b4b-22bb-47cb-84c4-420b6979eb49}} anchor set as {{formula:413795a7-444c-4bff-9aa1-c85aae5c1c8a}} . Each {{formula:7aa9a665-1f1d-452f-96da-102ed56af377}} contains nodes sampled from {{formula:e45339b3-8096-4b43-84a0-a0d0f1840898}} . We note that each anchor set can contain a different no of nodes. These K anchor sets create a K size position encoded vector for all nodes. These vectors are used along with original node features to encode each node. However, since each dimension in the position vector is linked with an anchor set, changing the order of the anchor set/position vector should not change the meaning. This constraint requires using a permutation invariant function aggregator in the GNN. So, PGNN introduces the following formulation for position-aware node representation. {{formula:c038da24-a610-48ba-8614-507c54cf08af}}
m
226fea43f317649572567ed823d512b5
Second, these already limited instances may vary significantly in pixel values. This is because they have different poses and illumination conditions, but neither of these factors are annotated or known. We also cannot resort to existing tools for pose estimation based on structure from motion, such as COLMAP {{cite:2675f97c2bf1a652c0afef9ebc7ec7b7545108da}}, because the appearance variations violate the assumptions of epipolar geometry.
i
c40e81388f254afb44ecfe073a56caac
Absence of any significant background modulation in the energy spectrum has also been verified in the present data taking for energy regions not of interest for DM {{cite:9a056c9d71a7b1cbf22967b387ba55d2135701b1}}, {{cite:ecf44bd93ad98b501284560a64b07fbbfe65aee9}}, {{cite:4fcc5bc82e949869746b6dc47307ae772a8493c7}}, {{cite:69a082364a6682a869e8fd912e10a37c0b0b9d96}}, {{cite:0a47d5c0d1646d0d221c025dc592aaaa02e0bd97}}, {{cite:260d10768c27be9e3c1fc614c4983799854f48b9}}, {{cite:78231ea9dd2d8210346a8ac03aa340050da8ac17}}, {{cite:ec9d945904b20cbd4016cfd4148cf72d7f6a3b07}}, {{cite:7daad4b9631b6346ccb096883ed72975166d2448}}, {{cite:6dba78398def32dffd4ef23d3e9490e5cb39bb35}}. It is worth noting that the obtained results account of whatever kind of background and, in addition, no background process able to mimic the DM annual modulation signature (that is able to simultaneously satisfy all the peculiarities of the signature and to account for the measured modulation amplitude) is available (see also discussions e.g. in Ref. {{cite:02153b54efa18620ee7344eee4c3e6d823ad40ba}}, {{cite:9a056c9d71a7b1cbf22967b387ba55d2135701b1}}, {{cite:ecf44bd93ad98b501284560a64b07fbbfe65aee9}}, {{cite:4fcc5bc82e949869746b6dc47307ae772a8493c7}}, {{cite:69a082364a6682a869e8fd912e10a37c0b0b9d96}}, {{cite:950044fef5f414ad88b5d734227aa8ee764fd25b}}, {{cite:86100496aaf726b152a317dac83dbd3747c36b2b}}, {{cite:260d10768c27be9e3c1fc614c4983799854f48b9}}, {{cite:78231ea9dd2d8210346a8ac03aa340050da8ac17}}, {{cite:ec9d945904b20cbd4016cfd4148cf72d7f6a3b07}}, {{cite:7daad4b9631b6346ccb096883ed72975166d2448}}, {{cite:6dba78398def32dffd4ef23d3e9490e5cb39bb35}}).
r
df9e14b9be3c0f5f2db02e680b7ecaa6