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This paper details the investigation of the KHI and null point collapse around an axisymmetric, linear null point, an idealised model of a real null point (such as that observed in {{cite:1aada1bb8bfccef875dce76971aa36ec0c8c4b5d}}). The impact of different null point configurations such as those with asymmetry (e.g. those investigated by {{cite:ed19a8a36222cea0dd8586ad134cd58ad698334a}}, {{cite:430e66ae3eef052c2dbb2fb87c8ee94a47809c4a}}) is unclear. Similarly, the simplicity of the driver used here is unlikely to reflect the true nature of drivers in the real solar corona. The impact of driver complexity on spine-fan reconnection specifically has been investigated by {{cite:90e18c23aa6977570d19cbe5f6c5397532e1991d}} who, however, focus on sheared drivers, as opposed to the torsional drivers employed here. It would be of interest to understand how different magnetic field configurations and forms of driver affect the formation and stability of the kind of current-vortex sheets studied here.
| d | 66dac8a244b02d6fb688b68164a2afbb |
Firstly, with the measurements of the central velocity dispersion and
the location of multiple images (Einstein radius) of a strong-lensing system, the ratio of two angular diameter distances
{{formula:44ad3e3c-002b-495a-b467-f1a266ed845f}} can be precisely assessed. Specifically, by
assuming a power-law model to describe the lens mass distribution
({{formula:04b2f63a-70d8-4463-9acc-ae0d8d391826}} ), the lens potential relates to the
moments of the stellar distribution function through the Jeans
equation {{cite:905f52c7f27ced70942d78c2e0d87e68067d5475}}. The combination of the lens mass and the
dynamical mass inside the Einstein radius ({{formula:872985f2-e157-4370-9d79-30417e6e7860}} ) yields
{{cite:c1ee580105779f5d06dc0d8456f076132a963ed5}}
{{formula:2def9143-8786-49b4-b1c6-85e1a1a7f9ad}}
| m | 2a91fe135e5947f1069cdf250a76cef2 |
Figure REF shows
95 percent confidence intervals for {{formula:527f4506-fd04-4861-8c42-e2ec8ca4b7c4}} for each state
from the marginal structural model in (REF ).
We computed standard errors as if the weights were known, which results in valid
but potentially conservative inference as long as the weight models are
correctly specified {{cite:2bab20b5aa6a25cdda12c781d2522f0c0263c8e9}}.
The estimates are mostly negative,
as would be expected, since
higher {{formula:2be9fa96-7102-456e-841b-4479640e38eb}} means less mobility.
Interestingly,
we find that there turns out to be little
confounding due to past deaths,
as the fits with and without the estimated weights (not shown)
are very similar.
Nevertheless, we
keep the weights in all the fits
as a safeguard.
In Section REF
we investigate this further by doing a sensitivity analysis.
{{figure:3a127b39-b624-4cd2-8285-32e79dfed4e0}} | r | 3352ec9a0357a14108a8d1217a088423 |
Theorem REF and the estimate (REF ) guarantee that the minimizer of {{formula:5b2b7f9d-36cb-4795-8b2f-bf64dcc2d89e}} can be found by the popular gradient descent method.
The success is due to the hypothesis that the desired minimizer is in the interior of {{formula:7c393adb-1bc3-4ccd-b393-0936fb7db33b}} .
We do not experience any difficulty due to not checking this condition in the numerical study.
However, to be more rigorous,
in general, if this condition cannot be verified, one can use the projected gradient method as in {{cite:91bc1a1ecc2ebc6d1dd72c54bde52675622555cd}}, {{cite:96fe82b3628c18a0dbf0776aaf6ea9cbba3cf446}} to find the minimizer. In this paper, we choose the gradient descent method because the implementation of the projection in the projected gradient method is more complicated while there are many ready-to-use packages; for e.g., the optimization toolbox of Matlab, for the gradient descent method.
In other words, Theorem REF significantly reduces our efforts in implementation.
Although the proof of Theorem REF is similar to the proofs of {{cite:bbd852c3c1bb81fc18a493a09a38aa56f47ab853}} in 1D case and {{cite:568c2f50b0a60966869c60c44471c6c1681b81bb}} in higher dimensions, we briefly present the proof of Theorem REF here for the convenience of the reader.
| m | 5f45c2ac551eac4d25589b7c1959420c |
This definition is equivalent to the concept of uniform stability defined over the on-average loss {{formula:5c9844ed-72c0-424e-9c3d-d8adf9cdabc9}} . Suppose that the loss function is uniformly bounded in the interval {{formula:919ade42-f487-44ef-9156-112eceeb6b84}} . Then essentially it has been shown in {{cite:2df4582002295b203f1ddd295558eccfbd718d9f}} that for any {{formula:a5975435-dc24-4c31-b3ef-84e39fb5f658}} , with probability at least {{formula:60857d0f-bc99-44f3-9ec9-ed46c6ef8136}} over {{formula:e8b5b4fe-5235-40b7-bc93-8df39316a06a}} , the on-average generalization error is upper bounded by
{{formula:50eb41a5-70d1-4314-9047-84d845140eb4}}
| r | da64107af0dd8dcb908d3b47b215e865 |
Development of such a model class as something which will scale naturally to large networks is of further interest. Computing gradients on arbitrary Riemannian manifolds may prove to be challenging when the positions are in fact latent. One promising approach we plan to investigate in future work is that of product spaces for latent space models. This geometry has seen considerable success in representation learning tasks {{cite:597ef32df9e76f194964e1136fda7dc4cbf17300}}, {{cite:0a138caf8a26663e5dd0c9a3bb3659258fca8940}}.
| d | ad2ca68a48d26daf8431579317c951fa |
Note that we can chose the smoothness {{formula:6f67b170-3270-4158-a314-cfb38b13a33b}} of the basis to be as large as required and hence will omit it in what follows. For more details about wavelets see {{cite:5e1485e53b3f383d1867784873b4e6ad76b95826}}, {{cite:21c873ac00e73dc9c8dce0ff044db33f6cfcb162}} or {{cite:d9e7cb67e9ad3a6fb02d6c4e1468acf600b5e919}}.
For {{formula:3f71d30c-76fe-4ce2-bbce-0ecc38d37cdb}} we have the following wavelet characterisation of {{formula:b89d63bc-6f32-4da9-a125-16fdd6443874}} norm
{{formula:a1b02089-174f-4240-b4d2-5bde13d41c73}}
| r | eae1d0a9be153d1d3d175e9240eb7ff3 |
The methodology proceeds by the translation of semiformal specification to Focus {{cite:5b2c31e2d25f91a1b4587ff566d2e4b7f6ecd703}}, a framework for formal specifications
and development of distributed interactive systems, preferred here over other specification frameworks, since it
has an integrated notion of time and
provides a number of specification techniques for distributed systems and concepts of refinement, as well as graphical notation, which is extremely important when we are dealing with systems of industrial size.
We represent in Focus two kinds of specifications:
system requirements and architecture.
This prepares the ground to verify the system architecture
against the requirements by translating both
to the theorem prover Isabelle/HOL {{cite:4258268ec475a3b23fd9feee34a551ba36ebeb00}} via
the framework “Focus on Isabelle” {{cite:d4796e7c4626cad8562d2a29011c99a4884b9d9e}}.
As the next step, we translate the architecture specification
to a representation in the CASE tool AutoFocus The AutoFocus homepage: http://af3.in.tum.de
to simulate the system.
The requirements specification can be schematically translated to temporal logic or specification patterns, which gives basis to model-check the model (cf. {{cite:e30764cb8d0b98c9c87d362e26121b03f314dc7a}}).
The integration of model checking in AutoFOCUS approach usability at the following points: tight coupling of verification properties with model elements, different specification languages for the formulation of properties, and visualization of counterexamples. Dealing with these issues leads to one of the first model-based development environments incorporating property specification, model checking and debugging.
Optionally, we can also represent an environment or a test model if this benefit the analysis of the concrete system.
Finally, we can switch from the logical to the real level, where we have to split our model into software and physical components.
Transformation to a corresponding C code can be done using the corresponding code generator: we have shown that the C program produced by our code generator is an admissible simulation of the model.
| m | 102f7ecb2e263d6155e7ec1193a901cf |
A fundamental problem in representation theory is the description of all irreducible representations. We are interested in the polynomial representation the invariant differential operators with respect to the generalized symmetric group.
We know that the direct image of a simple module for a proper map in semi-simple by the Decomposition Theorem {{cite:8fd85751b879e80cb694e66237c54d9f21895416}}. The simplest case is when the map {{formula:1ed94569-28c3-48c4-96e5-e92a39fcaea9}} is finite, in which case it is easy to give an elementary and wholly algebraic proof, using essentially the (generic) correspondence with the differential Galois group, which equals the ordinary Galois group {{formula:33f081c7-8944-453f-87cf-d870dcd0231d}} . The irreducible submodule of the direct image are in one-to-one correspondence with the irreducible representations of {{formula:f7b3eee5-e881-4f7b-bd41-3851117b5a2b}} (see {{cite:25b39f15b6853acd8728c0e8ffcc58a159d88f71}}). In this paper we make the differential structure more explicit in the case of the invariants of the complex reflection group {{formula:b2c18f45-1f22-4ccc-a024-9515f38e60de}}
We explicitly study the simple component of the direct image {{formula:5e7c773f-6759-493c-bc4d-9316cd6ac2d5}} of the polynomial ring {{formula:8fe7e61b-043f-46eb-8b45-5bb474d109f1}} as a {{formula:c04ecc20-74d4-49b8-b4e0-537d99a1e507}} -module under the map {{formula:0016931b-a6cb-4bd1-9645-f79fa946ccf0}} where {{formula:e9091d5b-d21b-41d6-8024-b46f4bf5b909}} the ring of invariant polynomials under the action of {{formula:34e49e02-c304-4a06-8a7d-7e916a1f3bab}}
We describe the generators of the simple components of {{formula:9b13aad8-ceeb-41b1-9027-71c28534746f}} and their multiplicities as in {{cite:25b39f15b6853acd8728c0e8ffcc58a159d88f71}}.
We thus establish the decomposition structure of {{formula:09377196-4aae-436c-b36c-d6bdac0be825}} by means of the higher Specht polynomials. This proof uses the fact that the irreducible {{formula:d606ae24-0481-44e0-8e77-76991704c7d2}} +({{formula:88ea6f4b-0d82-4dd0-a602-977beb5b2bf4}} X){{formula:0047c9f3-d809-4141-a0ab-9507472006c6}} G(r,n) {{formula:6a3c6867-6f8e-4691-97a9-6db726dd7a67}} -module decomposition of the polynomial ring localized at the discriminant of {{formula:ed88ce83-200b-4d98-bb28-be2857b9b370}}
| i | 0b58a85a43423ccb4204a0a45458e27c |
Perhaps the most important ingredient in this derivation is an analogue of the property referred to as “one-sided molecular chaos” in chapter I, section 11 of {{cite:fbc0cfc61034514cb035b815770842495c894bef}} — see also Sone's lucid presentation in Appendix A, section A1 of
{{cite:36d49be54e4ce09f6441b6c23a70cca8321dc1a0}} (especially the discussion between equation (A.5) on p. 485 and the Lemma on p. 492, and footnotes 12, 13, 14, of key importance for a good understanding of the foundations of the kinetic theory of gases). This analogue
of Grad's “one-sided molecular chaos” idea is presented and explained in detail in section below.
| i | e8fe322c3d6403510ce1b6456d56bb68 |
The density method does not involve the Ahlfors-Beurling operator nor {{formula:78e93a37-75d4-4864-9499-813464103c5c}} spaces beyond {{formula:bc9df394-8044-4702-aec8-69a77965aa9f}} , {{formula:57435331-25c6-4a27-89c3-e5c072d33389}} .
It involves the notion of distribution and the Sobolev space {{formula:bbfd367a-60d7-41fc-a866-ae125ca2796b}} , which serve in particular for the definition of quasiconformal maps.
It also involves compactness statements for quasiconformal maps: one about normal families, which is proved in {{cite:2c58880a33278a491fadaac339c93bc8a26de7b6}} by conformal geometry techniques; one about {{formula:cb1c4bd7-2967-4cbf-a2a0-19e1cae1859e}} bounds, which is proved in {{cite:2c58880a33278a491fadaac339c93bc8a26de7b6}} by proving differentiability almost everywhere and bounding the differential with the Jacobian.
| i | 3691e801ba86130846ebd939a7f5184e |
Non-parametric methods find the sparse network by repeating a two-stage procedure that alternates between weight optimization and pruning {{cite:98fb82ca8a1088a6a3b754f72c25b7e8a564cf68}}, {{cite:68742ce04d5a73d92aa19cd982584999ed0b3df0}}, or by adding a proper sparsity-inducing regularizer on the weights to the objective {{cite:91f269ef85b323f2b3fc1b4db77759cc8990bda9}}, {{cite:13498ebcfe1fbde34c7d8a59eed453d0f9844fbf}}. The two-stage methods prune the networks in weight space and usually require retraining the obtained subnetwork from scratch every time when new weights are pruned, which makes training process even more time-consuming. Moreover, the computation of regularized methods is dense since the gradients of a zero-valued weights/filters are still nonzero.
All the parametric approaches estimate the gradients based on chain rule. The gradient w.r.t. the structure parameters can be nonzero even when the corresponding channel/weight is pruned. Thus, to calculate the gradient via backward propagation, the error has to be propagated through all the neurons/channels. This means that the computation of backward propagation has to be dense. Concrete analysis can be found in Section .
| i | c07a39ae3380365f0826fc971dbdea46 |
Recent years have seen a lot of studies which focused on the application of network representation learning methods for recommender systems and the user response prediction. Motivated by the success of CNN and RNN, there has been an interest in developing neural network based models for the graph structured data. Considering three major challenges in recommender systems, scalability, data sparsity, and cold start, many methods have been proposed in the literature using graph embedding {{cite:59ae2840fb3f89884c3379b1b3d3c87dea21e084}} and graph neural network {{cite:5996080f0867345019a5e9c97881a32be55c2b9c}}, {{cite:c00e4792d3002f9889501ef12f5c37192506bb7b}}, {{cite:d22562616002ce56bac45af48bcc9224aac381fd}}.
{{figure:c1d57d4d-5d68-46c3-89e7-54158e266be2}} | m | 5481f44575662c7b52519394ab0c956c |
There exist two main trends in the literature when it comes to measuring improvements in the learning capabilities of agents. One approach consists in measuring performance after a limited budget of interactions with the environment. While this type of evaluation has led to important progress {{cite:9a35092940d5f33b14b8f90b5adb4271fd5d1780}}, {{cite:61f39396806ef5089592d36c5cfc41ed2a3635dc}}, {{cite:a4f5db8a6addcb775b75f8db6eddbfe9a6b0ce3a}}, it tends to disregard problems which are considered too hard to be solved within the allowed budget {{cite:16f89d9cbc6458a438d97148e642403683101c09}}. On the other hand, one can aim to achieve a target end-performance with as few interactions as possible {{cite:87c46edacc1789966ed3c6e212b1242b90c44643}}, {{cite:b210074db48cb7bd6a5c7d0b708201e53e3694c1}}, {{cite:93811a38cabdef135d8044f51f4fee30fa329666}}. Since our goal is to show that our new agent is as general as Agent57, while being more data efficient, we focus on the latter approach.
| i | ee6aa981dfe900dde8993f694dac15ab |
The main contribution of this paper is a lightweight transformer neural network that exploits only depth information of range images to achieve place recognition. Our approach is very fast to execute and at the same time yields very good recognition results. Based on the attention mechanism of the Transformer {{cite:45021e1afc9af960d6c7d2c844099b796ecb2e4f}} and the NetVLAD head {{cite:99312b30911bb01bb61fa7741bd8e88fa9f44dc2}}, our proposed OverlapTransformer compresses LiDAR range images into a global descriptors. We build the architecture of our OverlapTransformer to ensure that each descriptor is yaw-rotation-invariant, which makes our method robust to viewpoint changes.
We train the proposed OverlapTransformer only on a part of the KITTI dataset and evaluate it on both, KITTI and Ford Campus datasets with the loop closure metric in line with OverlapNet {{cite:4669ffe6cbbb90e683618af8a60aff8744fee6f3}}.
Besides, we recorded and will release a new dataset, which contains three different challenges including place recognition for long time spans, reverses driving, and different appreances scenes to evaluate different methods.
| i | cf8bbfac116722c8dc4a7d62600b346b |
It is becoming increasingly common for companies to make use of machine learning (ML) predictions in their services {{cite:3944fac99c875f06a867af774d0d952186fa6ed1}}, {{cite:f866393c5540e6593439421a63c4bd255bd851db}}, {{cite:fb72e3763b25d7db7f900446f7fa815cba4b24c4}}, {{cite:b5fc7fe4039e20db7f2c1f82c0dd99beae345e7a}}. When there are several companies on the market offering similar ML-based services, customers choose only one service they prefer the most, arguably the highest quality service within their budget. In this user selection process, the customer pays a fee to the company that provides the service, which naturally creates competition among companies on the market. As a result, competing companies strive to produce high-quality ML predictions to attract more customers, which leads to buying customer data or subscriptions to data marketplaces {{cite:2341260e149f50c041bbfd610761305e62cb2482}}.
| i | 9605b687e9446d44b11e5be020fec1c8 |
Predicting an answer in a KBQA system depends on the ability of reading-comprehension that is responsible for fully absorbing and understanding the question {{cite:3a3bf63a97974812f934f4100338d1d11da02f74}}, {{cite:a97434ee8b3d9e95f0e171ace798ed3a74fae527}}. This is achieved by conducting a semantic and grammatical analysis that is required for obtaining the encoded question, and then representing it logically in a justified manner according to grammatical rules defined by the system. The logical form can be validated by a semantic alignment for the structured KB or by simultaneously performing a logical analysis with knowledge base grounding. The logical models are then validated in the KB during partial parsing. Thus, the logic model of a KB is analyzed and the predicted answers are extracted.
| d | 5478b096c654b453774e17a5d8d4c93d |
where {{formula:b6925347-7a38-48cb-bf44-dd269d064481}} 's are the Darboux coordinates of {{cite:36bd53ba4cb85531c7a894ed3f985432b4b3c278}}.
The semi-classical analysis on the conjectured form of {{formula:c74a0476-cb0e-4097-8765-6756f5ddc972}}
would be interesting and illuminating as in Ref. {{cite:7be463e1791be75f679ed6a7a4d7a3f436387ead}}.
As noted by Gaiotto et.al {{cite:36bd53ba4cb85531c7a894ed3f985432b4b3c278}}, {{cite:86170f4e43a74afe68976a090a30e6977bb68c77}}, this asserts the much needed
continuity property of {{formula:1c311997-0b8e-44a7-a574-d42e91b7e941}} 's over the vacuum moduli space
that plays a central role justifying
KS formalism in the context of {{formula:1757eab5-0cc8-4fdd-9b49-943b097a5559}} Seiberg-Witten theory. Our low
energy quantum mechanics is consistent with this claim since
{{formula:495605c5-0dbe-4595-b86f-4cd6c2144ace}}
| d | 793450c4f9947c50611507eed4996b50 |
LDL on Discrete Datasets:
We evaluate LDL on three datasets–Texas, Purchase, and Location– with discrete-valued features.
In these cases, we used a {{formula:4822c0af-efda-4b72-bf55-224a18972106}} noise to generate perturbed variants of samples (Table REF ).
Although using LDL was effective in reducing the value of {{formula:fc0a845e-5f54-48f3-b4ae-f0e08d87121c}} for these datasets, it resulted in a simultaneous reduction in classification accuracy.
The lower classification accuracy could occur as a result of the additive noise flipping the label of the sample.
In contrast, adding a Gaussian noise to samples in the four datasets with continuous-valued features (CIFAR-10, CIFAR-100, GTSRB, Face) did not change the label of samples as significantly.
A possible way to maintain classification accuracy when LDL is used on datasets with discrete-valued features is to investigate the use of a noise generated from a discrete Gaussian distribution {{cite:fc7b247b7b005e4af7d78ff2d1f935471b0777de}}.
| d | ed09ca2f6d475508b9a4f7246e957e0f |
Black-box optimisation {{cite:4bb4d250164c9df36993c6c22af60ded05650b69}}, {{cite:40cc01c53d802fd6f456a1c563ceaa9ef77a31d8}} implies that the details of the objective function and its gradient information is unknown during searching optimal solutions. In HPO, hyperparameters can be evaluated on the objective function, but we do not have access to any information about the model. Random search {{cite:56906600b6dc202e534dc865f4a0b6ee69eef0eb}} and grid search are two simple and commonly used methods for HPO. Bergstra et al. {{cite:f2f1d34fa652b06fb31fa94e306397f5c87b0fec}} hold the point that random search is more efficient than grid search given a fixed limited computation budget for HPO. However, facing the problems with expensive evaluations, it is very challenging for random search and grid search to achieve satisfactory performance.
| m | 9a375b7dbb15cfa5fb6a8d3766cec3d3 |
We report an exhaustive comparative evaluation, comparing with several high performance but low parameters and multi-adds operations methods on five datasets, including FSRCNN {{cite:24d920eea74ac39d0f84d1deb93db2d13ce0d1cf}}, DRRN {{cite:968d9a0d94155cce51a4bfcce0ecf912b5928732}}, FALSR {{cite:4283834e6b0453d1215b1be63377b9e13a20d183}}, CARN {{cite:bdd222789e2978d3acb48ec20e4ab6a181ed48b0}}, VDSR {{cite:de9d1b2fd804e7fa67d68e4f9b080ad6d64aa9a0}}, MemNet {{cite:644a90dcad0e85d433d3a323b9c7f8275d2b4e9f}}, LapSRN {{cite:3d2301cda0e5ea6a1c0444e75672d89830a82108}}, AWSRN {{cite:81118f8dbe6bd2527d12b0a3b0a2503c6fc5a1ee}}, DRCN {{cite:a7fadae51d3a0d7967f33023a2cf6c00652106d6}}, MSRN {{cite:db2db11d708b1b1ec7b9a28d04d815b7ceb3285e}}, SRMDNF {{cite:bef3665ddebe85f04dc93836bca672febc54ce44}}, SelNet {{cite:67f8286cf5dc72918c98343d242509478e2b8f88}}, IDN {{cite:cf2008dc74fab7a8cf16042d53a8542776834af9}}, SRFBN-S {{cite:7c2e2b6805b26f71892ec10a24a84b12c4efdf86}} and so on. Note that we do not consider methods that have significant performance such as RDN {{cite:ab66640981371467d8cc2b147304fa67402f76b7}}, RCAN {{cite:9f18d2b4522e8daa4d693e64dcabfd61aa909d6a}}, EDSR {{cite:de73e13d45b67803ba855fe6888e189fecbe09a0}} for they have nearly even more than 10M parameters. It is unrealistic to apply the method in real-world application though they have higher PSNR. But we provide a supplementary material to compare with these non-lightweight SOTAs. To ensure that parameters of different methods are at the same magnitude, we divide the comparison experiment on a single scale into multi-group according to different parameters. All methods including ours have been evaluated on {{formula:4444dc25-185b-41a2-add3-098d7a5d2a8d}} , {{formula:fd08558e-50e8-4c91-8b78-9af88e72d124}} , {{formula:bf755dd8-c2bc-4d57-afe4-9c0f594788b3}} .
{{figure:e24b6cd1-3dce-41db-b8c1-4c4a56195828}} | m | a230211d6ba13d4c10881b648a68047b |
Similar ideas have been introduced to neural networks recently {{cite:c5e8dc4633993347aca8aad10a3c9107e00a4cd8}}, {{cite:63e0009458c9fb28624966c85c13f447befc0aea}}, {{cite:0f5b351b835ecd6e4d8d8fc28658764f551bf765}}, {{cite:16940b580b527a1d200f14c87b976d7ed8b29280}}. In a stochastic thermodynamics setting, the change in weights of an perceptron during supervised learning can be defined as a forcing term and the objective function being an effective energy function {{cite:d07454856891ca2371177cc37b317ae7036d5ad8}}. The thermodynamic efficiency during learning processes can then be defined in terms of the heat production due to weight updates and mutual information between the target signal and predictive output. In a deep unsupervised learning setup, convolution neural networks are trained to recover data destroyed through forward diffusion processes, showing how ideas of reversibility can applied to robust generative models {{cite:d86f53f0dcf9fa6ce0067b7aa5d8c8780bb9e497}}. On the other hand, nonequilibrium thermodynamics can be used to analyze unsupervised learning process of a restricted Boltzmann machine (RBM) {{cite:26013808208e634b3c790edcd4e070aabbce6b9b}}. The results show that fluctuation theorem holds in this abstract model and the learning process is related to the reduction of dissipated work. Interestingly, if we inspect the Hopfield's original simplified model with dimension analysis, one would conclude that the "energy" term has a unit that is closer to entropy production rate in nonequilibrium systems {{cite:c21447950432f918dffa7964767f291b493e11d5}}. However, nonequilibrium thermodynamics investigation is still relatively absent in biological network models.
| d | 8441a2af10b7b2a25c824ea54d633592 |
The advent of recent blockchain technologies brings opportunities to overcome the above challenges of services computing. Blockchain was originally designed for digital currencies such as Bitcoin {{cite:1b7c63cb6202ee43fe20654d92b8d3b03c537181}} and Ethereum {{cite:2a73d0d74d63d3f48f8f333b5b4a887589ee5def}}. Thanks to recent advances in cryptography, distributed systems, consensus algorithms, and smart contract, blockchain has evolved into a trustworthy and decentralized platform to support diverse applications such as supply chain, finance, healthcare, energy, intellectual property protection, and IoT {{cite:61ac00abb0d4c5f4c46a0a26c61162b88ad0df96}}, {{cite:6083c387377e2126716cdc09335d74c6e0801a7a}}, {{cite:8e45bc19e5655f5169e4f75dfd8251eea30ec174}}, {{cite:62d53bb70ab265fde36ee4804c8231fbefcafcc3}}, {{cite:5f6278e1f503a31c200ee686ceb7e6f3228180e4}}, {{cite:ec373e5151ca1497eed4eed07df1f54190b032ad}}, {{cite:9ed6f8905f29729ce350c583e22a8608bc62fcf2}}, {{cite:c37f848dbd833b3177cbab10157f297f0b329ea3}}. Blockchain can potentially solve the challenges of services computing from the following perspectives. 1) Built-in encryption and digital signature schemes of blockchain can integrate with other security countermeasures such as authentication and access control so as to enhance the system security and preserve the data privacy. For example, data encryption and access control implemented on top of blockchain can effectively reduce the chance of data misuse and privacy leakage. 2) Decentralization of blockchain can help to mitigate the security risks and vulnerabilities such as DDoS attacks and SPFs. Besides, the auto-execution of smart contracts can help to update the firmware so as to mitigate the security vulnerabilities {{cite:a301b7f2b070776d66e79b904baa2dd44a3d6e39}}. 3) Intrinsic incentive mechanisms may address the pricing and incentive problem of services computing. For example, developers who contribute codes or report bugs can be rewarded a certain amount of digital currency through the automated execution of smart contracts. Therefore, integration of blockchain with services computing can overcome the challenges of services computing.
| i | 140ef13e001d9232b7fab1921832a4fe |
Numerous studies have been proposed to address the problem of shape effects on the transport of particles in the continuum regime. From the pioneering theoretical work of Oberbeck {{cite:a338718a01afc3462ffa1a654b51efe890e5fbd6}} and Jeffery {{cite:3c76c9216e76308b4d0235c0b422deb78e009eac}}, who firstly investigated the motion of an ellipsoid immersed in a fluid in the Stokes limit, an increasingly growing effort has been dedicated to understand shape and orientation effects on the drag, lift and torque experienced by particles in different flow conditions {{cite:a42c706317856696b86e6d74f344397c4661029e}}, {{cite:ee05b6656ba519423caa3f6fb8b5fa034f91eb7f}}, {{cite:20e18573725b30401a32959ac8b9d5fd173b3df1}}, {{cite:5320a6789b96d7baca777a3a208a274e6423ce88}}, {{cite:2e76800088dce072c13685ceb493811e6cd0cf12}}, {{cite:68e562814b3c1051d5bf3be6202db50e7a89a51e}}, {{cite:1005ed32f7394a104ee07a2b9f372b72b5b191fe}}.
| i | aaed6186a46452a504c54fed83c86b8b |
In our evaluation, we assume that the query can include the target (e.g., individual {{formula:f1261277-9ac7-4c15-979a-6ebd3fac3674}} j{{formula:430ac581-5677-4b91-a500-9cbbf867b2a6}} ) with 1) a direct family member, 2) multiple family members, or 3) multiple family members, and other unrelated individuals. We compare our model (in terms of privacy) with the existing similar work (discussed in Section ) such as {{cite:bf656fe693009533e08e790d16860b2d3f7b38f5}}, {{cite:1be239c6ac5cf076cf49c752e76b239ee87e8798}}, {{cite:d491ee9ecd1e5121de13346115fdbcbf74af545a}}, {{cite:5be4196fd159c6696a95e7cd5e1d3cd9e719f4e5}}. Since Hidden Markov would not work to model kinship relations in a genomic dataset, we are not comparing our model with the mechanisms proposing Hidden Markov-based models.
In the following, we compare our proposed model (referred to as “GenShare" in the figures) with: (i) independent assumptions (referred to as “Independent Assumption" in the figures) to show that GenShare can be proven by preventing any client from utilizing the dependencies among the dataset tuples to infer more sensitive attributes about dataset participants (in other words, we are aiming at achieving the privacy guarantees of the standard DP assuming all the participants of the dataset are independent), (ii) the proposed mitigation algorithm in {{cite:1be239c6ac5cf076cf49c752e76b239ee87e8798}} (referred to as “Almadhoun et. al.” in the figures), (iii) dependent sensitivity mechanism proposed in {{cite:bf656fe693009533e08e790d16860b2d3f7b38f5}} (referred to as “Liu et. al." in the figures), (iv) Wasserstein algorithm proposed in {{cite:d491ee9ecd1e5121de13346115fdbcbf74af545a}} (referred to as “Wasserstein" in the figures), and (v) Group DP proposed in {{cite:5be4196fd159c6696a95e7cd5e1d3cd9e719f4e5}} (referred to as “Group DP" in the figures).
| r | bf80be5f894e3f29c79da580ff56301f |
Machine learning (ML) methods are now being deployed for decision-making in complex domains such as loan approvals and criminal justice.
In many cases, an available ML-based policy may not generalize to situations not encountered during training. In practice, it may be safer to defer to a human expert when using the policy may not improve outcomes. Many have considered the problem of learning to defer in myopic, non-sequential settings (e.g. {{cite:670e29118b908ee73095229f0ad55ff9bbdeb0b6}}, {{cite:93113003430fb2f4fa8972313ee059b439c7578a}})Preprint. Under review..
| i | 2cd69a12f5db1083e30061528711ad3a |
We applied the eigendecomposition-based standard DMD algorithm {{cite:c5fd208efe075c2491bfc0c5d364a53b4631eb04}}, supervised DMD ({{cite:f6c110979e63b23788658895d19f5c0c2e3eb5e9}}; we review it in related), and the proposed discriminant DMD to the synthetic dataset.
Each method was set so that it would compute a dynamic mode (i.e., {{formula:d642f7aa-88f3-4f3d-aca6-a6018070fd94}} )The true value of {{formula:4f9ae52d-be42-4849-b1ba-97ba408ffb9e}} is obviously 2, but we set {{formula:0d4ee06f-55c7-48d5-8d83-8887c6872701}} . We intentionally misspecified {{formula:9ce3771b-8f4c-41f8-8aff-55fac320ea87}} because if {{formula:8592b7f8-bc88-4514-9aca-d478a152ebca}} had been set to a true value, the problem would have been too easy..
Let {{formula:720dce87-55a3-4d95-9c99-693dd86eba59}} be the dynamic mode computed for the {{formula:bed0c685-f227-4c7a-814b-53a10c4479a9}} -th episode.
In fig:example:mode, we show the averages of the dynamic modes computed by the three methods for each label (i.e., {{formula:84037412-8ac5-4dee-aadb-beb720abbff8}} and {{formula:21b44d9d-5106-464c-a180-a1a1a1d3aaea}} ).
We can observe that the modes computed by the discriminant DMD are less occluded by the non-distinctive mode.
Moreover, we visualize the relation between the 20 episodes using the classical multidimensional scaling (MDS) with the distance function induced from {{formula:fd978c12-364f-42ec-8d3d-691f309237d5}} .
We can see that the episodes with different labels are well separated in the feature space induced from {{formula:090002ff-903d-4a8a-b0ec-2c161aa6da70}} .
Furthermore, we show the values of the two objectives of the discriminant DMD, {{formula:f61220bb-7b9c-45c0-a948-886ae3840a99}} and {{formula:c0021e0e-333c-4065-8726-ccd76b2f388f}} , achieved by solving eq:problem with different {{formula:f34adafc-6100-48f9-8134-920f2af4ab05}} 's ({{formula:8b1638ce-68ee-4c22-abfa-e4ecd340cd6a}} ), in fig:example:loss.
We can observe that the value of {{formula:5b8c2215-aeb5-42ba-a4a6-a3e8a538c5ff}} improves (i.e., increases), trading off the reconstruction error, {{formula:e8a933ab-dd3b-473f-885c-73ae4f39fbc8}} .
| r | 8a2155075d67b77fb10398234763d802 |
converge in distribution to the process {{formula:762ec432-c00b-473f-8787-6a35630e0cc4}}
whose generating function is represented by the Fredholm determinant with
the extended Airy kernel {{formula:e2ddb6c3-f743-4c84-acd5-b5e9cea08f91}} {{cite:2522068d0b7a9605a565f18164675c73a54e2de2}}, {{cite:f2ad10651ff148e809c7b86f2971616a9326375e}}, {{cite:27c79a5edd76c11d25e1d5478044ee04bc2715b9}}, {{cite:80abedb6cfc91109828abd131774ecd7e6345534}}:
{{formula:2e76aff0-fac2-40c4-8d0b-a1ecefbcd774}}
| i | 8ff310866c530d89cff59c695ece1d13 |
where {{formula:3f6da0e1-0487-40f0-ae08-9bf17192fa97}} represents virtual crystal
and {{formula:5cea6b68-2bbc-4885-8995-2d10104f567e}} is the energy dependent self-energy
determined by the coherent potential approach {{cite:ebe17ecc4c3a4c04bf6ab8e13b50bd54e68fa0c7}},
as the best known theory to estimate effect of alloying.
| r | 06a5b05163af8927b3bdbc01720cd0ae |
where the binary encoder and decoder {{formula:8420d661-251a-4ba4-80e6-7d3aa904ce99}} are chosen optimally such that the average expected length of the binary string is within {{formula:e0debe6c-b6ac-4b1d-a618-3a1385c464c4}} of the entropy per symbol; see {{cite:9fcff637bc42aaacc34b6110945c6835225440f7}}.
| r | cb5146af2d93cde7be079f6d3e5a2ccb |
Rubio de Francia's extrapolation theorem works for spaces of homogeneous type ({{cite:7cc1ae1c2373a930c0f2ae937ccd21113c94fc29}}). The arguments in the proof of {{cite:6016c8e8adeeb0424f346de78f086306e1b65c48}} allow us to deduce that if {{formula:bb643f94-f63c-41af-a997-b569e2c60b3b}} is an {{formula:ea6ca1ce-6475-4092-a3d0-7ea18fe18e09}} -valued Calderón–Zygmund operator on {{formula:9e776e1e-5535-4552-b937-bbf161ca9c3d}} , {{formula:9bf9decf-8794-4a6d-bf85-286db2e7429f}} defines a bounded operator from {{formula:973e8110-1ec1-41c0-9a3b-7cdd777d14fd}} into {{formula:933534b4-886a-4240-86fc-cb39f25036e5}} , provided that {{formula:6f89ba75-62f8-4e9a-ba45-5b5acfbfc87c}} and the {{formula:f808bc54-3be4-4984-92ae-0b200828c99e}} -Hardy–Littlewood maximal function is bounded on {{formula:4f5d02f3-b732-449f-9477-6f868334c888}} (see also {{cite:1e92d773c0610cce64c56114f368ba5a2b1e0169}}). We recall that according to {{cite:4eccb3b4e1364f4d37a3bb242417212228681b13}}, the Hardy–Littlewood maximal operator defined by the measure {{formula:a41eb732-cf99-46b4-9daa-a1a9c63cd69c}} is bounded on {{formula:dea436a1-41e3-4ecb-a699-8e7a64ccc1b5}} provided {{formula:2f7a4212-1b35-44db-adcd-c64cf4b1f5f4}} and {{formula:a4fdeb4a-5b3a-430c-9b5a-a9e2ea49439a}} (see also {{cite:87741c0d3f62ba48cf945a456a3aa6715cc8da6c}}). We also notice that {{formula:c1067055-e821-4c9d-8f62-e7fcfcea28df}} is well-defined for {{formula:68c16c00-4708-43e5-88ce-7712beb0254d}} thanks to the embedding {{formula:4aab0f20-aea1-4d01-971a-56aa2fe4c44c}} ({{cite:f6e3f15d8fcaee09de8282dcdc65357bb02138ea}}).
| m | e06eed6349e078999ccb1eb694e08661 |
Through this study, we gain several insights.
We find that normalization layers affect robustness significantly.
As shown in Fig. REF a-1, the better clean AP score the specific normalization layer achieves, so does a better CD.
Seeing such a positive correlation between clean AP and CD is expected, and the same observations are made for semantic segmentation tasks {{cite:b786f2b6d0240cea7fd9b1f4d98175aa28b47ebf}}.
The more interesting is the rCD score, which is reported to stay relatively constant in previous studies {{cite:fb3c2df23f49135b2e8a4545f75929083864b381}}, {{cite:b786f2b6d0240cea7fd9b1f4d98175aa28b47ebf}}.
In Fig REF a-1, we see that Group Normalization (GN) achieves a very robust rCD score. This observation shows that corruption robustness improvements are not only coming from better-learned representations of clean images. The model shows larger improvements for robustness than it does for the clean validation set.
We also compare models trained from pretrained networks and randomly initialized networks and observe that pretraining does not improve the robustness. As a result, we observe that models trained from scratch for longer iterations achieve higher robustness than pretrained models.
As presented in Fig REF a-2, the synchronized batch normalized model trained from scratch provides the highest robustness when evaluated on Cityscapes images.
| d | f889c96dc7488a157a0f3f3219f5b24e |
Results from the various SI models show considerable disagreement in the long-term evolution of TSI with estimated changes since the Maunder minimum ranging from 0.7 Wm{{formula:3d5f9d9e-e3f2-4eff-b3b9-0932e8c0fe83}} to 6 Wm{{formula:8e91e6bc-43a4-420a-b6fb-df94c2089d24}} {{cite:a5d64bcc2ca676e619020e0c1aa184dec2f48f5c}}, {{cite:d8269c5e81f2e7c3a400ccd565d00683303fcd3b}}, {{cite:d992161f88627b51a230b8d4f88d4364be2af39c}}, {{cite:a9f5b7e9f71fa81fbfd0221e611d9593e05ad643}}, {{cite:6bed6d715c3a4fed74d4aa234044670f2108112e}}, {{cite:0dba39069bf80873587b982843d380542262bc2b}}, {{cite:2b013d24c6af93f658128d9b7c3128b1006300e5}}, {{cite:48dcf55af90952ef12d7546bc5fa9fd27fa92aea}}, {{cite:16707bde9676cfcc67d4c717de59f64fc16afb14}}, {{cite:1f2a138b49a415ff605d1a8767a30907ac31a7c5}}, {{cite:ec67ccc712928ef48f22b317471512b08041ad3e}}, {{cite:d63d9ae8b05e16c638731bde7ad9e1c3c30615a5}}. The various SI models also estimate different SSI variations on timescales longer than a few solar rotations
{{cite:edd762293308ccce94ebe3a093b429c8218f914f}}.
In particular, for the SSI in the Vis range, most models suggest an in-phase variation with the solar cycle {{cite:ed99478ca670d221f4eac0be7723f4344dc27a50}}, {{cite:14bfae60156558a79c3e29b4bb7c63e2f0b713c6}}, {{cite:eb65b0f68fb3f0cff2ada9b13bc495449239b42a}}, , , {{cite:51ad8e2384c2f69f26e4bd4017873c88573a6582}}, although there are also models indicating an anti-phase change
{{cite:b2edeadb5189ceb84887df5ccde31594cb836ae5}}, {{cite:5a80eb67edc0659125112ec23b8ad2abc1854446}}, {{cite:75717e33f603d7e1c429473797a3d84e25c5fa1a}}.
In the UV, all SI models return variability in phase with the solar cycle.
| i | 421cec32e0668f31a457b9e72402f375 |
This section elaborates our proposed BLGCN model and the corresponding HSI
processing framework. First, we preprocess the input HSI raw data with the help
of simple linear iterative cluster (SLIC) algorithm {{cite:43e0b3adcb76941f314c8a6aaafed6b56e3552c7}}, and
construct feature matrix and adjacency matrix. After that, we train our GAN
network for the minority classes, augment the minority classes data, and update
the adjacency matrix.
We input the obtained features into the BLGCN model, and dynamically adjust
the training strategy by quantifying the uncertainty of the output.
| m | 1b72edd1d99b04468656e7d25724947b |
A similar idea was recently pursued in {{cite:e5d49a1173fa082972dfb1dc36862a29c59886c2}} for the task of dense pose prediction {{cite:0fbaa1654bdbaf00c39358a5931f74cc2569c5b9}}.
Just like 2D pose prediction estimates the location of a small number of distinctive object landmarks, dense pose estimation does so for a continuous set of landmarks, identified as the point of a 3D template of the object
(fig:splash).
The goal is to learn a canonical map, i.e. a function that maps all relevant pixels in an image to the corresponding points in the template, thus identifying them.
For supervised learning, correspondences between images and templates are collected manually, using a category-specific template for each example object.
As a result, annotations for different object categories are unrelated, which makes it hard to learn a universal, category-agnostic object representation.
| i | 1022f6ec481cfd2cbd54bed622af20bd |
The measured angles of a frequency-dependent {{formula:6c5ae8c6-2ecb-44cf-bb47-2953e70ee833}} for {{formula:06196db1-df10-46a6-b779-2d61ac930233}} GHz are shown in Fig. REF as a function of the fractional sky coverage {{formula:e8fe7d59-54a3-433f-bf56-b60f3b572913}} . The upper panel shows the probability distribution for the cosmic birefringence angle {{formula:737f1d36-2bd0-4682-a65d-00a3b8823022}} for each frequency band when we ignore the intrinsic {{formula:43014ec4-6996-418b-888f-f7554caa8759}} correlations of the foreground. We observe a decreasing {{formula:12d3debd-0441-46f6-85e2-f9965d1ef000}} as we mask more of the Galactic plane for 100, 143, and 217 GHz. This is consistent with {{cite:62eb00b636814e98d1efc5212cca966f82b510db}} where a similar drop was shown for a single frequency-independent {{formula:332d52d2-0ef9-4dd5-ad53-85b70919d525}} . We do not see this decline for the 70 GHz band. This band has a higher contribution from polarized synchrotron emission than the other bands, therefore, the mask-dependent contribution to {{formula:063e8ede-c5a5-4186-a715-b8edf6fdd469}} is less significant. In the lower panel of Fig. REF , we show the probability distribution where we instead use the filament model for {{formula:ca8de7f1-bbd7-49f1-8672-5fd723763ab4}} . The drop in {{formula:aed408f0-f070-4a94-84ff-60c9b5e01abc}} when we ignore the foreground {{formula:a14f932d-2f47-43a5-9a4b-65d470cf384d}} is mitigated when using this model. This reinforces the hypothesis that the intrinsic {{formula:47865c77-6066-4503-8482-087959d86cd0}} -correlation of dust is mostly positive for large Galactic masks as reported by {{cite:7ddc3ad984f8e09772a3aad85997bf8cfdbd5e95}}.
| r | 9d5eef4dc8d8feb95947132dba84b1f8 |
Now we present some details of the training and validation for the following four numerical tests. In the training process, all the parameters in the neural network are first randomly initialized from the uniform distribution in the interval {{formula:352f945f-d9b6-4584-80ee-b866165cdfa0}} . Then, we update the parameters by minimizing the loss in (REF ) using the standard Adams algorithm {{cite:1919a18ec52c5f002a16edc2ff6be215bb02a002}}. The learning rate is taken to be {{formula:81b2d660-c4b0-4188-99df-7b0cfd0d39c2}} and the regularization coefficient {{formula:b47fb0f5-758f-43a1-b795-dadca7311c22}} in (REF ) is {{formula:28ee344e-5a3b-468b-8b03-0f8485be6cda}} . Recall the training method following (REF ), we take the integer threshold to be 0.05. Besides, the total epoch number is {{formula:13fe3e46-63fa-4d0e-a14d-f02bb0d66595}} and the mini-batch gradient descent is applied with the batch size 10.
For the validation, we use the following relative {{formula:21e0d9d8-5760-4cd1-9a30-a54c9a1c8cac}} error:
{{formula:3ef96337-7ea3-475e-be8a-8551e823ac73}}
| r | 1e702232fb3a35370fd660e6af7612cd |
Repeated cross validation is not the only technique for evaluating candidate models.
For instance, the method of stability selection described by {{cite:f168851f2389ec9fffc8319c0a13361b9e3bf4a7}} is attractive for its theoretical finite-sample guarantees in controlling family-wise errors.
Alternatively, selecting features in groups can help overcome multicollinearity {{cite:a6275b035d9815510d364ba558f3827781542bb5}}.
Ideally group selection should also control candidate model sizes.
Without going into details, it is possible to project onto sets that limit the number of groups selected and the number of features selected per group.
The downside of doubly sparse cross validation is that involves searching over a 2-dimensional tuning-constant grid.
The percentile lasso {{cite:91283420938f0bebb87cd3f1579e585b80c32c3f}} is another attractive device for stabilizing model selection.
Our repeated cross validation procedure, similar to the percentile lasso, attempts to control variability by using the median of optimal model sizes across replicates.
The distributions reported in Figure REF suggest that adapting feature selection to account for the variety of models generated by replicate cross validations may, in fact, improve credible intervals.
Incorporating a Bayesian perspective into sparse VDA might be based on the the peaks in Figure REF , but again model selection is apt to become even more time consuming.
| d | e0a4aaa62dd50e3ea7be23446fc11c56 |
Interval Censoring.
We have made the “no gap” assumption in the current paper to focus on the right censoring problem for simplicity. However, in practice, it is possible that there might be gaps between the clinical trial and observational follow-up dataset. Thus, to fully deal with the problem, we need to extend our current procedure to the interval censoring case as mentioned in Appendix F (supplementary material). {{cite:c367160a8f3d5cc12e5e88b245bdad8d4768cd89}} has studied the problem of two-phase sampling for Cox models under interval censoring. Generalizing their techniques to the current linkage problem remains an open question.
Beyond CLAR and sensitivity analysis.
CLAR may not hold in certain situations.
For instance, if the data being linked is from another study, in which
the time to event variable {{formula:5d9d8512-ac58-4861-82d8-bf8061880b54}} may influence the chance that someone participates, then (A1) will no longer be true.
In this case, we may need to model the linkage probability that depends on {{formula:4e9e4627-0327-4373-9f4c-1bf9364f4960}} , which could be seen as a sensitivity analysis {{cite:7a044179854e3788a3afd80f46efd5eb58ef27da}}, {{cite:f20d869ae527431a7f455ade53a7ca56df072873}} on perturbing assumption (A1).
How to analyze the data in this case is left as a future work.
Missing covariates.
Another direction that we will be exploring is the case of missing covariates {{cite:a19e81865e6b1a7c03f0b988dcc89c351decda1a}}.
Missing covariates is a common issue in medical research.
When part of {{formula:e7deb54b-8a20-471f-8388-ef76b65adece}} is missing, CLAR will no longer be enough to identify the underlying parameter
since the linkage probability cannot be computed for every individual.
In this case, we have to impose additional assumptions on the missingness of {{formula:88c6ac17-4cda-47f3-b67d-0c4d77621c8d}} .
However, such assumption has to be carefully chosen so that it will not conflict with the assumption on the linkage.
| d | 4814947c852a030a6264c52b28a59bb4 |
This kind of methods have as aim to compress an image losing the several information starting from reducing the color space like chroma subsampling method and any Transform coding which belongs an important transform such as Discrete Cosine Transform {{cite:acde3e6fe73f4e3c9412a9369630933e2b795868}}.
| m | d776b09de989d34fd3cfc8c3631ef633 |
Figure 2(a) provides an UMAP visualisation {{cite:8ae5a3b49352049b45dba44178459c764f06649e}} which illustrates the class separability achieved using only the three most discriminant dimensions (umap1 to umap3) obtained after the dimensionality reduction of the HSI-LBP feature space. In Fig. 2(b) it is noticeable that the same UMAP dimensionality reduction applied on the “deep features” produce tighter clusters and larger inter-class distances than in Fig. 2(a). This suggests that the superior performance of the DL models relates to the richness of the information extracted from the patches using efficient feature extraction backbones associated with transfer learning.
| r | 25d0267b2e78cbf4dca6f24a47440227 |
Broader Impact.
Like most self-supervised approaches, our approach is data hungry and trained using a large amount of unlabeled data collected from the Internet. Our model in its current form is prone to learning and amplifying the biases present in the dataset, especially if the dataset in question is not carefully curated. While the data collection and labeling has been discussed in the original paper {{cite:1734175607219328b0ae9982103c3cbbada885e1}}, the community has focused towards imbalance and privacy violation in existing image datasets only recently {{cite:d1da0df1cbd352dcdd7322e8c37c1b00f518edf6}}. A recent study {{cite:a9ab3794e8372370da36facb029c88ed5e196ad3}} shows that 997 out of 1000 ImageNet categories are not `people' categories. To compare against previous methods and allow future benchmarking, we provide results on the 2012 version of the dataset with 1.28 million images in training set and 50000 images in the validation set.
| d | c38743e6561978930ad1bc3017a269fc |
We initially carried out first principles calculations using the generalized
gradient approximation (GGA){{cite:b6ede9e9b2444e6ce2e2a36694fbed1b32128a86}} for exchange and correlation,
which is implemented in the all-electron full-potential code wien2k {{cite:af9efe02df0afb709153f3879a5e686fcbfe4c8b}}.
The results for the AFM phase at {{formula:7683f944-fcd0-43ed-a079-e522e7147c17}}
were confirmed by another all-electron full-potential code fplo-18 {{cite:05fac59a570aa8294aa769a8daafe723aec13e78}}.
| m | b8cba1902642bd89e7044d09fcad30fb |
For each algorithm, {{formula:db677d05-10ad-4639-8732-29a84b2c0131}} is equal to PMI or a scaled log of {{formula:31437182-f4eb-4d7f-87c7-73ed1a334c82}} . Yet, the choice of {{formula:9a2a4e58-7df9-4e28-a724-9b48ec59f6a2}} in combination with {{formula:261658fc-d364-4ca9-9d01-fbd57c89cb07}} provides that every model is optimized when {{formula:f9cce96c-7bd4-4cf8-8779-e4d7c0f95a67}} tends toward {{formula:99d99978-96b3-4ddb-9a97-29a2e0071c96}} (with or without a constant shift or scaling). We demonstrated that the optimum for SGNS (and FastTest) is equivalent to the shifted PMI (§REF ). For GloVe, we showed that incorporation of the bias terms captures the unigram counts needed for PMI (§REF ). A similar property is found in LDS with regards to the L2 norm in its learning objective {{cite:72001d3aa619fb26b7a28e67c5ecfa17455c083c}}. Thus, these algorithms all converge on two key points: (1) an optimum in which model parameters are bilinearly related to PMI; and, (2) the weighting of {{formula:1ea20e4f-3d37-49d8-b7b5-5ef42465b23f}} by some tempered form of {{formula:8141463a-43c2-44dc-a370-21eb9cbb32a6}} .
| d | 3e5692b730d79d4fa372e3b90ccd9d9c |
The Hölder family contains a large class of smooth functions, and has been widely adopted in existing nonparametric statistics literature for various problems {{cite:e1669cbee2eb14ea68bbb54ff0977c1e64ec37ba}}, {{cite:7c5e0e88d362ad0bb8c696d729148cbcfddd0ad3}}, {{cite:b652046da99324bbb53a3be5346f1aaefcd418c0}}. For MDP, Assumption holds for most common smooth dynamics, as long as certain regularity conditions on smoothness are satisfied. For instance, a simple and sufficient condition is that for any time step {{formula:57c91085-2ecd-4999-b94e-8860c92c200f}} and {{formula:ca4edf31-8c1c-42ed-bf6c-6dbe856befbb}} , the reward function {{formula:5918c7f4-74df-4fe9-96b6-ee3ec3fa14a4}} and the transition kernel {{formula:95e97ac9-636f-4e8a-9a47-760f9f22972e}} are {{formula:e5ebf69e-c7bb-4f86-8039-1b717fc221e6}} -Hölder smooth functions. This implies {{formula:0fb24c57-96c0-4efa-9d68-f2bc83490574}} . In addition, Assumption may be satisfied even when the transition kernel is not smooth, examples of which are provided in {{cite:02cc19c99d407be2727407359c9ea952539f3dfd}}.
| r | bed6985695c5ff25b872a350c7765f63 |
In this paper, we address the above challenges by proposing a representation learning framework with multi-channel feature exchange for aligning incomplete knowledge graphs from different domains. To capture the multi-domain nature of KG entities, we develop a graph attention convolutional network that can combine the translated entity name (as the entity's feature) and the relational structure simultaneously. The attention mechanism allows relational importance integration, which helps mitigate the noise by focusing on mutual relations in the input KGs and ignoring the missing ones. Our proposed attention mechanism goes beyond the existing techniques {{cite:16a4cae1de01f31ad8af24cefee15958bdf0cd13}}, {{cite:dceb31d258fc2d7d4184189ebaf661e9d9746203}} by leveraging relation-aware attentive scoring, which helps the framework to integrate the KG edge information. To guarantee consistency across KGs, we develop an additional embedding component that encodes both entities and relations with the tradition translation constraint {{cite:26760b0e0b8696ed5182920f0d3f291dae942373}}. While many recent works neglect this `seems-to-be-strict' constraint {{cite:8ce2420365d68010440d043d3144b81adc36c207}}, it turns out to strengthen the local information of relational triples and mitigate the information dilution phenomenon in graph convolutional networks {{cite:592f7e1f2f4173e6b465410605db70575ef328c6}}. We also develop a missing links detector that consumes the two feature channels to exchange the knowledge from the two input KGs to discover and recover the missing triples. Finally, we combine these dimensions using late-fusion to instantiate the alignment result.
| i | 8e940c3280dccd9deb8c8bd71aaa3d08 |
The pre-trained language model is the uncased base BERT from Huggingface's Transformers package {{cite:234720b5cfaafbe1516db22af882b76ada68ffd1}} with an embedding dimension of {{formula:c805a2b0-f07e-4630-9f9a-68709940d549}} . The pre-trained word embedding layer is the cased Common Crawl version of GloVE, which has a vocabulary of 2.2 M words and the embedding vectors are of dimension {{formula:4124738f-cf5f-4549-a1e1-037191c5ff02}} {{cite:cede3357dbf717868f43075c3f3c798aa1e0e9ab}}. Both the BERT and GloVE models are frozen during training. We use NLTK's POS tagger for the POS tags.
| m | 77367bde06d5e2ec8e9c5ce3b884265b |
The adversarial attack to speaker identification aims to make an identification system wrongly recognize the adversarial voice of a source speaker as a targeted imposter speaker, where the adversarial voice, a.k.a. adversarial example, is produced by adding human-imperceptible noise to the speech of the source speaker. It shows great threat to modern speaker identification systems based on deep learning.
Existing adversarial noise generation methods can be categorized roughly into: (i) gradient-based approaches {{cite:db39fe2ffb8b94a1427f1807e8bf6c732a82a89f}}, {{cite:e48032fe0bc85208d47f8159e1ce583b45b2c2aa}}, such as FGSM {{cite:b1c53d022ccd058f4ad2eb4b1c5d8f907d410068}}, {{cite:0a98c0c959cc72abc25583ae1864e59163de270a}} and BIM {{cite:6bc778b8da4538d9c459329145a552d4e05db55a}}, (ii) optimization-based approaches, such as the C{{formula:fd723591-b00e-407b-b5ec-f67276d14091}} W attack {{cite:494f1641edc09424ccd412226ff12d01b9b7112b}}, {{cite:10a8ac50da39cdf71bc919a974e30cbe1f29953b}}, Quasi-Newton {{cite:5693149354f5ba9c4fce11daf31d4f0b22105bca}}, FoolHD {{cite:c16a0792a7065510791af14fbae3d694e05fdc91}} and AdvPulse {{cite:14c484ed4d1c3cc01ef421e20c03c4c0bf19b418}}, (iii) query-based approaches {{cite:afd905d76c45061b2232c33943213fd4b9286c15}}, and (iv) generation-network-based approaches, such as the Universal Adversarial Perturbations (UAPs) {{cite:cd5b92ab294961092298f262cf0be340597d1ac3}} and FAPG {{cite:abbc301462027057df7aca7a5cdd0cc5d19b4387}}.
| i | 73f57103d61439da44c02b62a6bbdd96 |
We present some recent tasks on the physical processes dominated by the magnetic field.
Magnetic reconnection can be calculated as a traditional megnetohydrodynamics (MHD) process. Turbulent reconnection was firstly mentioned by {{cite:f8a181d0b7261f9b59d703fe8be640052895bd6d}}, and it was applied to the relativistic plasmas {{cite:c7f99c97e5b22d04e1f6849824a9f76177188d5a}}. Stochastic acceleration is involved in the turbulent reconnection {{cite:0f2011e439df11ca96bd675e128090228c2a12fd}}. It is possible to use the turbulent reconnection to explain GRB phenomena {{cite:3bdc38e36eb6f4c638be5de351731144eb58f191}}.
Furthermore, the spectral feature of the kinetic turbulence in the collisionless reconnection was recently analyzed, and the spectral index has a range from {{formula:52f5c8cd-0238-4437-b9b2-b86994af9d44}} to 3 {{cite:f549721769f6d4ea076a0b013e6fee7787ad0ea9}}.
In particular,
{{cite:cf824be70dd1577fc536d7543d695ae67765294e}} comprehensively investigated the acceleration site and the particle motion nearby the reconnection region. Particles can be effectively accelerated by the electromagnetic field during the collisionless reconnection process.
Although the complete process of the particle acceleration in the reconnection region is complicated, it could be very interesting that the turbulent properties in the collisionless reconnection can be further investigated with the combination of the jitter radiation.
| d | 4abddfb9bea319a9214e242086a19ff4 |
Patch-wise weighted sum: Our fusion method uses attention mechanism also utilized in GANimation {{cite:2912ee748d8c6c225630220bdfa3891308d4788d}}.
Inside the fusion unit, convolution with shared weights is applied to each of {{formula:50414d78-9f66-4d53-b194-bc1fd4f14db0}} warped features and outputs single channel features.
Then, all features are stacked along a new dimension and softmax is applied to form the patch-wise masks. In this mask map, the sum of values at the same pixel location will be 1.
These mask maps and warped features are then multiplied and summed up to form a fused feature. Table REF shows the effect of this method and it is clear that these masks filter out irrelevant features.
| m | df092fb32b674ac4efcdb33f48108e44 |
Coupling two normal leads to a superconductor can give rise to non-local transport processes directly involving both leads.
Two opposite-spin electrons from a Cooper pair in the superconductor can be split into the leads via a process known as Cooper pair splitting (CPS).
The dominant transport mechanism that gives rise to CPS is crossed Andreev reflection (CAR), whereby a virtual state allows two electrons to be injected simultaneously into the superconductor to form a Cooper pair.
Additionally, single electrons can tunnel through the superconductor from one lead to the other through a process known as elastic co-tunnelling (ECT).
The ability to control these processes has important implications for two distinct fields.
Firstly, efficient CPS can be used to generate spatially separated entangled electrons, that can be used to perform a Bell test {{cite:5e3b5dd168ce4092200374d4f4949d02cf78e547}}, {{cite:d0a28ef98405d43c07c23ae1f6d6641bb2475ef6}}, {{cite:24156f03459796ebdd711de8138cabb737b7b2ff}}, {{cite:a26337eb9d542e6c04c1f38a0e3ad7cf0e9ef9bb}}, {{cite:1df18db5b9e03c5562daf23d1b432aa0261c99e7}}.
Secondly, in the context of topological superconductivity, it has been shown that CAR and ECT are crucial ingredients required to implement a Kitaev chain {{cite:e9cad2331c3150cb6568bc26ad0acda50942a4a8}} using quantum dot-superconductor hybrids {{cite:8b725b5b9c8befad2c39194764217e04fff6848c}}, {{cite:43b8568edd9adcf8e1214dc1a39e90b94891ace4}}.
| i | 29eeffddf46d2214ec4b0f04ed02a26d |
I will soon start from the beginning and define a matroid and its Orlik-Solomon algebra and holonomy Lie algebra, but first I will give some background from topology and cohomology. A (central) hyperplane arrangement is a finite number of subspaces of codimension one in a finite dimensional vector space over {{formula:8cbbd43f-491d-41f8-87e7-7e925d0c6dd0}} , {{formula:a3287202-c01e-40a9-aa14-a9c96d875cca}} X{{formula:bb33cd81-3a7c-4319-a0b9-e8074c439501}} Rn{{formula:0a07f243-4278-4ba8-821e-e1b2cbbb5a70}} H0{{formula:e7e52af0-ea1a-4a61-899c-0fe5be2666ae}} X{{formula:7fa26244-510f-40ce-bfda-83b7a495a00b}} |H0|{{formula:c2b471d0-e7ea-4aaf-ac50-551307a7b606}} When we change to {{formula:4e09cabb-a78d-430c-ae46-1c54d004502e}} we get something quite different. If we think of {{formula:29ab5103-a8fd-414a-9d2d-8def964597ac}} as {{formula:0cce1c2a-fe69-4cf4-9a2d-32a581eddc4e}} the {{formula:861a79af-d8c3-4290-b5d6-9270d91aa1eb}} -subspaces of codimension one now has real codimension two and the simplest case is the real plane minus the origin, whose first cohomology group is non-zero. In fact, the general complex case may be treated with deRham cohomology using a closed but not exact one-form for each hyperplane to get the cohomology algebra (at least over {{formula:d9193167-5369-4042-b792-8769bc450752}} ). This is called the Orlik-Solomon algebra {{cite:2a68ace32945dfbe6239cc2261a410a0d712d3f1}} (Brieskorn {{cite:dee58b6aa85f198f8f720c399e4ea8e7bb870c8a}} showed that the cohomology has no torsion), which we will come back to. The algebra is determined by knowing which subsets of the defining forms of the hyperplanes are independent. It is here matroids come in; the main example of a matroid is the set of independent subsets of a set of vectors. Goresky-MacPherson {{cite:201cb99058a0b1a6ab20f46b578a7a3e10243a6e}}, Björner-Ziegler {{cite:443de6580e4a2437eae3cc7a2522bdea43297151}} and Longueville and Schultz {{cite:8da2d448125876466657fe93f8edec241d14e009}} study general subspace arrangements in {{formula:cadf21d9-4b02-4c56-83a2-dd79881bd3b5}} , especially subspaces of codimension 2 whose intersections have even dimension. This is the natural first step generalization of the complex case. They prove that everything hold except that the signs in the differential defining the Orlik-Solomon algebra may be different from the complex case. This is interesting, since it gives us more freedom in defining holonomy Lie algebras (and my generalization covers also this case). I should perhaps end this introduction by defining the holonomy Lie algebra (it will be done more explicitly later with generators and relations). If {{formula:78aeb2a0-8ce6-4aea-b965-010564acd20f}} is the cohomology algebra of {{formula:601f969c-9287-4d04-b66f-49a6f481f986}} , with coefficients in some field {{formula:694adfa9-c76f-43c5-86ea-d7ab4a86cf7f}} , of a complex arrangement, we have that {{formula:7d55ade7-2c25-4a4e-9831-c6675caf7fa5}} is the enveloping algebra of the "homotopy" Lie algebra {{formula:b22b4d13-4596-49ab-a2e5-ef7ce69fccd6}} of the arrangement. The holonomy Lie algebra {{formula:03bb9250-46b2-4aea-950e-9ebf4e1d9b78}} of the arrangement is defined as the Lie subalgebra of {{formula:b98c94f1-af11-4299-ad15-84a9523f2001}} generated by its elements of degree one. The following result by Kohno {{cite:0f36de90266ce28772ba3275d08beb5e05a1bb1c}} highly increases the interest to study {{formula:3f50e5d2-1d94-48e1-b7d4-c30951bf4428}} ({{formula:658f3e38-3cde-4682-9a96-37731ade9a5d}} has characteristic zero).
{{formula:ab6925da-1e55-46e7-84cc-1d9e7dc35025}}
| i | 3b7e18746a7f03abc0052b562f5f51e1 |
A novel method is proposed to tackle the issues in modelling cognitive load, as discussed in the previous sections, followed by an empirical study to validate such a method.
Contrary to all the existing methods of cognitive load modeling, the method proposed here is self-supervised {{cite:6e88150146082c7d213ce5dc6ca2b9f0b40e9b6c}}, {{cite:8bb3147c8013cad29db24a9ebe49e6c21c2c0f95}}.
Self-supervision is an approach that autonomously learns from the data itself, and that is in the middle between supervised and unsupervised learning methods within the discipline of artificial intelligence.
It is not fully supervised because it does not require ground truth (an independent variable to fit), usually as a form of declarative knowledge.
It is also not fully unsupervised because it is not used for discovering patterns in the EEG data that need to be subsequently labelled and categorised with human intervention.
Rather, self-supervision refers to the fact that the ground truth is generated by some automatic methods applied to the available data itself.
Subsequently, some supervised machine learning algorithm uses this ground truth as supervisory data to train a model.
In other words, self-supervised machine learning can be seen as an autonomous form of supervised learning because it does not require explicit human declarative knowledge.
{{figure:a6d69cd4-78ff-45fd-9b2f-e5df361c94cf}} | m | 0b87f5f428181332989f669079c46126 |
Large-scale deep neural network models have an extraordinary capacity to generate linguistic continuations of natural language prompts {{cite:0b2aedfe359f7a4530267acc4ad8fd6ea2bd0812}}, {{cite:a5e69ec46191a1228945073b63bf5790f836b32b}}.
The models provide the probability of words given a context captured by preceded sentences that is similar to human predictions {{cite:8c0ae7a442758347ed015f72221690b98c5ae1d6}}.
Using the GPT-3 language model, we used sequentiality to quantify how much a story resonates with the expected or commonsense narrative for a story topic (Fig. REF ).
With the measure, we observed that a difference between experienced and imagined stories can be captured by differences in episodic details and differing reliance on schematic knowledge about how events in the stories should unfold (Fig. REF ).
Based on sequentiality differences, imagined stories have greater alignment with expectations and commonsense on the flow of sentences than autobiographical stories. Autobiographical stories contain more minor events than imagined stories (Fig. REF ), and they tend to have higher proportions of first person references, contain more adjectives, conjunctions, quantifiers, and words referring to cognitive processes.
Autobiographical stories also contain more concrete words and words referring to orientation in time with a focus on the past and present, as well as words relating to time, space, motion, and core drives and needs (supplementary Table REF ).
| d | f4a53c8d5b40afb86e002d38baba0b6b |
UNet {{cite:cbe80cb20e8ce026453e9a236e53229ef86028b3}} was originally proposed for medical image segmentation. We use a variant that adds residual connections in each convolution block as the backbone network in this work. Details of the backbone network is given in the Supplementary Material.
| m | 4bf396cc82dcc63fef9b9538aec80b96 |
We propose EdiTTS, a score-based speech editing framework that enables phoneme-level editing of pitch and audio content. EdiTTS does not require any additional data, training, or architectural modifications to the model. Unlike score-based image editing methods, which directly modify the input, EdiTTS induces editing behavior by applying coarse perturbations to diffused Gaussian priors while the score estimator denoises the perturbed latents along the trajectory that best aligns with the data distribution. We demonstrate the effectiveness of our method using Grad-TTS {{cite:fee506b931b6be4ebceb06da423eb5eea0ee8b3b}} as the model backbone.
| i | 640657a9fc09774af067152476b3b6d4 |
While the population synthesis models are often referred to as theoretical models, it might be more
reasonable to consider them to be methods that attempt to interpret observational constraints in terms
of the many complicated physical processes that are thought to be involved in the formation of
planets. As mentioned in the introduction, {{cite:0bbe65fa1ea2f474995bae38431e85782a1e7bc0}} have presented a number of possible modifications to the
{{cite:633d0d9b1d38dd2ee0a45eefc16e5eed0b51ed57}}, {{cite:b18b3ca4fdeae7ff03a8c4197fdfb9dd313ad02a}}, {{cite:1bd790c9bca3a15bfc2aac89c21827067dfc13f1}}, {{cite:6d4c3f55194283cac6206cf133b2ed5d498835cb}}, {{cite:706cd8513959c9dec2521c3fc09e4d240093c704}} and Bern group {{cite:7317f60521af482634eb80d169320fb882aee04b}}, {{cite:b1c49b523f64fd6eaa4cd396027c72c8f5c3fb0e}}, {{cite:e30b8fdf91c9ea70212fef6d87fca48ef1e0363e}}.
These include a number of processes that could slow gas accretion or terminate it well before the planet
reaches {{formula:41772c0e-acb6-46ba-8cda-80372531daad}} . These include heating of the gaseous envelope by the accretion of planetesimals,
a low disk viscosity, low disk scale height, or early formation of a circumplanetary disk. Runaway growth
is often thought to terminate at lower masses at wider orbits, so gravitational interactions between the
planets could transport lower mass planets to Jupiter-like orbits from the wider orbits where they formed.
| d | 9e6038d0477fef3d2e693d3bec76e553 |
Remark 1.2 It is well-known (see {{cite:f4eb4c05167a7866b620bf866f22c2bcbd6a8815}}) that convergence in {{formula:6e2c7369-4f88-408b-aaf4-9d147931ce7f}} does indeed entail pointwise convergence in the case of
Reproducing Kernel Hilbert Spaces (RKHS). Because the space of spherical
eigenfunctions is indeed a RKHS, again the point in c) may sound
counterintuitive. There is a subtle point here, as {{formula:79676c50-b1d6-4f36-beee-2d39b2eb0be0}} increases, we are
actually dealing with a sequence of RKHS; whereas it is indeed possible to
bound the pointwise norm with the {{formula:579b5dd5-7627-4dce-87d5-eedf4057f8cf}} distance up to a constant,
the “constant” does vary with {{formula:868e3470-6250-48e3-8aeb-01d06b6a03d0}}
and indeed it diverges to infinity as we shall discuss below; so no
contradiction arises.
| r | ad81fd7359cf696daa296f535a47a28d |
We compared our proposed framework with two recent methods designed for multiple OAR segmentation from head and neck images: FocusNet {{cite:a22c78bf72a1305b5da6a151f691dcbd2e99c459}} that is an end-to-end two-stage CNN adopting a segmentation-by-detection strategy, and 3D SepNet {{cite:ddb96b45e379fad077578d971c9c92ba50285760}} that applies anisotropic convolutions to segment multiple organs in images with large inter-slice spacing. They were also compared with six state-of-the-art networks, i.e., 3D U-Net {{cite:599167759b7b67abe8e96c9b3236e3c9d31ee961}}, nnU-Net {{cite:870d7ecdbb9229499415f4065e51c771d9a7aeb1}}, 3D Res U-Net {{cite:1d14128e41de91639ab6e2d2e0a8cccd866b9faf}}, U-Net cSE {{cite:ca6a91fa238186441881597b18314bca36a822f1}} that combines 3D U-Net with spatial squeeze and channel excitation block, U-Net sSE {{cite:d6fa85aa65623f6addf860ff294c356d20fb0a25}} that combines 3D U-Net with channel squeeze and spatial excitation block, and U-Net scSE {{cite:814f011f8ce63c0741b6a70c9f7b33adb032c51f}} that combines 3D U-Net with concurrent spatial and channel squeeze and excitation block. All the alternative methods were trained with {{formula:69b384c8-78f6-4e8c-a49e-d08963efd129}} . Our method using {{formula:54cdb176-d8ed-4a6c-8eb7-9b93ac5c85b2}} in the first stage and {{formula:22d2f9e8-0dbd-45b4-8eb6-025d40a8b667}} in the second stage was also compared with using {{formula:06d9acc4-52db-4d1a-9b44-4218f8f894a8}} for both two stages, which is referred to as “Ours ({{formula:1b41f9c7-2288-48a0-9ba2-720384149081}} )”.
| m | 316e5bd3315c938a502ab168f517d859 |
With the rapid development of deep learning in the last decade, deep neural networks (DNNs) have become the predominant models in various fields, including computer vision, natural language processing (NLP), etc. However, for a long time till today, DNNs have always been criticized as being excessively large to be deployed to resource-limited edge devices. To make DNNs more applicable in these real-world scenarios, knowledge distillation (KD) {{cite:b37ebaa87c3e7fbfc8445d1645b4734ef8f48690}}, {{cite:85a486b51fb2352985ddaec6b00ee889441db35d}} has been proposed for crafting the lightweight substitutes for these expensive DNNs. The main idea is adopting a teacher-student learning scheme, where the competitive lightweight substitutes, called students, are produced by mimicking some behaviors from well-behaved yet cumbersome DNNs which play the role of teachers. By harnessing the dark knowledge learned by teacher models, the lightweight student models are expected to achieve comparable performance, yet with much fewer parameters.
{{figure:0e14bc69-0595-463d-ab93-3d9dd39b076d}} | i | ecad4545b2fdf1f3224eb130e3ac74db |
As a general framework, Ask-RFFs also covers symmetric kernels, including PD and indefinite ones. In that case,
the complex measures reduce to real signed measures, i.e., {{formula:7602371c-0ae4-456b-9ffd-e9f260e4da64}} .
Then the proposed AsK-RFF is equivalent to that in {{cite:d9b2baa8dfda69de43ec93d38eba8644090f3792}}, where the kernels to be approximated are symmetric. When the positive definiteness is imposed, the complex measure further degenerates to a finite real and positive measure.
In this sense,
the Bochner’s theorem {{cite:21d1a1c4f1b7acd545bd51f0a8230ed36b16cc78}} can be regarded as a special case of the AsK-RFFs.
| m | c677ea0eb7d5263a9901b31f659c94e6 |
Our results are in line with {{cite:6580049c0ed21f141160bc4660564cfedf2d2e4a}}, who showed the improved convergence of Disc-Opt over the Opt-Disc approach on image classification tasks.
Here, we show similar properties for time-series regression and CNFs using several numerical examples.
These applications differ from classification in that the inference in these applications requires the continuous model.
For example, in CNFs, the inverse of the model is required for inference.
The continuous model is invertible by design, which may motivate one to prefer Opt-Disc over Disc-Opt.
Remarkably, in our examples, Disc-Opt approaches can achieve competitive loss values and (upon re-discretization) low inversion errors.
Notably, the Disc-Opt models in our examples were faster to train.
We also show that both approaches can be accelerated in similar ways using multilevel training.
| d | f1077f44dc6994b811fecab3f2bba02c |
{{formula:412e72e8-2906-4a8b-a0fd-d816d03803c4}} Doradus shows an excellent agreement between the frequencies found in photometry and spectroscopy. This has not always been the case for previously studied
{{formula:a195549d-b283-4165-abef-2616863bd733}} Dor
stars (e.g. {{cite:36a859d8a6e3cf9f96a4d2a23c741eb02847df7c}}, {{cite:36a859d8a6e3cf9f96a4d2a23c741eb02847df7c}}, {{cite:0ef9e35e748c4b163dbc55483830a044e9088540}}, {{cite:0ef9e35e748c4b163dbc55483830a044e9088540}}) although other stars show similar agreement (e.g. {{cite:78baa9c084f7c6550e3b9b9e28e438db2a951211}}, {{cite:78baa9c084f7c6550e3b9b9e28e438db2a951211}}, {{cite:900453e6bafc6aaa404da1e0b582123a3aa23865}}, {{cite:900453e6bafc6aaa404da1e0b582123a3aa23865}}). It is not known why such differences should occur, but this work continues with the complementary data from large photometric surveys and targeted high-resolution spectroscopic campaigns. The power of combining the techniques lies in the precise identification of frequencies from photometry with the two-dimensional information provided from the line profiles.
| d | 0452ae6e569fa493f52aee9066f689ac |
Then we confirmed the upper-bounds performance of the segmenter on the target domain and report it as Seg-CT. Generally, these results are comparable to the standard U-Net {{cite:f9bad2193df8dc43181c7f069ce31f0374b333c6}} and cascaded-FCN {{cite:5e7561e09a9004bbf8c29ad388ceb08fd2b7895b}} methods. Furthermore, comparing Seg-MRI with Seg-CT, we found a significant performance gap, which demonstrates the severe domain shift between the source and target domains. Furthermore, domain-shift problem inherent in cross-modality biomedical images is also illustrated by the degradation of Seg-CT-noDA's performance. This indicates that although the cardiac MRI and CT images share similar high-level representations and identical label space, the geometric pattern or boundary of each category or instance remains different, which makes domain adaptation extremely difficult.
| r | 1944ff4fc24c407ab2a310371b7349c9 |
To alleviate the exponential computation and memory requirements of training GCNs with multiple graph convolutional layers, and correspondingly improve their scalability, sampling-based methods, such as node-wise sampling {{cite:2a5680463024b1c0c8ffa8e4c882388845e443d8}}, {{cite:f0c7b4782c9ef3d5cf8ec24a18ea0bea8f0ee2d4}}, {{cite:541faa516941c252001465c3e383caf412485360}}, layer-wise sampling {{cite:068c029d4cbf884bd8b00d840658a944ab87b88e}}, {{cite:a8c20434763d9acb0ce563a24e4643447d6c8aab}}, subgraph sampling {{cite:0b4e930a4fa18e3312e56961fd9f9d93be22c413}}, {{cite:f88b27cfbd686b36d2cbcb49cbbd6956c3ad0406}}, bandit sampling {{cite:2318062f1fe851bc157d72ad84ba1b31a4b2081b}}, {{cite:cecb8f137f4859c1da623203096a74d81da04ae4}}, minimal-variance sampling {{cite:ce019e3f0a6ca221cf525c14f0af886c80db473b}}, and lazy sampling with recycling {{cite:c3526f1e9a6531869774c79d7472d5ccd1826395}} are proposed to be utilized in mini-batch training of GCNs to accelerate the optimization. The main idea of sampling methods is to reduce the number of nodes involved in the computing the representation of nodes and hence lower the required time and memory requirements.
| i | 28c952f6b82a7f0a3bc32ffe66babc27 |
Here, we only investigated outlier explanation for tabular data. Applying SPNs to the closely related task of image anomaly localization {{cite:ad599b003d7488381ae4e7d375e60c44292cb790}} is a possible next step.
For this task, SPNs suitable for images (like Deep Convolutional SPNs {{cite:17c94291dd4a0496e79d9dc3e2702b7a93f0cad7}}) together with efficient SPN training algorithms and implementations (like the recently proposed Einsum Networks {{cite:bd3b7f7c2d1db04fb073aba4299121b0cade8b44}}) are an attractive option.
| d | a95b7c3eae2ba586e46f3f914b071f35 |
Video analysis. Individual cells were cropped from the acquired video data using the cell wall PI signal using Fiji (ImageJ) {{cite:d41c3a7af032bc7c8b9f60f2d48aea42a4b1925b}}. The size of each video was scaled to the universal length scale 5.0 pixels/{{formula:3efffe63-d7da-49a3-b65f-4bd6d6dd6704}} m. We then extracted individual mitochondrial trajectories from the acquired video data using TrackMate {{cite:0271074fbad82eab40d4680742c081b9a8d35324}}. Typical settings used were application of the LoG Detector filter with a blob diameter of 1{{formula:598c5c54-f9c8-4d1e-a853-a121e20df66a}} m and threshold of 2-7, filters were set on spot quality if deemed necessary. The Simple LAP Tracker was run with a linking max distance of 4{{formula:57e6596f-2dc5-46fc-bf15-9a793af524e5}} m, gap-closing distance of 5{{formula:75d7fdf9-fece-40f1-87a9-b15394f3c9e4}} m and gap-closing max frame gap of 2 frames. In each case we visually confirmed that individual mitochondria were appropriately highlighted and that tracks were well captured, editing occasional tracks where necessary. XML output from TrackMate was converted to adjacency matrices using custom code (see below).
| m | a1e0043e6641dbf9e6a1742ce1c02d37 |
Finally, a very recent constraint comes from the measure of the radius of the massive pulsar PSR J0740+6620 made by the NICER x-ray telescope. This is related to how squeezable are the neutron stars and allows us to put a inferior limit to the radius of a two solar mass object. A inferior bound of 11.4 km, 12.2 km, 11.6 km and 12.2 km was found respectively in ref. {{cite:ee97ff5bace480893b91187507e8a79813ce1551}}, {{cite:b32552d66334aa3e84b0e8eed70ffff3cde99a7b}}, {{cite:1844a3789aca69250deeda50c8aa017bf8f43cdd}}, {{cite:e96bf4cfbf9388ddc3eefe188a056f5277d8ee0a}}. An average value of 11.85 km arises and I also use this value as a constraint to the EoS.
| r | 3630ac532c2104361a45a4ae9b08a79c |
This approach has been studied in various previous works {{cite:0c7abf17a063f37bba4d46af4b0daf0ff9caf870}}, {{cite:73fbb8d3c1419a8d4b6a2baeef1d1a94884350dc}}, {{cite:86e1c3d91e1cdfb0e5a8b3ef22107c52ddd11f9f}}, {{cite:3556c298932284eda93454d3ce7a5f153abb88e7}}, {{cite:db2ada80754a9991d29797df9dcce59faae0232b}}, {{cite:d392fda93891c18165c2def4c1b3925ad901e7e4}}, {{cite:185d375986736fa72fe653237297d73b0842e4c4}}. See also the treatment by Townsend and collaborators for dynamical string tension {{cite:d17d875354800789515445de8b104757cffd0222}}, {{cite:dc481e28501e421ec85b2429a1865f5ff666fb78}}.
| i | e9e68d3ec139444050a4a60b6d90297b |
As other types of transfer learning approaches typically require a large dataset for knowledge transfer (many based on deep neural
networks {{cite:dda7a2430a761ea1899553a865e811fe496004e1}}), it is not feasible
in our case as we have TMA images from many other cancer types but each with only a small sample.
{{figure:a642f77e-c11c-41e6-8ff3-41163d7ad12b}} | m | 68ad69c70003b2cb37998202f938402b |
In general, to constrain the parameter spaces of the present models, we have modified the codes proposed in the MCMC method {{cite:b2a5e4892b3d74e1516a74d98ad8a37754aac498}}.
There are three statistical analyses that we have done to calculate the best-fit parameters: The first was done on a non-interacting model so-called
{{formula:5e864baf-9829-469b-85c4-ea33d0d988cb}} CDM with six parameters {{formula:cd374f23-72a7-483a-84f5-c266baf5d1c7}} , the second was also made on a
non-interacting scenario denominated {{formula:44a59458-97fe-426c-b740-9841b7da3d49}} DE model with nine parameters
{{formula:15144cc1-70d5-4fac-ba0b-66ce66365538}} and an interacting model
with twelve parameters {{formula:2c3f16aa-e995-416c-ad24-7fbd9d9f9cd8}}
{{formula:4a850351-e363-4175-b19d-eaaacd4746df}} . Furthermore, the constant
priors for the model parameters were:
{{formula:1c5de9fa-4a20-4c1c-aa2c-4bad0d03f1fa}} , {{formula:b6e9fc26-26ce-40b4-8249-a04ad4e3c90c}} ,
{{formula:c1037093-fb79-440b-bc29-ff645463248e}} , {{formula:3a402f01-9742-4927-87a1-54be1e70bd24}} , {{formula:1c79ba6c-79cd-40d3-b827-9d05d7d32b61}} ,
{{formula:b4a49af9-5e1c-4847-a37c-2bc0e7fd350d}} , {{formula:26c65f58-005b-41b6-ac49-804b9ce57304}} , {{formula:53d823d5-7391-4e11-ab64-c53632ee54ca}} ,
{{formula:95983c07-8d7a-4436-9970-5c5a02cc5e9c}} , {{formula:e1ea684c-6680-48b8-acf1-0a8c6e67cd78}} , {{formula:298e3991-9099-4923-9276-4dc96cbd23a7}} , {{formula:e637123d-0386-4717-b839-4c58abd96ca5}} .
We have also fixed {{formula:5c1417e5-a472-4df8-9553-abc2e3454289}} , where {{formula:f8735ed0-9a10-4d1e-9564-6544d3671a5d}} represents the effective number of neutrino
species. So, {{formula:1ff49e83-4106-423e-9b0b-75f6801a4d89}} , {{formula:b58e3537-f6fb-4c62-a066-ea213ef6c893}} and {{formula:31dee978-dbb0-4145-a9fd-a1547bb5b26a}} were chosen from Table
4 in {{cite:32ad2084127849feeb0b4b10c2219bff64e31105}}.
| m | 5254ffed1a4fde67db20ea669f87d66c |
Even though a direct attempt at generalizing thm:dagnew to all directed graphs fails, one might hope for some analogue of thm:dagnew that does hold more generally.
One interpretation of the above counterexample is that the exact statement of thm:dagnew is not the “right” framework for getting a local-to-global shortest path phenomenon in general directed graphs.
To that end, we consider the roundtrip analogue of thm:dagnew, where the final path through every node is a shortest roundtrip path, i.e., the union of a shortest {{formula:c0ff02df-60dc-4c91-84e2-4574a64b0eaa}} -path and a shortest {{formula:2aa78ade-9e2e-4745-8656-b4bbe57686c4}} -path
(roundtrip distances are a common object of study in directed graphs, with there being much research, for example, in roundtrip routing {{cite:9fc08e5394344aecfe4c5c3a83a3b501e376d6e9}}, roundtrip spanners {{cite:e5ea12446880f039f69874dd05f18a4b05df526a}}, and roundtrip diameter computation {{cite:2f255dcdee16c342eb6e4a2c00353f139421d613}}).
Note that the above counterexample no longer holds for the roundtrip analogue of thm:dagnew since there exists a pair {{formula:90fd01e7-5d1b-41ef-b98a-6f425ad8e043}} of nodes such that the union of a shortest {{formula:e47431eb-3d28-40f7-bd39-ad8290909aeb}} -path and a shortest {{formula:df1f0d29-b134-44d0-b0dd-7e8a7fa10b63}} -path are both in the clockwise direction and thus contain all nodes in the graph.
| r | 5ff155916f1f576d8673588697ea0ed9 |
where {{formula:d3013820-c94e-4e18-83b3-382d51ce3484}} is the original image, {{formula:10c09b78-fd96-46e2-8845-796618ce33a1}} is the final perturbation, and the last summand is a constant term only depending on the size of the image. As {{formula:2a0323e4-db8b-4504-8e09-443fc1f0115e}} perturbs every pixel by a small magnitude, they add up quickly. The root problem is rather because PSNR is a basically {{formula:83e211de-63c3-42da-9ffd-cfa414586958}} : the first norm term is usually 1 since most pictures contain a white pixel, and the second term is solely dependent on the maximum {{formula:7e86deff-3fcd-48fc-b1c2-173d9889a21d}} budget. This is very relevant to metrics alignment {{cite:811bada2f86c0a589c4284e795928c1c49f9dfcf}}, and might explain the reason why {{formula:c4245c35-80e8-4018-ad76-d517f02f4ba5}} defenses are weak against {{formula:710a2240-70ca-46cf-b755-6c628cd5d10b}} attacks.
{{figure:5476f3b0-e508-489c-b6e7-cee0c32ca072}} | r | 93b2b8a55bf53c45217262116fdb4ba5 |
We tackle the computational bottleneck of GPR and introduce an ensemble approach in the spirit of the mixture-of-experts method.Alternative ensemble approaches proposed in the literature include the product of GP experts in {{cite:40b1b0c13c120d211cd1f55d080ffa00468b9c41}}, the generalised product of experts in {{cite:f10e5e35e41fef388f3f9ab1eb192a940254da1d}}, the Bayesian Committee Machine in {{cite:44009321e764a1ab152c7b3ab50d5026700fb50f}},
the robust Bayesian Committee Machine in {{cite:77485bef72ab3de472343891c662b4347436b062}}, and Distributed Kriging (DISK) in {{cite:52628c3f3bbea5c00dacdc9865f4e24d8ed0d37f}}. The product of experts approach obtains the joint prediction by the product of all predictions from trained GPR models, while the generalized product of experts approach adds the flexibility by assigning weights to the contributions from independent GPR models thus increasing/reducing their importance. These approaches are further generalized in the Bayesian Committee Machine and the robust Bayesian Committee Machine, where the GP priors are explicitly incorporated when combining predictions. In contrast to these product of experts approaches, Distributed Kriging obtains the combined predictions as the Wasserstein barycenter of the subset posterior distributions. Thereto, we partition the training data into subsets, apply a GPR on each subset in parallel, and obtain a predictive distribution conditional on the full training data by mixing the predictive distributions over the subsets. In contrast to ad hoc partitioning schemes used in the literature, such as random or clustering based partitioning, we use that our training data is naturally divided into monthly subsets. That is, we treat data from each month {{formula:3e9003af-2cd7-41de-a8a8-2da785d61a68}} as a training subset on which we train an individual Gaussian process {{formula:1a71a58f-d47d-4959-a445-7719da4423d6}} . Specifically, we estimate hyper-parameters by maximizing the log-likelihood function (REF ), and obtain the predictive Gaussian distribution of {{formula:92a45046-a53c-4d57-bd77-b2cb1ea1181e}} with mean and covariance functions {{formula:9be2708c-d348-44f8-bfe0-cdd88256bcd7}} and {{formula:911c6a32-65c4-411e-a6e6-21591bcb0a77}} as in (REF ) and (), with the training data {{formula:2885b71f-ca67-4338-b311-9ba3d7b1af7a}} replaced by {{formula:79e45f52-37e5-43ae-80b1-d306858c5c92}} .
| m | ffcdb0a08ab9409f38ee89caca34c42e |
However, there are optimization scenarios where even zero-order access is unavailable or unreliable. Indeed, studies have shown that it is often easier, faster and involves lesser bias to collect feedback on a relative scale rather than asking for reward/loss feedback on an absolute scale. For example to understand the liking for a given pair of items, say (A,B), it is easier for the users to answer preference-based queries like: “Do you prefer item A over B?", rather than their absolute counterparts: “How much do you score items A and B in a scale of [0-10]?".
Consequently, relative preference queries are extremely common in
domains such as recommendation systems, online merchandises, search engine optimization, crowd-sourcing, drug testing, tournament ranking, social surveys, etc {{cite:dc2e6abaaa5b2e547e539bc4063c5d0fcd1657d0}}, {{cite:71ed4f69222c2a10178ab38bd652307ea63b1937}}. This motivated the introduction of dueling bandits {{cite:5ee03dc5938451070a47a09021c82d82fa6f1ba1}} in the online learning setting.
| i | 818be16a92c1dd7c9bf0c02452beb7aa |
Compared Methods. We compare our method against 13 cutting-edge competitors, including (1) FPN {{cite:7e0b8abde4786f1d2c798aef808d4dcd242fc728}}, (2) MaskRC {{cite:a7da8f6082ddff02a6530ac96626ed225f38852c}}, (3) PSPNet {{cite:dc6f1eb4555cc6447d07ffd3dc73090e6329189e}}, (4) UNet++ {{cite:e4f770d84e5f5e561e3db5d449d9a7567ccdd1e9}}, (5) PiCANet {{cite:e6db42ae2f18a0dd7fff30ed1b4d83206d5f2bdf}}, (6) MSRC {{cite:0e45d492de874446e8062eb5b1589d24a96b2a4b}}, (7) BASNet {{cite:8b56ca4e31381c1daabbddf08aecf94334287005}}, (8) PFANet {{cite:027d1c809b775c10c3e1fda3452b3e4f3909f3f8}}, (9) CPD {{cite:baba50eda04ad213d7cd4f93b867cb9f84fc38fe}}, (10) HTC {{cite:cefcf401c632ac486d11a0b83e8bfffbcee5adfa}}, (11) EGNet {{cite:747574a2896246ecf93640d632fda7ffac3b63e2}}, (12) A-Net {{cite:7b09baf7312b4cc20a948dc338a32ff2ff5375dd}}, and (13) SINet {{cite:2f113267c36256bd0cf9035abdbd0509566f5d09}}.
As stated in {{cite:2f113267c36256bd0cf9035abdbd0509566f5d09}}, these baselines are trained from scratch on the COD training set mentioned in {{formula:41afee6f-9b30-40b6-b1f2-246a4b36c5da}} REF with the default parameter settings. Hence, we use the standard benchmark results reported in {{cite:2f113267c36256bd0cf9035abdbd0509566f5d09}}, as shown in Table REF .
| m | 05df4082146fc12ce94cde991fc2c961 |
Over the reals, Elekes and Ruzsa observed in {{cite:6298985bbc12d36536a19ae8836fc01f52088551}} that the Szemerédi-Trotter point-line incidence theorem {{cite:96c4f74306b99c0f3f73ca59b462884fe8b08960}} implies
{{formula:a1ba733b-ba74-40f7-8bd0-2e1378b1eeea}}
| d | 57ea835d3d2ee667c464f70a6da3fb04 |
Reflective and Transparent Surface:
Our depth estimation has limitations for reflective and transparent surfaces such as glass or water. An example of these limitations are shown in eqviews (Hill scene), where our method contains ghosting artifacts on the glass window. The Multi-Plane Image (MPI) representation has demonstrated its ability to reproduce the behaviour of reflective and transparent surfaces {{cite:2711056d6f461bda217dfa901d1f760e7372d98c}}, {{cite:5809bc455968af77b99eae1030e4cef60d837058}}, {{cite:afbb9cb975120faec2ea42d0601b948810f8129b}}. Adapting similar methods into our pipeline to separate the transparent layers would be an interesting next step.
| d | f7e3318effddbcabf0bde2b5f9907ba6 |
Compared to the existing game-theoretic models for explaining oscillatory behaviors, our pairwise game model does not require three or more species {{cite:6fc847eec4806437a5dd845f5f6f312af91ad34a}}, or seek for other complex mechanisms such as mobility or conformity {{cite:d491026a72460438c65145236501cf70acd2f1da}}, {{cite:46e4bc46fce4e1220c5efbd5a705b0353d74544b}}. In this sense, our model provides a relatively simple framework to understand the emergence of oscillation. Given the omnipresence of incomplete information scenario and the non-Markov process in the realistic games, our model may provide a plausible explanation for a range of oscillatory phenomenon.
| d | d847bb7d1ed6d69ec159e6ffd0435ab5 |
Paired setting. In the paired setting, we use the Structure Similarity Index Measure (SSIM) {{cite:0783f17182a96a59e252fb2f630a7e10146b56b9}}, the Peak Signal-to-Noise Ratio (PNSR) {{cite:739cd4d455374c17cac0d8015165292807e34ee2}} and the Fréchet Inception Distance(FID) {{cite:9bdb40f5f2344e4bc63963fa9b4912c348c6cb2b}} to measure the similarity between the synthesized image and ground truth image. The Inception Score (IS) {{cite:86378a8e49b95be42bc5b57bbd972dae36da8abe}} is applied to evaluate the realism of the generated images. We take the target image (the same person wearing the same clothes) as the ground truth images which are sued to compare with the synthesized image for computing these metrics. It is noted that PFAFN and WUTON were removed from those measurements as they need to take the target image as input for inference.
| r | b64ac79120268ab20fd35ff3538fcd1d |
Image understanding can be described as the process of automatically analyzing unstructured image data in order to extract knowledge for specific tasks. Automatically assigning images to pre-defined categories (i.e., image categorization) is one important form of image understanding and an area in which we observed substantial progress in recent years, largely due to innovations in deep learning {{cite:8556bf299a22939d6ed0249fe52c95bde2b599b6}}, {{cite:613553cf8e63155d424ff7ff9517662896a0a1a2}}, {{cite:a5754ea4e069f084020130cb12b2352dbf88e0c5}}. Nowadays, one standard way of developing an image categorization solution for a specific task or application is to rely on pre-trained image models and to fine-tune them with application-specific data for the particular problem at hand.
| i | 1b0fb9e095b5a23a0292f1f01ba664b4 |
We combine our loss function with open source SOTA methods (FIDT {{cite:93ad20e28063dbbd2c44f9341bb826d6134990c9}} and FDC {{cite:a9e273ed90d023f6409a6628d445c70123b2efd7}}) by using our loss to replace L2 loss in the counting regression of these methods.
For FDC, we reproduce the experiment with ConvNeXtS as the backbone network and give a better result than the original method with ResNet18 {{cite:ec8210dc2bfb506961804689fd73f8ab3b83fbc5}}.
Table REF shows the fluctuations in MAE and MSE contributed from our loss function, where MAEs decrease across all data sets and methods.
| m | fe4a8a3eb74c322be4c5b62c4c757021 |
Furthermore, we have compared the eRAR with the alleged universal functional form of the RAR (i.e. Eq. (1)), but not the actual distribution of the sRAR (i.e. {{formula:44736e98-c6a2-4ef7-ab8f-ef68b165cf53}} ). In fact, our objective is not going to compare the distributions of the {{formula:7975a71e-e99a-4912-9efd-d11f1ae9687f}} between elliptical galaxies and spiral galaxies. We aim at showing that the acceleration scale {{formula:16dcff0e-6877-4172-b200-5c108f48e625}} might not be a universal constant for both elliptical and spiral galaxies. Since the acceleration scale {{formula:63296e27-c9b7-41d3-9f0b-4f6bfeba3370}} is primarily defined under Eq. (1) (with the smallest possible scatters) {{cite:be48f105f1255f628cdc251643104b564bef45c6}}, we finally compare our distribution of the {{formula:9bbd76eb-9365-465e-8ae6-d7cdad6ea680}} in elliptical galaxies with the functional form of Eq. (1).
| d | 5a837fcb3b9b9387a6bc29f6a365cfb6 |
Let {{formula:534ce4af-075d-4bf9-8935-025d97e0c17a}} be a set of parametric components and {{formula:a0d33b7e-1e17-450c-a77f-e16122f581d7}} a mapping. Then, the equivalence problem for FOEIL sentences over {{formula:abb82707-259b-403c-b338-a3287b6b5b36}} w.r.t. {{formula:5a2f7291-37ae-4aac-92d3-d321d53f1a00}} is decidable in doubly exponential time.
Let {{formula:c7c15353-9095-4e4e-8740-27581464feb8}} be FOEIL sentences over {{formula:c9eff82c-eb12-4ac7-9d31-e9a0480f98a3}} . Then, by Theorem we construct, in exponential time, finite automata {{formula:94dfffd8-8934-436f-a310-de0e4801b974}} and {{formula:e78c5fd9-2eb9-4cd5-81da-7048f5703b93}} such that {{formula:b0037d8c-e542-46f9-b56e-b5175b1092ef}} iff {{formula:2314f712-730b-4c73-bd77-5d2c1ed794db}} for every {{formula:5cc1ff82-42fa-451e-b8d9-10ca8d6f3b4b}} and {{formula:7b22eb0b-75a9-422a-b4a9-f59d10bc8af4}} . The finite automata {{formula:1b3d9745-b252-4263-b9f9-b3b7b9a2ab3a}} and {{formula:af25672b-b6af-4f08-b0d8-bce38bc60098}} are in general nondeterministic, hence by Proposition (1) we construct complete finite automata {{formula:598a0779-57e0-41c3-866a-6e581f21a3a4}} and {{formula:b84187de-a3ea-4f3e-96bc-bca229175d7f}} equivalent to {{formula:43a6b958-cf6d-456c-8f7b-7fbdf7fabe6b}} and {{formula:2980089b-19df-447a-a670-6660863eb89f}} , respectively. In this construction another exponential blow up occurs. Finally, the decidability of equivalence of the complete finite automata {{formula:bf66201a-00d1-40d0-ba35-0bb0d5b2ac01}} and {{formula:3b6b4d51-ade3-4a94-9772-eb5e0f09a3eb}} requires a linear time (cf. pages 143–145 in {{cite:f96f2549dce8b6b5a4ab10451fc2610f77bd9ce6}}), and we are done.
| r | 10e194ee6d50efbcb1b762778119b504 |
The observed vertical patterns of velocity ellipsoid help us to revisit the nature of the disk flaring. We find that the flaring of the disk begins near the solar position, which agrees with the findings of {{cite:8ec926550f0e2a7d02e24f4de6e60b9390e6a745}}. The position where the flaring starts to manifests itself is not settled. For instance, {{cite:845de9ddcde90ee7fc9ed785329a2642729a6174}} found a strong flare beginning well inside {{formula:dab8dc29-ad13-4547-bd0a-1f7c85cb7aa5}} based on 2MASS red clump giants. To the contrary, {{cite:3284a187ac4a1260a30705a4c477923a9014f0b3}} and {{cite:2f0543afd6020dffe1487f4b517ffe3c5098df43}} found that the flare begins at {{formula:b8c80da7-d21a-4b65-8daf-543ead310637}} by using samples of SDSS-SEGUE F8V-G5V stars and LAMOST OB stars respectively. In recent studies, the flaring of a disk has been detected not only for our home galaxy but also for the external galaxies ({{cite:b81a34595aba6eebdc710682388016ed3dfb8b1e}}; {{cite:771255a69635935a1dd356f6589bd873314d6eca}}; {{cite:c23376408c27219e19a7390f1c5eb065851f1e4f}}), which means that a flared disk could be a common structure in disk galaxies. The drivers of the formation of disk flaring is still unclear, one hypothesis is the minor mergers {{cite:5e7c06167dfb1304c5b956a77bd9d7d959c164cb}}.
| d | 884d5cd0fc80dff70b80484e0c82693e |
Neuromorphic computers perform computations by emulating the human brain {{cite:0bcfa62de1c01fd9f8d442252609788fd59bfcee}}.
Akin to the human brain, they are extremely energy efficient in performing computations {{cite:1d3fe463d2650c3bcf69a3cb858680070f9a7c3d}}.
For instance, while CPUs and GPUs consume around 70 W and 250 W of power, a neuromorphic computer consumes around 65 mW of power, i.e. 4–5 orders of magnitude less power than CPUs and GPUs {{cite:c6054fa69795c3529ed25c51477af70f5bc08133}}.
The structural and functional units of neuromorphic computation are neurons and synapses, which can be implemented on digital or analog hardware {{cite:92def904031285ca81b8b8ffc43b12c2b8f91738}}.
They impart critical characteristics to neuromorphic computing such as co-located processing and memory, event-driven computation, massively parallel operation and inherent scalability {{cite:ad5d660a2ccc47bf7b3116642e633d36a892c9bd}}.
These characteristics are crucial for the energy efficiency of neuromorphic computers.
For the purposes of this paper, we define neuromorphic computing as any computing paradigm (theoretical, simulated, or hardware) that performs computations by emulating the human brain, i.e., by using neurons and synapses, that communicate with binary-valued signals (also known as spikes).
| i | cbb825ff40d5159382fad26df954175e |
We mention experimentally obtained material parameters of a double-wall
nanotube structure{{cite:40c60af3fcd2fca5c76e811c7867ed495ca90e58}}. Nanotube length is 10nm and the intertube
gap length is 0.3nm. The diameter of a nanotube is 10nm{{cite:bab58dc9323c1bdded3438b49490083a6563f8ef}}. Q factor{{cite:857a268b77ae7c684645a60c26c4424040e8b3ef}} is of the order of 100. The inertia {{formula:e7a8dc67-2f3c-4371-99c3-ccb9f1c9b57c}} is 10{{formula:f48dcfd9-69c3-4fe1-bbc9-57ff3c989303}} kgm{{formula:a61075d7-c3cd-479e-b7ea-b39c833bab58}}{{cite:b65eafad857b08bb2564c12be37f59d2e36a9582}}. The rotational frequency is from 1MHz{{cite:857a268b77ae7c684645a60c26c4424040e8b3ef}} to 100GHz{{cite:40c60af3fcd2fca5c76e811c7867ed495ca90e58}}.
| d | 152b84adde3677c88273ea19c82e6d2f |
To intuitively illustrate the topological magnon transport carried by chiral edge states, we choose some unit cells of the kagome lattice strip as a center region and set the rest as two semi-infinite leads in equilibrium at temperatures {{formula:5c48d33a-ef09-49d9-b4be-ad54dc9706d3}} and {{formula:722e5a86-1766-48cf-8016-fb744c9866ef}} , respectively [see Fig. REF (d)]. We then apply the nonequilibrium Green's function method {{cite:411ba5203b8026e72ba312d044018d547bb61d0c}} to calculate the local density of magnons and the local energy current density of magnons. For the nonequilibrium magnon transport in such system, the Hamiltonian can be written as follows
{{formula:8a33ac49-6882-425d-ad42-8fb648568724}}
| m | 97c137c92d8766307b24fd81c96ef8b5 |
Ultrahigh energy cosmic rays and neutrinos are of interest as possible probes of new physics {{cite:ad903cbe9150c72ca839f9bf83db1dfa1d39bbb7}}. In particular, some quantum gravity models predict that Lorentz invariance may be weakly
broken at the very high energies, leading to potentially observable consequences. The possibility of
using ultrahigh energy cosmic rays (UHECRs) to probe for a small violation of Lorentz invariance was
suggested over a decade ago {{cite:b029255090d4a13e6c07b336e05d265172afe813}}. Indeed, a detailed analysis of the effects of LIV on the
UHECR spectrum has yielded the tightest constraint on LIV to date {{cite:f29b039cfe7d6a03a60097286cfdbdc9335eac77}}. Shortly after the
discovery of the CBR it was pointed out that photomeson interactions of UHECRs with photons of the
cosmic background radiation (CBR) would result in a sharp steepening of their spectrum above E {{formula:69a17778-7ead-4d0c-973f-b49b9f4b03ef}} 50 EeV now known as the "GZK effect" {{cite:fd0b380797f9ad3a8c17209759b2c3b98119b260}}, {{cite:96b03e6c9824595ab8ae65a1d9779f78fbf2aad7}}. However, even a very small amount of LIV will kinematically inhibit some of these interactions. It has been previously shown that a possible signature of LIV in the UHECR spectrum would be a recovery of the cosmic ray spectrum at energies greater than {{formula:f6013adf-1846-430c-b48b-8b908b3cb4d7}} 200 EeV ({{cite:f29b039cfe7d6a03a60097286cfdbdc9335eac77}}, {{cite:b9815d71f448fc57188e163196fdaa63acce9370}}).
| i | c327b84dfbb80352f50a6a707945b2c7 |
We remark that there has been a few works that draw attention to the potential problems of widely used graph datasets. Specifically, {{cite:abdf30accb9d74f619e2b2b5d5760fcc9d6fcda1}} observe that even by using simple graph features such as the number of nodes, they could achieve similar classification performance on common benchmark datasets compared to early graph kernels. Their results show that we cannot solely rely on these data sets to show the performance of a graph kernel. However, their work focuses on attributed graphs, while our work focuses on non-attributed graphs. Very recently, in an independent work by {{cite:05405d10fa660d87c34444c8b743e14f93e80f1c}}, the authors hypothesize that the nonlinearity between GCN layers is not critical. They remove the non-linearities and develop a simple network called Simple Graph Convolution. This network works well on text classification, semi-supervised user geolocation, relation extract, zero-shot image classification, and graph classification. While our work shares some similarities with theirs, our paper was developed independently.
| m | 13d9f3f01c47c479fb77200f21ed004f |
It is well known that including delays within a DE model of population dynamics can lead to major changes to its behaviour, such as causing instability, oscillations, and extinction,
which are not observed in a corresponding ordinary DE model {{cite:a7dbccfcb114f22d99f1cf22d650a53afc651b98}}. The famous Hutchinson equation is one such example. It can be compared to the logistic equation where the carrying capacity is always a globally attractive equilibrium for all non-trivial positive solutions. The inclusion of a delay in the Hutchinson equation can cause the carrying capacity equilibrium to become unstable for certain values of a delay.
Other examples specific to harvesting models can be seen in {{cite:c6899844e31af376be07c9852094c0c801f8e48a}}, {{cite:27b7afede42a10fc858e72cecb0a5f734c38eb96}}, where delay is incorporated into the continuous harvesting terms.
| i | f64d2e2b51b8cfb3fb9b5924f1c5fb89 |
Both our misalignment-induced splitting and the slight upturn at low temperatures are consistent with the distortion-based dipolar spin-ice model (d-DSM) {{cite:d0376a2b839fb15b4637c2290ddbe1b9cfecf855}}, which builds upon previous theoretical models {{cite:5ede464c9456e6d95dc308a6932e7a62f4c3202f}}, {{cite:3dc50cead020e6e7a61cc3406091f46f21bfba97}}, {{cite:6d7c56bb898f630ef402210c05b41197e1ff5e41}}, {{cite:85ae7b256bc2882372e65e479f58a902e130dd6b}}.
This slight increase of magnetic susceptibility on cooling is observed in magnetic fields of both [111] and [110] orientations, above 1.5 T boundary of the intermediate phase (Fig. REF ). It is generally believed that a spin polarized state is achieved above the intermediate phase, in which case rf susceptibility should be zero {{cite:164e560d5f1a42f8b6e7d326268579b6fc10dc44}}. Non-zero value suggest that the magnetic polarization is not complete, at least up to 2 T.
| d | c24ae9dc30e4cd4d59afa09d9b5fee18 |
In this section we describe the fitting methodology that
is used in this work to map the EFT parameter space spanned by
the Higgs, diboson, and top quark data.
In addition to results obtained with
the Monte Carlo replica fitting (MCfit) method
presented in Ref. {{cite:f515b9662ac5e86979e90af25c6fcee78d4b0d94}},
now we also determine the posterior probability
distributions in the parameter space
using the MultiNest Nested Sampling (NS)
algorithm {{cite:fc160b7a85606a8f9758a6a94653a462a51f53da}}, {{cite:5e9e3630eea2b5b4cac75eccf747630b18e0f692}},
a robust sampling procedure that is completely orthogonal to
the MCfit method and that is based on Bayesian inference.
| m | b454bfaaa38444df0dc78bdab3ed34e7 |
Our model is based on a standard framework of firing-rate neural networks {{cite:dc4b2c63215374e1f0babc94840f97b145403303}}.
It consists of {{formula:ebaaf9ba-ffab-4a9c-99eb-e64b564ba685}} recurrently connected neurons, with {{formula:21dda288-3bf9-44f9-928f-72cc84c9c6b3}} the synaptic connection strength from neuron {{formula:115afad7-2b8a-4a0a-9071-3a27add43c95}} to {{formula:ee95373f-d0e3-4edf-87b5-962f060ac513}} .
Each neuron {{formula:f273c11b-9502-4a59-8be4-c0c5583fd044}} transforms its input {{formula:9669af68-93e1-402e-a794-a10d58fb4254}} into firing rate via a nonlinearity {{formula:bad0f9ed-3a2a-4f50-8d89-c094d5e81b69}} , where the state vector {{formula:69ba8a70-4354-4428-8ee7-0ac75d35786d}} evolves as
{{formula:185628f4-5449-4fc4-af13-a2e6df02df79}}
| r | 7b24b32544f662647e04c1b0492cef1a |
All experiments are performed in POLARIS GEM e2 autonomous vehicle platform shown in REF . It is equipped with Velodyne VLP-16 LiDAR used for localization and mapping, dual NVIDIA RTX 2080Ti GPU for GPU-accelerated edge computing, and drive by wire systems for steering, brake, gear, and acceleration controls. The entire communication interface is set up using ROS noetic {{cite:39b5a21a8ba8735e62544fb84b8694e4ce768b46}}. For simplicity, the initial configuration is always (0,0,0,0) and the goal configuration is provided as per the experiment. Table REF compares the desired goal configuration and the final configuration generated by the planner. The error or drift from the final configuration is computed using the distance metric presented in Equations REF and REF . Table REF summarizes the drift values observed for all the experiments. For the videos of different navigation maneuvers, click HERE
{{table:d2fdf27a-3c6c-407b-96d1-ccd3543b130f}}{{table:bafbb32c-0135-4fe0-9b33-e7e8fc51fe28}} | r | 8a22729e855cc1867ac792ec09aaa5d9 |
The phases of the minima are dramatically changing in this system. The variations of the pre-whitened light curves indicate that the spotted areas are not stable on the component. In the pre-whitened light curves of the season 2003, two minima are seen separately from each other. In the season 2005, the pre-whitened light curve has a very strong asymmetry. The variations seen out-of-eclipses are similar to the variations exhibiting by the young-fast-rotating stars, such as YY Gem, ER Vul, SV Cam, CU Cam and CM Dra {{cite:71084a62719d1041fa9507e0ba8b2ef8ba152983}}, {{cite:6949ee812ea3875116b117f48e03650364f16fe2}}, {{cite:e8571edc1c4d71d93c6b64780f494e13163bc6c4}}, {{cite:a873d303e65369f5bfa057eb364e8b315909c0b6}}. Therefore, the spotted component (and the system) could be a young star. On the other hand, it must be noted that there are many systems exhibit an unexpected cases in contrast to this approach {{cite:29f78e69db98986bcebbe8863c00cd0406bb35a3}}.
| r | c3766a15d04189b425b08e3e26b4aad4 |
THE discrete cosine transform (DCT) {{cite:8c1cb61fb4ec9ed5dab35b5f674276500f971385}} is one of the most common tools in various signal processing applications.
Among the eight types (I to VIII) of DCT, type II is known to be especially effective for image processing and has been used in many practical applications, such as image/video coding (JPEG, AVC, HEVC, and VVC {{cite:7c1c09b2d62bd96949256b11e8d2d46536001a4f}}, {{cite:d385910a79f047e4a88b9881f54b8817414db232}}, {{cite:1dc13c1deb0b69405616ea28ceff296aae75957f}}, {{cite:ba2b95c65be354deec8ee4efd53a5522fff17ec9}}) and restoration (denoising, deblurring, and so on {{cite:30f029cefe00ce0920b8fc3deecca2eee5a0b4fb}}, {{cite:e251fe198adf5905198c4b313e6a8d6b0fa56f5b}}, {{cite:958853174e97fd829bcf79782241ad80392889dc}}).
In this letter, we focus on the type-II DCT; hereafter, we term it simply “the DCT.”
The key properties of the DCT for image processing are as follows.
Firstly, the DCT has fine frequency selectivity, which is suitable for natural images.
Secondly, the DCT satisfies the regularity condition: if a linear transform satisfies the regularity condition, it does not leak the lowest frequency (DC: direct current) components into the high frequency (AC: alternating current) subbands.
These two properties contribute to the DCT producing a sparse image representation.
Thirdly, the DCT has various fast algorithms {{cite:15968177ddb1eff1071cef7127b83839ce21c094}}, {{cite:3a6b51d0b5981cf48936b152ee979fea7f40721a}}, {{cite:746cb8c77d2dae7b9fbfbafc1f4411963557454f}}, {{cite:cfcf17260a592bdb1b905b71d065b2d59219db18}}, {{cite:7b56d38ab1e874ec7d14571c0a29bb7c3552ca38}}.
The traditional rotation matrix factorizations {{cite:35492ce972265dcd85c5b72edb270089526e826d}}, {{cite:bb80513be4ec7c2414187c8d204b1e886a7fd61a}}, {{cite:c74cdf74a0309dc7282d5a1a27e5d679723da89c}} are the underlying methods of many fast DCT algorithms.
| i | 9bfbfa11e19637e3cc90976f38879e6b |
To derive low-energy effective Hamiltonians, we performed first-principles calculations based on DFT.{{cite:2cb0443574083a7fd4ffa185c77e9baf9b26a516}}, {{cite:0686e7a873191e476cc9e102977f50d1691275da}}
We used the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) as the exchange-correlation functional.{{cite:d77d7bdba8a66a69933ebe88269c90a1515c5e2c}}
One-electron Kohn-Sham equations were solved self-consistently using a pseudopotential technique with plane wave basis sets adopting the projected augmented plane wave method,{{cite:2453c1afa8d2b07b51b6e99e0768d69fd98fc4cc}} which was implemented in Quantum Espresso (version 6.3).{{cite:00ceaab1d5ed2757daae2fd2a218ecdb33f36a38}}, {{cite:93fd6d4df2fafd9a593ca31adc284625217235ca}}
The cutoff energies for plane waves were set to be 55 (48) and 488 (488) Ry in the scalar (full) relativistic calculations, respectively.
We used a 4 {{formula:deb5be06-dc91-4be2-983f-38ee31c13180}} 4 {{formula:4f9a1aeb-0837-4bc3-8bbc-e03105c6a4cd}} 2 uniform {{formula:822c2793-8a91-4c61-beea-4c29935f7b52}} -point mesh with a Gaussian smearing method during self-consistent loops.
For the calculations of the density of states (DOS), we used a uniform 18 {{formula:02a33f39-bbe0-4a1e-aba8-a5ac3c838227}} 18 {{formula:b85d6fdd-a9a1-44de-9238-9a2fb53e3862}} 2 {{formula:db761121-ea81-4d04-9566-d62c5c32ec21}} -point mesh.
In both scalar and full relativistic pseudopotentials, the valence configurations were 1{{formula:e8ac507a-19d9-47b1-bc49-c86c7d83d95c}} , 2{{formula:cb7194ec-a12d-414c-b957-8856f06ff7c3}} 2{{formula:af8b4b18-4cd5-4922-bc17-c7b8dae4c5ca}} , 3{{formula:bd1e1951-0b85-4e31-aab3-b7b61c98f90d}} 3{{formula:0e318a2b-e501-4823-9b9f-3ce63333644b}} , 4{{formula:3f3126da-31e4-4704-b6ad-247f1eea53e9}} 4{{formula:6530a8d2-2a2d-4684-8986-69648e2fe958}} 3{{formula:067589a9-9f7e-4cc2-8064-879325279e64}} , and 5{{formula:9729cc90-cf4c-40ce-b841-d0d46ee46053}} 5{{formula:7c8df314-9efd-498c-89d8-61dd0c32a389}} 4{{formula:0d3d09d2-f192-45c5-aeba-6a59680d6097}} for H, C, S, Se, and I atoms, respectively.
The pseudopotentials were generated using atomic code (version 6.3){{cite:8c9ac7f3bcf73fa5a4e479bf18a9ae0d961142d1}} with a pseudization algorithm proposed by Troullier and Martins.{{cite:afb0100b8b14e632b69d7f3242eba0a698d959f1}}
Using the Bloch wavefunctions obtained in the first-principles calculation described above, a Wannier basis set was constructed by using the wannier90 code.{{cite:cf559fdd0ff6afe95824c8a14b91b96320556ac7}}, {{cite:3633d07487c6c5cad648c4222df233210d276549}}
| m | 65753d309a1d11d5d5859cdc21d02df9 |
The sideband signal encodes
the position-fluctuations spectrum of the mechanical mode.
At low drive powers, the area of the measured peaks with blue and red pumping (Stokes and Anti-Stokes sidebands) are proportional to {{formula:16619390-2731-4f7f-829f-0be3855365d2}} and {{formula:74bf5ac1-ee50-4146-8187-473be36c5c51}} respectively, with {{formula:a8d881df-b4d4-451c-bff2-20c92b424e29}} the Bose-Einstein population {{cite:d72b2a59425bfd8d47cb5675eda9cccf4e7a7786}}, {{cite:1fd603caeee7dea68581c710c9cc041016c1f6f6}}.
It is therefore convenient for the experimentalist to define
from these areas
two “effective mode temperatures”:
| r | 88066c0e904207ad74d4d704e039c913 |
Direct numerical simulations of SCF satisfying the Navier-Stokes equations were performed recently {{cite:b724e72a70acc3a7365fd57211eef1f2050658dc}}.
Using the equilibrium states obtained from the simulations as seeds, the spiral states with {{formula:659ba04b-1ade-428c-a605-8ec6616ebe33}} , and 2 were solved using the Newton-Raphson algorithm, and hence, so that the angular phase velocity was also specified numerically {{cite:186430d785ea6b44124f1d2ba7e0624d8b0aebc1}}.
The flow field was expanded into a series of spherical harmonics and modified Chebyshev polynomials, as used in Ref. {{cite:b7507390a79f2999054d39d223181618fc58d018}}, {{cite:d781fa47419317658b56901a26dcf50ba9fea309}}, {{cite:d44b27761135e40ba59393672846b4e8630862c6}}, and the Helmholtz equation equivalent to the Navier-Stokes equation was solved numerically with the aid of LAPACK libraries {{cite:076c46f4dce1532dd99a3f84102d1a0b52886c22}}.
The dimensionless frequencies calculated from the spiral states with {{formula:25da346a-509c-4aff-a3d9-f102638cbda1}} solved for {{formula:5e994bb1-8153-4f0e-aeca-a3bae3491af7}} and {{formula:7cda5a6a-d0f3-4976-b900-e7c8fc36bf10}} are plotted as dashed curves in Fig.REF for reference.
Although not shown in the figure, those of the spiral waves with {{formula:284067e2-26bb-4d6a-b008-e0f710a90dab}} and 2 were in the range of {{formula:bbcd3681-16e1-4edd-89a4-73a29837f5a7}} and {{formula:2d1cf45a-57cc-4f4e-a3ad-862d6c3aaac7}} , respectively, for {{formula:1ab6db62-47ed-4c66-ad15-887e8a44402d}} .
For reference, Ref. {{cite:eaa0151a4791a8caf28b717399d29e8c4b17e62c}} reported 0.614 as a typical value of the dimensionless frequency of a sinusoidal perturbation with the azimuthal wave number as {{formula:0da93f47-8884-415f-a331-b3b346c6d97f}} .
A comparison of {{formula:699aca67-d09f-4910-835d-813b41aa3e7f}} and {{formula:e2a78305-eec1-4e49-9953-e765811b0431}} in dimensionless frequency suggests that the present state that was realized experimentally corresponds to the spiral state with {{formula:c41a4e8d-c8c8-4bd9-9e7a-6238360b94c0}} , which remains within a relative error of 8% of its value for various Reynolds numbers.
| r | 56ea6263a4d0419c72abb53d0aaadf8f |
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