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This continual learning idea has inspired various machine learning strategies. In domain adaptation {{cite:79d890b7f3a3c8a44f6295426d9ebda069155ab7}}, the goal is to transfer the knowledge from a given task (i.e., source domain) to another task with few labeled or unlabeled observations (i.e., target domain). In the case of multi-task learning {{cite:228b756727477453cbdee2742c68452d11fadfc7}}, the goal is to set a good performance on different but related tasks simultaneously. Concerning lifelong learning {{cite:beb50069cc8bcd57d9fbae45f72c47aa6128c550}}, {{cite:48604d0ab155c7acf880a87f3bb9c331d6a45864}}, the learning procedure can be viewed as a continuous transfer learning procedure over incrementally available tasks from the underlying distribution.
{{figure:8dd45ac7-0232-4089-88d4-536fcb07ddc5}} | i | ff27d3e1254256a581ab8e120cee3b9b |
Availability of simulation data for a finite time interval or the need to approximate the system behaviour over a finite time interval led to the development of finite time model reduction methods. These include methods such as Proper Orthogonal Decomposition (POD) {{cite:a2fa5412b08d21453eae56e8e825518c3fa7dfaa}}, Time-Limited Balanced Truncation (TL-BT) {{cite:8c0aa8d252be5db841d2baa40322071c622dfa4b}} etc. Error bounds for TL-BT are proposed in {{cite:5f5bf841b9dcbaac99340deea246797132f3eabb}}, {{cite:84d9633faa61584e9f400dfa48e7764859ddfbba}}.
References {{cite:df0b91343ebf1eaebe9513236cd7f2d99a23d4dc}} and {{cite:06ab75e66574166fd862bc8a06e4461e74df584e}} deal with implementation of TL-BT for large-scale continuous and discrete systems respectively. Lyapunov based time-limited H{{formula:76f69c00-88b8-4e87-bf78-8cf542785063}} optimality conditions are obtained in {{cite:a5f43c78c85672aa4d17db24b15e6475926d1d37}} using a time-limited H{{formula:94b2bfac-7e10-49d6-a035-06b6f60f43f5}} norm. The same paper proposes an iterative scheme similar to TSIA {{cite:2b51f8a385980fabfaf34b68f6d24b7e0aa764b4}}. We refer to this scheme as TL-TSIA. Projection-based algorithms like TL-BT and TL-TSIA fail to exactly satisfy the time-limited optimality conditions. Reference {{cite:34b77ac451d18783cc01d77fd23f2102e0beb482}} obtains interpolation based first-order necessary conditions for time-limited H{{formula:b71fb96d-709e-474e-909d-5af5479b866e}} optimality and proposes an optimization algorithm named FHIRKA. This algorithm produces time-limited H{{formula:4309c264-4fe5-4b9c-8463-b838c156b35d}} optimal models but is valid for SISO systems.
| i | f1392065bf8fad96fdf5b871df84e797 |
Recently, researchers have explored this issue popularly. Zhou and Feng {{cite:c6ee5ec0694665b690615ee80db83f0ac8269cde}} proposed a deep forest framework, which was the first attempt to construct a multi-layered model using tree ensembles. They introduced fine-grained scanning and cascading operations and constructed a multi-layered structure with adaptive model complexity. However, the representation learning ability of deep forest was difficult to explicitly examine. Later, Feng et al. {{cite:99dea6e23c9825333948564fff36ea465247231e}} proposed the first multi-layered structure called mGBDT using gradient boosting decision trees as building blocks per layer with an explicit emphasis on its representation learning ability. mGBDT was learned via target propagation. Specifically, targets were approximated and propagated by a set of inverse functions corresponding to the forward functions. Both inverse and forward functions were constructed by GBDT. Such explorations showed the feasibility of learning hierarchical tree ensembles. Their results demonstrated that tree ensembles were beneficial from multi-layered representations. Several methods of differentiable and probabilistic decision trees have been proposed {{cite:3b1b021cc3302c1193c9f0abb552a7430d40a667}}, {{cite:e04e1c85012fa6f9a93c1ee078c7e5dce6302265}}, {{cite:2f027941a652d361997a0bd55754646708487722}}, {{cite:68852c5b0265d2670529e6ea4e547c6f4f1ec073}}, {{cite:63db1802ce5923a9974cf418e2e632573d2d71e1}}, {{cite:7d5785312c7ac3f9370470ad2424c0377e4f1bc6}}. The probability of going to the left branch was determined by the inner product between inputs and learned tree parameters. Training this kind of decision trees was similar to training neural networks. For traditional decision trees used in GBDT, the left branch and right branch were split by a threshold along one of the features in a deterministic manner. Since probability decision trees are different from the ones used in GBDT in terms of hypothesis space and training methodology, {{cite:3b1b021cc3302c1193c9f0abb552a7430d40a667}}, {{cite:e04e1c85012fa6f9a93c1ee078c7e5dce6302265}}, {{cite:2f027941a652d361997a0bd55754646708487722}}, {{cite:68852c5b0265d2670529e6ea4e547c6f4f1ec073}}, {{cite:63db1802ce5923a9974cf418e2e632573d2d71e1}}, {{cite:7d5785312c7ac3f9370470ad2424c0377e4f1bc6}} are outside the scope of this work.
| i | f8d3988883603bc5489f719f314f0c55 |
It has also been suggested that high ionization parameters are the result of high SFRs, which lead to a larger reservoir of ionizing photons {{cite:2d4143943f26847d34a0e4d96c2f74071d1d1f88}}, {{cite:e291f317ca584697b986f904ba8f74b398304a4d}}. This would be in agreement with the observed enhancement in SFR in the rims of the holes. Hence, the observed difference is likely a result of the enhanced SFR taking place.
Another possible effect at play is the dust absorption. On galactic scales, {{cite:afc6fef867df820275924852cf9025aefc63a98e}} suggest that the ionization parameter can be suppressed by selective dust absorption of ionizing photons in the regions where U is highest, decreasing the observed ionization parameter. This suggests that the ionization parameter we observe could be higher.
| d | 24666ec91d9300322c818236e62aef5e |
One branch of EBM works uses MCMC-based Maximum Likelihood with persistent initialization of MCMC states. Persistent initialization uses samples of prior short run EBM trajectories to initialize the current sampling trajectory. This approach is introduced by Persistent Contrastive Divergence (PCD) {{cite:7de59328f63024cb611ce0eb10a23b093593dacd}}. The IGEBM {{cite:06c73b872abb611937d2423bfee96061d03949f4}} is trained using a bank with 10,000 images to hold persistent states. States are rejuvenated from a Gaussian or uniform noise image with of between 0.5% and 5% probability before being returned to the image bank. The Improved CD EBM {{cite:ad98e232a16ddc3f3881fcd1d2ade067c83e1034}} builds on these results by including an approximate KL divergence term in EBM learning to minimize the difference between the data distribution and the sampled distribution, and by rejuvenating MCMC trajectories using data augmentation instead of resetting states with noise. The Joint Energy Model (JEM) {{cite:aca8dd7d81acc60d469cd2d0fa417b4027c52e56}} trains an unconditional EBM and a classifier model simultaneously with the same network using persistent initialization with noise rejuvenation. The use of persistent states in our work differs from prior work because we use persistent states to update only the generator while the EBM is updated by states generated from scratch in the current iteration. This is done to increase the diversity of samples used to update the generator, which is essential for enabling the generator to create distinct appearances for different {{formula:73150877-a3cf-42c0-8faa-aea1e5ad0fd0}} early in training (see Appendix ).
| m | 52443106b0ef9570b01bd255b091e459 |
Irony is a pragmatic phenomenon that can be defined as a sort of incongruity between the literal meaning of an utterance and its intended meaning {{cite:326b73667ab93345fd169e209aaef11e791b00e3}}, {{cite:7557cc0800b4a64d913b078c5d0bcd02492d838b}}, {{cite:0a46e7ddb7a38efcb8027f6f64b2ab1c42ec56a2}}. In text processing, the challenging nature of irony is mainly due to the inherent features of the phenomenon itself, that may assume a large variety of merged forms and facets. Several semantic and syntactic devices can be used to express irony (e.g., analogy, oxymoron, paradox, euphemism and rhetorical questions), and a variety of different linguistic elements can cause the incongruity, determine the clash and play the role of irony triggers within a text.
| i | cf07fdac897c80cab44c40ea1e0314f1 |
DAIN with MobileNet V2
The CNN module of the two stream network can be replaced by other state-of-the-art deep learning methods to further improve results. To demonstrate this, we change the CNN module to ImageNet pre-trained MobileNet V2 {{cite:5804c7845a3ce1c2758fa778a8674384e1e829fa}}. Combining feature maps generated from the bottleneck8_x (the eighth Bottleneck inverted residual block) with training batch size 64. The recognition results are shown in Table REF . After replacing VGG-M model with MobileNet V2, the recognition performance improves for all the methods. But still our DAIN network architecture performs better than the non-DAIN methods. Notice that sngle view DAIN achieves same recognition accuracy with smaller variance than multiview CNN with voting. The best recognition performance is the multiview DAIN (Sum/pooling) with single view images ({{formula:f75d0c78-1159-416c-aace-07afcc791e66}} ) and single view differential images ({{formula:21ddd9b2-4eb8-4294-a06e-d9c091201bc5}} ) as inputs, which is 86.2%.
{{figure:ec470b8a-11fb-4f7c-847b-9a31adc6a8d1}}{{table:8ae86f0f-42df-47f4-9d0d-41134fe69cb6}}{{figure:32556564-545d-4a6d-a54e-8a00a105d97b}} | r | 600f149fd9f8d0b506710da10ebacb89 |
ABC approaches also rely on the definition of a set of summary statistics. In this paper, we derived these summary statistics based on their biological meaning. More automated methods have been developed in the literature {{cite:97c5b22250cc3dde4eb0491af7e5f8dcb88475ef}}, {{cite:453544cb74d00ec148dc33b6e107eaf9ee92c6be}}, {{cite:7ce9a05e8524fb4d5b9a2a874b0eb2945eb7cc77}}, {{cite:a0f75161ff79e5e02aab40cc85a3945588458559}}, but they could not be implemented in our case due to their high computational cost. In high-dimensional settings, {{cite:f55398941f9e7825ddc13f94cd7292e8f70b275e}} recently proposed an approach based on rare events methodology and sequential Monte Carlo, which allow to decrease the computation cost.
| d | a316874a42bd973de08f47fcdc16aa28 |
In contrast to Theorem REF and Theorem REF below, th:main-partition does not assume {{formula:324db518-bffa-45b3-a1ff-ced549ba7133}} is countable. The reason is that the former two theorems use Kronecker factors via Furstenberg's correspondence principle, and the theory of factors requires the group to be countable. There are two ways to think of a factor of a measure preserving {{formula:2dbaf5d8-e90b-429c-b0a4-91ba2001f51e}} -system: as a spatial map or as a {{formula:f55f2783-d800-4bd4-929f-a055955d78ab}} -invariant sub {{formula:c9e47c03-c7cd-429b-96f1-7db7adb3531a}} -algebra. The latter can be obtained trivially from the former, but the converse is not trivial, and requires the group to be countable (in addition to the {{formula:7fa78a80-db88-4814-8b40-569332f9e259}} -algebras being separable). For instance, the method of proof of Theorem 5.15 in {{cite:531fdff55cee86757a17ef23e1ab6cbc6c2ca50a}} requires {{formula:4e6aa580-4c0d-4a57-8c06-5fdc50a3d3ab}} to be countable.
Since Bohr sets contain 0, th:main-partition implies that the equation {{formula:7bb38c1a-1155-43e3-85d3-9cb4127e8793}} is partition regular in discrete abelian groups, that is, under any partition {{formula:6e10ec3d-ecaf-4997-83bb-6bc346aa435f}} , there exists non-zero {{formula:62b15cf8-c0c8-4574-977e-e88ada8d1f2c}} in the same class {{formula:ad636a2f-e156-465d-b97b-7231ec1ea6bf}} such that {{formula:f096f378-be05-41db-ac9f-36b40213b2bf}} . (To see that we can take {{formula:509e2dce-31da-4f57-9ddd-21b06ba09a14}} to be nonzero, give 0 its own partition class.)
If {{formula:0a118a27-813a-4230-8d22-95662205695e}} , then {{formula:6ba69b95-4b24-4fba-927d-ca8a4a99391a}} is not guaranteed to contain a Bohr set as remarked after th:br. In particular, the analogous version of th:main-partition for sets of positive upper Banach density is false.
The hypothesis that {{formula:60229221-624a-4dbe-9c5b-a62e3c791ef7}} has finite index in {{formula:4793644a-e17e-42cc-a125-de45f7de30f2}} cannot be omitted. For example, taking {{formula:db81f8ac-a2d6-49a9-81f1-9dd374ac2060}} and {{formula:66984f02-5e28-40b6-b514-0933ce9b3c64}} for {{formula:73ce44e2-b5cf-40bd-adf6-d4aaff5a94e5}} , the sumset in Theorem REF simplifies to {{formula:0bf79fba-d4ae-40bd-9190-62c0841a2b42}} .
The question of whether the Theorem REF remains true without the assumption that {{formula:a9066d5a-f7d6-4893-881b-68046b531648}} is finite is essentially q:kr: we may take {{formula:812e82fa-538b-4541-8b11-965cc25a012e}} and {{formula:04321f0e-c42c-472c-a2cf-497cc4311cc2}} for all {{formula:905bcf0c-7645-408c-b8bf-8e9971202ad5}} , and the sumset in Theorem REF simplifies to {{formula:2acbc8d9-0fcf-4d17-b6aa-1f124a18074e}} .
Similar to th:main-density, the hypothesis that the {{formula:4fdc617e-1586-4c7d-acd5-4665c803945d}} commute can be removed if one of them is an automorphism.
| r | 1ba35622283e4f72f938208deb10c2d2 |
In this paper, we have have studied the asymptotic safety of the simple Higgs-Yukawa model with non-minimal coupling, in the symmetric phase {{formula:af216d45-3238-4ea1-9569-ab94b2dedcf2}} .
In the Higgs inflation using the SM criticality, the typical value of the Higgs field becomes close to the Planck scale {{cite:d192094d1c6e1c1b5582ccddf628d3e5ba103302}}.
For such an application, it is important to extend our analysis to the broken phase {{formula:87cac9df-2488-4695-938f-9bcc6dc7225f}} .
| d | eb05288d4b8bf89a6df1ca8b34a55665 |
From the results of Top-{{formula:57da03be-7f1c-49b9-a609-41b49b6a7a4b}} , Nucleus, and Contrastive, we see that solely using the unsupervised language model without conditioning on image inputs can hardly generate meaningful captions.For stochastic sampling methods (i.e., Top-{{formula:69e27629-d6fd-4d52-8e17-4e13ac251bef}} and Nucleus), we report the results averaged over 3 runs with different random seeds. We refer to Appendix for more details on the numerical results. On the other hand, the results of CLIPRe show that the ability of measuring image-text similarity enables CLIP to retrieve captions that better correlate with the test image from the training text corpus. However, the performance of CLIPRe still lags behind the current SOTA method, ZeroCap, by a large margin due to the data discrepancy between the training and test sets. Lastly, we observe that, on both benchmarks, MAGIC achieves the best performance on 11 out of 13 metrics, demonstrating the clear advantages of our proposed approach. Notably, while outperforming ZeroCap on 12 out of 13 metrics, MAGIC achieves a nearly 27{{formula:bfd229d2-eb99-47ba-a7c5-4a9912d76707}} decoding speedup. This is because, during the decoding process, MAGIC does not involve any computationally inefficient operations like gradient updates {{cite:135dd1fcac9203eec70f2ccb966d5af6aeb231c2}}, {{cite:d8baf447b5d86f20cab211c1cf54e4531b7aebd3}}, which further validates the practical usage of our approach.
{{table:0b056947-a092-421c-a6a7-d923251351bf}}{{table:d1fa0683-ca65-4768-a926-803ba2e95499}} | r | c8d6377dfd895e38c9debd3ad3297747 |
Mass estimates and kinematics of PNe that experienced a CE phase can be directly contrasted with theoretical predictions {{cite:46bce06320919ddf6dda74b37f77379556fff0ae}}, {{cite:7fb05e415470048c2b06dd5c7206e90b629f9216}}, {{cite:3c865365e5ff6bb916c70cfa81a571db404a9d77}}, {{cite:15092025f33480b4aca2910f26b6154370a6e6bd}}.
The mass-loss rate of the jets of M 3-38 is about one to two orders of magnitude larger than those reported for the jets of PNe with post-CE close binaries {{cite:fe580cebfa4d5331fd7c1b2cf4b891a105331f20}} and for the jet in NGC 2392 {{cite:d600a4f7d5e136c546fd2177a032c85dc4a00ab6}}, but consistent with those of the late AGB jets in BD{{formula:d6111123-eb3e-4328-b723-649d2b627c95}} 46{{formula:cbfd3e50-7018-4d4c-858f-a7b7156408e1}} 442 and IRAS 19135{{formula:8bc029ff-0b3e-4764-8e04-ce6ab3c9090f}} 3937 reported by {{cite:61ce40dd967afdadce072b2b4612b3536277d436}}.
The linear momentum and mechanical luminosity of the jet in M 3-38 are in the high end of the range presented by those authors, but still notably smaller than the values reported for outflows in proto-PNe {{cite:62b8ec8d4726867cfc5a889e79ab66df431b1e30}}.
| d | 4b7df6f504dc483dd16e7d55634af3c4 |
The three games differ, however, in whether the cooperative outcome obtained through mechanism design is stable even when the planning agent is turned off. Without additional incentives, mutual cooperation is not a Nash equilibrium in the Prisoner's Dilemma and in Chicken {{cite:be2b831fb601ef3141d398f9a3db1190b6dd778c}}, which is why one or both players learn to defect again after the planning agent is turned off. These games thus require continued (but only occasional) intervention to maintain cooperation. By contrast, mutual cooperation is a stable equilibrium in Stag Hunt {{cite:be2b831fb601ef3141d398f9a3db1190b6dd778c}}. As shown in Table REF , this means that long-term cooperation in Stag Hunt can be achieved even if the planning agent is only active over a limited timespan (and thus at limited cost).
{{table:05e478df-00fc-4c3b-962f-c7d78a0f4d2c}} | r | 8c6c70699c17aea0794c656c170a3532 |
We limit our evaluation to only autoencoders as we find comparison with methods that rely on SSL {{cite:57f65f7580e255896d0218527d1caeef15ae7904}}, {{cite:e0dd32ea7dbd3a1828d3957cc7d2c65f0e8d5879}}, {{cite:7c37186717980f1744da96827d8ce0fabf5c5759}}, pretrained feature extractors {{cite:379786b5145acc277a0770e2d69b24ef9fc72b5e}}, {{cite:df5c013e59800a0f15ae90635ed5ee4e7a565601}}, {{cite:7c37186717980f1744da96827d8ce0fabf5c5759}}, {{cite:e0dd32ea7dbd3a1828d3957cc7d2c65f0e8d5879}} or computationally expensive inference {{cite:57f65f7580e255896d0218527d1caeef15ae7904}} are not easily comparable on AUCROC alone across multiple datasets. It has been well documented that using pretrained feature extractors and SSL losses result in improved performance. However, they typically require orders of magnitude more parameters {{cite:58eaad8edcdeaef766ade8963a15c531acbb7db4}}, and are not easily applicable across datasets or evaluation strategies. Furthermore, we regard the simplicity of AEs a crucial attribute. This is in contrast with the significant augmentation found in {{cite:128934bb8f65829c0d8e04ecd0276f530a87b7d0}} and the challenge of applying patch-dependant methods {{cite:57f65f7580e255896d0218527d1caeef15ae7904}} to different datasets of varying resolutions and anomaly types.
| m | a2b3b7e21fbc2d5fd16993663ade94fe |
Second, noting the lack of DS robustness in CNN-based prior models for driving TTA, we posit that simpler prior models may (a) suffice to improve task performance under the considered acquisition-related DS, while (b) themselves being more robust to DS as compared to CNN-based priors.
With this motivation, we model the distribution of the normalized training images, {{formula:b606503e-9469-49c1-91b0-be82c5225584}} , using a Field of Experts (FoEs) {{cite:8e52dacba704d9eebac58bf6ef81c6c371fc181f}} formulation.
FoEs (described in more detail in Sec. REF ) combine ideas of Markov random fields (MRFs) {{cite:7c3fc775730336062d24fc68abf09cff3a340e65}} and Product of Experts (PoEs) {{cite:c2b100591845545490801968af1e19ab46a99400}}.
FoEs enable modeling of complex distributions as a product of several simpler distributions.
The simple distributions are those of the outputs of so-called expert functions, which are typically formulated as scalar functions of image patches.
We propose to use the task-specific filters learned in {{formula:f3eb970a-a708-40d5-bb89-9e8d4bd2537e}} as the FoE experts (Sec. REF ).
Further, we augment the FoE model with additional experts - projections onto principal components of patches in the last layer of {{formula:528a25ab-27cd-4b0a-bc02-05377e184851}} (Sec. REF ).
| m | 98f0140b327b29eee95408a2e5a88b4a |
Alternatively, we adopt a racial bias analysis methodology that uses facial phenotype attributes for face verification (one-to-one facial matching) task {{cite:a42081ed3d53fd25b3591d9ee8cfb201069a1f5e}}. The study categorises representative racial characteristics on the face and audits these attributes: skin types, eyelid type, nose shape, lips shape, hair colour and hair type for two different publicly available face datasets: VGGFace2 (test set) {{cite:66ae0c52d4f5b8f6b53900e2136f2581c24eacdb}}, and RFW {{cite:617a0175d5322990324ae6ec11674df6539d379b}}. We show each of the predefined phenotypes and their categories in Table REF . Moreover, this methodology provides different pairing strategies for face verification to draw attention to the importance of pairing for comprehensive evaluation. It introduces attribute-based pairings, which contain same-attribute grouping pair combinations to compare individual attribute performance for face verification. Additionally, the study shares cross-attribute pairing combinations between each grouping to measure false matching rates between all possible attribute category pair combinations.
{{figure:5fe4aff0-0c01-4512-92bd-39b462f66938}} | m | 98800328ad500278968caa2ef9854473 |
The proof of this result can be found in {{cite:15aa922ed0998f708980297c94f010de4f78110e}}.
{{formula:577ef935-2ffc-4294-8c2a-80c1865e47b5}}
Lemma 4.4
For {{formula:4ec88b58-fa34-4b0a-b537-0c0e72d7aad9}} ,
there exist a
constant {{formula:dbbb21aa-56a5-4c5a-9990-691f8d962b03}} , such that
{{formula:0569b316-9274-422c-a63a-b851b5f65f5f}}
as {{formula:2392e82d-3c11-4dc9-ad06-c33bd8987d8e}}
| r | 486c1e49fb80e25c8deba9c30b04fc55 |
Ensemble methods are very easy to apply, since no complex implementation or major modification of the standard deterministic model have to be realized. Furthermore, ensemble members are trained independently from each other, which makes the training easily parallelizable. Also, trained ensembles can be extended easily, but the needed memory and the computational effort increases linearly with the number of members for training and evaluation. The main challenge when working with ensemble methods is the need of introducing diversity among the ensemble members. For accuracy, uncertainty quantification, and out-of-distribution detection, random initialization, data shuffling, and augmentations have been found to be sufficient for many applications and tasks {{cite:d4be62a2180a1f902b0e57057035d4bac9d4dd94}}, {{cite:fe2a18af51f71b82e04cd85a509c54cd65c45d31}}. Since these methods may be applied anyway, they do not need much additional effort. The independence of the single ensemble members leads to a linear increase in the required memory and computation power with each additional member. This holds for the training as well as for testing. This limits the deployment of ensemble methods in many practical applications where the computation power or memory is limited, the application is time-critical, or very large networks with high inference time are included {{cite:60193445b43bd1d1131ecdc0979f1c486ca9ec4e}}.
| m | 18511da3796892e5651f3c2135190588 |
By incorporating the changes described in the previous sections we arrived at a single model type, with a single set of hyper-parameters, that was trained to reach new state-of-the-art performance on CLRS-30 {{cite:497c87b29196d728d54ec5bfc7179f5d8eecc74f}}.
Tables REF and REF show the micro-F{{formula:99268113-80b3-4400-9725-f0e3decb7ed2}} scores of our model, which we refer to as Triplet-GMPNN (an MPNN with gating and triplet edge processing), over the original CLRS-30 test set (computed identically to {{cite:497c87b29196d728d54ec5bfc7179f5d8eecc74f}}, but with 10 repetitions instead of 3). Our baselines include the Memnet {{cite:b2651c126c739bdac12e3cb3897737b2198ba903}}, MPNN {{cite:da69ff9b6ad7bb9f83aaf7accce74b37f79bbcef}} and PGN {{cite:70878f1e11d6743115d0b5142133cceeef7b8b18}} models, taken directly from {{cite:497c87b29196d728d54ec5bfc7179f5d8eecc74f}}. Figure REF displays the comparison between the improved model and the best model from {{cite:497c87b29196d728d54ec5bfc7179f5d8eecc74f}}.
Our improvements lead to an overall average performance that is more than 20% higher (in absolute terms) compared to the next best model (see Table REF ), and to a significant performance improvement in all but one algorithm family, compared to every other model. Further, our stabilising changes (such as gradient clipping) have empirically reduced the scale of our model's gradient updates across the 30 tasks, preparing us better for the numerical issues of the multi-task regime. We finally also note that though we do not show it in Tables REF & REF , applying the same improvements to the PGN processor, leads to an increase in overall performance from {{formula:d343188b-ca1d-489d-8ba2-de43d85388bf}} (Table REF ) to {{formula:96cb7e1e-9b20-4694-b771-dea057eca794}} .
| r | b6b1c85122af4f693cffd07265f31d35 |
For comparison, we compare our model with the standard Barabasi–Albert Model {{cite:d6794f9b3e184b2760d0e34236f05222c4c1732d}}. The Barabasi–Albert (BA) Model is a method for generating scale-free networks using a preferential attachment mechanism. Since our model also applies preferential attachment mechanism so it would be interesting to compare it with the basic BA Model. In the very basic form of the BA Model, the network begins with a small connected network of {{formula:9a48997d-6a9d-40d2-b05d-6ffe1776b795}} nodes. New nodes are added one-by-one at each time stamp and connect to {{formula:0302a9da-0937-4a93-b029-1aef3150bae0}} existing nodes with a probability that is proportional to the number of links that the existing nodes already have. In our implementation, we start with a small connected network and connect the new nodes with {{formula:bf8d9b4b-c7b6-4aa9-9f52-00c896dbacba}} number of existing nodes using the preferential attachment method described in {{cite:d6794f9b3e184b2760d0e34236f05222c4c1732d}} where the value of {{formula:88094070-6529-45d8-a2ab-18986664659f}} is adjusted such that the resulting graph has nearly the same number of edges as that of an original graph.
{{table:0bcf4790-51cf-49f8-93aa-36b43aa0ae31}} | r | 3b8e3829809ea7ce9c9cd04a308e9b61 |
In the third observing run, the Advanced LIGO detectors operated with roughly 250 kW of resonating power inside the arm cavities {{cite:51ed94c66ed4d1a7ec8135233f0ebfe2236a4d79}}—still only one third of their 750 kW design power. Recent tests in both detectors have shown that as the injected laser power is increased, the arm cavity optical gain severely decays due to increasing internal loss {{cite:51ed94c66ed4d1a7ec8135233f0ebfe2236a4d79}}. The source of this loss has been identified as sub-millimeter, highly absorbing defects in the optical coatings known as point absorbers. In situ wavefront sensors have detected their presence on at least four of the eight currently installed test masses {{cite:51ed94c66ed4d1a7ec8135233f0ebfe2236a4d79}}, {{cite:b5b578da9bfcfa498cfe6ac02dfd3516af0ff17d}}. Point absorbers appear to originate during the coating deposition process, although it is still not understood how these contaminants enter the coating nor to what extent they can be eliminated. Each point absorber absorbs roughly 80 ppb of the total incident power, or 20 mW when exposed to 250 kW. The extremely localized heating induces a sharply peaked thermoelastic deformation of the mirror surface, which scatters power into higher-order spatial modes {{cite:b5b578da9bfcfa498cfe6ac02dfd3516af0ff17d}}. To achieve higher operating power, point absorber losses must be mitigated.
| i | 8cfed0db71b4d4bf01197d671b040547 |
The impact of limited liquidity on optimal trade execution has been extensively analysed in the mathematical finance and stochastic control literature in recent years.
The majority of the optimal portfolio liquidation literature allows for one of two possible price impacts. The first approach, pioneered by Bertsimas and Lo {{cite:a70788b8eaa9468d115e61af940fc1841516df16}} and Almgren and Chriss {{cite:6a675efb2bd76fa56a43d4900206b51152910021}}, divides the price impact in a purely temporary effect, which depends only on the present trading rate and does not influence future prices, and in a permanent effect, which influences the price depending only on the total volume that has been traded in the past. The temporary impact is typically assumed to be linear in the trading rate, leading to a quadratic term in the cost functional. The original modelling framework has been extended in various directions including general stochastic settings with and without model uncertainty and multi-player and mean-field-type models by many authors including Ankirchner et al. {{cite:a18c3e7fe9e558f044e598edf42809464c9b01ac}}, Cartea and Jaimungal {{cite:9eb96d2b2351918e6e8a6af95408624d90078113}}, Fu et al. {{cite:3cf581be2472848a7ee3ba7d115ba324ae89aa44}}, Gatheral and Schied {{cite:742d14ee23dda166a28f218003ccc615ebe209cd}}, Graewe et al. {{cite:3e2f90d3b260fe72f920ed0a7dc3c13e7bb387f3}}, Horst et al. {{cite:68f374bfb78ed3a4c92c6a2d5fb324436030ede6}}, Kruse and Popier {{cite:43c714cc8f32366a81c32121a45db401ef1addb9}} and Neuman and Voß {{cite:824d5804d35af75a5dbf1372706ad92c11368bdc}}.
| i | ab3a5d240dbcf737f4b1c392a39ad580 |
Concentration inequalities are a powerful set of methods in statistical theory with key applications in machine learning. This is due to the fact that in many machine learning applications, a learner often estimates some quantity solely based on samples from an unknown distribution, and would like to know the magnitude of the estimation error. The typical example is that of the mean {{formula:8650216c-c7cb-43fd-b2fa-cbc3f08784bb}} of some measurable real-valued random variable {{formula:969afd1f-307d-4d58-9bff-ae1f27b8a406}} , estimated by its empirical mean built from a sample of {{formula:0a8fba33-ac5a-420b-b4af-4bac359a5f8d}} independent and identically distributed (i.i.d.) observations. We refer the interested reader to the monographs of {{cite:ef9e040c7d0419da566cce3728351a5c5fa30bfd}}, {{cite:6334661e06e37e3e8e2a38f3f90df9aeea9f6233}}, {{cite:9e44490e6c3c2eab9d2cb5682c04318264762582}} for standard results in this and related topics.
| i | a7ba94233ff1a613a291520b95f5335b |
Previous researches have shown that the self-force effect and other interactions would prevent the black holes from being overcharged and overspun {{cite:663963f98598c428993b9be347c40c31916733ef}}, {{cite:bb09fa5aca657f44703b43a05b1e30978ba8bfd5}}, {{cite:2398f6648ef6667822794aba2438b46c1de30a25}}, {{cite:f05186d75af218e34e7af1145cab367e1fae0bc1}}, {{cite:9cd74d17608813eabc0c49a1e673c7e2948f9b2d}}, {{cite:82d8b2e7dd1163ef2dab00720e8d782e41ab48e3}}, {{cite:9e0a43b0276d9025b70d9757136ccf35d73ecd2e}}. In our investigation, due to the infinitesimal time interval, the self-force effect and other interactions were neglected, and the black hole can still not be overcharged.
| d | e93a1b165b7f40a720b25a1b93bc1939 |
We believe that this disparity can be explained by a strong bias in selecting videos for this dataset. In their paper introducing the challenge,
{{cite:418156b90a065ee931d6e7928400aba08711b859}} explain that the videos are machine-generated and selected for precision
“While the labels are machine-generated, they have high-precision and are derived from a variety of human-based signals...” {{cite:418156b90a065ee931d6e7928400aba08711b859}},
before being subject to additional filtering to improve precision.
The dataset, therefore, is strongly biased towards videos that can be classified with high precision based on associated “human-based signals”.
If we make the reasonable assumption that videos with clearer visual and auditory content also have clearer human-based signals,
then it follows that videos from the dataset will be easier to classify than the average YouTube videos.
Further, if these signals directly depend on video or audio data, the task reduces to us attempting to learn another machine learning model.
| d | 8b1a80ac989bd9422615708e7d3c4952 |
In the case of distributive lattices and Heyting algebras the lattice of all upsets is isomorphic to the canonical extension.
The representation of lattices as clopen filters leads to two kinds of completions of a lattice: (1) by taking point generated upsets of the dual space of {{formula:f0201a4e-b25c-47b8-b0ed-8ddf832d96d8}} we obtain the filter completion of {{formula:b849ae11-953e-4c29-88c9-32d707e7c532}}
and (2) by taking all filters we obtain a new completion of {{formula:143bbcc6-21f7-4604-b23b-2aaea77c1e4b}} that we call the
{{formula:7e5523e9-4a01-48dc-ae50-8781947f4559}} -completion. The canonical extension of {{formula:81e43362-17df-4cd8-b116-d5412b9a72c0}} is a completion which is situated between these two, although as we notice it is not a sublattice of {{formula:5e24a815-d29d-4a54-b6df-67b5def0ebec}} -completion.
Our main results are preservation and correspondence results.
Using a duality technique similar to that of Sambin and Vaccaro {{cite:e7fb909b094a2610d23823efd5a9f1654b28ebff}} we show that every sequent is preserved by filter completions and that every Sahlqvist formula is preserved by the double {{formula:180a4c8d-9e03-4f51-ade9-d3c78e90a284}} -completion.
The former provides a purely topological proof of the result by Baker and Hales {{cite:5fd7a32b7b95820a002b579584a3fd2b6040e8eb}} that every variety of lattices is closed under ideal completions.
An alternative approach to Sahlqvist correspondence and canonicity for non-distributive logics has been undertaken in {{cite:a16405352b0119b08ac40f3b6b57d075b52b5b72}}. But this approach is purely algebra based and is not concerned with the
relational semantics and duality developed in this paper.
| i | 7a2696dd27db9ad4a04f15a752ab09f7 |
One advantage of subspace-based methods is that the calculation is simple and efficient. Similarly, the linear correlation alignment (CORAL) minimized domain shift by aligning the second-order statistics of source and target distributions
{{cite:6941f561a4a526b4c65458bf1c891f492338b97d}}; it solved the following optimization problem:
{{formula:cab6605d-ef25-49b1-ab36-573d236ba95d}}
| m | f7e869b32c7e2bbe420550623dd83291 |
By the spectral theorem {{cite:f89378ede14e393f6f95134842780dff592d2110}}, this can be expressed
as
{{formula:0f2c226e-74fd-43a6-9c6e-e51c0900ba1d}}
| r | 52f53a1fa4fd6a351ad3a81228f1f211 |
Another critical issue in Bayesian and other model-based clustering is the issue of model misspecification. In particular, clusters may not have Gaussian shapes or may not even match with more elaborate kernels, such as skewed Gaussians {{cite:eb3b8a11a6a8b762fc71f8e0e214a0a1853094fa}}. There is an evolving literature for addressing this problem in low dimensions using mixtures of mixtures {{cite:6e8956edefb0b24c54c0c01c306337aee89a562a}} and generalized Bayes methods {{cite:06a6e25bf2b316f1b93ed91fbb80ed46ed97e6ae}}. However, it is not clear that current methods of this type can scale up to the types of dimensions encountered in our motivating genomic applications. One possibility is to rely on variational Bayes methods, such as variational autoencoders {{cite:561a60012c4aee961473ef7f19ff68fc3adbd2a9}}, {{cite:1fcce744d3e1de1b17c647e092b83ab9c87be349}}; however, then one faces challenging issues in terms of obtaining reliable algorithms having theoretical guarantees, generalizability and reproducibility.
| d | 7f9f4d009660026045fe8df5e56abc71 |
To measure the rotation rate we applied the following procedure. In order to decrease the uncertainties due to noise in the magnetic field maps, the linear size of the cropped patches was reduced by a factor of two by binning 2{{formula:ada37b3f-eab0-4da1-8c4b-aaf80c278728}} 2 pixels. Then the flux-weighted centroid positions of each magnetic polarity were calculated. To decrease the uncertainties only pixels with absolute values exceeding 100 Mx cm-2 were used in the calculation. The positions of the centroids were further converted to Stonyhurst heliographic coordinates using World Coordinate System (WCS) library provided in the IDL SolarSoft package. The longitude of the tracer, {{formula:48b83aa1-7ae3-49ab-9457-c4e7c2b738b4}} , was determined as the unweighted mean value of the longitudes of positive and negative polarities. This is the difference between our methodology and procedures widely applied in the majority of the previous studies where the flux-weighted or area-weighted centre of the tracer was considered with no respect to leading and following parts. {{cite:5155d0581fdc5cb82cb1cc7565e057ce712aa93b}} argued that due to different decay rate of leading and following polarities the area-weighted or flux-weighted centre of an active region shifts toward stronger leading polarity as the active region evolves {{cite:5155d0581fdc5cb82cb1cc7565e057ce712aa93b}}. This effect may cause fake proper motion of the tracer yielding polluted rotation rate measurements. An example is shown in Fig. REF . The total unsigned magnetic flux of NOAA active region 11066 is plotted by a thick grey line in the top panel of Fig. REF while the flux-weighted longitudes of negative and positive magnetic polarities are shown by blue and red lines, respectively. Green line denotes unweighted mean longitude of the active region while the flux-weighted longitude is shown in black. The differences between the mentioned longitudinal positions and some point rotating at a constant rate are shown in the bottom panel of Fig. REF . One can see that, as expected, negative and positive polarities disperse from each other as the active region evolves. Meanwhile the flux-weighted position exhibits motion toward the leading positive-polarity part of the active region as decaying proceeds.
| m | a8d24792cf0956852d2570546968b097 |
When there are finite number of algebraic singularities on the circle of convergence, the final result can be extended by
adding up the contributions from all singular points; see Szegő {{cite:2ae9759d9cd4b4ec0dfbcd5fceb751e024304293}} and Wong {{cite:ca47722ff6d9c0818ec55473995350a2cd208e89}}.
| m | 186730d97e850bc3fb4fccc870219c71 |
The voter model describes a simple process for opinion dynamics and consensus in a population of agents that can hold one of two different opinions ({{formula:038dd91d-b514-4b2f-963d-74e0fb2b34f4}} and {{formula:55c53baa-5034-4062-b24c-73a3291ab217}} ) {{cite:cf0aad0f42217308378d36b8a0c33f785fde7aff}}, {{cite:5459aa0e93559e685d2750493ea7165b36207004}}. In a single step of the dynamics, a voter chosen at random adopts a random neighbor's opinion. This step is repeated until voters' population eventually reaches a state of consensus in a finite system, where all agents share the same opinion. Due to its simplicity and analytical tractability, the voter model has become a paradigmatic model to study basic properties of opinion diffusion, and the dynamics of elections {{cite:b5b6f85d8041d4d319a690e1008850a7199fd180}}. After its introduction in two independent works, by Clifford in 1973 {{cite:cf0aad0f42217308378d36b8a0c33f785fde7aff}} and soon lately by Liggett in 1975 {{cite:5459aa0e93559e685d2750493ea7165b36207004}}, many extensions of the voter model have been proposed in the scientific literature to mimic more realistic or complex scenarios of social dynamics, such as considering multiple opinions {{cite:70f44a715aa0e2ae437c32d328aedb08d21ef870}}, {{cite:a1169a184c357489f314b29fb1bb2156f3620fdf}}, {{cite:c5d793a99086a2f95944784550a565c6572d52ce}}, heterogeneity in transition rates {{cite:d87cd561a1f980d9f71ff2f93317d0f1e219c57d}}, {{cite:60c7147ff8c14c6092d1154abbb6ff105a23d5be}}, and complex interaction topologies that are static {{cite:5ab7586f2a0585399086417b9e7899875defcfa1}}, {{cite:825fe13c245c26856a5e84b5330e0528027771cb}}, {{cite:80a350c629c2c71a14942b19bc853da881e2d87e}}, {{cite:5a7bd53c4e2971bcca87af03486ea2103807405e}}, {{cite:c3b68e335e79d69fe291d8c35b8b04b78e2d0e30}}, {{cite:6f53d6d82248f705464bb7f015222baf9e24a72b}} or evolve in time {{cite:4d6e093b7a1ec9f771a01f266236b6b0ac87bfe1}}, {{cite:1a8ce42eb6fb04433965c1b252779160a72e8d90}}, where clusters of opposite opinions coexist. Other works have studied how the presence of agents that never change opinion (stubborn individuals) affects the dynamics and consensus properties of the system {{cite:c8969ce9ac9cae7dba79af2fd1734a25da922fa7}}, {{cite:63ba0d11a910fa816ee0851d6b6361b81f40e590}}, {{cite:06f290e2d60cb24e4ca0ff2eb2684088e83749e1}}. Moreover, the introduction of personalized information {{cite:958346dbd1c2bd209b05ec54d094ce58fb6ce5d3}}, reinforcing the political orientation of an agent when its opinion changes, has shown to prevent global consensus for strong captured information change, showing the phenomena of strengthening political positions observed in many countries. This polarization behavior has also recently been explored through multistate voter models that include a mechanism of opinion reinforcement, which is a consequence of exchanging persuasive arguments {{cite:8389a906ae90c427ade9390920b8a099f7da8320}}, {{cite:8c36153e53d3298ac825cf5335ca6fd722c664b6}}, {{cite:267879cdd51c90dedd7d6e19383e0a47cd472391}}, {{cite:e1dc2d7f0a06bd97cc5ed4e7fd9732cf86a7acb3}}. Another implementation of the voter model has investigated the role of confidence in individuals by introducing two states per agent, its opinion, and its level of commitment to the opinion: unsure or tolerant and confident or intolerant {{cite:49872f266221190fa3879291b397c75716b4efd6}}. After interacting with an agent of the opposite opinion, a tolerant agent can change its opinion, while an intolerant agent becomes tolerant but keeps its opinion. It is found that consensus is achieved very quickly in a mean-field setup (all-to-all interactions). At the same time, in square lattices of finite dimensions, the system reaches a metastable state where clusters of opposite opinions coexist for very long times until consensus is eventually reached.
| i | fa0ecd6e0cde9cbde2d6d3f1655366ca |
A significant uncertainty in this study is due to the poor knowledge of the Galactic magnetic field. Different observations, like Faraday rotation measures (RM) and the intensity of total and polarized diffuse synchrotron emission, are used to constrain different magnetic field components.As described in {{cite:0c351913640074022f5c95f4f42525cde75806d0}}, the regular field component contributes to both polarized emission as well as to RM, while the isotropic random component contributes only to the total intensity of the diffuse emission. The striated, or `random ordered', component contributes to the polarized emission but not to RM. These observables depend on different projections of the magnetic field, along or perpendicular to the line of sight, and other not well known quantities like the electron density along the line of sight, what leads to different uncertainties affecting the coherent, random striated and random isotropic components (for a state of the art review of Galactic magnetic field modelling see {{cite:a3cc3d935ab14269a58b6160c857fdbba6620de9}}). For this reason, we have presented separately the results due to the regular component alone, for the regular and the striated components and for the complete field including also the random isotropic component.
| d | 5f99076fca69bd495ff9e6e0585597f1 |
Ablation Study. In Table REF , we show results on the test set of AICITY22 Track 4 made during the challenge. We can see that ViT, U-Net and CBT metric based approaches leads to the best results. We can see that the base ViT model has a relative improvement of 107.1% which is significantly better that the Baseline EfficientNet-B0 {{cite:401ebf044329c6a05c94baace41b608ca841fc2f}} model. Despite achieving the same F1 score at final test set, while experimenting on the then released test set, ViT scored 10 points higher than Efficientnet-B0 on same configuration. So, we didn't pursue EfficientNet any further on CBT metric. Next, after segmentation and contour selection we see a relative improvement of 44.8%. Performance improvement is also observed after removing the duplicate frames. Finally, using the CBT metric in combination of other test set preprocessing steps, we get our best model which has a F1 score of {{formula:f570af51-111d-4db7-a395-a8fb4bb88435}} .
| r | 26e426991c0684087d28436a8a6e4e91 |
Except for GB 1508+5714, these objects have {{formula:ea77d2c1-d95c-4981-8bc5-7e0b3778ae40}} . When considering spinning BHs, which have a high radiative efficiency, there is a great challenge for the formation of such large BH masses even from seeds with masses {{formula:243b8df3-bc1d-4266-b79c-d4a67e16f7a9}} (e.g., {{cite:603de29cebfc7a3f269aeb9fac90303d7c5bcb4b}}). At the same time, the relative dominance between the radio and optical bands seems to evolve strongly with redshift (e.g., {{cite:85f4d48c0f1938c949837b26e099e4a63bc398ba}}), which results in significant changes in the observed frequency of radio-loud quasars with redshift and UV luminosity (e.g., {{cite:313e338e18b36ed93236eb0970f01f16350a458a}}). Furthermore, as the degree of radio-loudness increases with increasing radio luminosity, it would be possible to explore the connections between the efficiency of the formation of relativistic jets and accretion power, which may, in turn, depend on the combination of the evolving accretion rate and black hole spin (see {{cite:20e7da1189cbea4f409f1ccd20ba200cb86506cb}}). It is worth noting that, apart from J0131{{formula:b70480b7-c8d1-43ac-99d4-2515c889b918}} 0321, the BH masses of the other six objects listed in Table 2 are all based on the C IV emission line, which could be highly uncertain due to nonvirial kinematics in the high-ionization C IV line region {{cite:beca1f4c381d1a307d6a756a6decbfde17c02933}}. The BH mass of J0131{{formula:6b872ad9-daa9-4435-a894-84ac0437d735}} 0321 is based on Mg II, and thus should be more reliable. For radio-loud sources in general, if we cannot eliminate jet contamination, use of the size - continuum luminosity relation might overestimate the size of the broad-line region (BLR) size and hence the BH mass {{cite:c50e6a8b6b2aace9e7dbcbd0ba7c7671614f4bd6}}. The broad emission lines, however, can be seen clearly in all spectra, which suggests that the beamed relativistic jets may have a small contribution to the UV/optical continua in these sources.
| d | 8c0a8ffa063b23b3ed1bf3054a540f9c |
We have shown that substitute model black box attacks are not so effective against 01 loss models when the substitute model is convex or 01 loss. There are however other black box attack methods that rely on just labels and try to estimate the minimum distortion of adversarial examples (an NP-hard problem) {{cite:90247ce26d41b40754c063030a42c1c7608afec8}}, {{cite:32a53b55d2b2feb1a60a79bd677d9454521b48a1}}, {{cite:c6f929eedf48ab2bcb66afb4d505713ebe98ae22}}. We obtained the implementations of the Boundary Attack {{cite:32a53b55d2b2feb1a60a79bd677d9454521b48a1}} and HopSkipJump attack {{cite:c6f929eedf48ab2bcb66afb4d505713ebe98ae22}} to determine the minimum adversarial distortion of our SCD01 boundary. Both of these start with an adversarial example and make incremental changes until the example is just at the boundary of the target model. In our initial attempts we found both codes to crash before reaching convergence or their default maximum iterations when we attack our SCD01 and SCD01 majvote models. While we need to revisit the attacks both are slow even for a single example. This is not surprising since finding the minimum distortion is an NP-hard problem and thus hard to solve in practice.
| d | 31584ceb54375053ac614fc0ee542c48 |
We measured the detection results using the official WOD detetion metrics: BEV and 3D average precision (AP), heading error weighted BEV, and 3D average precision (APH) for L1 (easy) and L2 (hard) difficulty levels {{cite:7ce05daf2f3271dfc82aef5bb151df03e8d63bcc}}. The official metrics used to rank in the leaderboard uses IoU cutoff of 0.7 for vehicle, 0.5 for pedestrian. We report additional AP results at IoU of 0.8 for vehicle, 0.6 for pedestrian. Large vehicles that have max dimension greater than 7 meters are also reported.
vehiclepedresult reports the main results on validation set, additionalvalidationresults reports additional results for high IoU and large vechiels on the validation set, and testresult shows the test set results by submitting our predictions to the official test server. Results from methods with test time augmentation or emsemble are not included.
| r | 81c04501e4d162235c3219ca7baef58f |
Gauge equivariant neural networks {{cite:0ebb9360fe05932f82ff0fd545a6bdcf63eac8bd}}, {{cite:1e66a30ea22123bb722b2a51231e49a4eb272a13}}, {{cite:676fac48b85dc0c6d3beecdc4fbfdeb5a746ef0b}}, {{cite:96f94ee662b88f0d55fbb2a430824cce71690dbe}} are instead designed to respect local symmetries. For example, computations involving vector fields - in meteorology or other areas - require vectors to be expressed in components. This requires a frame; a smooth assignment of a basis to each tangent space. However, the sphere and other non-parallelizable manifolds do not admit a global frame, so the computations must be performed locally, using different local frames for different regions on the manifold. It is then important that any numerical results obtained in one frame are compatible with those obtained in any other frame on overlapping regions. In other words, the computations should be equivariant with respect to the choice of local frame, which is a viewed as a gauge degree of freedom; a local symmetry. Gauge equivariant neural networks have also been introduced for problems exhibiting other local symmetries, primarily in lattice gauge theory.
| i | 5818b2c55cc0a493f259e5229561f2dd |
We have performed an extensive numerical scan sampling over {{formula:32b04189-e7d5-4c54-83d4-16da496e74a0}} points using the free parameters in MFS. From this scan, about four thousand ({{formula:b57c5a14-1761-4a8b-a7bf-1a575b43af31}} ) points survive which satisfy the latest measurement of {{formula:e6d47292-77cc-4284-8339-1da6aafc1b39}} at Fermilab {{cite:2ee074b883810d88270cd65b8a9f230baa9dc13b}}, {{formula:ad0330ea-7745-4bf0-a9e4-ce26526d5cce}} given by Barkeley laboratory {{cite:b0d266c8e38177b07541af9ec944ded7d559327a}}, {{formula:c79fa6e8-168a-4d70-8f3b-01848ee32a52}} published by LHCb collaboration {{cite:ef483e3f9fb94c1207516ded3e3ca1699bc5592b}}, up to date results of {{formula:257858c1-64e6-4b48-ab83-d8b78f4d207e}} for the both lower and central bin values of {{formula:8baa7586-d9b8-4d56-9567-3532071df0d0}} {{cite:fb928e2b71084f993afc98e24c3f48968626355e}}. Moreover, we incorporate relevant constraintIn our economic scenario constraint from Br({{formula:492c9323-8561-431f-bb87-8f0437d8d75c}} ) is not relevant, because it is dominated by the WC {{formula:db5c29f5-91ca-446d-9de5-e357ed376f7a}} . However, in this scenario, the WC {{formula:dc125877-e6da-4064-b0f5-eb966d5b519b}} gets the NP contributions for {{formula:f6eda25a-ffdd-47e7-98f5-3462df462e4a}} transition whereas the WC {{formula:52ad5c52-8753-4481-90ef-ab27af102a2d}} receives the NP contribution for {{formula:b5c6c6d3-46c2-43d1-9ffc-b9b479dc300c}} transition. from {{formula:fffe5c43-07f2-495e-a59f-27b51014649c}} oscillation data {{cite:21487680a8667983164839fc715cb4e4be6e3190}}. Additionally we have also imposed the constraints from the leading angular observables ({{formula:d0323566-d532-4703-8d3c-b2b6b7cdb120}} and {{formula:8334c82e-89e7-4195-b65c-c6ce4df99568}} ) of {{formula:1b1be34a-346b-452e-ba25-ee9246ebc5e1}} decay mode {{cite:73c9b13b527c70c657cab6b94b33f70539cd870d}}. In the left panel (REF ) of Fig. REF we have shown the allowed parameter space in {{formula:ea164f91-6a67-42cd-8f57-62747f909c8a}} vs {{formula:f4c0523e-cda6-45b5-8f6d-9d29f55b5d37}} plane with allowed values of the mass of {{formula:8a862e48-2406-4f27-b39d-40265f2dc1d8}} boson (indicated by different colour code). This pattern can be explained if we consider the similar argument as given for the Fig. REF . However, in the case of Fig. REF apart from the case of {{formula:c7379a4d-2e8d-4d55-a9b9-7245eea1b88b}} , we have to consider the NP contributions to the WCs {{formula:b1a0e129-6595-4ce7-b154-33a43c7ed544}} and {{formula:0a4f43b7-63ef-4d32-b13b-9bd4b0978e2c}} for {{formula:1d833a55-f1b7-4f99-8caf-9e171970e7c1}} -meson decays. If one looks at the Eqs. REF and , then it is evident that the NP contributions to WCs {{formula:9cf1bf4f-ad8c-48bd-bdda-e92e2c87d3ff}} and {{formula:1e2380b1-5cc7-4048-8941-1c96a5b2a78d}} are proportional to {{formula:ca458397-ab59-4401-93ca-384e3212eea6}} and {{formula:ed1e396b-d6ba-4f4f-9eba-73567047cfe1}} respectively. Therefore, if the values of {{formula:1a663970-9a1f-45a4-9a48-5cf0847c7d69}} and {{formula:9771e233-282b-4518-866e-c7755ec87c3d}} are increased then in order to restrict the numerical prediction of the observables within the allowed range, the values of {{formula:7535aeea-09d0-4868-8c21-ce397c2bc6b1}} will also increase to suppress the propagator effect and it is depicted in the left panel (REF ) of Fig REF . Similar argument also holds good for the right panel (REF ) and it is evident from the Eqs. REF and . Hence, following the previous argument and from the Eqs. REF and it is clear that with the increasing values of {{formula:489a5977-2645-462a-916c-adec3c64e267}} the values of {{formula:4813b049-8d13-48e6-b68c-b14a84d386a1}} will also increase and it is reflected from the right panel (REF ) of the Fig. REF . If we relax the constraints from angular observables of the {{formula:6acc1c3f-4d73-4a43-86f5-0d2fd37aecd2}} decay mode, we expectedly obtain an enlarged allowed parameter space and these additional points are depicted in grey in both the panels of Fig. REF .
| r | 4ae5bc99ff90f66130d2038f5d806140 |
Moreover, to demonstrate the effectiveness of our blob-level curvature-based SDF description for robust change detection, we provide another baseline (FPFH in Table REF ) with a point-wise variant of the proposed method by replacing the 3D voxel validation step REF with the point-based FPFH {{cite:b9909dca7bd15831acd5249eae95aba645c4f68b}} feature matching using the Open3D {{cite:81c79c065057a5f3cd71ff5738610716474c1246}} implementation. As our selected key voxels are not located on object surfaces, where off-the-shelf point feature extractors cannot be directly applied, FPFH features are extracted for every point in the original point cloud that contributes to the fusion of the SDF. A point is marked as changed if its source FPFH feature cannot be matched in its target neighborhood.
| r | 264137daceb5e078a780e491a3eb698d |
Recently, there has been a line of work that argues for the geometry of the loss landscape as a major contributor to generalization performance for deep learning models. A number of researchers have argued that flatter minima lead to models that generalize better {{cite:85f471751f20ad891c1bd72eed0a8266a271afed}}, {{cite:5bf284d5bac915c99e8abcc5c820bf6e6943e77f}}, {{cite:acfd66361cf6d219117b5e90d128229081c0e212}}, {{cite:6581182c5a516e8b6a624cf95c00a3ec1d9c69bc}}. Underlying this work is the intuition that small changes in parameters yield perturbations to decision boundaries so that flat minima yield wide-margin decision boundaries {{cite:820bcc53980073c35153d81c04c122aa45fb8048}}. Motivated by these investigations, {{cite:c906f47becb9ad493cb7d2b75d02b57b8a718e47}} propose an effective algorithm - Sharpness Aware Minimization (SAM) - to optimize models toward flatter minima and better generalization performance. The proposed algorithm entails performing one-step adversarial training in parameter space, finding a loss function minimum that is “flat” in the sense that perturbations to the network parameters in worst-case directions still yield low training loss.
This simple concept achieves impressive performance on a wide variety of tasks. For example, {{cite:c906f47becb9ad493cb7d2b75d02b57b8a718e47}} achieved notable improvements on various benchmark vision datasets (e.g., CIFAR-10, ImageNet) by simply swapping out the optimizer. Later, {{cite:ff0f54c9843fd2f33d73ae2690e8981a13378900}} found that SAM improves sample complexity and performance of vision transformer models so that these transformers are competitive with ResNets even without pre-training.
| i | 6ff1074ba4536eb1d45d23007c9a6e6e |
More recently, deep learning methods have become predominant for guided super-resolution. These approaches work by parametrising the non-linear mapping from the two inputs — guide and source — to the target as a convolutional neural network, and learning its weights directly.
The deep joint image filter {{cite:c85beb8ce52bfceadfefccb9890531e977abb6ba}}, {{cite:4e961e36579775a93117e6c87fd70f0076b8b79f}} feeds the upsampled source and the guide directly into a standard encoder-decoder architecture. The deep primal-dual network {{cite:0c590d92c5af8a6c56e67c20a121770772f65b49}} follows a similar strategy, but outputs a residual correction to the naively upsampled source. Additionally, the output is refined with non-local total variation, unrolled into a sequence of network layers.
The Multi-Scale Guided network (MSG-Net) {{cite:c1953ba754ed1e9284d62c399a292b53b0c37a95}} implements a new strategy, to encode only the guide, extract rich hierarchical features at different levels of the encoder, and append them to the corresponding levels of a network that decodes the source into the target through a final reconstruction layer. This integrated multi-scale guidance from the guide to the upsampled source allows to resolve ambiguity in depth map upsampling.
This design has inspired several other works: PMBANet {{cite:2cef82727fd1ac979e8d67381de23ccc1885e9af}} adds multi-branch aggregation blocks; the Fast Depth Super-Resolution network (FDSR) {{cite:c1be31e04412a4124faf47a71cd2ab3dad5fc869}} adds a high-frequency layer to extract fine details from the guide, and strives for a computationally efficient, yet effective design. DepthSR-Net {{cite:72c8cc01154c1aa3efde7a1b3a9b64dc708c5cdf}} integrates the idea in a residual U-Net architecture {{cite:87216fe5c6556078a6870cc61b1cd7568a69a1a0}}. First, the source is naively upsampled to the desired resolution, then the residuals between this naive interpolation and the corresponding target are learned using the hierarchical features as input pyramid in the encoder structure. In {{cite:98410beaf185e522859c7d4948c62a920fe65afb}}, an explicit coarse-to-fine cascade of networks is used to iteratively refine the output and progressively add high-frequency details.
In {{cite:26ac17a65bc4725dc8b6e9b9c378bfe39d5f384f}} two networks are trained collaboratively, one for monocular depth estimation from the guide and one to super-resolve the source. Furthermore, there is an auxiliary structure prediction task to mitigate differences between depth and intensity discontinuities.
Also in a very recent work, {{cite:bdf29a68986ff938bd97ecfc55a46648f28f01ff}} explores learning depth super-resolution from unpaired data, using a learnable degradation model, and surface normal estimates as additional features to obtain more accurate depth maps.
| m | 25c3b8479924605b8ef01e7e2c19fbf9 |
[leftmargin=*]
Political books {{cite:829a78be455016cf3a41f7987a505e5a86f82c75}} ({{formula:470a5822-1f10-40ee-b92e-00b72eafd837}} ) – network of Amazon book sales about U.S. politics, published close to the presidential election in 2004. Two books are connected if they were frequently co-purchased by customers. Vertex features encode the political affiliation of the author (liberal, conservative, or neutral).
Primary school dynamic contacts {{cite:15d2845065eb4d5761674e3fd7c38f81166760a5}} ({{formula:a3cc8620-26ec-407f-9978-8009bf520b34}} ) – network of face-to-face contacts amongst students and teachers at a primary school in Lyon, France. Two nodes are connected if the two parties shared a face-to-face interaction over the school-day. Vertex features include class membership (one of 10 values: 1A-5B), gender (male, female) and teacher status encoded as an 11th school-class. No further identifiable information is retained. We choose to analyse just the second day of results.
Facebook egonet {{cite:3efd7ad3258fe093ef8567d69e4f773b90317341}} ({{formula:5be003d8-3e20-4a2b-a600-12ce51683e90}} ) – an assortment of Facebook users' friends lists. Vertex features are extracted from each user's profile and are fully anonymised. They include information about education history, languages spoken, gender, home-town, birthday etc. We focus on the egonet with id 1912.
| r | 2bee8c15bba8193d0351edbcdf9ad546 |
Reachable sets originate from the evolution of set of states in system dynamics. Therefore there are two major system model based methods to approximate reachable sets numerically, i.e., set shape approximation{{cite:9a9e2cade972f4fc42d4c123543eb84521c14f37}}, {{cite:aafcec79c8faf5a362e4996d3045defaf5adae76}} and system dynamics approximation{{cite:3500be12925c4d3389b52687c7dffc24141afe24}}, {{cite:e3b8636c693fd7b033af7897c2af591d8abc9506}}, {{cite:1598a412f34df52940fc0be5f9c4f7a349e9e1e8}}. Apart from model based methods, data sampling is another alternative to approximate reachable sets{{cite:3b2e003eacd6ca482841ca393d61acf6d40a9129}} or their control invariant subsets{{cite:ace6350d0dffd099a5b9ec8b02f519fc513364f3}}, {{cite:e3e6cee3791e85ba8e32c98cb0eda0ff64753266}}. Set contour approximation{{cite:0a64c53fe2f970636012971072d28b6461b39a6a}}, {{cite:b32b29cf8f14219e60579685b4e10a13080a1bfc}}, {{cite:9d9876e6a6fba4da3d746d05f2e3c3823bc50615}}, {{cite:0e2e90816e3b6b1b4f6e6a3fb31427136dab2929}}, {{cite:e1dbc2e06c383b9fda03768e98832fb8a3c0dd10}}, {{cite:9b534e897cd83d2bf1db3a17f86d7a2776795d0a}}, {{cite:fc495584ada3c0a1ec39a02e362d7c366e47b616}}, {{cite:d12ac09745cb3cf48f433f29f2570d363792813c}}, {{cite:e6af617b2d566544b49dffabf468295cb254a575}}, {{cite:ec235683a084cdfc572c746eb9c150878f89a7fa}}, {{cite:aafcec79c8faf5a362e4996d3045defaf5adae76}}, {{cite:9a9e2cade972f4fc42d4c123543eb84521c14f37}}, dynamics approximation{{cite:83fcf9c130924c8265d88ba21c4012a34c347f2d}}, {{cite:2e32a079eab7e05739458734e33bb452e872a0f3}}, {{cite:fb19bd1fada3c1153faaed2946ce2c1ead1d7d6f}}, {{cite:e2235d704048bd1c1e0a1d4aa5f73929583aa464}}, {{cite:6c76652e92057bf6c1cc38725b6e7ced3e217b6b}} and sample-based approximation{{cite:3511821ffd009765db1631959634a3914bde394f}}, {{cite:ace6350d0dffd099a5b9ec8b02f519fc513364f3}}, {{cite:e3e6cee3791e85ba8e32c98cb0eda0ff64753266}}, {{cite:a932fe496b0d10c63568d7ab3962ccfe1e87f997}}, {{cite:3acc51b9db5a97f0cd2353a3f19c848a1191b527}} are all viable numerical options. A summary of methods used in primary studies are listed in Table. REF . Academic competitions for reachability analysis exist, such as ARCH COMP{{cite:f07de0b86638714dd76f3576919bd266dc219b04}}, which is a competition of scientific software in the context of algorithmic verification of continuous and hybrid systems.
{{table:c47bc28d-2673-4dea-bf10-fa05b8f5609c}} | m | 6cf941151090971e9ec54fb3af5e0ebd |
Influence of average pooling. In contrast to the original memory networks {{cite:ff116feeae98805127d239aa351b8fe4dc09993c}}, we add an average pooling layer inside the memory layer, which takes advantage of the spatial organization of the information in the video imprint. Figure REF demonstrates the influence of adding the average pooling layer. We can see that the recounting maps are smoother and more reasonable, especially for TCG based video imprint. In addition, with benefits from finer resolution of input feature maps, the epitome based video imprint can hold more spatial information, and the recounting results are more reasonable than TCG based video imprint.
| r | cc6fca14a3d844d870281354bac32e77 |
The recent work of
{{cite:bebdb4eee447dcf00946fa84f30d36cf2a8d6e05}} proved that the {{formula:d6b05974-93bf-48e4-afe3-81364c7f028b}} norm of the error is bounded as {{formula:0e39cdb6-714e-40fd-80d1-3953071dcbe7}} , for a two layer neural network with ReLU activation functions in kernel regimes. {{cite:ea544b9e26404403e81a5a3c45e4c474b1917933}} decomposed the {{formula:7b075ab7-a884-4a32-81cd-7fd4383c3822}} norm of the error into a series corresponding to eigenfunctions of the NT kernel and provided bounds based on the corresponding eigenvalues. our results are stronger as they are given in terms of absolute error instead of {{formula:ffe829a9-a47e-45ce-b878-2dd3a312c2ac}} norm. In addition, we provide explicit error bounds depending on differentiability of the activation functions.
| d | b5ce89dbe7b3a3fdd0a1b8a001236ed7 |
The aim of this analysis is to model the energy distribution of the sample of 254 FRBs detected at CHIME. The FRB population model used here is presented in {{cite:756ff4895e3984302e52a0b77398759f1fd98e9a}}, and the reader is referred there for details. We have modelled the intrinsic properties of an FRB using its spectral index {{formula:422c2b42-0bfd-44d3-ae27-b4a1632cacb4}} , energy {{formula:943527d8-998c-4768-9667-e67d758e5eea}} and intrinsic pulse width {{formula:80f84867-b972-4863-8c66-7d3bd944c1ef}} . The pulse width does not figure in the present work, and we do not consider this here. We first consider {{formula:509269b9-7410-49e1-a108-e3a166484c60}} the specific energy of an FRB which is defined as the energy emitted in the frequency interval {{formula:d3af4084-c986-45c9-b999-80cdc3115578}} centred at the frequency {{formula:7dcf127a-4467-4daa-9f4a-343732145bb8}} .
We model this as
{{formula:b527e6ce-2e06-4779-acf6-cd0cc24f53e9}}
| m | 1ced39b8d460f35500651985d5b2ebc0 |
Avenues of research have begun to open up on how to prevent this hallucination and how to inject additional knowledge from external sources into the transformer-based language models. One promising avenue is through the integration of knowledge graphs such as Freebase{{cite:fee0b520d5553853e71bae65ba8f83a523ca5f0e}}, WordNet{{cite:3c331ce09dc953dde18a8e005ccadcf004c24ca8}}, ConceptNet{{cite:21fa504162457e93bc787eee00d073bf1862b5bd}}, and ATOMIC{{cite:3e50e52476efd3653120ba711642e34346ed5c5f}}.
| i | 60806d93f9afa24faf95522fc367f383 |
The motivation for this paper comes from the close connection between spaces of vanishing traces and the pointwise multiplier property of the
characteristic function of the underlying domain under consideration, and more particularly, the importance of this connection for interpolation for spaces with vanishing boundary conditions.
The first interpolation theorem for such spaces is due to Grisvard {{cite:d8f4fa35bb934ad4ae3f7a12af041a52de1c9213}} for {{formula:0d9b1a2c-3e93-44d9-a96f-852cbe8bf529}} -based Sobolev-Slobodeckii spaces and the real interpolation functor,
which he subsequently extended to the {{formula:6d26d09d-b41d-4156-9ef7-7411c8c0cc9c}} -based setting in {{cite:c3f65a81c263ab0ed6a141318ed4ec91a8fb21b4}}. The corresponding result for the Sobolev/Bessel potential scale and the complex interpolation functor was subsequently obtained by Seeley {{cite:46d4c37b1aeb3567e39c632a6f50bbf1bafd1f04}}, but also see the more recent works {{cite:89f2b41f436e2ac4d7b14e437e7b31e21840c221}} and {{cite:d56ed7907ff7c4a6e0ae2d049ca949decd3510fb}} and the references given therein.
| i | bf62dfa0408d019c5dffc6ecd71cae3c |
Similarly as it has been demonstrated for liquid-infused porous structures with regard to confinement-controlled phase selection {{cite:dffc925c26a9350b015a5f431ee9ebec8c41c327}}, {{cite:fce43892a6fb494797ff5ab7b3792a670c2aeda5}}, adaptable surface wetting {{cite:cf53fc5254d24fa3d5d33deaa4072c98f4b89e18}}, {{cite:23bd692b86f935d5a8fea4c8c33e4a8691661b0c}}, topography {{cite:4c4af2cad2e81926fab3116a02adf25fa9821b19}}, photonic {{cite:ef12d50873c1dff3ca152cdf324f5fcfd63bab90}}, {{cite:72f3dba074a53f394848358f535dca16e67383a5}} and mechanical properties {{cite:8b4f866df0b068b631d7ef7b4d977b7bf35476be}}, {{cite:4642963219b099aedfe6159b54f37401cae0f872}} our study indicates that electrolyte-infused nanoporous solids allow for a quite simple fabrication of materials with integrated electro-actuorics.
| d | 3f45bddd81cc9ce795057deb304036b2 |
Nevertheless, beyond all the problems surrounding quantum gravity, there is an extra fundamental question concerning the application of quantum theory to cosmology. As we know, in the usual Copenhagen interpretation {{cite:35d074dc8a311409ee13f326ede3a0aeba19cd86}}, {{cite:071aa89e6bc40f0935b45dca03cb83b0ac07256f}}, {{cite:a20c33c41e94d29f71a1e367becfb844588e9e79}}, the wave function gives the probability density amplitude for an external observer to measure one of the eigenvalues of a Hermitian operator describing an observable of a physical system in state {{formula:ce1facf0-8bd9-4f6f-a9ea-39e20d26ded8}} . In the measuring process, the system must interact with a measuring apparatus. In the quantum description of the whole process, the total wave function describing the system and apparatus bifurcates into many branches, each one containing one of the possible results of the measurement. However, at the end of the measurement process, just one value is obtained; hence, the total wave function must collapse in one of the branches. This a non-unitary non-linear process that cannot be described by the unitary quantum evolution. The intervention of the classical observer imposes a break on the quantum description, bringing to actual existence the many potentialities the quantum state describes. Of course, one cannot apply this picture to the Universe as whole, as, by the definition of Universe, there is nothing external to it that can bring to actual existence all the potentialities described in a quantum state of the Universe. In this scenario, quantum cosmology does not make any sense; it cannot describe the objective reality we experience in the world; it is an empty theory. One should then abdicate to apply quantum theory to cosmology, in order to use it to solve the classical cosmological problems. This is a good example that corroborates an important criticism of Einstein's concerning quantum theory in the Copenhagen framework {{cite:8e76f3eb79c664faf1eb7f7fb8abba7e13879d9c}}: `Contemporary quantum theory … constitutes an optimum formulation of [certain] connections … [but] offers no useful point of departure for future developments.'.
| i | 97677cfea5025979709017b25da459de |
Secondly, we will prove that inequivalent families of solutions
correspond to inequivalent embeddings (not related by conjugation in {{formula:62eaafc0-9db5-4dcf-9460-1b5b9beab01a}} ).
The problem of determine all possible three dimensional subgroups of a
simple Lie group has been solved by E. B. Dynkin in {{cite:1931a7d16e3c4bbf1c4b62d2153fa57cdc061fb8}}. In
particular, in that paper, all possible three dimensional subalgebras of the
exceptional Lie algebras are written down.
| r | 1484f2a91d2432a03363b23986baaf26 |
The possibilities of detection of wormholes have been studied in {{cite:6dc480fc95ba2218234116e1dbc8c21cc6327d4b}}, {{cite:09c8afcdf561885fe29da8d23e9f2c216a875312}}, {{cite:73fccd62353811c0d6cfa442606d4fe6b73ce7ff}}, {{cite:871e26e0ac1c2a3c3e4a463dcaa26a3e633128cd}}, {{cite:e73b725f5d460beba4194252bb2229bd798b24cf}}. A possible way of observing a wormhole may arise from the idea of the flux being not conserved separately in the spacetimes joined by the wormhole structure {{cite:8f74d276dd16f86111dbad10a7b82778a13afdfb}}. The idea may find application in studying this effect of wormhole on the orbit of stars near the black hole at our galactic centre. The lensing effect due to wormhole, identical to gamma ray bursts can suggest a possible upper limit on mass of wormhole {{cite:5614cc159f15d5f487ef38153dbf724cb25b3f66}}. There may be a possibility of radiation pulse emission from wormhole which may be a possible mode of detection {{cite:235ec7f0f250194265c534f10cf82f1ae907c1db}}. The investigation of scattering properties around a rotating traversable wormhole can differentiate it from a black hole either by exhibiting super radiance or non-identical quasinormal ringing at dominant multipoles {{cite:ef4ccc8af2b79c77b33afd0ef6d56810dae71e2a}}. Also, there may be existence of background quasinormal modes with a long lifetime for wormhole having variable redshift function {{cite:1fe3372a8385a6ad1cfec6e22d8221a8ffd32903}}.
| d | 40d61b791982ac0ea9447636d5369682 |
Deep Reinforcement Learning (RL) is a powerful general-purpose framework for learning behavior policies from high-dimensional interaction data, and has led to a multitude of impressive feats in application areas such as game-playing {{cite:57c18c783fac11fdfa5da7ab99fd01727f1e0dfc}} and robotics {{cite:905244778d73c649b05cff7789501dd677d9eec8}}, {{cite:0b9bfd176e567d5623eb5ca9579202132a6a4d91}}. Through interaction with an unknown environment, RL agents iteratively improve their policy by learning to maximize a reward signal, which has the potential to be used in lieu of hand-crafted control policies. However, the performance of policies learned by RL is found to be highly dependent on the careful specification of task-specific reward functions and, as a result, crafting a good reward function may require significant domain knowledge and technical expertise.
| i | dce22aa33a834588645c01f3f38281ad |
One-stage methods directly predict the bounding boxes and most of them adopt the extract-and-fuse pipeline. RCCF {{cite:a1501f404714adb8c47e329d0fc66da424edd075}} uses a cross-modality correlation filtering on visual and textual features, and ReSC {{cite:d4f200eb1b083133e2373abb586e1d65db6edaca}} proposes a recursive sub-query construction framework to handle complex queries.
With the success and popularity of transformers {{cite:c57e087d363425bf8fc177b7c88418e44e912646}}, recent one-stage methods have adopted transformer-based fusion modules and have achieved state-of-the-art performance {{cite:8cf6b576b58b51832f462873bb62dd9b6aa5093d}}, {{cite:fda0de2235bee38f106179af479dc94d856758fd}}.
| m | 419b5ab9d934664d199dfa86a9b9c9ba |
We can see that {{formula:2a4861b4-e856-4543-86cc-133b66e13528}} -descent condition (REF ) means that the graphs of quadratic functions {{formula:7c94d4ff-50b6-4865-826e-27d74988a12a}} lie above that of {{formula:a8627ccb-1f10-409a-9b33-294d7a37546d}} for all {{formula:9b307e2a-2db9-4dcd-806c-336978f79411}} This condition is equivalent to the convexity of {{formula:5424686c-46d5-4ebb-a8be-d12c0a0b8355}} {{cite:f48a3cb1061547d6a4995f53f6c1dff4ea33bc50}}, while being a direct consequence of the {{formula:18f4c620-da50-478f-97e2-8a43d64460a7}} -Lipschitz continuity of {{formula:ff5a22a5-b233-41fc-8c2a-14dc73d615da}} , i.e., the Lipschitz continuity of {{formula:cac07532-ec56-429f-b15a-5036772ed132}} with constant {{formula:ed6feada-fd23-422e-8460-de238aadb31b}} ; see, e.g., {{cite:c9c72b06aba8fecb16b1a04517db97ff233e1de6}} and {{cite:88ba7460e461933d578a9c1ed53391d1992fe656}}. The converse implication holds when {{formula:6f6cbf25-0e38-479d-84fb-b45791e735db}} is convex {{cite:11006d222df5a592a31ff69bcc51474d0fa608c4}}, {{cite:f48a3cb1061547d6a4995f53f6c1dff4ea33bc50}} but fails otherwise. Indeed, the function {{formula:d7d31187-65d6-41ce-a60a-a67a454a9a11}} does not have the Lipschitzian gradient, while satisfying the {{formula:ced0931c-bcfa-4505-93d4-e2c6c9113ef9}} -descent condition with {{formula:80333fc2-d295-4b80-a07b-839c13d0450c}} since the quadratically shifted function
{{formula:dbe7423c-c6f7-4691-afa7-45d9276c264a}}
| m | 15fafabab1a7bd4f18b60fc382aabb7c |
Influence of Encoder Backbones.
Table REF -(b) compares the performance of our model with different architectures, pretrained weights, and resolutions.
First, we replace the video transformer in PAVER with TimeSformer {{cite:13e4f71d78487e0934df38521e50fc9d8a552008}}. It shows
inferior performance mainly because the model is trained with a larger temporal hop size, as capturing subtle movement in scenery is essential for better saliency maps in the Wild360 dataset.
When we use DINO {{cite:3de152606f15e4d124178b1d385bbaa61e9bb503}}, which requires even no labels as the backbone of our model,
it shows better performance compared to the SOTA models.
The model with a smaller patch size reports better CC by 4%p, which is presumably due to higher fidelity of the saliency map.
Using ViT-Ti/16 {{cite:a0d7f46b068d6a6671a53887fde6ae0566643041}}, the performance drops by 6.6%p in exchange for 15{{formula:d2e716d0-4347-423f-8461-23b6483d82ae}} fewer model parameters.
This is still better than existing SOTA models for all three metrics.
| r | bf68e51b1d59cdb6f6c5409107efd06a |
On the other hand, associated to the Legendrian link {{formula:e96acc6e-ceaf-4080-9fc5-549956e46614}} with additional data {{formula:31070553-8ae5-45d7-b786-5a82808a91e2}} , Floer theory assigns a differential graded algebra {{formula:57b8fd20-ef04-42ab-8464-2036cb5e8fa8}} (Section REF ), the Chekanov-Eliashberg DGA {{cite:b7c0568fa37a082870ef6c358fa09fbe5ed32124}}, {{cite:a444b04b2db07492892bd9a3b7e3338050679a66}}. Morally, this algebra is generated by the Reeb chords of {{formula:2943508a-ece5-44af-a71a-e91407cc4899}} , whose differential counts holomorphic disks in the symplectization {{formula:5f13862b-4821-4f54-ad9c-62e39aab7865}} , with boundary along the Lagrangian cylinder {{formula:b5ab3119-5d3b-45d5-8d0a-9ea30d458fa3}} , and limiting to Reeb chords at the boundary punctures.
For any base field {{formula:cd109c9a-3987-487c-90e9-206c7e612338}} , the {{formula:8f2007b4-fd81-4fb3-8935-fb09f59cc97e}} -valued augmentations of {{formula:abda3c26-599e-4b03-878f-7d650c6db991}} form an affine algebraic variety {{formula:0e0a355f-d08c-4c5b-9eb2-7a9d073f9d41}} , the augmentation variety (Definition REF ). Depending on the choices of initial data {{formula:a388679e-19eb-4096-9071-da2f5b8bc96d}} , two versions of augmentation varieties are considered: {{formula:6128e151-2304-4f6a-8561-b0efe5182760}} and {{formula:90ff6d48-e389-444a-9c27-9dbc05efa36a}} (Remark REF ). For a {{formula:1662df77-56b5-494c-940a-dfe931795734}} -strand positive braid {{formula:7c261455-0d4b-4cf8-b13d-cdcf41169d57}} , the augmentation variety {{formula:ad3c66bf-e075-4467-8245-38ed9e0306f1}} admits a natural action of the torus {{formula:14a1d625-2e61-408b-a64d-b26addd96ea3}} (Definition/Proposition REF ).
| r | a849526d19b77b587ad038a33b290c77 |
In the last decades, evolutionary theory on complex networks has attracted significant attention from scientists in many areas, from economy to physics {{cite:b60ec111054bd36e75780c16ef59fdaff6208979}}, {{cite:eea36a7f0418e128028229e54c41d1b51eb5a5af}}. Prisoner's dilemma (PD) is a game in which two players acting selfishly will ultimately result in a suboptimal choice for both players. Two players, separated and unable to communicate, must each choose between cooperating with the other or not. Thus, in the game, we have two types of players, i.e., a cooperator (denoted by {{formula:057c5676-47e9-4bb0-b7c8-f695daca8737}} ) and a defector (denoted by {{formula:280d0db5-42ea-49e7-94d1-ae36aa6bbec4}} ) {{cite:32b78b170ec779b54e7558b30bf4d8e38b1e23bc}}. Cooperators benefit other individuals at some cost, whereas defectors attempt to exploit such shared resources.
| i | 6c1b1b5b057b905632fea7bdb50b7ee2 |
In training, we use the smooth {{formula:4eebafe4-3251-41a8-a792-845d2ae04da0}} loss due to its robustness at disparity discontinuities and low sensitivity to outliers {{cite:fd38973d76af2ab5322ec47659f70ce32c0a0e04}}, {{cite:0f02b3654d5035b9f3f85e930f3c6bb6be492747}}. Given the ground-truth disparity map {{formula:7ca8ec40-cfbb-4de2-934f-2e753acdce5c}} , the loss is defined by,
{{formula:e4598979-b3f1-412b-a6ea-7ebf7a11a4d0}}
| m | 4b0365942953fcce238be67414b41469 |
Fact 2.1 {{cite:c299bc34d714ca852fe369989f99494152b4f1ae}}
Let {{formula:4db27963-4631-456b-bdc6-069909d01421}} , {{formula:9a8563b8-b4f0-43b2-b5dc-fbd8f83c4dc0}} , {{formula:5e67d72b-19ce-4601-99fd-9e2eb2108f30}} , and {{formula:fb71e76d-edbe-4cc9-8469-3b63fc321d99}} be sequences in {{formula:05339640-0cf6-4b22-88e6-5a7fa6ad0087}} such that {{formula:6f7c2a96-a3e3-4aee-bf9e-25639b6a7eab}} , {{formula:9e90aa34-8c92-4a39-8293-fcfb15f225df}} , and
{{formula:69a31f57-2adc-482b-a5a2-a70e127a833c}}
| r | cf19359624cb1af41d2bc75d209e2ce2 |
One of theoretical issues to study valley excitons is to include external-field
interactions to the exciton model. For a Wannier exciton, which consists of an
electron and a hole bound by the Coulomb interaction, the system is
similar to a hydrogen atom in external fields. The electric-field interaction
can be included by the dipole-field interaction and the magnetic-field interaction can be
included as the vector fields in the kinetic momentums of the electron and hole. For
the valley excitons in 2D materials, the exciton Hamiltonian is constructed by the
Bloch-electron wavefunctions solved from diagonalizing a Dirac Hamiltonian or a few-band
tight-binding Hamiltonian{{cite:f4ad77f6df5e5ed8332563151b16c4495a5c74eb}}, {{cite:1028555c01d4c4914da87054aa53396f94817106}}. However, the
Dirac Hamiltonian or tight-binding Hamiltonian with including external-field interactions
is much more difficult to solve, such that the exciton Hamiltonian under external field
also becomes more difficult to derive. To simplify the problem,
approximations are necessary. In fact, a similar problem had been intensively studied in the fields of relativistic few-body
physics{{cite:6ba23af4c9f5052483c5bd0ac3baf378c1978bc7}}, {{cite:58f4126f89dc792b9f6c163f3835f6c4ab95a484}}. A relativistic particle which is
described by a three-dimensional Dirac fermion under external fields can be reduced to a
nonrelativistic particle with relativistic corrections in low-energy limit by the
Foldy-Wouthuysen (FW) transformation{{cite:58f4126f89dc792b9f6c163f3835f6c4ab95a484}}, {{cite:a5f8bfb3071e1341cdcfc267baaf2354bbef3129}}, {{cite:a69290b2e99b284a4d411191d54446737ab5cdde}}, {{cite:370b62f25a0ecb7bed2b362a38bac1f5b5c2cdf5}}, {{cite:bb1947516111f894e281c152ec80de809d74b6a2}}. A relativistic few-body problem,
such as a real hydrogen atom in external fields, can be studied by solving the
nonrelativistic Hamiltonian with including the relativistic
corrections{{cite:0be8eca21d6b477282a327d7f47189fb3b4453bb}}, {{cite:94186e0400b2ee7e0f0686d5550040eef0f5028e}}, {{cite:894c50e69800837573ebdcc4cb9a12ff4bbcf616}}.
The approximation scheme can achieve extreme accuracy in prediction of energy spectra and
fine structures. Following the same strategy, the 2D Dirac fermions can also be reduced to nonrelativistic form
by the FW transformation, and the valley-exciton Hamiltonian can be approximated as the
Wannier-exciton Hamiltonian with band-geometry corrections. The valley excitons in
external fields can then be studied by the corrected exciton Hamiltonian.
| i | 48cfc7957f64669ad206f081edd16951 |
First-principles calculations were performed using the Vienna ab-initio simulation package (VASP) {{cite:bb4638e85e31040e0b348a59f395094754a481de}} within the framework of projected augmented waves {{cite:9ae73d52ca6a27936ef8b5364e8064b7055983fe}} and Quantum-ESPRESSO (QE) realized in the basis of plane waves.{{cite:021cbd6d9c46b2a3a7ea24138cafd2d1e7b2bdca}} The calculations were carried out using local density approximation (LDA) {{cite:749ef28a85a010ff43eff6ea409f21191b799814}} and generalized gradient approximation (Perdew-Burke-Ernzerhof, PBE,{{cite:aa1b57daca5c75505d945c0b83c0b22b550b5a7d}} and Perdew-Burke-Ernzerhof revised for solids, PBEsol{{cite:dbb4b74ca0b44089c4c5ddfe78d333f522854e0c}}) for the exchange-correlation potential. The calculations in QE were performed within ultrasoft and norm-consrving pseudopotentials.{{cite:f045898ae33eb01a6df798f168e2e45865f4b0a6}} For all calculations, the valence state configurations were {{formula:ad6b7ebd-19a0-4cb7-a5e2-2f84196ed69b}} for Zr and {{formula:06c41597-faec-40fc-8299-26cce4efdc3b}} for I. The plane wave cutoff was set to 500 eV and 900 eV for VASP and QE, respectively. The Brillouin zone was sampled by a Monkhorst-Pack {{formula:62454f90-3668-44c3-80e1-02826c4086d2}} -point mesh,{{cite:9837f4d8e720e2c401d62364344bfcafa0301de1}}{{formula:e9239c60-c34b-4a84-9b08-f4c3c332e3b2}} for the T{{formula:737120f7-c732-41bb-b4e4-37b86b1ea64e}} and 1T{{formula:abfe7bc4-b910-476c-96a2-ff9817a78740}} phases and {{formula:153f35c6-34d8-4c6a-8c9b-079714ece3f9}} for the T{{formula:fe594d3c-cc06-49dd-818d-23ab9edeb1e0}} phase. The convergence criteria for the total energy calculations was set to 10{{formula:a3ba8e6a-a51a-46e1-b18a-8aec42fc466b}} eV, and all structures were optimized with the total force convergence criteria of 10{{formula:630155ab-f008-4522-b847-e4581fc8dcfb}} eV{{formula:cb391994-d4e8-4648-bff1-cb87b8d667f6}} Å{{formula:e5bc764d-0ac1-4f38-befd-be3892b6efe9}} . The optimized crystal structures used in the main text are given in Supplementary Table 1. Electronic band structures of the T{{formula:539f0e15-2093-4373-88ee-c95777978822}} , T{{formula:1a118ec5-0123-48c8-a623-8441698d5f94}} , and 1T{{formula:60346111-864b-4a64-b24e-4427c8896bba}} phases calculated with LDA, PBE and PBEsol are shown in Supplementary Figure 1. The effect of spin-orbit coupling was shown to give minor changes (see Supplementary Figure 4). Electronic correlations in the Zr {{formula:a52e2c0b-8aff-4d86-b051-1709c967c5ec}} shell were checked within the LDA{{formula:c91e8656-f3d2-4767-819d-8d935e342f7c}} method{{cite:e364d5d2502e8121b4ecf5e448bf80fce628af99}} and shown to give minor changes.
| m | 45c16d9fe01dc4f10ec9ba35c6753f71 |
The MLR-SNet learning algorithm can be summarized in Algorithm REF . All computations of gradients can be efficiently implemented by automatic differentiation libraries, like PyTorch {{cite:a393b564db5438411d81e146547aa1fd91d8f07a}}, and generalized to any DNN architectures. It can be seen that the MLR-SNet can be gradually optimized during the learning process and adjust the LR dynamically based on the training dynamic of DNNs.
[H]
The MLR-SNet Learning Algorithm For SGD
[1] Training data {{formula:0523e5a2-583a-431a-84a4-73a3ee1319f1}} , validation set {{formula:64e5f096-5403-40cd-b905-64fa94bef68f}} , batch size {{formula:76893672-1cca-4564-a964-6c5d31e231d2}} , max iterations {{formula:f4c67357-5cb2-42a9-8b04-f16f53982e74}} , updating period {{formula:3be4c827-9f57-4df7-8608-a2b2a72980dc}} .
Model parameter {{formula:45c8db0f-2ea8-49e1-a000-9184738a045c}} and MLR-SNet parameter {{formula:be62362d-5cbb-432f-a219-e956b279fe2d}}
Initialize model parameter {{formula:27df406f-8459-4196-9787-b43bd357dc8e}} and MLR-SNet parameter {{formula:2c1e0e75-bf6d-416a-935a-b174b5975591}} .
{{formula:2e074375-a994-43b9-8c4f-716792d0059f}} to {{formula:a9a7a2d7-a31a-4c2e-9e9f-34bdeb5c4058}}
{{formula:7e226b80-a4ad-4130-a09e-f274ce1dac6f}} SampleMiniBatch({{formula:f2743dad-784c-40f6-87a0-523b3ba006a3}} ).
{{formula:4677ab32-8637-4dfc-8943-fb1a944f76e7}} ,
{{formula:7d4b1a10-46eb-44b4-8816-4adcab7c8814}} SampleMiniBatch({{formula:bb239b16-839b-4dfa-b4d0-ac62b7281626}} ).
Update {{formula:9038e671-6d19-4392-889d-5027b8666e44}} by Eq. (REF ).
Update {{formula:beb60a87-ad55-4c63-8ae7-ba3b7f785171}} by Eq. (REF ).
{{figure:ea8218c8-777d-4832-9179-5ce960e72b2b}}{{figure:b9ebd665-b5ef-4205-974a-ddaf5bdc0236}} | m | 848166f2121362ad006e070555486a6d |
We ultimately envision a continually learning robot that uses symbols to learn skills and skills to learn symbols in a virtuous cycle of self-improvement.
One plausible path toward realizing this vision would start with a set of manually designed symbols, as we did in this work, or skills, as done by {{cite:38c8acb7542290a2f04d4c58a413b16f9a8efb88}}.
Alternatively, we could start with demonstrations alone.
In this case, we need to answer the chicken-or-the-egg question: which should be learned first, skills or symbols?
Here we present very preliminary results suggesting the viability of learning symbols (predicates) first, and then skills from those learned symbols.
{{table:50663cfd-d045-489c-b3fe-9708b98cc879}} | r | 7d4536be32c8615c72bf85956d31ac68 |
Taking all these limitations into consideration, we propose a novel forgery localization method named Contrastive Forgery Localization Network or CFL-Net, based on recently proposed contrastive loss {{cite:3ee10550cdd499febab1ba27f026349483c1ed6e}}. Our method relies on the general assumption in underlying forged region localization that there remains a difference of feature statistics, i.e., color, intensity, noise, etc., between untampered region and manipulated region {{cite:89154e8f14517d0c48079cd0bf27de38aef0d927}}, irrespective of the forgery type. In this paper, we focus on leveraging this difference in the feature space to aid in image forgery localization via contrastive loss. Specifically, our model learns mapping into a feature space where the features between untampered and manipulated regions are well-separated and dispersed for each image. Thus, our method does not focus on specific forgery clues. Also, we calculate the contrastive loss for each sample. Hence, our method treats the forgery clues of each sample differently, which helps in generalization. Our main contributions are summarized as follows:
| i | 5e39322803db8ed267c30712bae7caff |
where {{formula:086d8185-ab82-430c-8561-b8ab378b59df}} is a common close-set classification loss function such as the cross-entropy loss; {{formula:9a415433-74a4-4b62-be90-37e59dd83286}} represents a continuous surrogate loss for AUC optimization such as the square loss {{formula:692d5581-9766-488b-98b2-1ed18cb0d6e5}} , whose details can be found in the recent survey {{cite:0d3c6474a8d54784ea53fdba243c40210faae7d8}}, {{cite:3051e9bf9a8fd238a8a9d5b8cb119da01ff3f48d}}, {{cite:6178fa68b9d1cd43be53935e8fa9e4c3c34bfb84}}; {{formula:75eedfcb-1243-4187-ba6c-7f053e4ccd5d}} acts as the switch of {{formula:f659f768-878f-4edf-a259-b7be0111c000}} and will not be updated in each epoch. Note that there exist no open-set samples in the training set. Inspired by {{cite:e8d15fb0072cc5fbb6dc95df3ed1b5590b43df92}}, we adopt manifold mixup {{cite:0776145bea85dd4f5c834bd0646e34078ef3dcc8}} to generate open-set samples. Specifically, the convex combinations of samples from different known classes are regarded as open-set samples:
{{formula:9bad643f-3471-48f8-9ff4-5d30d0d787bf}}
| m | afecd7a4179061cd9f77b16705a4f013 |
Partially neglected for a long time, dendrites have been recently shown to treat synaptic input in a surprising variety of modes{{cite:5a436e960d50bc3595046c3119f5163b23bbff51}}. One particularly striking example is found in pyramidal cells of deep cortical layers. In these cells, a coincidence between a back-propagating action potential and dendritic input can trigger voltage-sensitive ion channels situated on the apical dendrite more than 300 {{formula:d87ea4c6-8fc1-43b2-b9ba-1c40bdbbda63}} m from the soma {{cite:e069d9dbd3c01f46e5208de966c8ad34eb83d89a}}, {{cite:83b97023c963a73f8e5d482daec15b0bfd2eb2ab}}. The somatic membrane potential increases only after the activation of dendritic ion channels. This often resulting in a burst of action potentials. Bursts in these cells can therefore signal a coincidence of input from the soma (down) with inputs in the apical dendrites (top). Such top-down coincidence detection is one computation that is attributed to dendritic processes. Other allegedly dendritic computations include subtraction {{cite:30d1e511b580c70958110d5710f0c7938bcde251}}, direction selectivity {{cite:540465624840ff2098cae8ebd331aef5cc99bffa}}, temporal sequence discrimination {{cite:d769994e438cd5d97bd5263d7673fe156d2ed66e}}, binocular disparity {{cite:a6547f7962733eebb22e09b271b86fe7c67f21d4}}, gain modulation {{cite:b84186b1b85462d4ae6e0a737e34123509ac9ef0}} and self-organization of neuron networks {{cite:99ca92795d351d71fa10d011f5b414bf152da313}}.
| i | 8c63645a98bfe35c36909ac789869cdc |
Furthermore, removing {{formula:9df59517-32bf-40ac-a0ee-d3f42f9e7716}} when computing the
centroid of the true speaker makes training stable and helps avoid
trivial solutions {{cite:b590fc5069d124484f30022c30969c291d58237a}}. So, while we still take the arithmetic mean of the embedding vectors when calculating negative similarity (i. e., {{formula:abfcc5b2-b9a8-44d8-b492-cac6c0486088}} ), we instead use the following when {{formula:297cd5bb-1980-490f-804d-af7c2e3ab842}} ,
{{formula:26f5d271-69ca-4d63-a167-3d44ac480834}}
| m | 59be7bec3f701db5a828ce4785a8aad5 |
In artificial intelligence research, artificial neural networks (ANNs) have made huge progress in the past decade with summation point neurons as the fundamental building block.
Some question whether the trend of "just scaling up" by adding more computation and parameters will lead to more intelligent models.
A neuron on average transmits action potential or operations at the rate of 1000/sec while a CPU can do 10 billion/sec.
The method and efficiency of the way human brains process information versus how computers process information is fundamentally different.
The past few decades of AI research has shown that pure computer science based AI research has led to many dead end paths such as expert systems, ontologies, symbolic AI, among others.
If we are trying to emulate human level intelligence, then studying human brains seems very reasonable.
Demis Hassabis has been advocating this approach of neuroscience-inspired AI to reach the next level of intelligent machines and they have taken this approach at DeepMind {{cite:f7fc9ba280193370fb942db8c605a91729c0d90c}}.
Many innovations in deep learning were inspired from neuroscience findings such as convolutionl neural networks (CNNs), point summation neurons, and attention mechanisms.
Grid cells offer the potential to be another building block to build new types of ANNs in a wide variety of applications.
| d | 727b6aa6adc97c9035b7f41ed738e02d |
With the advent of gravitational wave (GW) interferometry {{cite:7ef4062e6f0f1d21bbe435c3346971fbe41d4714}}, {{cite:98f5747240568489222a5f8db2969b2c15256110}}, {{cite:c9b10b5a509a43f39e52e063e86639d403e14f5b}}, {{cite:c98281891997931cbe68a85218de006cc011455c}}, {{cite:f9ae7eb00d7f8d585272e8b8e108f4f5cd683b3d}}, {{cite:f4b9898965419a09c4f96b3d72c88576541b7664}}, {{cite:314d6eec2afef74b3e362c06317d1009b0a6f775}}, {{cite:673a99ecd500556c1cd1ef5e9017f5dc169ea692}}, {{cite:d98e84453e55bdf289ae820ff189d374e4807611}}, it has become possible to probe a dark sector through its GW imprints {{cite:5c94e85f27ca2952aa473f18963375326aa27c11}}, {{cite:ec1390c20c5a0256a65317e4f5b003a8e299fdc9}}, {{cite:b3765f9690dea0c28ed285b1b038eb4740b6dff8}}, {{cite:b06bca2b62c5c83230e14a15e02c39fd40dceeb3}}, {{cite:ecec43086e2dfc2e38a91bed2410ee1e2781c070}}, {{cite:e605d0ce60cc6d4a5fc506e68b0044c6d765e729}}, {{cite:dd8730f03b5afb8b87f78d5aa2f2f808ac594abf}}, {{cite:92f98265b3fad8223ba506bf3ee0bbfe01755b06}}. In this study, we aim to study the possibility of a strong first order phase transition (SFOPT) {{cite:77c66ac6638cc25a1487bec581666f9b8e1ff0fe}}, {{cite:74ef6914fa35d2793483ad78c395d6168ccd2b0e}}, {{cite:52726c3b4bdf1202e0b2f58f729b0f49f8627dd8}}, {{cite:5ec60d0b0a49b585270d7b8ed93eb8185932ff29}} and the GW spectrum from associated with a sub-GeV SIMP framework. The model we take up is where the SM is extended by the scalars
{{formula:68ee1d08-b09f-494d-a01a-82393d402cef}} and {{formula:6b502bd6-87d2-4532-9ed8-b7d0a8a1889f}} that are singlets under the SM gauge symmetry {{cite:23013a68a5a255139872c034c3eaeabe51f4d6a9}}. The scalar {{formula:3c66a8d8-224b-4e7c-9dcb-e3b271169ee9}} , stabilised by a governing {{formula:3deddb9a-389b-480d-a60b-f214bc85520c}} symmetry, becomes the DM candidate here. The number changing process for this case that is consistent with the {{formula:1f80bea6-648d-4eef-8c5d-ac77f474ab4e}} is {{formula:767162bb-45fd-4bc7-9c16-1abdb8ebaf8d}} , where {{formula:4df7dc25-d2ea-40b2-bf6d-454895a1114d}} is an admixture of {{formula:179384ac-7a7e-490a-b897-261d002fc55d}} and the Higgs doublet {{formula:7bea99b6-7609-45dc-8924-57b148168ea6}} . The scalar {{formula:0f03c717-00f4-40ba-851c-2471ac75c9b5}} and its interaction with the DM {{formula:8a387531-42c0-4f66-945a-7ceaf3bfcb16}} thus play crucial roles in generating the observed relic density through the aforesaid {{formula:44aa79f7-e528-4de4-9c47-ba6103d1b090}} dynamics.
Given the importance of {{formula:6890803b-9084-4470-9f18-dd29d0d8d752}} in this setup, a pertinent question to ask is whether the same can trigger a SFOPT and how strong is the resulting GW amplitude. We plan to explore this possibility here by incorporating finite temperature corrections to the scalar potential along the direction of
{{formula:ca733d98-a7ac-4bdc-8f34-9862e67ea070}} .
| i | d576541bca043384747315e2412898c8 |
In this section, we describe our SPT-augmented CNN-based method for robust and accurate LV quantification. At a high level, we decompose each slice in a CMR image sequence into a steerable pyramid with three orientations at two scales. We then use a five-layer CNN to map the pyramid representation of each slice to three oriented feature vectors, which are fed to a shared long short-term memory (LSTM) {{cite:78b596d0542c2bd6176a757c773fda7b5772afba}} to predict the eleven structural LV indices. The learning of the entire method is driven by the mean absolute
error (MAE) and a regularizer of the multi-task relationships. The system diagram is shown in Fig. REF .
{{figure:2dd68d55-a1b6-4b6e-ad05-b042a1b989e8}} | m | 946627f189998ebeb45ea84059259afd |
We incorporate the LR and HR image features in two other methods, which were also discussed in {{cite:90f61354b09a6503bdb417892ae85bda807be93c}}. In summary, the image features {{formula:1f7a6b1c-518e-49aa-9573-c22668fbd655}} and {{formula:e7541abc-9a21-4e51-a830-f29b926c13ba}} are merged in the following three methods
{{formula:3fb4933c-75d6-47bf-aa3a-6f286274c8cc}}
| m | 672218470349eb08b273d1e347278fb4 |
where {{formula:9939da94-4bad-47c1-9f27-f311ef56470c}} is the azimuthal angle of the {{formula:6e84eb23-f363-4dd9-8dda-bf512663e05b}} particle and {{formula:830dbb2e-2375-438b-b2a3-85dc5e4de7bc}} is the measured multiplicity. After calculating {{formula:4ad4dfbd-b1f3-4c6d-b2cb-63aeecfb740b}} , events can be sorted into large and small ellipticity classes, where small {{formula:72b1f321-6e71-4154-a37d-5f208109df79}} events are highly isotropic and large {{formula:f7b5fda7-c0dd-4dc2-8df7-ea7d4ca2744a}} events are highly elliptical in shape. When comparing the charged jet spectra from these classes, it can be seen that the ratio of the spectra is compatible with unity, as shown in Fig. 1 (left). This result suggests that a fully corrected jet measurement is relatively insensitive to the radial flow of the underlying event. By further incorporating the jets' dependence on the event plane angle, one can study the question of path-length dependence described above. It is expected that very elliptical events will have more extreme differences between in- and out-of-plane path-lengths than very round events, and therefore a more extreme difference in energy loss between in- and out-of-plane jets in the case where path-length dependence is a significant contributor to energy loss {{cite:626b7f3ea30357107c3c04ee44bf32fffabe4eb2}}. It is shown in Fig. 1 (right) that, for the low- to mid-transverse momentum ({{formula:7def5693-1df2-42b4-a6a5-4168dc56242b}} ) range, out-of-plane jets are more suppressed than in-plane jets in high {{formula:33493ce2-1cec-4954-a50c-70314e1be3ce}} events than low {{formula:f1a0b0bf-6411-4d3b-8a2c-41a7a8e93b54}} events, corresponding with the expectation of increased suppression. Note that while the {{formula:0a8b2057-ffd9-49cc-873e-b735846c1e72}} values used in this measurement were obtained from the V0C, events in which the V0A activity would indicate an opposite classification were rejected to minimize the contribution from auto-correlations. Additionally, these results are corrected for the event plane resolution using the three sub-event method {{cite:ece5115338ac7a92dfdc251eec7c7cf06a4db22f}}.
{{figure:552a7166-c75a-4d09-8ae0-acbf8c9e7cb2}} | r | be0efb2b5aec59b6651e26c200e7dfdd |
The method is as follows: for each crystal structure in the input database, designated as a potential “endpoint,” we find all other compounds that share its anonymous formula (e.g. “ABC2”), and perform a pairwise comparison between all materials to detect commensurate structures using the StructureMatcher in pymatgen{{cite:8e06b517db14e13ea98555a9aef6676b8d0b33a1}}. A pre-filter is performed that checks for detected space group, calculated with spglib{{cite:c4742f29d90275d774ea28434df3bb0f7c3dbaf8}}, using both tight and loose tolerances. This pre-filter is imposed with the logic that it is a necessary but not sufficient condition that two commensurate crystal structures will have the same space group. After a pair of crystal structures are identified as an endpoint, information is extracted such as the alloying species, including oxidation state, and whether the alloy is isoelectronic, and stored as an instance of an AlloyPair class. This definition of “alloy” does not consider alloys formed through interstitial alloying additions or other types of alloys.
| m | ce1fba536cbb46d211d62b0c0cf12507 |
The study shows that contextual embeddings generated by transformer architectures generally perform better than static (e.g., FastText embeddings {{cite:2fb889b16b12a7ae586e3663ec3e48b163397e2f}}) and among them BERT showcases the best performance. Since all of the keyword detection experiments are conducted on scientific articles, they also test SciBERT {{cite:c5afec22a9d2e688b3bf50a4842547abe43d6678}}, a version of BERT pretrained on a large multi-domain corpus of scientific publications containing 1.14M papers sampled from Semantic Scholar. They observe that this genre specific pretraining on texts of the same genre as the texts in the keyword datasets, slightly improves the performance of the model. They also report significant gains in performance when the BiLSTM-CRF architecture is used instead of BiLSTM.
| m | eac79daca796f76cfc880e7f0ddf030e |
with respect to a suitable integration measure {{formula:f4f5a50f-a41a-4b04-9123-a7d56a724fc5}}
on {{formula:5366e879-4e06-49f8-833b-5a60ec47fece}} These CS are constructed for that space with {{formula:d680a63a-12b3-469f-b025-042869359676}} having either a
discrete or continuous basis in different ways {{cite:0735c38b773211388948f4f95e38ac7971c2bfb4}} : “
à la Glauber” as eigenfunctions of an annihilation operator; as
states minimizing some uncertainty principle or they can be obtained “
à la Gilmore-Perelomov” as orbits of a unitary
operator acting on a specific or fiducial state by appealing to the
representation theory of Lie groups {{cite:20183b46c487d240f21e0b9f68c3b59d23c31be5}} . Their number
states expansion over the eigenstates basis of the Hamiltonian has also lead
to a generalization which is known as the Hilbertian probabilistic scheme {{cite:5c7138e6aa7b43a760ca25e3982a9c123f1d59d5}}.
| i | 88470ecfa2a701f6962c8fdd52fdf16d |
Understanding how opinions are formed is as important as ever, as the spread of misinformation becomes more prevalent every day. Assume there is some new innovation being either good or bad that is introduced to a group of people who want to form their (binary) opinion about it. Following a key insight by Rogers {{cite:e88c7569ec24b7d7353e5c4532113eb4c42b2df0}}, the opining forming process can be modelled as follows. At first, a small set of so-called early adopters, or experts, forms their opinion about the newly introduced innovation. Afterwards, they disseminate their opinion to all other non-experts in the network.
| i | e50acde1fd3bf380d076388cb10bd5fa |
In this paper, we generalized the study on the EN electrodynamics
by taking into account the dilaton scalar field in the action. We
first proposed the suitable Lagrangian for EN electrodynamics
coupled to the dilaton field and in the presence of two
Liouville-type dilaton potential for the dilaton field in all
higher dimensions. By varying the action we obtained the field
equations of {{formula:3a9ed14a-78ac-4ad4-8b8e-716f2f725d00}} -dimensional EN electrodynamics coupled to dilaton
field in Einstein gravity. Then, we constructed a new class of
higher dimensional static and spherically symmetric black hole
solutions of this theory. When {{formula:a9123fde-dfad-4088-aae5-46a0280daed8}} , our
solutions reduce to higher dimensional EMd black hole solutions
{{cite:97e3620f9a201b19fbde0d3eb43e9a071b39e92a}}, while in the absence of the dilaton field,
({{formula:38a6e15d-9201-4154-a99a-8f0d0895f6c5}} ), they restore charged black holes coupled to
EN electrodynamics. Although the behavior of the electric field
near the origin depends on the model parameters, however for large
{{formula:26db3435-49c3-489a-81ae-6370ad434b19}} the asymptotic behavior of electric field are exactly the same
as linear Maxwell field. Interestingly enough, we found that the
electric field of ENd black hole is finite near the origin and
diverges exactly at {{formula:b55ed229-f938-49b4-9698-729a2aacf4d5}} depending on the model parameters,
however its divergency is much weaker than Maxwell field. Besides,
in the absence of the dilaton field ({{formula:509ab963-cb3f-48f5-9645-023edf4083e2}} ), the electric
field has a finite value near {{formula:4f1b831a-38d9-4819-90c0-9f20fa492282}} , while as soon as the dilaton
field is taken into account ({{formula:0d241d63-1197-4e23-a7a2-a9e5b8f43cd4}} ), the electric field
diverges as {{formula:7f39baaf-46f9-4c2d-8ffb-e5ebb62e88cf}} . This implies that the presence of
the dilaton field changes the behaviour of the electric field near
the origin where {{formula:58b8ce82-dd69-4079-b208-b4959616c1df}} .
| d | 0dfa266239e16cb5c304f11b6590ef6c |
A classical code {{formula:1922586a-d335-4577-894e-078783477abb}} is testable if the syndrome of a proposed code word {{formula:fd31b6f1-4365-45c3-939f-5171ae0251d8}} reveals more than whether {{formula:ac8739fc-5135-40f0-87e8-f9ca7df98edd}} belongs to the code: the relative weight of the syndrome is also proportional to the relative distance of {{formula:901be5b0-33e4-401f-9f72-a6a4eca6619f}} from the codespace, and their ratio is called the soundness of {{formula:a0f06eb2-35b5-4794-ba12-53ec56614117}} . A code is further called locally testable with locality {{formula:ec509a54-ea65-42ff-8835-45fc64199cb1}} if all of its checks involves at most {{formula:0dce34fb-fe25-4aa2-9fa1-dda967fbbfab}} bits from {{formula:8bdfbca8-8488-4d22-854f-80b68c39edbe}} . The theory of code checking, which began with the pioneering work of Blum, Luby, and Rubinfeld {{cite:12ca5a04016f3616988a2d4b7334051ae572b693}}, has grown into a widely successful area of the theory of computing, affecting PCP theory, combinatorial optimization, combinatorial property testing, program checking and even cryptography.
| i | 89e50911cc0e34145c9ac4beb9ab63c8 |
We used the experimental setup illustrated in Fig. REF to test the robustness of our algorithm with regard to baseline elimination and wave delineation. In the first step, time locations of the R peaks were determined, which in our case were either already known (from simulated data) or provided by the database used {{cite:b51541d900827e60dfe23ff0f110c298e9786fd9}}. Of course, one could also use computer aided R peak detection, like the well-known Pan-Tompkins algorithm {{cite:e8c4b4d1164195bd3f880ab565d5cf3af8d8c756}} or more recent methods like {{cite:633f5288f7a064a983b65922d68258d429df664d}}. Then we distinguished between a training and a test set, the former one defined to consist of 100 beats preceding the latter one, which represents the ecg sequence to be analyzed. As illustrated in Fig. REF (b) the training set was divided into single beats, where the time instant for slicing was defined to be distance
{{formula:11b485d1-0576-4257-be3e-0c464326e546}}
| r | 7c214f2c02b08e082536978987da2049 |
Although we focus on how information geometry can supplement traditional maximum likelihood based inference and uncertainty quantification, primarily through visualisation, it should be noted that concepts from information geometry have also found application in the inference context from a computational efficiency standpoint. For example in Bayesian inference, by defining Monte Carlo sampling methods on a Riemann manifold, the geometric structure of the parameter space can be exploited. Simulated paths across the manifold automatically adapt to local structure, facilitating efficient convergence, even in higher dimensions and in the presence of strong correlation {{cite:ae3bce2508999ab066146e20b46bfca8663d30e1}}, {{cite:108ed27f6b8e8f114ba8491fcd7fb6fe9ac73add}}.
| d | dbafb6d38e3ed53c2bb339482a01fecc |
Estimating the linear model parameters depends on the models and the strategies used to reduce overfitting. With algebraic methods such as the Centroid Classifier
and generative probabilistic models such as MNB, the label-dependent parameters {{formula:aa3a4f9a-e1e4-40b1-9e76-b8ffd6d51efe}} are estimated for each label independently,
while the bias parameters {{formula:43c5c738-4e44-408a-a9e5-8625d04b787d}} are assumed uniform or estimated separately. With generative models, {{formula:67f64e2e-2c4c-4f32-b147-7df85718ef9f}} are label-conditional
log-probabilities, {{formula:7be60307-f4fd-4745-b220-a8349c6556bc}} are label prior log-probabilities, and both types of parameters can be smoothed and scaled to correct for overfitting. With
discriminative classifiers such as LR and SVM, the parameters are estimated by minimizing a regularized error function
{{cite:dd5d28ed53b68f6096c243a82246b93b875ec052}}, similarly to learning the regularized linear regression.
{{table:5e479351-4d5c-48ff-8d19-164e76386865}} | m | 4ef0f35b1da73854ffb0f5bf6ed4e27b |
Tensor decomposition has shown to be a great tool for image clustering and latent feature extraction due to its natural representation of images as higher order tensors {{cite:f1f1ebcb03707cde206f46ffcc3733fe5c10ed56}}; for example, brain FRMI {{cite:18bddd1fdc480a763e593bd7a6df16d3d2b26a2c}}, head and neck cancer {{cite:580a7f42c7122f4e3992f8e7bc92cf2e4fdd4d5e}}, and breast cancer {{cite:c37dcf5ce6181b772f3738de6b9c6bcbc6c35440}}. However, there has been a lack of literature using tensor decomposition for skin lesion classification problems. One reason behind this may be due to the heterogeneity of lesion shapes, locations, and sizes, which makes implementating tensor decomposition challenging since it is infeasible to stack the images together {{cite:ce5647273931186d95692fff38d7cd6fb61aeb5a}}. Therefore, this motivates us to consider a novel image registration method {{cite:bf86b2d2bd9502555e8de210a2cc503f6cf85b67}} to align the lesion information to effectively implement tensor decomposition. Medical image registration is very popular among radiology {{cite:7819b4c577bf9e3f67bb85c5d1112570ea040092}} and brain FRMI {{cite:18bddd1fdc480a763e593bd7a6df16d3d2b26a2c}}, primarily to register patient images across different time periods, angles, or modalities {{cite:bf86b2d2bd9502555e8de210a2cc503f6cf85b67}}. However, medical registration is still lacking for dermoscopic imaging {{cite:bc1fadeb82edaa091774d3e6c5e763c0e05fcf95}}. In this paper, we propose modern techniques such as neural style transfer to bridge this gap.
| i | 458c2050fe82b1ec2f04805e7d789692 |
The first-principles calculations presented in this paper are performed using the projected augmented-wave method,{{cite:9e1777fb49845d8bac222dde168e2e8ae217742e}} as implemented in the VASP code.{{cite:b5f5391319ba605a5bb17ebb906ccdb7030c3222}} The exchange correlation potential is calculated using the generalized gradient approximation (GGA) as proposed by Perdew, Burke, and Ernzerhof.{{cite:e38ba5fef9e59224737182c48fd233ca037ca65f}} We have included the strong Coulomb repulsion in the Eu-4{{formula:dafa0a8f-cd5c-481d-9a94-39d95a55bcd0}} orbitals on a mean-field level using the GGA+{{formula:f2b35165-3ff3-4726-9b38-510f9f968680}} approximation. Since there exist no spectroscopy data for RbEu(Fe{{formula:b20c14d1-a976-4672-b4e2-b959f6cc2a48}} Ni{{formula:36755e06-fee6-4f73-b2d2-942900e153a8}} ){{formula:ff4732bd-977f-416b-bdcf-bde81ce96467}} As{{formula:a3ff5066-8c63-4ac9-a1fa-dc37e967741a}} , we have used a {{formula:9afe8371-a1af-4204-8de9-41620ecc8f8d}} of 8 eV throughout this work, which is the standard value for an Eu{{formula:13ce5598-c180-48d3-82e4-ebad8409b468}} ion.{{cite:29fb0ccc70528571c8dbc39d7dcd8f5f77809c53}}, {{cite:67d88f73caec4fd3a89c247c29b7ff41449b0db7}}, {{cite:f372e377b8d995ff3899668eb48f3f3915ff0118}} The results have been checked for consistency with varying {{formula:314c5c4c-2b29-4b6a-bab8-f49202fe2d1d}} values. {{formula:1fd874ef-a2fb-4deb-96d5-736d56ae44c5}} is not applied to the itinerant Fe-3{{formula:28662983-6342-4936-ace8-d9738bb00b83}} and Ni-3{{formula:81910ab6-7c63-4e94-8ab6-c8fd87df9f12}} orbitals. Additionally, the spin-orbit coupling is included for all atoms with the second variational method in the calculations. These calculations are performed using the experimental crystal structure, as determined by the neutron diffraction measurements.
| m | 2df16f2d2c2d4af5894729d7be7da9fc |
Rendering speed comparison: We compare the inference speed of our method with the baselines in terms of number of image frames generated per second. In table:recontablesynthetic and table:recontablellff, the inference speed for NeRF {{cite:e40efd1fc0fe3eb7897f54ad976907ce113f93ec}}, NeRF-SH (no-cache and plenoctree) {{cite:2f309db01cfaabc65c05fcc74f100540ce348721}}, AutoInt {{cite:fe039b5e0e31d66b372596c2090962d6c7c33b98}} has been meaured on a single Nvidia V100 GPU. FastNeRF has been measured on Nvidia RTX 3090, while JAXNeRF+ Deferred and SNeRG have been measured on Nvidia RTX 2080 and KiloNeRF {{cite:811f7c21e7ad0009fdf52f89654ae289b4cc8baa}} and DiVeR32 {{cite:30a44840f26e5d72305b238e95036e18bf44b183}} have been measured on Nvidia GTX 1080 Ti. For the purposes of comparison in table:recontablesynthetic, table:recontablellff and table:cachegeneration, we report our performance on a single Nvidia V100 GPU. We also report our inference speed on Nvidia A100 GPU in table:v100a100.
| d | 9089c7a5bb478e50d62cd2003d68e6ea |
A number of prior works on learning {{formula:c16de6c4-63fc-4af5-9a75-1beb9d72239a}} (e.g. DualDICE {{cite:f046090670e3096d0cb624fb89f8a009db1d5c94}}, GenDICE {{cite:4b055b63b82477700f9657185c92c93945fb40f2}}) can be viewed as variants of the above minimax objective, with some additional regularization terms on {{formula:f7e55bd3-8dd6-4c33-bde8-db98a20b968e}} .
For example, there is an additional {{formula:2587c560-2644-40cb-b12d-2efc0f8d3aa6}} term in DualDICE to penalize {{formula:cddd86d5-b74a-4464-a0e9-4d1f998e51ec}} so that the resulting MIW values {{formula:46a7d188-1009-44b9-b942-fc0b37128644}} will not be too large.
This term thus serves as a regularization.
| d | de37cce854bd39efceb82619ddba38d9 |
Use {{cite:d8faccf18d41215182bdcc1c8e38d6c34757b44b}} and the fact that an {{formula:91d0f909-214c-453b-bba6-803a759b0a5d}} –cofinite module has finite Bass numbers.
| r | 7e85b6c9097b1ec267ca62aed1630d59 |
This is the first study to use ML models to better understand and interpret the clinical meanings of characterized WAI regions that are closely associated with middle ear transfer function and further facilitate its clinical application. Two feature selection methods (i.e., random forest and statistical significant tests) were used in this study to extract the key regions from the WAI. The extracted regions could guide the clinicians to decide whether the case is normal or OME. Lai et al. {{cite:72498c115c8435c09ddc8605bdcbfc39158d9f0b}} investigated three other feature selection methods to extract the dominant features to distinguish cases with temporal lobe epilepsy (TLE) from healthy cases. They are independent sample {{formula:c2455085-0081-4dfb-adb1-0e9335052a60}} -test filtering, the sparse-constrained dimensionality reduction model (SCDRM), and the support vector machine-recursive feature elimination (SVM-RFE). By using Support vector machine (SVM) to determine abnormal brain regions in TLE, their results indicated that the SVM-RFE achieved the best results, followed by the SCDRM and the {{formula:b55b1add-3d58-422c-8e1f-d70f67dd1daa}} -test.
More advanced deep learning tools such as attention mechanisms could also be used to extract the key regions in our future studies {{cite:b04ebd872cc972fcc237800d2ea252716f67c01d}}. With attention mechanism, the neural network can weight features by level of importance to the classification task, and use this weighting to help achieve classification with better accuracy. Guan et al. {{cite:367cc300b6250f20c9960010ad5d118fe70b0ce3}} showed that the performance of automated classification of thorax disease on the basis of chest X-ray images using attention mechanisms was improved in terms of accuracy by cropping out the discriminative parts of the image and classifying both the global image as well as the cropped portion together.
The size of the key region extracted and driving the classification decision is approximately 5% of the whole WAI image (as shown in Figure REF ), i.e., around frequencies from 1000Hz to 2670 Hz and pressure from -50 to +100 daPa, approximately 5% of the whole WAI images. This result provides important guidance to ENT physicians, audiologists and other healthcare professionals in terms of WAI data interpretations and subsequent diagnostic process for identifying middle ear diseases in the clinical setting. The small size of the key regions suggests that dimensionality reduction techniques could be used before classification to decrease the size of the data, allowing efficient computing, simplifying the complexity of the problem and possible improvement of results {{cite:78320552c87751252f1432fb71dde0874b1c9e9a}}. The study by Zhao et al. {{cite:722b27ffa99358e88092f7a1f275cf0ee68b6f2b}} analysed the characteristics of 2D WAI plot configurations in ears with normal middle ear function. The results highlighted that the frequency region with high absorbance; 1.1 kHz (SD: 0.3 kHz) appeared related to resonances in the middle ear system, where sound energy coming into the external ear canal is transmitted most efficiently into the cochlea {{cite:78c5e08a507109ca6e9e2cae16c6879d015744ef}}. A previous study by Beers et al. (2010) {{cite:2580164c0c58f8d60f62bc67272f73b202b3e936}} found that the area of the ROC curve was 0.9 at frequencies between 800 Hz and 5 kHz, with the best result at 1.25 kHz. 96% sensitivity and 95% specificity were achieved at the absorbance cut-off value of 71.7% in diagnosing childhood OME with WAI. Their results also imply the importance of areas around the middle ear resonance frequency.
Furthermore, Zhao et al. {{cite:722b27ffa99358e88092f7a1f275cf0ee68b6f2b}} found another region with high absorbance in the high frequency region (Mean: 3.4 kHz, SD: 1.5 kHz). They suggested that this region might be associated with the external ear canal resonance and middle ear structure. A recent study by Jungeun et al. {{cite:340215bc558c06deeccd0b419766cb63774810b7}} concluded that the otitis media group with high viscosity effusion had significantly less absorbance from 2.74 to 4.73 kHz in comparison to the otitis media group with low viscosity effusion. In addition, the amount of middle ear effusion affected the absorbance at the frequencies from 1.92 to 2.37 kHz. However, because of the complexity of 3D measurement results obtained from WAI, very few have explored the ability of WAI to differentiate between normal middle ears and OME, although a pilot study by Wang et al. {{cite:36833a66f4caac29f2052a0526d489f48a19bb8c}} investigated the dynamic characteristics of the middle ear system using 3D image analysis in ears with normal middle ear function and in the OME condition. They reported that the areas in the frequency range between 1.0 and 8.0 kHz with normal middle ear pressure appeared important in terms of distinguishing normal from OME. Absorbance in the high frequency region under high positive pressure were significantly decreased in ears with OME.
In the present study, the contour of averaged absorbance in the frequency-pressure plot in normal ears is generally consistent with the findings of Hougaard et al. {{cite:7aeab2ebc6eb89fd5570318946f4564504deae72}}. The averaged absorbance increases from 50% at 1.0 kHz to an absorbance peak point around 75% at 3.5 kHz under positive pressures between +50 and +150 daPa, followed by a sharp decrease at higher frequencies (Figure REF a). Averaged absorbance in ears with OME were significantly lower than those in normal ear conditions (Figure REF c).
In comparison to the variance found in the normal ear conditions (Figure REF b), significantly higher variances were found in absorbance in ears with OME around the frequency from 4.0 kHz to 6.0 kHz in the positive pressure region (Figure REF d). Jungeun et al. (2020) {{cite:340215bc558c06deeccd0b419766cb63774810b7}} also suggested a large variance in absorbance between 2.0 and 5.0 kHz in ears with OME of various type and amount of effusion. In a theoretical analysis using the Finite Element model of the middle ear, Koike and Wada {{cite:c78923cc87dc4e1a021c7f981baf7d9ec5fb9121}} suggested that positive pressure in the middle ear cavity had a greater impact on sound transmission than negative pressure at frequencies beyond 1.5 kHz. Therefore, the area with greater variance at the region of high frequency and positive middle ear pressure should be used as an indicator of severity in the OME condition.
| d | 2c571114830ba21b51ccf14763c2078e |
Our goal is to learn a general-purpose data representation {{formula:d430df65-1030-44b0-b5fc-42d95b039031}} that maps data {{formula:81567739-3ab2-468b-aba7-9ec9869b63e3}} to feature vectors {{formula:bab84b23-a56f-4103-bc5a-3caca5dc8de4}} .
In the supervised setting, representations are learned end-to-end as components of larger systems that solve certain tasks of interest, such as image or video classification, under the assumption that supervision is available to drive the learning process.
When supervision is not available, representations can still be learned via self-supervision by means of suitable pretext tasks.
Among the latter, noise contrastive learning is one of the most popular and successful ones {{cite:8c54709ec30f9fa1c21f9391c7ce1b6adf6d3ee0}}, {{cite:50fa7d7522e8c5cc662c01905180f4661370a8b1}}.
We summarize this background next and discuss our extensions in the following sections.
| m | e91526aaeb427f839945e470efbce0d0 |
Dynamic graph streams, which allow for sequences of both edge insertions and deletions, prove to be more difficult.
Edges that arrive in the stream are not necessarily in the final graph as they may later be deleted.
In fact, it is well-known in the community that it is impossible to deterministically return a single edge of a dense graph without storing all of its edges.
As a result, almost all dynamic graph streaming algorithms rely on counters which use {{formula:5ce52e3c-60f5-486f-94b0-29cbba7c7225}} bits of space or they rely on {{formula:461053de-7ab4-4c19-83e9-220720aa20b4}} -sampling which optimally uses {{formula:9f73af34-4a80-4feb-af2f-43708bad658c}} bits of spaceThis optimal space bound applies when the probability of success is at least {{formula:c7170443-5e7b-440f-8356-9628c4a16706}} . {{cite:f491bcb8d48ff2fa6f244574433362c2c39dac5b}}, {{cite:e869ef926b16e0685129a6c03f2366cb9ddba103}}.
In essence, counters are used to solve the problem of determining whether an edge is present in an edge induced subgraph {{cite:32134c6534d9f2e43715c76146b3abfb3df6eddd}} (see also {{cite:70d1641f00494541fa8f7d809f6ab3d59a31b1a2}}), whereas {{formula:999065e9-3764-4d02-bb2e-6f3766658b48}} -sampling also returns the identity of a uniform random edge if one is present {{cite:13e9565c4ae907aaf16b877204f868ec992c0d9d}}, {{cite:c076e4efcc43e455913f653c9080a676780f4269}}, {{cite:92ecab1466a647a04718dc74bbe7d904d06cc9c2}}, {{cite:70d1641f00494541fa8f7d809f6ab3d59a31b1a2}}, {{cite:1ca0cc976a6d8bc48fe23b57121ef7a48d11cc8b}}, {{cite:718376835bb2a2102a9efc5ec6996c5a71d6c21b}}, {{cite:2ec296f8c2496b763af17f6d47df513c09043767}}, {{cite:a825737f4158ce53512e9b896cdf9956549a249c}}, {{cite:b0f242280bc2ec05bcb66f518e8711e420578157}}.
A notable exception includes spectral sparsification {{cite:7441700fe7573fde93815b7b62a858fe4d06e484}}, {{cite:870b66c7c1567459415fc24b0e006399f1024fb3}} which relies on {{formula:cd427c08-da21-4211-926e-f28ac41dc373}} -heavy-hitters (non-uniform sampling).
| i | a27d012251b053c3518d997837e66f6d |
Optimization-based Carlini and Wagner (C&W) {{cite:7571881b6b81c06a9992a462f08d2e1848f0e5f8}} attacks are more powerful as they are more imperceptible and have less distortion in the produced attack than other methods.
Besides, the implementation of C&W attacks can sometimes be tricky and needs to select parameters efficiently to obtain the desired data.
Cisse et al. {{cite:c529e578e1ab2d7cc2b72872e8047a31a7e3d8d5}} showed a flexible adversarial attack named Houdini based on DeepFool's structure.
The attack gets the loss value between the true target and the prediction and then the forward-backward processes to seek the adversarial examples on DeepSpeech2.
The result shows that the adversarial attack causes misclassification with {{formula:38ea35ad-e210-4de2-9947-14aad33b0325}} of WER on the Librispeech dataset; however, the exact perturbation was not investigated.
| m | 4bf9f370594037a9a1f11f86ec2acf45 |
Object detection is an essential yet a challenging task in computer vision field, despite the recent advances using deep learning based techniques. While object detection demonstrated significant success in many applications, those applications are mostly limited in domains using ground taken images. ImageNet {{cite:9a116b7b3629f9da788106fe89338af2b4444986}}, COCO {{cite:3665d48427152d82aaf0c5789b16fb8f9b2917c5}} and PASCAL {{cite:1a8e6a3b513cd454c9bd6a98118568bd2786bfb7}} datasets are such major datasets driving the deep learning based object detection algorithms and they contain images taken predominantly on the ground. Consequently, they do not include a large variance of the object properties as observed from air. Furthermore, such state of the art object detection algorithms are designed considering the problems associated with the ground images mainly. That is why even the most recent works focusing on aerial images such as {{cite:e6172a7b772b803fb512e1f10553b94892c4aef6}}, {{cite:3e061942c7c7a05df528cfd6b1ceffd2c82976be}}, {{cite:f89056ee2beae4c118b6e43bb7997d1f331134d0}} cannot reach to the level where the state of the art object detection algorithms perform today on ground images. With the motivation behind deep neural networks and how object detection is being performed, performance of the state-of-the-art object detectors suffer mainly from two reasons in challenging settings: (1) the images captured has a non-uniform distribution in terms of object types and (2) scale, orientation, shape and the features of the objects can significantly differ from the ones appearing in the ground images.
| i | 5bf5268765e42471abcc969f07759a78 |
Remark 2.2 The well-posedness and convergence of the AH scheme was shown in {{cite:d0179a36f6c5c7e13b996d18c6bbb929b8664c74}}, under some assumptions on the parameter choices for {{formula:b94a2151-cbdb-4548-b035-cc7f1b5fed3b}} and {{formula:1ea6f7e2-0f30-4791-bf97-f17499cf5edf}} . Under similar choices
and additional data restrictions beyond the small data condition, the AH method was shown to be contractive in {{cite:ac4cebfccbc7b7f1b022891a1017d6a5773afd6b}}. While contractive, the linear convergence rate is rather hard to decipher from the analysis, which is rather technical (although still an important step forward). Indeed the rate could be very close to 1, and in the computations with the AH method in {{cite:ac4cebfccbc7b7f1b022891a1017d6a5773afd6b}}, it appears that it often is.
| m | e5151797c38472404b786a637cc59f30 |
However, as discussed in Section 3.3.1, because of the higher-order Balmer lines and Balmer continuum in the {{formula:0219cb00-4aab-4693-b24f-17c98a4abbf6}} filter, the unreddened slope in an {{formula:ee24514b-c989-4c87-9609-e795f0e22223}} vs. {{formula:6bf5eb9e-5f87-4b77-9f24-053d65c92d70}} plot will not be 1.07 as predicted by Eq. 3. The {{cite:28297302c2de62fc0149bc593bc5b21616d0e9c4}} and {{cite:ade8441a4c0d4dbf5d5ffef07e2f869a2659e786}} reddening estimates are thus lower limits. Using an unreddened gradient of 1.18 instead gives {{formula:9c4e7cec-1834-42e0-bd18-27f462f5a958}} .
| m | 928094b6e81f6e12e79bceda87c7800b |
A Lie superalgebra (see {{cite:304c7114e8b14b26bff1a8cc03fd9b72e8504aba}}, {{cite:40872c0a866a938bd825720c04ff071c1e6b8375}}) is a superspace {{formula:f8755cad-8e20-4d8c-bcc6-e37c372660e6}} with a bilinear mapping {{formula:74e53601-0aba-40ff-9c81-4ed4a79ce810}} satisfying the following identities:
| r | 4d0e5acee8e46b21ce28fd3480cd0a70 |
To further substantiate our study, the values of the Hurst exponent {{formula:9c70d9a9-309e-4a6f-b60d-532e58775dbf}} and of the fractal dimension {{formula:2d55efe1-9510-4934-ac29-2a8d4cfeb8e4}} of the satellite images as those in Figs. REF -REF will be validated against the the relationships linking {{formula:c3e600da-133b-45dd-81b5-572f8b60c629}} and {{formula:d79b45ad-ebb3-4871-999b-be166e9536fd}} deduced in Refs. {{cite:9450e3ac3cdb3189b4ccc0280b2c2639e5277999}}, {{cite:f3a9e41ee5a01d2e21fecf1e98c9c1a6081c4fa5}}, {{cite:9ea8ec119e84c604e8710ac6e22c8aa7e2573c66}} briefly recalled below.
| d | eaab8d1bd6882a20393bf6ea1cf42993 |
VSOD. Recent development of large-scale video datasets such as VOS {{cite:3440c0efb40b44213248a4693febf2dbf6ecfac1}} and DAVSOD {{cite:73dd9337b699bf4c59ffdd1f8e8767bb784ed727}} have facilitated the development of deep learning-based VSOD. {{cite:86d4d87e75d6cf857009ce767cd94fc316e9286d}}, {{cite:9bc485f6257b39c2ae0a88f281df7c38ce3bd97b}} and {{cite:9f1937e54fd70f4dc5c5b6bbf30bc73afe22ede0}} modeled the temporal information by combining optical flow. SSAV {{cite:73dd9337b699bf4c59ffdd1f8e8767bb784ed727}} mimicked human attention shift mechanism by proposing saliency-shift-aware ConvLSTM. COSNet {{cite:eb4e3f254b812422cd98b1c6a30b248e03c36fcb}} learned mutual features between video frames with co-attention Siamese networks. PCSA {{cite:4584cd42e33b9de249b156fd98c505bfbc767281}} applied self-attention to learn the relations of pair-wise frames. More recently, TENet {{cite:5bc892bbcbcbdffe234b9b53b6ebbd4dfbe14fca}} proposed new excitation module from the perspective of curriculum learning, and achieved top performance on multiple VSOD benchmarks.
| m | 65e5879c64d5f865b761cd4d7c3380f1 |
The reduced-basis (RB) low-fidelity model {{formula:1eaec3f3-541d-4ad8-a868-691a8688e40e}} is constructed using a greedy strategy, as described, for example, in {{cite:65bbcddad9a7aa3c1a8d3c1db90626e804ea5262}}.
We employ the implementation provided by RBMatlab.
It has been shown that greedy RB low-fidelity models have exponential accuracy rates for problems similar to the thermal block {{cite:65bbcddad9a7aa3c1a8d3c1db90626e804ea5262}}, which is what we use when fitting the error decay.
Once the reduced basis is found in the offline stage, evaluating the low-fidelity model online entails solving a dense linear system of size equal to the number of reduced bases to find the reduced basis coefficients.
Therefore, we model the evaluation cost rate as algebraic in the reduced-model dimension.
| m | 147fab12627004eef6db33df928e5c87 |
Experiment #1 shows that although saliency maps are predictable, GradCAM scoring 43.9% accuracy despite no context being provided, the utility of its predictability cannot be ascertained. Among the methods, GradCAM and Excitation Backprop having the highest accuracy can also be attributed to the fact that GradCAM has highlights large regions of the image where boundaries may not be well-demarcated {{cite:d4ee18d24260e607cd072238c9b34dcc528476bb}}. Excitation Backprop is also helped by the same fact and also that we are using the contrastive variant, which gives well discriminative saliency maps. All the other methods provide pixel-level saliency maps except FullGrad, although it also provides a finely detailed saliency map. The fineness of the details of the saliency maps may have had counterproductive effects. Added by the fact that the model itself tries to discriminate between classes by specific features like object parts, textures, colours, even backgrounds {{cite:8514d88635571bc512b5add893d1afad37c771ec}} {{cite:15eccb9641aa223946173b0c7781a3d864a74f59}} and not strictly focuses entirely on the object of interest.
| d | 44889853b48331f63b27c77fa5cc1c1e |
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