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This study was built on PyTorch version 1.8.1https://pytorch.org/, and using a PC with an Nvidia GTX 1080 GPU. We trained the feature extractors using SGD optimizer {{cite:ab7d9be639266ee899dc641eb1551d973da87da8}} with a momentum of 0.9 and cosine annealing learning rate {{cite:f46da79ede090d1561bb34861210db0b0518af16}}. The cross-entropy function was used to calculate the error. For model evaluation, we used F1-score on the 5-class BI-RADS level. F1-score is the harmonic mean of precision and recall. For multi-class problems, F1-score macro, which is defined as the mean of class-wise F1-scores could be used. In our experiments, the results are appraised on image-level for BI-RADS classification.
| m | 455104e109bffd3bdf4fec55f1b369a0 |
We solve these equations with the renormalized Numerov propagator method
{{cite:8c3e5ea7c02dcb39dbb0ce25b396cca0c4d84d1d}}, {{cite:3680f278fc6c27fc817884008e4b2e676d5482b7}}. This method implies that one defines an
equidistant grid {{formula:bd87caeb-af36-4a5a-8541-656b7da80442}} and propagates the matrix {{formula:3c3ee22a-6792-447b-bbf0-9118db166eff}} ,
which defines the ratio of the radial wave functions in subsequent
grid points {{formula:34105086-ae5e-43bc-aef9-d6afead5e03e}} and {{formula:efe1a504-c561-4084-911f-f8d1bca9416c}}
{{formula:89305ba4-377f-4241-8b37-119f8bb7c13f}}
| m | cf764c3c9b521a5d4b52e2ad910c874a |
The presented dataset augmentation technique was not compared directly to other strategies due to a lack of readily available alternatives. Through a literature search, shown in Appendix 1REF , it was found that only a single paper was published which performed dataset augmentation on structural connectomics data, specifically for the classification of multiple sclerosis patients on binarized connectivity graphs {{cite:31e5b278ea00d8490ae635f419ab9f952542e634}}. This work adapted a generative adversarial network (GAN) architecture, a structure that is commonly used in other domains of data augmentation. Published applications using GANs or other deep learning approaches for image data augmentation have reported increases in classification accuracy from {{formula:f3e33b39-2055-4b93-8453-42549baa5926}} {{cite:06ac5960faf1fd4db5076f32936c1c4cce8d702d}}. Given the average improvement in performance of {{formula:7cad314f-b607-47d8-9ba7-eb82610671e0}} presented here, MCA-based augmentation can be considered consistent with the other types of data augmentation when used for classification. The data-agnostic and training-free nature of the MCA approach also enables this technique to be combined with other forms of dataset enhancement, such as directly in GANS or through the addition of realistic noise, when available. MCA has not been tested for other common applications of data augmentation, such as object detection or segmentation.
| d | 7a413c4588b44557fa7350d4ab1aa6c4 |
On the level of {{formula:ef735177-0a3a-4959-ad5a-ecd9cdf25fc4}} -modules, we will use {{formula:6a97056c-f899-4ba9-9685-897f39a9e8f4}} and {{formula:f918799a-ba0f-47d8-9284-c74bd3e62512}}
for the usual and proper direct image functors, and {{formula:6594f7df-8fea-4183-ace2-f024c13ecab6}} and
{{formula:6f8ebd41-b4b5-4cf0-a05a-d37b0d35a888}} for the usual and exceptional inverse image
functors. For reference and comparison,
our {{formula:b08d2561-c717-43d1-8c51-55c39b14296d}} -functors {{formula:d1e688ee-9fa8-419e-913a-6fb24e7413f3}} are (in
this sequence) denoted by {{formula:a862e40b-e8ec-4568-ba7c-dffbac4e6198}} in {{cite:61901057d135b4c7fc91d5f06859b68e9813148d}}.
| r | 7fe385a5176dffc01c064052fdcb8e05 |
According to {{cite:6196a41f019ce689aeb9fba653ccc5b06243c3eb}}, we can upgrade Prokhorov's theorem to be sequentially compact with the Wasserstein 2-metric if
{{formula:e5049e56-3e45-43cd-aceb-4b080976eb43}}
| r | 530f6d04fea58fc53c9dcb80d2a59043 |
We can obtain a similar result by the technique of completing the square. Since we know that a scale and shift on a function argument does not change the function shape, i.e. scaling and shifting a Gaussian will give a Gaussian curve, we can use the technique of completing the square to recognize the mean and covariance matrix {{cite:b88080a5cc8eff24d7602a16b40b6cf2b9f8c86b}}.
| m | a9b7627f2307cfdfd0b88f44e2ee2c2b |
The proximity effect in superconductor (S) – ferromagnet (F) hybrid structures is known to be responsible for rich variety of exciting interference phenomena affecting thermodynamic and transport properties of these systems {{cite:717610e1508331b434cc810fad2964420b47ffff}}, {{cite:1fd3b46431dbb62bf6237654c44b21eaf9303212}}, {{cite:eb2640fec65fef8bfcace92083347bde87131307}}, {{cite:59275cffb1d9ae7ab106459bf7de2be9313be10d}}, {{cite:c4f6b8559a3496de6b3a91023dfc8d9accc4a1c1}}. The Cooper pairs penetrating the ferromagnet change their spin structure and become spin-polarized under the effect of the exchange field so that the superconducting correlation function contains both spin-singlet and spin-triplet components. This spin transformation results in the non-monotonous dependence of the critical temperature and the in-plane critical current on the F layer thickness in planar S/F structures {{cite:966c61b57d987154caec5f41ba3b86edd5e757ac}}, {{cite:4dbe86eabfd98138503bb2d1ff0ee37c31558d8a}}, {{cite:8d27946ee56dec4d235dd38fdae6941e785da16c}}, {{cite:a6d52814e6dfd4abced8ba65c598bdd60e0ceecf}}, the formation of Josephson {{formula:1caa0fa9-1063-4995-943d-c93788f92770}} -junctions {{cite:377e749b1b2a6d9a4709a6138ccb0f52df78da55}}, {{cite:ede51a3431d7b243d1d8c7ebb7a650817052b6b1}}, increase in the electronic density of states at the Fermi level {{cite:102cbf437629b38fe7e8bfd97eeabf600c90e128}}, {{cite:5690fc9bb843a6582ab6e7333f55b4585dabf57a}}, {{cite:11e1b64a816db09cb501bcdb36454ce9bc24b008}}, {{cite:189504aac9f19571b754265c15befc559c150712}}, and so on. At the same time, the F layer affects the superconductor by inducing different types of magnetic ordering there. There are two dominating mechanisms responsible for this back-action. The first one is related to the penetration of the spin-polarized Cooper pairs from the ferromagnet back to the superconductor (the so-called inverse proximity effect) {{cite:00f46734cee1f44233981b5ac31db6eace43a210}}, {{cite:72b908c8d4825d028ddd2a449cd1be71e09051ee}}, {{cite:8f22249f93e619a693ff095c7cc1bec9bb2da5d1}}, {{cite:a2e2d51430aa45df5fa86f11aa1919840f1993e5}}, {{cite:9cff5382b195aca8ce4fd6de2e03c81e3b4aece1}}, {{cite:3af1b5d688f06fd40a2e4638167fc2fc54a5cefe}}, {{cite:4c74c4f9534a973c5979474d40564eae6c609059}}, {{cite:dc54169555cf9fa3f281f21c63be64d7ad228443}}, {{cite:eedc61feae03483a593a172db036ba24b385b4c7}}, {{cite:975bbc4339771b89639f16be6ddc2c50ac388c2f}}. The resulting spin polarization in the S layer is localized at the scale of the Cooper pair diffusion length near the S/F interface which has the order of the superconducting coherence length {{formula:3c33452c-3373-4aec-a1f0-957f7efc1aa6}} . The second mechanism originates from the effect of the stray magnetic fields produced by non-uniform magnetization of the ferromagnet revealing through the generation of the Meissner screening currents and vortex structure in the adjacent superconductor (see, e.g., Refs. Aladyshkin, Eremin, Milosevic and Ref. Aladyshkin-SuST-09 for a review). Note that for S/F structures with the uniform in-plane magnetization in the F layers both mechanisms predict negligibly small magnetic fields arising in the S subsystem at distances much larger than {{formula:4a7de2f8-072b-4f76-9d79-b553af471246}} from the S/F interface.
| i | 59ad6f89ecfe1f1cc59e496d63809e67 |
Robustness to adversarial distortions.
We extend our analysis on the robustness of CNN-GRU and LipForensics (two of the baselines for temporal DF detection methods {{cite:dad2e609e482c34cede37ba91be426624a2b67ec}}, {{cite:01b887e7f159c9f7c49caca77e3018bd2c1d64a7}}) to black box attacks {{cite:ec7a206d706f0aee5dcc1574a0ce0719aee320af}} on FSh {{cite:962944854546f9d32597f997666b35e26ccaf2bb}}, in addition to the CDFv2 analysis presented in Tab. 2 of the main paper (see Tab. REF ).
This black-box method utilizes Natural Evolutionary Strategies (NES) to estimate gradients between the input and output of the network without knowing the model weights.
This is done by applying small perturbations to the input image in the form of Gaussian noise, and observing the change in output result.
With an input image scaled to the range of [0,1], we use 40 samples per step, and take a step size of 1/255.
At most 25 total steps are taken, with a total perturbation of at most 16/255.
Consistent with the original work {{cite:ec7a206d706f0aee5dcc1574a0ce0719aee320af}}, once the adversarial perturbation reaches a 90% confidence of fooling the detector, an Expectation over Transforms is introduced.
This step applies random Gaussian blur and translation to the video before each adversarial step.
| r | e1b0f8055681a45dcf14fd731f87c94a |
where {{formula:40b21f20-6a17-4e3c-92a3-27788d281327}} is the medium gluon number density.
A great amount of abundant experimental data {{cite:d822825cb6a3c51ac8c88fca052f5b335b8caeb1}}, {{cite:a98e136dc11e2d61d11fc16cadc48a30b8d21c5e}}, {{cite:a96fcf79aa893f500d19a75d01ec3d6f66f98545}}, {{cite:c83521f87d3eb5673e8bd066dfd4445dc82acb39}}, {{cite:06d9a43f25a874de76588d670011d1932020147f}}, {{cite:e2a6463916065079dd645de078853d672160376c}}, {{cite:b0c32ca6673a96d9c572ac4a5a9228633de58d6b}}, {{cite:cf7d16187f8f06088a464fb94be9a8ac01d54e73}} make it possible to accurately extract jet quenching parameter.
One notable work on the extraction of jet transport coefficient {{formula:feb118d8-0f3d-4817-b3ef-b4cffd8da27f}} was performed by the JET Collaboration {{cite:f9351aa2f0d52d0d355531db83097e5e2a202d24}}, which compared several different energy loss models and extracted the {{formula:3d485874-858f-4ba4-80d3-792ca91aa999}} values from single hadron suppressions at RHIC and the LHC energies.
Besides, phenomenological investigations have been carried out to extract the initial jet transport coefficient and the mean free path at the initial time simultaneously {{cite:622eb03c1be1a7fbd2a5a5d938aec0c2118bd424}}, and consider bulk matter evolution {{cite:2118f8383c29565f6d85317fab745ffea95641bb}}, {{cite:90a83b0556294b71f0ef93c3e8cb80f75c04e85c}} for large {{formula:97da2cc9-9614-4740-90f0-2576ebb6789a}} single hadron suppression and other jet quenching observables, such as dihadron and {{formula:46a55014-3781-4c0f-8843-1d737101b310}} -hadron suppressions {{cite:2022838bbda065ed42d8e9c09cdd51c5a3ed049e}}, {{cite:905eb19c8767138bffe5d2fdaa08aa543117f638}}, {{cite:a5570fe6855291044dba5bad9520d65badf7c2d4}}, {{cite:966fcc081a596ac2f3b5952de3409d20fa48d2ee}}.
More recently, the jet transport coefficient extractions are continuing via the improving theoretical approaches with opacity-resummed medium induced radiation {{cite:38d994f189a88d035be83b3ec4d17cea0a7c9f5c}}, the quasi-particle collection for QGP based on the linear Boltzmann transport model {{cite:6564027dc4b9584b0ee13a5702278d7b2aa50a81}}, as well as the advanced analytical technique within JETSCAPE framework {{cite:1d5e0f3bff605826c674ef706e7d05681ebf3c77}}.
It is important and necessary for a comprehensive and thorough understanding of the QGP properties to evaluate the systematic uncertainty of jet transport coefficient, which is given by different theoretical methods {{cite:f9351aa2f0d52d0d355531db83097e5e2a202d24}}, {{cite:38d994f189a88d035be83b3ec4d17cea0a7c9f5c}}, {{cite:6564027dc4b9584b0ee13a5702278d7b2aa50a81}}, observables {{cite:90a83b0556294b71f0ef93c3e8cb80f75c04e85c}}, {{cite:2022838bbda065ed42d8e9c09cdd51c5a3ed049e}}, {{cite:905eb19c8767138bffe5d2fdaa08aa543117f638}}, {{cite:a5570fe6855291044dba5bad9520d65badf7c2d4}}, even hydro evolution information {{cite:2118f8383c29565f6d85317fab745ffea95641bb}}, {{cite:622eb03c1be1a7fbd2a5a5d938aec0c2118bd424}}, {{cite:966fcc081a596ac2f3b5952de3409d20fa48d2ee}}, the initial parton distribution functions and the final fragmentation functions, etc.
| i | 07b718692ac926067a7bd42187d8bc16 |
Inspired by the collaborative training scheme proposed by {{cite:98b593d5d52270cd730f7bf283a9bd1891a65376}}, {{cite:e1aab8d7bec4a8127b40a523ad60275117c85d13}}, a co-training network with a noisy label filter has been utilized to more explicitly enhance the network robustness and greatly alleviate the selection bias, as shown in Table REF .
Moreover, we incorporate a novel self-supervised learning scheme towards the global relationship alignment of samples in each batch and local clustering of each sample, which could maximally utilize the detected noisy labeled dataset (e.g., noisy label or hard samples). The experimental results demonstrate that this strategy efficiently improves the utilization of training data and improves the model performance.
Fig. REF shows that our self-ensemble network with two regularization losses could detect the noisy label more efficiently by properly dividing the noisy and clean dataset.
{{table:6a960bfd-ac56-471f-96d8-b2c0d59a8341}}{{table:e84e8908-5d49-4ee9-8441-d9d5bb86fbde}} | d | 5de5d6b0b684af894338e322cd0ad7db |
To address this limitation, recent research has started to focus on generalization approaches for RL.
Ideally, these general agents should be capable of zero-shot transfer to previously unseen environments and to changes in the problem setting while interacting with an environment {{cite:771107d3d53162e5ebc0a7357ef8dd86500462c2}}, {{cite:7025b2671cacb8cc5b688edf9509422f39abdb27}}, {{cite:da5009891f962fd08fedc0f987dcc75c3c7d477c}}, {{cite:50cf219f9c5836d02ff279adf03c7361b24d5ef6}}, {{cite:4062e0308fccd01dd00a890ad9c7a71cb067fc23}}, {{cite:0395e33d70838d6bbfad47fe99ae1c8f2122998a}}.
Steps in this direction have been taken through new problem settings where agents can test their transfer performance, e.g. the Arcade Learning Environment's flavors {{cite:346fa4107d43e79cb9807ea12569192437054f02}} or benchmarks utilizing Procedural Content Generation (PCG) to increase task variation, e.g. ProcGen {{cite:199362fefd92264019c685adf215ae9df28cf402}} or Alchemy {{cite:80b4169087f1d81271d9ab47b4df2a39d5c71e1c}}.
| i | 6787413cb722d6ef7eeab35590803a3e |
In addition, all models were trained with the Adam optimiser {{cite:605a6dadaf74fb9de84ce556608c25aa388215e1}}, through the weight-decay wrapper provided by Tensorflow-Addons in order to implement weight-decay regularisation compatible with Adam{{cite:012fdc2a55292cb1a8c947c7ba1d1063e70f41e6}}. The value of the weight-decay was optimised during the hyperparameter search loop. Furthermore, since the the Deep-SVDD cannot have non-homogeneous learnable parameters, i.e. biases, we implemented a non-trainable Batch Normalisation or otherwise the learnable mean would effectively behave as a bias term and lead to trivial collapse solutions. Since preventing trivial solutions requires not using saturating activation functions and learnable batch normalisation layers, one would expect only shallower networks to be successfully trained in order to avoid vanishing and exploding gradients. To mitigate this, we allowed for the gradients to be norm-clipped to a value to be optimised.
| m | 925eb0e2661fb7f093136cc378f9f80a |
User Study. We undertake a user study comparable to {{cite:a7890fe3d4526c32e1f35eac1c503277dc0bd809}} to dig deeper into the six approaches: AdaIN {{cite:c4884572e8455d2d23064da1c91c270793ae5c24}}, SAFIN {{cite:a7890fe3d4526c32e1f35eac1c503277dc0bd809}}, AdaAttN {{cite:abccb846746b6c8105d75a653269baa77ff7d236}}, LST {{cite:fbce06f29aa3fe728e2768129c999187ea1343bc}}, DeCorMST {{cite:7a7515011d5a7c1a6b9b52a9cf5a49a52c60ff98}}, and DFR. We use 15 content images from MSCOCO dataset {{cite:925a6e9ffe493314372d021f2608728f19be14fe}}, and 20 style images from WikiArt {{cite:ca6ab2075ce12794e551c3db34d05260ddefc941}}. Using the disclosed codes and default settings, we generate 300 results for each technique. 20 content-style pairs are picked at random for each user. For each style-content pair, we present the styled outcomes of 6 ways on a web page in random order. Each user is given the opportunity to vote for the option that he or she likes the most. Finally, we collect 600 votes from 30 people to determine which strategy obtained the most percentage of votes. As illustrated in Fig. 5, the stylization quality of DFR is slightly better than AdaIN, LST and worse than the attention-based method. This user study result is consistent with the visual comparisons (in Fig. 4).
{{table:11ede80f-18fe-4411-b2d6-550142d1652e}} | m | 1b6ae9a458f104c90b3230539e5c1206 |
Finally, we have reached to our prefixed destination, but this is not our final destination because the model runs throughout the assumption on unchanged population size over time. However, evolutionary dynamics and ecological process, those
are dependent on frequency dependent selection and demographic fluctuations, should be altered in fluctuation of population size (see {{cite:ec7f27fcb177ee68063871851c5a9199e5d95959}}). In this connection, we also know that the adaptive network dynamics in which node states and network topologies dynamically change adaptively to each other is well-establish an area in computational network science where coevolution rules aim to integrate the adaptive network dynamics into the framework of evolutionary games – for useful reviews see {{cite:163aabdc171a8aa7f0810d652574fa6e536735a8}}, {{cite:2660ab2eb5f1ab73b6f84c75b34072cd311a8b84}} and for details see the references therein. Therefore, it is time to come to face the real great challenge to derive the analytical procedure to measure the evolution of cooperation in the fluctuation of population size; that will be a base model for the corresponding adaptive network simulation. In doing that we will drastically have to change the basic structure. Our surgical endeavours would surely lead us toward our ultimate destination; however, it will take time.
| d | d914fc4043f35acff33701903e15e742 |
The InPTA experiment aims to use the unique strengths of the Giant Metrewave Radio Telescope {{cite:f7b572c8bb8e94d235cf0f215171627cd8cb2d9c}} after its recent major upgrade {{cite:4ae0fe74e8244233c6ea1262929838f347fef40c}} to complement the international PTA efforts by providing a unique low-frequency view of PTA pulsars.
Such low-frequency observations are especially relevant for characterizing the effects of the interstellar medium, which are strongest at low frequencies {{cite:7a872af015f4087d3341581bf165723d1d988dcc}}.
The broad bandwidth and high collecting area provided by the uGMRT at low radio frequencies make it an ideal instrument to characterize such effects {{cite:0ba878d8d01a9cfe8c915e648480f45e2c729b72}}.
| i | 14748c76bb21df4679f1ca1a89563c12 |
These findings have later been leveraged to provide powerful unsupervised computer vision algorithms {{cite:477dc7990396240529421e6566b0222f3ee6c006}}, {{cite:bef4f749423d8c2dac18e70ad7df26ec03ad0d09}}, {{cite:e882aa5d4b04453a822055bfb9bf10a08e41b59e}}. When applied to images, these pioneering techniques usually require each image to be landmarked, i.e., to have annotated points on their most essential features {{cite:8facd13bef3af443e9f68701b612e87b8ac37ca5}}. Another critical set of work, e.g, the works in {{cite:ff9f5500191c0f5a232b10ad4803fa00cc20586c}}, {{cite:df444650b022d9c416763e41da64383e4714e98e}}, {{cite:8e8dd98b8448f17b8e73de2a5f6e0676f2e749fd}}, {{cite:02c3cdbc33c544010da22fbc41e80b1df09076f5}}, {{cite:7c5be383aa21f5bed6f0704212ef6dd21d171a4b}}, focused on visual appearance instead of shape. They proposed the development of features that are invariant to specific transformations. However, it was noted that extracting these features reliably and consistently is not easy {{cite:9ba503214c5faccd617c17a434e739f505ab7c0a}}.
In the same vein, the use of the Dynamic Time Warping algorithm on flattened images has been used to understand and compare images being the results of transformations {{cite:550d761eab32abc3b6f47ebb7851e757df52290f}}, {{cite:e50ecf7e54a90de3356d75c8e9275e0535dae5d7}}, {{cite:f9ad20d443d631c8db2f236e9fef0dfed2921081}}.
| i | 6a03a0ba997ed49b1ae69891e689d33a |
We believe that the practical applicability of BERT-based re-ranking models is currently limited to offline scoring or domains where users are willing to accept multiple second delays in their search workflow. Future work will likely focus on the gap between the contextualized and non-contextualized models – both in terms of performance and effectiveness. Another path is to speed-up BERT and other transformer based models, for example with pruning {{cite:994191c96e14bcc0039281b6af06326595b8637d}}. Therefore, we argue that it is necessary to provide the replicability infrastructure with tools to take both performance and effectiveness dimensions into account.
{{figure:88b09146-bebe-49c7-bebd-aac239b6758d}} | r | 1ee20250b90f4f9822ffe684ff50a7fc |
Our understanding of the link from scattering amplitudes to classical solutions has matured. It has become straightforward
to construct the linearised solutions associated to massive three-point amplitudes in four dimensions.
The technical developments which have clarified this link are the KMOC formalism {{cite:96f0e23eb3d62c69f9a7c95faf6245beedc156fa}}, {{cite:85caa7f5f01ac68f82538d6fcc31315fa98a724a}}, {{cite:f9d6e2118172e5a04259e3fc2be2230fc991c5bd}}, which constructs classical observables from amplitudes,
and the analytic continuation {{cite:d60fdb41145d3b437f7c1182093464f9daeedc9c}} to split signature metrics.
This second step allows us to use the methods of KMOC in the context of three-point amplitudes.
| d | 77b85e61172020ac47f2ae88ea17aad4 |
An important aspect to consider in analyzing the results is that the individuals' movement patterns seem unique. This is not new, and several papers have exempted the individuality of human walking and running {{cite:4f2d658222f522f556178857258d225691176063}}. In this sense, since the biomechanical patterns are probably grouped in clusters {{cite:98b84e7d32238f861a80d40846ede65134b987ea}}, {{cite:c9d69215c758081d4cc68f30c999835e0fa8a11a}}, standard hypothesis tests applied to the whole sample are not the best way to establish biomechanical differences. There are some discrepancies between studies when examining these issues. Also, in the biomechanics literature, as in other biomedical literature areas, there is some controversy about the use of p-value {{cite:abbb5881d24566007092e5c47b9b58bd2465f4bc}}, and the use of other approaches such as effect size {{cite:f9b6c8120af6f31bdc4a5f9ec9a86f051b96c1d1}} or e-values {{cite:aef47554113a163e62c05d126cc8b88c48553bff}} may be recommended.
| d | 3ce129c8f8ac0410d29cdba48b9bf8ce |
Finally, we have only considered finite-dimensional parametric sampling score and outcome models. Recent advances in the machine learning literature have expanded the tool box for causal inference. In particular, TMLE {{cite:a1f197988a6daa5a9473819dfc7baf26bdbe3ba6}}, {{cite:749a22ebbbe580907f73504c3770054cc2fb2460}} and double/debiased machine learning (DML) {{cite:e2743c6c03819984ff8aa8fea5722d4f8fa8c08a}} represent two powerful frameworks that integrate flexible machine learners to estimate the nuisance functions and alleviate the bias of causal effect estimators due to model misspecification. These frameworks have also offered theoretical guarantee on root-{{formula:b98b0d0d-b16c-43c0-bc1f-fe4c1cd67540}} convergence and provided consistent variance estimators through the efficient influence curve or the Neyman orthogonal scores {{cite:137e3e73625e2cb0a9421378a742463e7926df39}}. It would be of substantial interest to apply these more flexible nonparametric estimators to improve our parametric implementations in generalizing the ACTG trials.
| d | 0098e5b585ceb666cfe2c0000dc31571 |
Due to the emphasis on the symmetry, quantization of gauge field theories are usually performed in the Lagrangian formalism, rather than in the Hamiltonian formalism. The standard procedure for fixing the gauge is the Faddeev-Popov method {{cite:66ba4cdc7593dec2bdaf9ea5589d059f90bae648}}, together with its associated Becchi-Rouet-Stora-Tyutin (BRST) symmetry {{cite:ba2dc6064cbbd8c866d9ee8c5eee39f05376108a}}. Nevertheless, the quantization of the Hořava theory using the Hamiltonian formalism deserves to be considered. In particular, the quantization of the nonprojectable case is a delicate issue since it is a theory with second-class constraints. The analogous of the Hamiltonian constraint of general relativity acquires a second-class behavior in the nonprojectable Hořava theory, which can be related to the reduction of the gauge symmetry. The Hamiltonian formalism provides a natural framework for the quantization of theories with second-class constraints. Indeed, the contribution to the measure of these constraints is defined in the phase space {{cite:f4fb59f511835b00d29707055cb48a1530224a0c}}. Analyses on the Hamiltonian formulation and the dynamics of the degrees of freedom of the Hořava theory can be found in Refs. {{cite:2a26ed731862575ec94d7419b32be9124f2623bc}}, {{cite:dfe13ff2ff24c97f537f567c7f675348440f2f2d}}, {{cite:bf691f2a025bf78020aef6d615d70462456e0a68}}, {{cite:4d032d47dade89a308e4b987dc9508ead5f17b7f}}, {{cite:7b765f13fd99c22bd86eded731cbab5420bc9c01}}, {{cite:aa0f1540218ca7fad810f5557ef62169cec943a9}}.
| i | efa29f87284c976d1309923ffb999f75 |
The determinant quantum Monte Carlo method {{cite:8e0ab257b834679a91814733aca860191c7e4204}}, {{cite:d984e64c4dc4c31672773efba9e4d74c18973095}}, {{cite:7e3b9d1916cd131268f984119f321c660e0f354b}}, {{cite:ae2911fed1f7984e959ee64b2accafd63285efbd}} is a powerful technique to find equilibrium properties of interacting fermions. It is controlled, in the sense that the results are guaranteed to converge to the exact answers upon increasing the computational effort. Unfortunately, in many cases of interest, the applicability of the DQMC method is limited due to the fermion sign problem {{cite:5f891c96c52b37b175e07a00a8120a59390d2798}}. In these cases, the computational cost for a given accuracy increases exponentially with the system size and the inverse temperature. The repulsive Hubbard model suffers from the fermion sign problem in DQMC at generic values of the filling. Below, we briefly review some useful results that were nevertheless obtained using DQMC, either for special parameters where the sign problem is absent, or by employing very large computational resources to overcome the sign problem.
| r | 9ca47b6722fe0d45b2e96a45b103fed8 |
Training and evaluation.
As in {{cite:76f6e0dadd7844daeb854edf5ba4a5c31e66dc65}}, we use a {{formula:9832180c-49c9-45e4-93b4-0ae95144d1f7}} -wide {{cite:4529d9bbbdcf4b42c3a1ef11d14836a3ccf4afa2}}, selective-kernel {{cite:ae5e3c11fed5a20f79603916015f2c7fb21ff3f7}} ResNet50-D {{cite:4f74d7a8579f02a6191c807ae87de7ecb4c56ee2}} network with squeeze-excitation blocks {{cite:4ff99ec7f1a0965b5ce8af3599b5ab4862a11a5a}} as feature extractor, and a three-layer multi-layer- perceptron (MLP) as transformation network. We train for 1000 epochs, with a batch size of 628, using the LARS optimizer {{cite:f3f6543d82ef51e9feaa316a2f826933713f9ddf}} with a cosine schedule {{cite:821e983253f3e81bf5122d2abe3713e7ee06f388}}, ten warmup epochs {{cite:1887874e4ea3caf8daa66f3e36981eca4f5d92e8}}, and optimizing the NT-Xent loss {{cite:973d2368c068a737f3cc0bcc2d294235f56bc273}}. Training takes half an hour on four NVIDIA 3090 GPUs. The code, pretrained models, and training results are openly available at {{cite:322b0820affe11060c550a898e5ae6fc439c37af}}.
| r | afb3c9f1388c20dfea546dad93c073b5 |
For the purpose of generating plots, we choose {{formula:547e5ef3-ec3b-4451-9363-f1c76df89200}} and {{formula:592e5ed1-067f-4add-9780-4a70dea0686c}} as obtained by matching MIS with the holographic description of {{formula:ad3ebdde-95c8-4801-bda7-ab611b755217}} SYM theory at infinite 't Hooft coupling and for infinite number of colors {{cite:027b204d6ef7801b890b8bc138af8d2055e0cea5}}. Also we choose {{formula:23d47ad2-0f4a-40a9-9db6-fadd6d425ca7}} , and {{formula:6d5e7df2-10a8-4438-94fb-2a03c5dc7537}} in units {{formula:0424a8aa-0f33-47fe-86d9-c06f86181049}} . Likewise, we will count our proper time, {{formula:6d11c0e1-aa67-4ecd-9e7c-40bf60ecc37c}} , in units of {{formula:1eae8c7f-6301-409e-9eda-68fe220263b2}} .
{{figure:f6647744-6dc2-42fa-9195-495f1867ceca}} | r | d3b902bbd4139a948039a1ae411a8467 |
Let {{formula:19fec2e3-4f35-459d-9991-4029cbba1d3e}} be a transcendental meromorphic function such that it has either at least two poles or exactly one pole which is not an omitted value. For such functions, there are infinitely many points whose iterated forward image is infinity, the only essential singularity of the function. This is the reason why these are called general meromorphic functions. The class of all such functions is denoted by {{formula:72784d56-73ca-437c-8b21-00590f5eac09}} in the literature {{cite:d058cd245f4cdec45b7886a4f62e184484953188}}. A family of meromorphic functions defined on a domain is called normal if each sequence taken from the family has a subsequence that converges uniformly on every compact subset of the domain. The limit is allowed to be infinity.
The Fatou set of {{formula:2ad6a209-778b-456e-8c6d-8aac21343869}} is the set of all points in a neighborhood of which the family of functions {{formula:c5e1b9ae-bdae-49a2-af7f-73a7225e5675}} is well defined and normal. For general meromorphic functions, normality is in fact redundant. More precisely, the Fatou set of a general meromorphic function is the set of all points where {{formula:f443a44b-9c6d-4673-9e6c-8afe990e5d05}} is defined for all {{formula:28f40df2-9783-478f-9fa4-99175482ad46}} {{cite:d058cd245f4cdec45b7886a4f62e184484953188}}. Its complement is the Julia set and is denoted by {{formula:5036a968-a185-4485-aa31-0fe91f1ab700}} .
| i | 9b4457ab078f9d2b2e0f52f37696cc2f |
Despite their state-of-the-art performance on object classification tasks, deep neural networks (DNN) are highly prone to shortcut learning {{cite:e49b61ca4471b7f8d1a6b2584c5883ac4d98b9cb}}, {{cite:e5a53f651c1ad0c5525e71ec53fc7cb5348e63a7}}, {{cite:a30a362b5155ecd29dcfa99efcd1d4e6bb2d6e7d}}.
Instead of learning holistic representations and decision rules
that can generalize beyond the training data, DNNs overly rely on so-called shortcut opportunities (SO), which occur when the target class is highly correlated to one or very few easy-to-represent input factors {{cite:413e5ce0dc7c87d3291d85c656dd6d2abf57465e}}.
This leads to poor generalization on many out-of-distribution (OOD) settings, e.g. ImageNet trained DNNs are biased towards texture and fail to generalize under texture-shape cue conflict evaluation {{cite:e49b61ca4471b7f8d1a6b2584c5883ac4d98b9cb}}.
{{figure:862a37b6-31ce-440b-b274-e823887e72c4}} | i | 10f81446ed6ead2b86377987e148befc |
One may also consider the related concept of local rigidity, where there must exist only a finite number of realisations (up to isometric transformations) in the given normed space. This has also been studied intensively for many years in the Euclidean case (see, for example, {{cite:969b24e46b949372d86551f3691adbf9270d41e6}}, {{cite:da40b7228738fc3de14c48fcc0e21819599809aa}}, {{cite:3ae36eb10beb29d86b071efd81bb8bbde01aa29c}} and the recent survey {{cite:5ff072231e78a047a5ad0904bce40a1c40a55355}}), and research in the non-Euclidean setting was recently initiated by Kitson and Power {{cite:6b7dbd7e50389c3e80fa961ebf063c2b933711d4}}. Indeed the main result of {{cite:6b7dbd7e50389c3e80fa961ebf063c2b933711d4}}, which we describe below, will be important in our analysis. Their work influenced subsequent study of a number of related rigidity problems, including for polyhedral and matrix norms {{cite:63de186be4221636ce46513da32b7684e1e46b56}}, {{cite:43c51e97061958b8e99dbcae15baae308ddcb4b4}}, general normed planes {{cite:dbf61c5b50ae2214c7f9c66bca6f67584a708710}}, higher dimensions {{cite:131f8093468aa47199bde3917e6fd2c068d08fa6}}, and in the presence of symmetry {{cite:17d748944a0f28e653e1583dd2a79364e2854c17}}, {{cite:eedbac609c98201e6db9519f4dec6ca6f4426dc5}}.
| i | f95075a7e1456ad92d066de8d5c463e9 |
This effect that, as mentioned, has been largely unnoticed does not
have any implications for interferometric experiments
such as LIGO or Virgo {{cite:14c988eb25dfdb97cc14c81d389f2b4cd60e133b}}, {{cite:04241712a772bb118d8b494f9f0a13b442a6468d}}, {{cite:67dac592e55f142e0b622f7278e57933875a9bc8}} that depend only on the
GW frequency, but it may be relevant and indeed observable in pulsar timing
arrays (PTA) {{cite:6059d11705e3e61a4ff2bd02893e88237bb0d61c}}, {{cite:6a3cae29bf72e724094f079583f220f570e8227a}} where the optical path is much longer
and therefore sensitive to modifications in the wave number vector.
| i | 6912d8354f578f23f01ed1dba1ee61f5 |
With the help of these exchange interactions, we have calculated the ferromagnetic transition temperature (T{{formula:4f22ffe8-157c-40cd-bf3c-0b3ad66c5dea}} ) using a classical Monte Carlo (MC){{cite:7436bf3c36c5455e02134c0991117f02f4277dda}} method.
In this technique, we first set up the magnetic lattice. In SFRO the Fe atoms form a face centered lattice. A system size consisting of 16 {{formula:70aee4e3-1dab-43c1-ba2d-72c60ae902ee}} 16 {{formula:1258e2d2-566d-4655-af03-325aa0e68260}} 16 spins is considered. The extracted {{formula:bb71a0d2-dd1f-41fd-9272-483c1134588a}} 's from the procedure discussed above are used as inputs for an extended Heisenberg model.
During a single MC run, random orientations ({{formula:185af8db-cd15-4db8-b2e0-41eedc7e7abd}} ) for a spin at {{formula:098e6acb-b539-49bb-be06-6a91fdcd2234}} -th site were considered and the energy of the system was calculated.
Then a new random orientation of spin ({{formula:a210649a-0026-40ca-8462-d9265cb047fa}} ) was created and the system energy was again calculated. If the energy associated with this new random orientation ({{formula:8a49dba3-9f4c-4bf0-822f-ad75f2834959}} ) was lower than that of ({{formula:425fab37-1108-4154-9618-3d3c8cff0c5c}} ), then ({{formula:2876d527-80aa-40bf-8f1e-64a39cedc6a4}} ) was accepted. Else, Metropolis algorithm{{cite:c97800b7b994124bd4faed97efd9a9f6f787dce3}} was employed to decide whether to accept or reject ({{formula:327fd31a-f42f-4ec8-9c24-b3a4386d231c}} ).
This procedure was performed over all the lattice sites {{formula:6fec4a72-8f14-4d7d-b940-ac5e371f6804}} is one Monte Carlo step. The magnetization M(T) per spin was calculated only after bringing the system into thermal equilibrium. Total 5 {{formula:1e4e426e-b2a7-4872-b1a8-19102c570c65}} 10{{formula:504eb96e-b1e4-4f19-abfe-2747e08febfb}} Monte Carlo steps were used in these calculations and results were found to be well converged with respect to the system size as well as the MC steps.
| m | 075a1b9548803e8bdfcaf2cdd2d2a8c9 |
The appearance of this emerging local scale symmetry has two consequences. First, it implies that the NR action leads to one equation of motion less than its relativistic counterpart. It turns out that the missing equation of motion is important, as it corresponds to the analog of the Poisson equation of NR gravity. We will see that this equation of motion is recovered by considering the NR limit of the equations of motion of NS-NS gravity, so that taking the NR limit of the action is not equivalent to taking the NR limit of the equations of motion. Secondly, since the zero torsion constraint (REF ) is not invariant under local scale symmetries, it can not arise as one of the NR equations of motion. We will indeed see that some of the NR equations of motion that we find amount to algebraic and differential equations for {{formula:e3048dcf-78ac-4329-acbd-a7c7e8ce8c83}} allowing as a solution the following set of constraints that is weaker than the SNC geometric constraints given in (REF ):The second constraint is sufficient to define a globally well-defined co-dimension two foliation, called integrable distribution {{cite:d2168fd3e1859b6ea0b943472bc42ee330594ac1}}.
{{formula:efadadff-4bdc-4642-946f-feaa439fed9e}}
| i | fe58b7f4290d4dfa613da810bb0cd931 |
We extended the calculations by using the covariant (relativistic) density functionals (CDF). The widely used parameter sets,
nonlinear parameter sets NL1, 2 {{cite:5b48b53a43cb0f25f072d57721f4a09ecf00de16}}, {{cite:2e1d23664e7bd4a5b922bb6913c4a1e490e9aec3}}, density-dependent RMF (DDRMF) parameter sets DD-ME1, 2, PKDD {{cite:26a7fe9a6bb74243fbf80914b63443c442ffd500}}, {{cite:72eb159ff2edda02e7d0bf61f2fa0ffbd708f4e7}}, {{cite:baafcf8e9a6d6140a2538c7302bb97b0d2e56c28}}, {{cite:a90ea1d47cc22ef1e9eff55de2e046387868f550}}, and density-dependent relativistic Hartree-Fock (DDRHF) parameter sets PKO1, 2, 3 {{cite:737c209d2d99070815c9582c4f61467486a60fc9}}, {{cite:c479a3b0f9fb1b1083fcca15b0307616fc2f6fc3}} are shown in Fig. REF .
The relativistic results generally scatter along a linear trend and show a somewhat different slope from the SHF results. Taking {{formula:52adfa61-aa43-4663-a531-93f10b9554ce}} mb as an example, the SHF and CDF results would give {{formula:b2fe9f8c-d72e-47ae-b7bf-09f3b698027e}} and {{formula:5f24c65b-9b41-4734-85b0-f5a2253a4232}} MeV, respectively. The SHF prediction is about 61% larger than the CDF one.
| r | f681ff930d2a99fa726d92b2243eeb87 |
Most of the previous works on QG focus on generating the SQuAD-style single-hop question, which is relevant to one fact obtainable from a single sentence. Recently, there has been a surge of interest in QG for more complex multi-hop question generation, such as HotpotQA-style questions {{cite:4f74bc4adce950af210a96f570ec07d1eb61be6d}}, {{cite:86b6d58e7f806f719c0e01250b0636423bb3e2b2}}, {{cite:79bc5e2edde6def78a3f22212a22422d3e083cc0}}, {{cite:79831f7b4877a3c46e224b04efe6c6f3c3350dd0}}, {{cite:5d4d5ced78fb5f9d059acd2f1b9f99c8d50b8bdb}}, {{cite:1e3070b7be0c07fb7d86fde794f49de14b4e549a}}, {{cite:90f588864e644862c6d328899c22fdade4d4ca6e}}. This is a more challenging task that requires identifying multiple relevant pieces of information from multiple paragraphs, and reasoning over them to fulfill the generation. Due to the multi-hop nature of MQA task, different models {{cite:86b6d58e7f806f719c0e01250b0636423bb3e2b2}}, {{cite:79bc5e2edde6def78a3f22212a22422d3e083cc0}}, {{cite:79831f7b4877a3c46e224b04efe6c6f3c3350dd0}}, {{cite:90f588864e644862c6d328899c22fdade4d4ca6e}} have been proposed to introduce graph-based networks into the traditional Sequence-to-sequence (Seq2Seq) framework to encode the multi-hop information. However, some of the most recent work has shown that the graph structure may not be necessary, and can be replaced with Transformers or proper use of large pre-trained models for multi-hop QA {{cite:d7d9965e9e951781e4dd3bf47ee94bc4a23ab377}}, {{cite:f57140089c4efa530ca827053d9226335f41fc0a}}. This motivates us to explore Transformer-based architectures for the relational reasoning requirements of the multi-hop QG (MQG) task.
| i | 12d237db4a73b876a91f3243173181d3 |
We present a simple and intuitive approach to semi-supervised learning on (potentially) infinite streams of unlabeled data. Our approach integrates insights from different bodies of work including self-training {{cite:c08f557afac206c3dd65325c05723c8b922052f1}}, {{cite:0b0e3f5448ddddfd825bf035de7b4572d66a62c5}}, pseudo-labelling {{cite:a546cad1c681b7ac1de058ab17653ce22ff0124d}}, {{cite:697621f83ea468de57e9886d7153ad1968b1ae33}}, {{cite:b738f90c42cc64100ca559e6eea937886cf05610}}, continual/iterated learning {{cite:5617fef28c3bbbaa5cfe8ad52be8cfd84c736daf}}, {{cite:fcfcd238a167c02c13c32f1a932cf9dbe93ea91e}}, {{cite:c5784c8b7c7bbec61f018a868157952c1fd94257}}, {{cite:da15dadb388f64fa81bc97e627e711d6319b082a}}, {{cite:35879ee76f32164cadfddbe72d119c405d66ddc9}}, and few-shot learning {{cite:775ad8866d3183f853470698e9b38916ca0eacf3}}, {{cite:dbb2ac32cbdb5ac20ad811dba594690bd68ea5cb}}. We demonstrate a number of surprising conclusions: (1) Unlabeled domain-agnostic internet streams can be used to significantly improve models for specialized tasks and data domains, including surface normal prediction, semantic segmentation, and few-shot fine-grained image classification spanning diverse domains including medical, satellite, and agricultural imagery. In this work, we use unlabeled images from ImageNet-21k {{cite:48f06804386317b22d3d6af25ad7a116174b25da}}. While we do not use the labels, it is still a curated dataset that may potentially influence the performance. A crucial future work would be to analyze SST with truly in-the-wild image samples. This will also allow to go beyond the use of 14M images for learning better representation in a never ending fashion. (2) Continual learning on streams can be initialized with very impoverished models trained (from scratch) on tens of labeled examples. This is in contrast with much work in semi-supervised learning that requires a good model for initialization. (3) Contrary to popular approaches in semi-supervised learning that make use of massive compute resources for storing and processing data, streaming learning requires modest computational infrastructure since it naturally breaks up massive datasets into slices that are manageable for processing. From this perspective, continual learning on streams can help democratize research and development for scalable, lifelong ML.
| d | 8af61baaff39a6f89fd494b18094cd62 |
In the following, we will start by a summary of the canonical quantization of the free electromagnetic field in the Coulomb gauge using the LP field in position space and its equivalent in momentum space to make a link with the standard notations of the quantum optics literature {{cite:f42996eeef679d44a99bd2e137137f9f65f735f8}}, {{cite:55225dc96ee2b61a0b1bfcf7ed39b6c8587eb826}}, {{cite:50bf25fc146b59c6e70df16cbd7f6e38e920370c}}, {{cite:d754dbe9edda5301aa153d244cd5a49de1eb976e}}, {{cite:dd3c58ed459f05b30faa307f2f0948c13c1f1ae1}}. Then we will introduce the BB quantization using a slightly different notation than the one used originaly by Białynicki-Birula, which is more convenient to write the isomorphism linking the LP and BB quantizations. After giving the explicit formulation of this isomorphism, we will show through a few examples that the two quantized theories are indeed equivalent and that the passage from one to the other is explicitely given by the isomorphism. Finally, we will discuss the time evolution within both theories, by explicitly linking their quantum Hamiltonian operators which represent the total energy of the system and the generator of the dynamics. This step ensures that the equivalence is preserved at any time.
| i | d0b14998310511409b0ff726abdbe378 |
There is a range of GNN variants, that implement different aggregation strategies. In this section, we focus on standard graph convolutional networks (GCNs) {{cite:083cb01c53f4bdc69615b2ef023b51bc7f262f2d}} and graph attention networks (GATs) {{cite:a25387635eddaebbc53f361386354e00002506d9}}, since they are the core of both RDGCN {{cite:3ea0249802642738338c3a76e74cbeffd0265b6e}} and RREA {{cite:8fbd218dee50dbf5fc9ceef52a12a8aedfc12fcc}}; two of the proposed methods that we evaluate in this study and describe in Section REF .
{{figure:ee1ef8ef-f697-4e40-9cf6-828ed178c5e7}} | m | 75f9d4a6c9de94bcca4545dbc1a14f03 |
There have recently been attempts to test the idea of braneworld against
observations {{cite:666f400e688405edea917296c9094df6ac068e6f}}, {{cite:dde3eefb594717f80a0f1d414807a8bf0903558c}}, {{cite:07a00396f5cd5fae63bfab3ad4a1c19e30c7351c}}, {{cite:9302670b86b5f5dba824578802b9d5b0b11abfb0}}, {{cite:f285503c9fccff064121ae781d0b4c4786b35e07}}, {{cite:b5961e578fbbb85d38ef55abb60f67757196b765}}. There have also been a
number of recent investigations on possible ways for detection of wormholes {{cite:2d9db6a99a9788b787b309ade747ca41d31da217}}, {{cite:e7e6a16a8d39b810ce001910ffd7043bc246e948}}, {{cite:acc04b90dc613e7258481f39921dcaf38fca83ef}}, {{cite:a7daa211002b5115cf7ea0bf22e43b09a475019e}}, {{cite:aaace488aad64612eb2991d94ba8996b7d198ccb}}, {{cite:730afcfbde7dc0d65fcb19b15d7db7608fe74404}}.
Our theoretical model of brane wormhole satisfies all the properties required to describe a traversable
wormhole without requiring exotic matter. It also imposes two very important constraints on the
brane tension,which is one of the most crucial parameters involved in the study of braneworld
and more importantly, both the constraints are in confirmation with ones obtained from studies
on different aspects of braneworld including fundamental aspects and also aspects related
to black holes. Thus we conclude with the notion that the Kuchowicz metric potential provides physically
acceptable and theoretical sound solutions and showing consistency with both wormhole and braneworld in presence of ordinary matter. More boldly we can claim from our analysis that if wormholes do exist in nature, then it must be true that our universe has a very high likelihood of being a 3-brane embedded in higher dimensions.
| d | 9b0a96d66fdc74f711374c9823d44d66 |
In the prototype, we represent each clause in a proof state only by its size and order number, applying a logistic regression as a Q-value function. We will need an elaborate feature extraction procedure to complete this oversimplified model to a competitive ATP. We plan to use graph neural networks similar to those used for lazyCoP {{cite:725ce5eeb383772621680ff5ce38167366861a9f}} and then compare and combine them with the graph representation of clause lineage pioneered by Deepire. We also plan to test training algorithm interchangeability by using IMPALA {{cite:5ca0b54c9706f4d9007887c140f64cb857edcc5b}} and Ape-X {{cite:e23c803511db0882e30214155ecbdb7fe2bba275}} in addition to DQN.
| d | cd92d5760e1d139ef45c3019c867524e |
Although no available measurement of the {{formula:248df951-4c0a-4e36-a5fc-d55717a91fdd}} {{formula:40f0b04b-85bb-45a2-8911-1953501f592a}}
{{formula:41790225-694f-47e9-9a63-54208d801308}} decays is enumerated by PDG so far {{cite:5d94e8627021c7cfc48745b6488cf9e77982c316}},
there is renewed experimental interest in {{formula:fbf1d891-6699-4b7b-8eb5-faf58975ee9e}} decays
with the advent of high statistics {{formula:988dfbd1-813a-431f-8ae7-9f85ae8f6e17}} experiments.
For example, some {{formula:8df5df0d-9a89-4b5e-9def-98327ef70ffc}} fully reconstructed {{formula:2a9a6945-9f64-4551-8e45-3f90417acaba}}
events per day can be reached with WASA at COSY {{cite:1441ee842d1d503651cd8d432ed8ec757f9696c5}};
Approximately {{formula:5aa0a6ef-2db9-423b-b098-bae3f2f523ae}} {{formula:d080e4fc-0e7b-44ae-b778-07f94246aebb}} events per hour
are expected with Crystal Ball at MAMI {{cite:24a47ba04c891406141277b8ee7c84f041c0cea0}};
With one year's luminosity at {{formula:ab8f2d6e-9fd5-4c58-8879-c5c468fb36e0}} peak, some 60 million
{{formula:cf1c0360-972d-4c0f-84bd-7b914eee3e4a}} events could be collected by BESIII at BEPCII
{{cite:66b2ccffcd481552addf67cd7856d6c8105a963d}};
KLOE-2 at DA{{formula:3c4409d8-058c-4e5f-8fba-f842c17c812b}} NE experiment expects to increase this sample
up to about a few {{formula:99f7c6ef-d1c6-48ef-8104-2e0905f2262a}} integral luminosity per year within
the next running {{cite:18b0d58ce09a4f0db41fbe281f00d6af6d1b64c3}}.
We take BESIII as an example to estimate the production
rate of {{formula:c02d6106-c683-4c69-a0b9-b39d1f580a0b}} {{formula:7a32d4bc-bff0-4cfc-8bd9-03f1d587a13b}} {{formula:ea234885-81f2-4f83-bcaf-a4e27a0ba3c6}} decays.
It is estimated that there are more than {{formula:8bce7a6e-6b6b-4c23-8006-4584b18a56f7}}
{{formula:c67ef958-52f2-4afe-a3d7-ba8e8aeab21f}} sample, corresponding to the radiative
decay {{formula:71cb8de4-9311-4ea6-9c6d-d78cd0f774a6}} {{formula:6d4666f7-33ac-419e-ad84-f3059eea90e5}} {{formula:3cb5253d-3d99-4f37-be9e-37f13fd80886}} with
some {{formula:06c79569-8c5d-4ccc-9645-fa7580e94df8}} {{formula:c25333fc-378a-49eb-8677-338efd835463}} dataset accumulated at BESIII
{{cite:66b2ccffcd481552addf67cd7856d6c8105a963d}}.
Given the detection efficiency for {{formula:a5d2bd6a-56f9-48f5-b5cd-d40bf715e5e8}}
{{formula:2b9ca213-b57c-4ea3-9850-7a51d8c4260c}} {{formula:39d5040f-7b6d-4eb7-b819-9905b193f161}} is about 17%
{{cite:839542a7efe019fe7c0055643462e30d7a5db4c1}}, some 2000
{{formula:37122e26-6dad-49b0-8bcb-0cc6c4852189}} {{formula:152b8994-270f-4eb2-ab6c-acc4b5def60f}} {{formula:9b254e7b-01c2-4709-aab4-e000191dfccb}}
and some 100
{{formula:ba2e959f-9c85-4d40-933c-ea608d1dae47}} {{formula:ff623df7-9282-4559-ab31-6ca4996cdda9}} {{formula:af0e61c4-7b6f-40f2-a353-79f2ab0754a8}}
events could be observed at BESIII[7].
[7]
In fact, the {{formula:07a56566-2476-4e8e-a3ec-9e0e1e0838fd}} meson decays mainly into
{{formula:fbbc39c9-990b-4929-bdc3-69c2ae17e278}} and the neutral pion decays mostly into
two photon. So the detection efficiency will be less
than 17% for {{formula:6221d0bf-d2d2-41fe-a892-ac4ef032b6c2}} {{formula:f9628c50-522a-497e-a967-cb83ed142dd4}} {{formula:7f800829-b15c-4611-b2a7-d568dd90ca52}}
decays due to much more final states.
According to the referee's suggestion, the reconstruction
efficiency of each photon is {{formula:4f4c7744-f9df-4cde-80d6-f7bef3618541}} 80%, so the
about 100 events for {{formula:4ce9c8f1-320c-4826-b2b7-8293a6bff007}} {{formula:246e02fe-a308-44ae-abf3-6c68752a4187}} {{formula:1854680d-5ad7-4202-82f4-d95fef65cbcb}}
could be observed at BESIII.
The corresponding distribution of dilepton spectra are
displayed in Fig.REF .
Our studies also show that
(1) the influence of the mass and width of vector mesons on the
normalization distribution of
{{formula:284abee1-77bd-41d8-a8e9-7c3463cdd241}}
is small[8].
[8]
Here, the maximum invariant mass of electron-positron pair is
{{formula:12b56770-3c32-47a2-9414-0f628359c3bc}} {{formula:e3cd3733-8cf0-47c0-b605-4108b6236464}} {{formula:7aea589f-67b9-4445-a3cb-e7cbd85d7ef8}} ,
so {{formula:644fd0d2-e3fe-47f7-89a7-881b75fff4bb}} {{formula:7417a7c9-e725-4d59-a38e-8346ef203f91}}
{{formula:4f16653a-4cee-4069-9afc-35bb2c380f66}} {{formula:f89b1359-7208-4286-a58f-22e02d52baa9}}
{{formula:8c0a1d8a-8294-4129-b3d3-4f202ab57ec1}} is less than {{formula:4dfd607e-7ba2-4826-ac57-1497a337645e}} .
In addition, the ratio {{formula:9b129074-dd8e-4bd8-ba75-5dbbeb116524}} {{formula:11e6e157-9046-4665-bb88-7b2d8b142417}} 1% for
{{formula:31588b14-0d5d-47a5-8eb3-9d30166cd15b}} meson and {{formula:293fbb1d-40d0-4904-8c68-044930ecd58d}} 20% for {{formula:2d35c015-a7ae-4afd-9b1e-15ca48afec8f}} meson,
so with {{formula:4a9f908e-abd1-4ef7-bc8b-3db83a28bd58}} ,
the factor {{formula:28cce886-b42d-48d7-a7e8-77948db939ae}} {{formula:5e6d8a4d-ad4a-4228-a393-69de57f816f3}} 1.11
for {{formula:0aac310a-060e-47c7-bee2-0c9d8209af3f}} meson and {{formula:903a2629-eb2a-40ee-b90a-b2573839cd2d}} 1.07 for {{formula:7e0444d5-ff9a-4021-8018-cb9f24c7480f}} meson,
that is to say, the effects of the mass and width of vector
meson are about 10%. At the maximum position in the
dilepton distribution {{formula:a37779ce-931a-4983-b454-8e4f26a628f9}} {{formula:a8440b3c-7d39-4b6a-96e6-5c1a7e423346}} {{formula:1b739c02-f095-4934-adaf-e88987cb78e4}} MeV,
the factor {{formula:03912bd1-5a46-4d66-a7bb-47d4545e71c1}} {{formula:0a7aeb05-b8d4-4380-b665-1259253d8093}} 99.99%
for {{formula:cff76f2e-a372-4c92-b2f0-35da512323cb}} meson and {{formula:5aef266e-c73c-493b-b45d-d9bd7ac146b6}} 96.44% for {{formula:5e37e1aa-ad24-4574-9075-fe4cebad7692}} meson,
that is to say, the effects of the mass and width of vector
meson are ignorable tiny for {{formula:cdcb4c6d-40c1-4947-a8b0-b036c7c729dd}} meson and less than
4% for {{formula:e936281a-d97c-4920-9960-90e0c8fc5378}} meson.
(2) The maximum position in the
distribution is near dilepton threshold[9],
[9]
It is shown from Eq.(REF ) that the differential
width is proportional to {{formula:bd3544bd-f614-4305-8993-a4153338f43a}} ,
so the spectra lineshape tends to the maximum with
{{formula:eb9e92ea-b895-4637-8269-63e5cc2e562a}} moving to the dilepton threshold.
In addition, because {{formula:68f5424c-6587-4456-8316-5887f611bc80}} is far away
from the mass of the vector resonance, there is no peak
near the tail of the dilepton distribution and
the shapeline is falling down smoothly.
i.e. {{formula:0e1099b5-f6a1-4f2a-bd5d-b84f80dd43fd}} {{formula:a7a2e50c-f14a-4919-9997-c4924245832b}} {{formula:e5857eab-1b5f-4a8e-9823-1c7deafda65f}} MeV,
the corresponding common momentum of vector mesons {{formula:980a913b-027a-4242-88c5-3fe85ab22fc9}}
and {{formula:21c360ce-eb8f-4d05-9e76-b16550d94c4c}} in the {{formula:cd59eb07-ff3b-4004-8fe2-6a28435d5a14}} rest frame are
{{formula:1e9f0a54-4fc0-4cdf-89e3-9c4306e2fdbe}} MeV and {{formula:bae0e60a-5c01-4a53-83be-4681303e5fd3}} MeV, respectively.
This distinctive feature will be helpful to distinguish
signals from backgrounds.
| d | f2931a0b71faaf4766e3bbd711924103 |
Cloud computing has allowed massive data collection from users, forming Big Data for machine learning in 2010s {{cite:7f0936323592d86706432cf8ee4f03af66b4c7aa}}, {{cite:51bc08de429ba9e86288302a37a374c074a78d61}}. However, because of the privacy concerns, such as (1) utilization of them other than the original intent or (2) leakage of them by cyberattacks, privacy related regulations are getting severe these days in order to protect especially those who are not information literate including children against unintended use of personal data{{cite:421b6bbcc2f88986bb9322f8eb0492bef26ea74e}}, {{cite:2165c0704c5e9d7d294c8b4f566716dce2004ce8}}, {{cite:eddbca2e78b35e9649cf6f758c20d467c8131adf}}, {{cite:b7dd5799ae5f0237a4fd34a2655334ee07c66b55}}.
| i | 779c8bc1abda9636d01b06368ca08c85 |
Humans possess a remarkable ability to parse images simply by looking at them.
In a blink of an eye, a human can fully analyze an image and separate all its components.
People can perform several tasks simultaneously by analyzing an image, e.g., object detection and contour detection.
Furthermore, humans can easily generalize from observing a set of objects to recognizing objects that have never been seen before.
Although humans enjoy an inherent capacity for generalization, they lack the processing power given by computers.
That is, to process a large amount of information (e.g., images) in a reduced interval of time.
The separation of an image into its components (i.e., join pixels into regions) according to some features is called image segmentation {{cite:567430fe5479cd0c37b5051cc47c00168d25d3d5}}.
Reproducing this process at or above the human level on a computer is not an easy task, and several approaches have been proposed to address it {{cite:da13073ff6e4a0816079d712d5b60ac9b2104993}}.
Nevertheless, the segmentation task continues to be challenging mainly due to variability, i.e., when the visual tasks are performed on a computer there is a considerable variation in pose, appearance, viewpoint, illumination, and occlusion throughout different instances of the same image.
Thus, a type of segmentation commonly used is semantic segmentation (SS).
SS is an essential part of the pipeline in computer vision projects.
It extracts and analyzes useful and meaningful information, in addition to classifying the regions obtained within an image.
In other words, by improving the segmentation stage, the computer vision's final output is also enhanced.
{{figure:250edcb3-8ec3-454b-a3a8-c6701568028b}} | i | 0531d7503be7ac01a428b1d1787eb726 |
Hioki and Maeda {{cite:2c9d34e3284c0a939b0baece51415f4e556fca9f}} characterized the distortion and shadow size by proposing the two observables, viz. {{formula:e1280375-fdd3-4a9c-963c-f98e6b4cd9cd}} and {{formula:55749970-ad0e-4d14-b974-3babed9d2634}} . They approximate the shadow by a perfect reference circle, with {{formula:5ecef5c9-25ff-4cb6-b85c-a46eaffafeb5}} being the radius of this circle, and {{formula:37c94d9f-9c39-469d-8cf3-4e136eeabe4e}} , the deviation of the left edge of the shadow from the circle boundary {{cite:2c9d34e3284c0a939b0baece51415f4e556fca9f}}.
The shadow reference circle coincides at the top ({{formula:1ad312a7-0293-40f4-9976-06809e1e538e}} , {{formula:cd076cb3-9340-48e9-a138-bbfb3873e583}} ), bottom ({{formula:2acee965-dcf4-407c-9e17-698835446f81}} , {{formula:3214fa5d-b923-4a56-bc22-0ced9a8011c9}} ) and right ({{formula:95ebf61c-d53f-4392-95db-95b06883eb88}} ) edges with the shadow contour {{cite:c220c76a5d155f20dfbed212e75b8e17a6092fe9}}.
{{figure:d1cd69e1-c159-4870-83a6-a816b79e99db}}{{table:2b3f7c06-7e47-4477-8c46-0499d870d03d}}{{figure:63561bb0-e9fa-44a8-a78a-62dafe26c7a0}} | m | 2d7982df85a8f96dd67d4e51a7f7164d |
Our results in this paper apply to de Sitter geometries and inflation, at tree-level. Indeed, our MLT and the ansatz we employ for our partial-energy shifts follow from de Sitter mode functions. It would be interesting to extend our results to other accelerating FLRW spacetimes, with help from the recent generalisation of the COT to backgrounds away from de Sitter space {{cite:9dfb8f809500cf4633ab1c727163d97ccd6d511b}}. The ansatz that we work with, for both the three-point and four-point functions, are also applicable to tree-level only. We expect the MLT constraint that we derive in Section to be valid away from the tree-level approximation, however technical difficulties in going beyond tree-level lie within writing down the appropriate ansatz. Indeed, a rational ansatz is very important in Section such that we can use Cauchy's integral theorem. We leave the interesting generalisation of our results to loop level for future work.
| i | 39adb20901d05e305aaa8178bdb0c51d |
Other approaches, such as GradCAM {{cite:13f4d355ef4f868bea059c165ae8b6eb7076e9e0}}, calculate gradients by back-propagating the prediction score through the target layer of the network and apply them as weights to combine the forward feature maps. These methods are generally faster than RISE since they only require a single or constant number of queries to the network {{cite:2ac24a0d351b7de2a4c2689384a91bcd332be1b8}}. However, results of GradCAM merely reflect infinitesimal changes of the prediction, and these changes are not necessarily reflective of changes large enough to alter the decision of the network. Naturally, a question arises: “Can one method produce results that truly reflect the model decision in a more efficient way?"
| i | ed2ac053af6191d5be364f71596fb02a |
(1) First, we encode relation instances in {{formula:74bcb6ad-6b75-4fc9-8f7c-c0d90664c8d9}} and {{formula:a1261e69-7d85-4fa4-a592-724b661f0c42}} using the entity pair encoder implemented as the pretrained BERT {{cite:6b937ffe94ef068ad218e2add20d2b352068eb88}}, which takes relation instances {{formula:4b70d439-d4b2-4e1d-ac49-4fa9205c3732}} , and {{formula:c9af80cd-731b-41e6-87a9-12848e01b90f}} , as input, and output relation representation {{formula:077e930c-e221-439e-8eaf-9f93639ddcb7}} , {{formula:0467cdae-7964-45a4-bd1c-836c51d7957f}} . However, high-dimensional {{formula:22591255-a28b-4b1a-9931-18f2b18194b1}} can encode a mixture of various aspects of linguistic features and the derived clusters from {{formula:41e493f6-9e65-4e88-8ba4-aa5b8cb3c8a4}} cannot explicit align with desired relational classes.
| m | 3597c6968ae185f4dd72d92687756016 |
Transfer-MAML The transfer meta-learning model introduced in {{cite:21abd44978d2e4feff54fb5b8b10df358e7b547b}}, which learns a global model on the Train S-Set, and then transfers the global weights to learn the MAML.
| m | 0649a3509de871025bf34843960263f3 |
We conclude this section with a few remarks on the above complexity results of UCGS.
First, we note that UCGS is similar to FGM in {{cite:2de56db4e44f4d557265a20536b6bb622dce010e}} in the sense that the number of gradient evaluations generalizes the accelearated gradient descent method in {{cite:18a2b03a1384328e0133b6d6553cebf03d2fad82}}. From Theorem , number of gradient evaluations required by UCGS to compute an approximate solution is {{formula:a044a35f-039e-4e04-920b-f3e6d3bc5169}} . In the smooth case when {{formula:f7cf471c-4e44-42e2-b82f-dd2d7d09eeff}} , this becomes {{formula:794da722-0071-4b14-8ae0-d9679e402f1c}} which matches the complexities of gradient evaluations in n{{cite:2de56db4e44f4d557265a20536b6bb622dce010e}}, {{cite:18a2b03a1384328e0133b6d6553cebf03d2fad82}}.
Second, unlike FGM that requires exact solutions to projection subproblems, we have a bound on the number of linear objective optimizations required to solve the projection subproblem (). From this perspective, UCGS is a generalization of CGS in {{cite:d9b5a269991b877ff36e389afa9a6c3c9c14c8b8}} as a universal method that covers not only the smooth case (when {{formula:2f4644cf-d7e7-457c-a902-f4585e9da982}} ) but also the weakly smooth case (when {{formula:046037cb-d9c1-421e-90af-443c017e9773}} , without requiring any knowledge of Hölder exponent {{formula:164f97de-961a-44b9-b491-1b5039511553}} and constant {{formula:a041caa0-ec27-4678-86e7-f19e3a65636f}} . Indeed, when {{formula:23d84304-beca-429c-8bfc-8ae2902cccbd}} our complexity on the number of linear objective optimizations is on the order of {{formula:ef53653e-53c6-4874-9cee-43d034612752}} , which matches the that of CGS in {{cite:d9b5a269991b877ff36e389afa9a6c3c9c14c8b8}}.
Third, the number of linear objective optimizations and gradient evaluations when CG is applied to (REF ) was shown to be {{formula:b652e6fb-52c3-4966-9326-4aa0fa2b2050}} in {{cite:746f919bc93a3ea8a8f32601932585c607fa66c9}}, {{cite:3ce13366637e6d8a7138e8625ffdb43c09d990d2}}. In view of Theorem , UCGS benefits from sliding and only requires {{formula:d500c17c-eac2-47ae-b625-1a40e1146ef7}} gradient evaluations and {{formula:9c8c2dcf-a2c4-4d76-86ff-570b37bbc39a}} linear objective optimizations which are both improvements over the results in {{cite:746f919bc93a3ea8a8f32601932585c607fa66c9}}, {{cite:3ce13366637e6d8a7138e8625ffdb43c09d990d2}} whenever {{formula:029cf9c7-85d8-4d84-bab2-d60ef28f91b0}} .
Fourth, our proposed UCGS method is not only a universal method generalization of the CGS in {{cite:d9b5a269991b877ff36e389afa9a6c3c9c14c8b8}}. Indeed, there are more features added for practical implementation: it has an implementable exit criterion and allows for an approximate solution to (REF ). Note that such added features of the UCGS does not affect its theoretical complexity.
Finally, we use the same accuracy constant {{formula:3286aaa5-15f2-45f8-8c9e-697d64ce4c30}} for approximately solving the linear subproblems in setting the parameters {{formula:0d978714-8484-432d-b987-94de8545b6ae}} and {{formula:5b6e96fb-3c3d-41d2-92f4-5be038315ef4}} . It is easy to change the proof if we use different accuracy constants for {{formula:0d759a9f-4a9b-4f36-8ee7-345883c2996b}} and {{formula:557ed6fe-9ca5-4fc9-bba6-162aa2805614}} .
| m | cfe0bc10231d8f8db227b829661d6fb3 |
where where each {{formula:0842ba7c-22f4-4614-890a-52294401291e}} represents the oscillations of the function at a different length scale, and our tensor {{formula:7c44131d-595a-4efc-8483-a514f93e6a4b}} explores correlations between different length scales. This implicit renormalization scheme is a discovery of the quantum computing community that has not been sufficiently exploited so far and which may empower many recent developments in the field of quantum finance and probability distribution analysis {{cite:c77bca3b10107ac9c08fd72319f27c2ba5635563}}, , {{cite:3f3384eab4c4f3f1b10a9cd8f4359b01e9aaf472}}.
| d | 7fb5021fc07cca034ab6e4d61c9853f9 |
Datasets and Baselines:
Evaluating treatment effect estimation methods requires all potential outcomes to be available, which is impossible due to the fundamental problem of causal inference. Thus, following {{cite:c81e267652c27695e2b2a99605f7dd99edad04b2}}, {{cite:30e729f98d0eabb55a8513bcc6226463d6e7e7e4}}, {{cite:a9e5058f3b45d2ab1ce63216566d2897daa91367}}, {{cite:fa10ba97be52ae5f3e033927aeac0aa7b86a317d}}, we experiment on two semi-synthetic datasets–Twins {{cite:f609281fb2552edf277c8d3ae4182d57c48aff0e}}, IHDP {{cite:e1f461cc814c448d911e7ece99c82e7b5fe8ddcf}}–that are derived from real-world RCTs (see Appendix for details). For these two datasets, ground truth potential outcomes (a.k.a. counterfactual outcomes) are synthesized and available, and hence can be used to study the effectiveness of models in predicting potential outcomes. We also experiment on one real-world dataset–Jobs {{cite:a6a763520de55e39130112b2ad1894f677a47044}}–where we observe only one potential outcome. Each dataset is split 64/16/20% into train/validation/test sets, similar to earlier efforts.
| r | d8d726b93ca6fa14ba2c8b9f1457274f |
Data Granularity.
For some coarse-grained tasks,
their pre-training dataset, e.g., the ImageNet{{cite:47ca2c2c8daaac4fe5e80f0bdac4e052add9ae32}} for image recognition,
usually has millions of images distributed over only thousands of classes.
This relatively dense distribution implies that a training batch may contain two different images from the same class,
but the contrastive model will still pull them away and sequentially make a mistake.
As for our benchmark,
it is almost impossible for an individual to appear twice in GaitLU-1M since the videos are collected around the world,
varying in locations, dates and photographers.
Therefore, we consider that GaitLU-1M contains only one walking sequence for each subject,
meaning that GaitSSB would not mistakenly pull two different sequences owning the same identity away.
Considering Eq. REF ,
we assume that the ability to pull negative pairs away learned at the pre-training stage is not misleading and thus pretty useful for gait recognition.
Overall Similarity.
The overall visual similarity often dominates in the final representation for contrastive frameworks{{cite:ce570f9aca80a4e047b2003f8e1ea012b8ed9d0a}}.
However, for gait recognition,
it is a similar camera view rather than the same identity that usually makes two silhouette sequences alike in overall appearance.
Hence,
using negative samples is a good choice since it tells the network needs to pull the negative pair away,
even two sequences similar in the camera angle.
| d | b8e04e72d9dac5d041a3423a56933c86 |
While dynamical systems theory is a natural language with which to frame DNN optimization, the complex dependence on optimizer, architecture, activation function, and training data has historically kept efforts in this direction to a minimum. This has led to a reliance on heuristic methods, such as iterative magnitude pruning, whose basis of success is still not clear {{cite:14b7860eb05a8f49acc1843c4ae5c795c4e200a1}}. Other groups have attempted to more principally examine DNN behavior by studying mathematical objects, such as the spectrum of the Hessian matrix {{cite:b763d3288614e30e2f3b593fb372519496b6f905}} and the spectrum of the principal orthogonal decomposition {{cite:4172f58f43469f575ba6343e342f16ffb69f2b98}}. While this work has been influential and led to new insight, the connection between these metrics and the (future) dynamics of DNN training is not direct.
| d | deb77d56a1720986091441a1d39b2887 |
The nebular Heii{{formula:582c28e4-fbf5-415e-bf0d-df5b65f0e19f}} 4686 emission observed in some SF
galaxies has often been attributed to X-ray emission from HMXBs
{{cite:7127c6c855fd032d6aa790c512fe6a8fba498f3d}}, {{cite:24538526f605df8c2fb4d0621ad068ccb3959d4b}}. This hypothesis has been critically
tested by {{cite:4b001922419cdaed7893bb7a0bb33c0cbf4037a3}} using photoionization grids
accounting for the combined contribution of HMXBs and young massive
stars for metallicities from Z=0.02 to Z=0.001 ({{formula:10ee9d2b-a3f0-4ff1-91fa-20acd7d47fcb}} 5{{formula:40e05b9a-8ea0-4166-a51e-ea57ca58d569}}
solar), and provide predictions for the Heii/H{{formula:233d4be5-c574-4163-b8f5-55966d1b100a}} ratio
that correspond to a range of values of the {{formula:55c2ea06-e434-451b-bf9e-7b174730174a}} /SFR
ratio. We estimate a SFR of 0.14 M{{formula:553bb3dd-5422-4573-a734-0b425999ad15}} yr{{formula:f60d0140-2b3a-452f-afe6-2413598cea87}} for IZw18The IZw18 integrated {{formula:05a3e7cb-1c29-4a3e-a05d-04f9a4d4e41a}} =4.36{{formula:735ff09f-6f05-4f45-adc1-6cf8d933a683}} 10{{formula:597f899b-7948-4954-8b51-ae8be7e075a3}} erg s{{formula:82d81f3d-39c9-4ff2-b0a0-ac07978f4e56}} cm{{formula:b499654b-fd7e-4fa0-9ffb-da640ebe3b15}} (K16) was translated to {{formula:b52405d1-02a9-4ab5-9141-5a90e0483e0c}} assuming a distance of 18.2 Mpc.
based on its {{formula:f5d62a0a-9627-4a17-962a-d57d553702a1}} =1.73{{formula:a222132d-dac6-4b5b-83a3-3959ba445f3b}} 10{{formula:1acb3c7f-de37-41a2-9dc7-f81217c97bd7}} erg s{{formula:7b5efe8b-7278-40ff-afa9-69cd9a3f43f5}} (K16) and
the widely used SFR-L(H{{formula:e23e23e5-4b7d-4397-b78f-4bcf9a525538}} ) relation from {{cite:32305392b4d9f79260577b02679201c5c1cc103d}}. Therefore, taking the
{{formula:dd84d46d-d45d-40a0-ab6f-1da23501edda}} value in Table REF derived from
the 2002-04-10-XMM-Newton data set, this implies an observed
{{formula:6e6ee5a7-05fe-4aac-b258-2d0add9c8c38}} /SFR of 9{{formula:b2644884-7b93-4c7a-a641-fe5a8fcbabe1}} 10{{formula:a80a941d-330e-4005-8595-07912d94b4b2}}
erg s{{formula:5d09cd99-135e-47cd-b63a-de1b3ee00ea7}} /(M{{formula:7e234f30-ec04-425c-be55-c326a309b843}} yr{{formula:27b47aea-a9ba-4719-9c9b-b6692f55ff18}} ). According to S20's
predictions, this {{formula:c447fc26-44d5-4e30-aab6-426d55d576cd}} /SFR value results in Heii/H{{formula:500a926f-c03e-46ad-9ea0-5b00525875c0}} between 0.0004 to 0.0025, regardless of the metallicity
assumed in the models, a value well below the observed Heii/H{{formula:a6944e29-7c54-435e-95d8-ab5b368859f5}} of
0.023{{formula:8af9211c-bcfd-45cc-8f4b-db4a75f159ea}} 0.004 in IZw18 (K16).
To reinforce this result, we have computed the total Heii-ionizing photon
flux {{formula:7b524f18-1776-4f77-a8bb-5fc0aabda727}} (Heii) from Kerr BH and irradiated disk models of the X-ray
emission detected in the 2002-04-10-XMM-Newton observation.
The thin accretion disk around a Kerr BH model including a
Comptonization component provides an extrapolation to UV wavelengths
{{formula:aa719051-16cc-47d3-8d64-b8008a1c3cfa}} 228 Å similar to that of the multicolor disk models
used by S20.
The best fit for this model has very similar parameters to those reported
by {{cite:ae766ea7d76df2dbed77dcb4c82b873aa3953146}}, with an acceptable fitting quality ({{formula:a8b91b9b-3afe-4d81-8671-20d45d1c2d26}} /DoF=0.90).
The intrinsic (unabsorbed) {{formula:e47aa55b-f40f-4a9b-b517-e24761a1c75c}} (Heii) for this model is
{{formula:212a52a3-33f1-411d-a3ee-dd6d330b0f7e}} 48.4 photon s{{formula:8dd59936-286e-4102-95b2-a20fcb95819f}} , i.e.,{{formula:bbd6f74a-fe50-4d96-9ca9-98c8910b3fb1}} 50 times lower than
that of {{formula:5c8a09de-10c4-4e3f-9cf1-c8e097e4f80c}} (Heii)=50.1 photon s{{formula:f03744b5-755f-4aba-a8b0-7f29c1456d87}} reported by K15.
Meanwhile, the emission model of a disk irradiated by the Compton tail
{{cite:d2f78bcf4f265d403f84e1cbea33ba75f12b00d8}} is of particular interest, as the physical processes of
disk irradiation provide a meaningful description of the expected UV
spectrum to constrain more reliably {{formula:66c2dc3d-9bee-4c75-89bd-8fae30a2e1bf}} (Heii) {{cite:e90861845c27ac2a0eca1be2a191bbbb602c4fd8}}.
The best fit for this model has a slightly better fit quality
({{formula:153cd0a6-0224-4040-8834-fa7baa063558}} /DoF=0.93) with a local {{formula:5463e9f8-17cd-41f2-bb0f-7cccd2b7fe3e}} =1.5{{formula:c8ce28a1-1641-459d-95ae-e7cd71f379d4}} 0.8{{formula:3f99c139-388f-47e7-a6ae-a03ad36454f9}} 10{{formula:908794d2-eb3e-4419-a05f-5755e395e3c0}} cm{{formula:1ed0f4cd-f811-4bd7-aad9-acb75eb3a823}} ,
inner disk temperature 0.55{{formula:4acb505d-37d6-4c06-b380-78a569a1e642}} 0.25 keV,
photon index 2.9{{formula:1b60cad0-c763-445d-9527-52882ba6a964}} 0.6, and irradiated flux fraction of 2.3{{formula:475c2a92-17ea-48b7-9f38-28199879c6f4}} for the
{{cite:d2f78bcf4f265d403f84e1cbea33ba75f12b00d8}}.
The resulting intrinsic (unabsorbed) {{formula:407af5b6-253d-45d8-83a8-3ae37e2bedf4}} (Heii) is
{{formula:74a809a6-41b6-4038-bdf2-b88e349ee176}} 49.1 photon s{{formula:508f82a2-5cd1-4203-bb71-49490ef6e871}} , which is still 10 times lower than
observed.
It is worthwhile noting that the {{formula:54d62fa1-d43c-4f3e-8680-bfd4735fb7d6}} derived from
these models is very similar to that derived from a power-law model.
| d | fe409b3692bbb3f48e69cdefd0ac7549 |
In this section we review the classical definitions, algorithms and convergence results from convex optimization (mostly referring to {{cite:3a7df28d352f1f511eb3b0d79a299a87068d4f51}}, {{cite:20dd65c7183f158ef839af24ba92f766d9e3289f}}). As the scope of gradient methods in convex optimization is extremely large, we only introduce here the notions that are relevant to our connections with algorithms for MDPs.
| m | d7839c987f656af56367bab4ff22b886 |
Finding Steiner trees and related network design problems were intensively studied in undirected graphs, directed graphs, and planar graphs, from the viewpoint of approximation and parameterized algorithms {{cite:54616d54670c08d22b66a51b7f5ecd06d465fddd}}, {{cite:0e7c7242b720350168dfc8c82f47c2866b3f1140}}, {{cite:3a345fde5a6470851c6ffe223b0840c6c1649cc5}}, {{cite:f6001e5b0bd302b2b08835cb09cc03001dfc4ed0}}, {{cite:47633bbc48c589c36810f15900f55df723181376}}, {{cite:dd029097116152ab5fbd68a4e4989c1288198da3}}, {{cite:d02a50cbea6e7893cb857836bb760beff0ede0da}}, {{cite:ddae16fba6058bf0c4b2fd8a58208bb17cc580b0}}, {{cite:9e1a52b636278cfbe5909fa64ffcb76112ffab66}}, {{cite:d5708e2d90c65276977491321cae846a4cec290a}}, {{cite:f69c4cae715e1a2f303e5410ad9989cf3f29e4d7}}, {{cite:c13e98805e14b863850bcdb7e85252214cb422a3}}, {{cite:257c10af8d2d5cedf8f72202fb64cc7aef6717ba}}, {{cite:e2e8a98de4018e5055a925051e57a078a6e47f5e}}, {{cite:49d88dacc07117bae842cd371facd116f6fc1bad}}, {{cite:5a0a4f355b3aa79b6e9a4e31f597d2acdea4ac4a}}, {{cite:040c4a96b47c7a580dece1ae6db8bf2a1135e80b}}, {{cite:fff4d511888746dd0566f5496db523ade99f49ff}}, {{cite:7fc5867ae84c77c4aede558f1717d71e5eafaa8b}}, {{cite:6b81e4426da444510ef5dcab01da61564e9cce59}}, {{cite:3a8288e5c70563a1ace9731802479bea570a5d80}}, {{cite:1241e273bc26c811ed121e1816d7836beec94d53}}. The simplest problem of this type is Steiner Tree, where given a graph {{formula:d5eccbcb-54d0-4dfc-820b-9b9a901d659f}} and set {{formula:5a66272d-54d8-4933-89b2-ae46abcc2ffc}} of terminals, the task is to find a tree with smallest number of edges that contains every terminal. This problem models a network-design scenario where the terminals need to be connected to each other with a network of minimum cost. Steiner Forest is the generalization where we do not require connection between every pair of terminals, but have to satisfy a given set of demands. Formally, the input of Steiner Forest is a graph {{formula:3f6b4640-3086-45ee-8b23-8dea54684a45}} with pairs of vertices {{formula:bb119e12-a1c4-4b80-acbb-04eed1934b33}} , {{formula:699096d8-8926-4872-a946-609d87bffca4}} , {{formula:8607d8fb-b715-4aa6-aa7d-79a0f232a4c4}} , the task is to find a subgraph with the minimum number of edges that satisfies every request, that is, {{formula:578cbfe3-19ff-4a1f-8b3c-bb7375d91d87}} and {{formula:39444819-4cbd-4e55-ab4b-2905b923745a}} are in the same component of the solution for every {{formula:b60b9950-79d3-417e-96d8-f11d933dff7d}} .
| i | b735f3ac45f6bfdfd7e58bc07f8ab4f1 |
A variation over the previous iterator is the accumulator. Instead of directly applying the chosen gates to the target qubits, one defines an accumulator qubit, which is at state {{formula:517dc9ac-2b0f-4756-b1f1-904d19dba405}} until we control on the selected value of the indices, and stays {{formula:288e0e2e-65cc-41fe-b94b-1f60eed540a8}} until the end of the iterator, at which point it can be uncomputed since at the end the accumulator will be at disentangled state {{formula:74ea384a-6d1f-40f3-9a8a-fd3c344634da}} . A picture of this variant is figure 8 in {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}. This accumulator is specially useful because it will allow us to apply the Majorana fermion operator {{formula:19d4ba41-0b29-4494-b3fb-7f8b9ed4be79}} , as can be seen in figure 9 in {{cite:b8670a873d1a4ddfe034b70b6c459837b58e476a}}.
| m | fecba2f2584b4dcb433daec818cdaaf1 |
given some desired {{formula:bbe3ae5c-fc51-4664-a09b-8f34109c3216}} . The ranks found for {{formula:a2dea5f9-2da9-4c83-983f-63ba208db9c6}} are shown in Figure REF .
The POD bases for {{formula:9a7bdec6-2b52-45bf-bcb4-f54854701832}} and {{formula:2593651d-de3b-497d-b38a-2afed5df24bb}} reach full rank {{formula:cc6c84b6-bb7f-4db2-8d96-a12c8b87bda6}} at {{formula:368483a1-e078-4e71-bd33-cc07fcca3032}} and {{formula:1b2ca11e-8609-4dc3-87d8-0da3d8c6492a}} , respectively.
Full-rank is not found for the basis of {{formula:7b390439-c2f9-496a-9fb3-608557416122}} until {{formula:cd9b369f-a272-42b0-95ee-a6fefaec6dc1}} .
This behavior is expected since compared to {{formula:4676f12d-b8c0-4226-a38d-3cb4564fc392}} , the full ranks of {{formula:86cbc49a-1dfc-4517-837f-ece6d4f5e113}} and {{formula:85108a26-6cb4-457c-9f79-b69d1c263aed}} are relatively small. The singular values of both {{formula:eecc2c8b-4678-4710-94b8-c0eded3eb6a4}} and {{formula:92911ad2-cc56-4c08-9fbd-6e40e769567e}} also occupy a smaller range than for {{formula:6f84c9b9-afe6-41d3-9f2d-e1afbc3ff024}} .
Another notable behavior is that {{formula:9d477ea3-ba9e-4004-bb29-fa14b5be7ab0}} for {{formula:fbf7cea6-6134-47d9-b78e-086064d589d6}} , indicating that the solution contained in the time range over which {{formula:8b6cb38e-337a-4591-a503-f05530fa340d}} was generated is the most difficult to represent with few POD modes.
This is to be expected given that {{formula:bbd05654-1bf9-4265-9273-bb075523b8b0}} accounts for the solution during propagation of the radiation wave from the left boundary to the right, which is known to be a difficult phenomena for the POD to represent with low rank {{cite:e0bf581280e46b108921bda2f79981fb4f7b1e37}}, {{cite:38bafbb66022eb55886cbede81ac9c34d389a00f}}. Let us note here that the rank of expansion for each timeframe in the F-C test is exactly the size of the linear system that solves for the coefficients {{formula:ec6b3afe-6092-4684-9c0e-d9dde038069d}} (Eq. (REF )). This means that when using {{formula:72b0fe74-bc9f-40e3-a1e5-91a42a064a3c}} for instance, the largest linear system to solve in place of the BTE is a dense {{formula:8cfc574e-3219-4951-8375-8add69f76581}} system with {{formula:154adc93-b7ea-44d5-ad31-8ac9ffd7efc1}} , which is of significantly lower dimensionality than the original BTE ({{formula:e58fea47-6c41-4d9a-9ed7-935bf6dd9072}} ).
{{figure:5f703f6d-6a49-4387-b1ba-b1ef2469915e}} | r | d40cf50759257a312f22f09c5bbbf4dd |
In Section , we rigorously construct the (sequence of) statistical experiment(s) generated by the observation (REF ) under the dynamics (REF ) that we denote {{formula:904af4de-215c-42b7-a3fa-9fba96b008f1}} . It is well defined and regular in the classical sense of Ibragimov and Hasminski {{cite:d53d5e6c4a12f517b10f938a86946f5ecf80a416}} under strong integrability of the initial condition {{formula:7d830929-4ca8-4121-af9f-8355efc410b9}} and standard smoothness assumptions on the drift {{formula:a2297c73-df2d-4acb-a261-caa6f917783d}} and the diffusion matrix {{formula:76563f93-608f-4752-aeda-7ba4c9fd4e13}} , see Assumptions REF , REF , REF and REF and Proposition REF . The deep study of the identifiability of {{formula:dc54136f-0751-4cda-bf83-d6cca41a571c}} and the non-degeneracy of its information matrix {{formula:ef8fb611-8bc6-4d82-9659-9a3bcf8c1c7b}} is simplified via the accompanying experiment {{formula:da660557-b91b-49a1-a842-2c54be456129}} , where {{formula:a3e4c173-f1f5-45e3-baed-c36b68a0a01b}} is generated by the continuous observation of a solution to the McKean-Vlasov equation
{{formula:d9d4f80f-f121-4a63-b1aa-c5edfde9af1f}}
| r | 15cd6e9f64c1b2d28786208f9f02f504 |
In this paper, we introduced DETRtime, a novel time-series segmentation approach inspired by the recent success of the DETR architecture {{cite:7b2a96ea75b5aad8d58a65aa5dacc3c7a1256fea}}. Furthermore, we showed that deep learning models designed initially for image segmentation are also well-suited for EEG time-series data.
| d | 3a4930105d8978bf67590615d4b0b6ca |
Our proposed cross-view affordance knowledge transfer framework for affordance grounding is shown in Fig. REF . During training, we first use Resnet50 {{cite:1d1e330f027052e1e5daef6b1d595a77d49612f8}} to extract the features of exocentric and egocentric images to obtain {{formula:c068ac60-4530-4066-89fd-560fa728876b}} and {{formula:183f0efb-b718-49e1-9504-039c8b3a1158}} , respectively. Then, the Affordance Invariance Mining (AIM) module is introduced to extract affordance-specific clues ({{formula:7ae2a331-5675-4a66-ae55-efd2ab9560b5}} ) from the exocentric features (see in Sect. REF ). Subsequently, the Cross-view Feature Transfer (CFT) module is proposed to transfer the affordance features extracted from the exocentric to the egocentric view (see in Sect. REF ). Afterward, the features of the two branches ({{formula:b3a3ccfe-51e1-46df-91a2-e16b4964d59d}} and {{formula:8378846d-271e-4d27-9544-0bebf116f634}} ) are fed into the same convolution layer to obtain features {{formula:8481606e-f639-4cb1-a9a1-b42ea58a2101}} and {{formula:88a49c0f-8af0-4da9-9d7b-0c17fb8f4131}} respectively. We average the {{formula:71d3b3ca-a74f-45d5-b28d-b9d813ca6e8c}} through the global average pooling (GAP) layer to obtain the {{formula:961b41df-0846-42c7-bfd7-4663e87102fd}} and pass the {{formula:f552af19-8ae1-44f2-b780-0ae1e825aad4}} through the GAP layer to get the {{formula:ac37ec55-4aad-41e3-843b-479ae61a72a4}} . Later, {{formula:632fc9cf-c4b6-46e0-86ce-c6f3208c4ba5}} and {{formula:ada851b2-6ddd-4bc1-8401-9403e4a81713}} are fed into the same fully connected layer to obtain the affordance prediction. Finally, the Affordance Co-relation Preserving (ACP) strategy is devised to enhance the network's perception of affordance by aligning the co-relation matrix of the outputs of the two views (see in Sect. REF ). As shown in Fig. REF , during testing, we feed the egocentric object images into the network only through the egocentric branch and then use the CAM {{cite:f1c3b0e495a78059b0dfd588dd51b84ccb5c937d}} technique to obtain the affordance regions of the object (see in Sect. REF ). Table REF shows the dimensions, definitions, and meanings of the symbols used in the proposed approach.
| m | a60682c43e9ee2e3dc91e202ecc8f447 |
We thank S. Hilgenfeldt for helpful discussions over the course of this work.
The authors acknowledge support by the National Science Foundation under NSF CAREER Grant No. CBET-1846752 (MG) and by the Blue Waters project (OCI- 0725070, ACI- 1238993), a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.
This work used the Extreme Science and Engineering Discovery Environment (XSEDE) {{cite:8363c775ba16484f7743325328e9a9d9b76bd2b2}} Stampede2, supported by National Science Foundation grant no. ACI-1548562, at the Texas Advanced Computing Center (TACC) through allocation TG-MCB190004.
| m | ffd172aee20f6c199ef239d9182d680a |
The other school is metapath-based approaches.
A metapath means composite relation connecting two objects at the network schema level.
It has been adopted to capture semantic information {{cite:d258c0d8950b0769288d8b4462cfd981ef70d9ea}}, {{cite:be8f6060f7f8cc703c5d82e339bb71ea4e521d52}}.
Taking the movie data in Fig. REF as an example, the relations between user and item can be revealed by the metapath User-User-Movie (UUM) for the co-user relation and User-Director-Movie (UDM) for the co-director relation.
However, as stated in {{cite:4854b2fba77d8aa1289f97099529f867e9dbae1f}}, metapath-based methods, heavily relying on explicit path reachability, may obtain bad performance when path connections are sparse or noisy.
Also, rich structured information of nodes outside metapaths (e.g., their neighborhoods) is omitted in these approaches.
| i | 7dbbe2a193589083f2dc251ec6f9f914 |
Neural Timeseries to 2D: We divide the process of creating images from EEG signals into the following three steps.
Window Extraction: EEG time-series signals are extracted into windows of 2, 4, and 6 seconds. For example, if a signal contains 24 seconds, we get 12, 6, and, 4 no of windows respectively. Varying window length identifies the information content and plays a significant role in discriminating the classes. In some applications, we have the luxury to extract varying windows sizes depending on the task.
Power Spectral Analysis: Power spectral density (PSD) is estimated for the extracted window using the Welch method {{cite:8681c6c5990c0fc90c17d5615e670b7c02f9c322}}. Welch’s method is also known as the periodogram method for computing power spectrum, the time signal is divided into successive blocks followed by creating a periodogram for each block, and estimating the density by averaging. Oscillatory cortical activity related to meditation primarily observes in two frequency bands, theta (5-8Hz) and alpha (9-12Hz) {{cite:13a156e8ee07476dcd5d4e9f6a73c79b9fa064b2}}. These bands are further subdivided into theta1(5-6Hz),theta2(7-8 Hz), and alpha1(9-10Hz), alpha2(11-12Hz). For every channel, PSD is computed for the mentioned four bands.
Topographic (2D- 3 Channel) Plot: We use the topoplot function of the EEGLAB that transforms the 3D projection of electrodes in a 2-D circular view using interpolation on a fine cartesian grid {{cite:8605337535360e5cdbfbdff54279c74571e5b2c9}}. Topographic plots were earlier implemented in Bashivan’s work {{cite:7ff7b038f11a34ceb06fabe02db8856c1bd57c2f}}, and they combined plots from three bands to form one image of three channels, whereas we create one image of size 32 {{formula:fbab3e8f-43ed-4ba5-a175-5d883eb4813d}} 32 for each band having three RGB channels, and this might help to understand the significance of each band in the specific cognitive task. This plot preserves the relative distance between the neighboring electrodes and their underlying interaction, generating task-based latent representation using convolution.
{{figure:c3e556db-3cab-4fd5-9af1-910c15f9e891}}
2D to Prediction: Our model comprises 4 Blocks as shown in Fig. REF (b). The first two blocks are introduced to capture deep feature information and the third block for reducing the computation. The major components in these three blocks are regular Conv2D, depthwise spatial Conv2D, depthwise separable convolution, max pooling, ReLu(Rectified Linear Unit) activation function, and batch normalization.
Conv2D to learn richer features at every spatial scale. Depthwise convolution which acts on each input channel separately and extremely efficient to generate succinct representation {{cite:deb7fb98216b06510223ab1b2d7da42ee4a6ea2d}}. Depthwise separable convolutions factorize a regular convolution into a depthwise convolution and a (1,1) convolution called a pointwise convolution {{cite:8fc12011d3685857f85c2d1d8f7caac9d2b66116}}. This was initially introduced for generic object classification {{cite:7552a2ecc986ebe34fb794327992f13abe6fdb94}} and later used in Inception models {{cite:9ac6c1d280f10a25551e48a3934d77a2f760edc0}} to reduce the computation in the first few layers. Kernel sizes for the initial two blocks are 3{{formula:e3f00acd-ddac-4161-9d59-9a803f09740f}} 3 and 2{{formula:9ba1ef79-6a6e-4fe0-a417-a80c9e82c71f}} 2 for standard 2D convolution with 64 filters and 2{{formula:8898c12b-de7f-4bbe-8bfb-8b17f27eb52b}} 2 for Depthwise convolution. The third block comprises standard Conv2D and depthwise separable convolution of kernel size 2{{formula:cd335309-b365-4e72-887e-55a73e5e393e}} 2 with 64 and 12 filters respectively. ReLu activation is introduced in the initial two layers to prepare the network to learn complex representations and to generate faster convergence and better efficiency {{cite:fc9f2e8589c2b534453f3f76acaf8515d7587e3b}}.
The output of ReLu is processed by the Max Pooling operations for spatial sub-sampling, which downsample the feature maps by generating features in patches of the feature map {{cite:deb7fb98216b06510223ab1b2d7da42ee4a6ea2d}}. Batch normalization is performed at last in the three blocks to minimize internal covariate shift, which subsequently accelerates the training of deep neural nets and enables higher learning rates {{cite:9ac6c1d280f10a25551e48a3934d77a2f760edc0}}.
Fourth block contains flatten, two dense layers and a softmax activation function. A dense layer is employed to combine all the features learned from previous layers where every input weight is directly connected to the output of the next layer in a feed-forward fashion. Since we are doing multiclass classification, the output layer has a softmax activation function. Softmax as an activation function is used because the model requirement is to predict only the specific class, which results in high probability. To find out the loss of the model, categorical cross-entropy is used to predict the probability of a class.
Deep learning models are trained using tensorflow(keras) {{cite:616c2d39937156972f22e86f2b356e65d889bc85}} and machine learning algorithms employ scikit learn library {{cite:2693662158e497e6bbf3393f3f2572370d941f89}}. GPU NVIDIA GTX 1050(4GB RAM) are used for this study and the batch size are set to 30 because of memory constraints and kept the maximum epoch to 30 to maintain the timing constraint as well as to avoid overfitting and for optimal training and validation loss.
| m | 6f8571598f82a3ece93f3c224ca36b9f |
Weighted Boxes Fusion (WBF) {{cite:f80a07ccfa3adf876c8076497550006d6b24127d}} targets specifically at post-processing the bounding boxes from different models. Instead of selecting one best bounding box (NMS) or keeping all of the bounding boxes (Soft-NMS), WBF produces a weighted average of the bounding boxes in terms of position and size, so all of the to-be-fused bounding boxes can contribute to the final bounding box and no redundant bounding boxes are introduced.
| m | 059747e48d4d498c5fd3d41a5c159e23 |
Although there is a significant amount of literature on applied transfer learning procedures {{cite:f7b9cdc06cf62d4267e865f9527c860bdf785a71}}, {{cite:2af57572bf6773dc73392fa5a1b1305aacb91c5b}}, {{cite:a44daf6f539394945b1f07065f5c827cc0771c53}}, {{cite:21ee15239aa5afc148a8c1939640c89ea26ef750}}, the literature on rigorous mathematical formulations that lead to minimax optimal estimators is limited.
{{cite:830d814e70cc0c15025f6a107608c471965e2010}} consider transfer learning in the context of a stylized non-parametric classification setting under a different set of assumptions including a model that only allows posterior drift.
{{cite:7b726c6030a25e05847c2c6730d06a3643b0325a}} study classification settings similar to that of {{cite:830d814e70cc0c15025f6a107608c471965e2010}}, albeit under covariate-shift assumptions on the difference in source and target environments.
In strong contrast, while our methodology is parametric, our analysis is not limited to classification problems and it further supports more general environments including more general drift conditions between the target and source models, where indeed our analysis of the underlying geometry explicitly accounts for these differences.
| i | e6be79d449355c1b27852d095c48fc2b |
Some of the most recent state-of-the-art approaches to keyword detection consider the problem as a sequence-to-sequence generation task. The first research leveraging this tactic was proposed by {{cite:1e711859fc8209e3272746dda7d7b188f8a7b1c7}}, employing a generative model for keyword prediction with a recurrent encoder-decoder framework with an attention mechanism capable of detecting keywords in the input text sequence and also potentially finding keywords that do not appear in the text. Since finding absent keywords involves a very hard problem of finding a correct class in a set of usually thousands of unbalanced classes, their model also employs a copying mechanism {{cite:ccd2976d3efa2f6ab33b8cdbab5f163ed376fcfc}} based on positional information, in order to allow the model to find important keywords present in the text, which is a much easier problem.
| m | 00cd2d6e043a2582af6e82ca8751a266 |
In REF , the first term is the data fidelity term, the second term acts as a regularizer and {{formula:7db3b052-2598-4b29-861f-47a5de25e0bb}} is a regularization parameter. {{formula:f3c2b7fc-9613-4efa-b0d8-36e07dc762a0}} extracts a patch of size {{formula:bbbc3635-0c68-4efb-94b9-bafee697d8e4}} from the location indexed by {{formula:a4289aa2-956f-4d46-b00e-8be63eec7048}} and vectorizes it. {{formula:aa7a3e2b-9521-4b8d-96fb-f317bca1595a}} is a CNN parameterized by the weights {{formula:f8640dc4-73f5-4833-b153-6f5098993901}} and {{formula:9c15f784-8598-4b0d-9d2d-3db1e2ef2265}} is the input to the network. According to {{cite:7d791e0619dcee71bf168756d6e7a9a658199643}}, a deep neural network with randomly initialized weights and random noise as input can be used to fit any degraded image under an observation model. Accordingly, we also assume {{formula:c4dbcaa1-1205-4f79-8128-342c64b66d33}} to be uniform random noise with variance 0.1. {{formula:366053a1-fe94-4798-9aad-df59eda5d044}} is a diagonal matrix where each entry (corresponding to a voxel location) is inversely related to the number of patches covering that voxel. Multiplication by the diagonal matrix is necessary to ensure that the same {{formula:8be81288-07e0-49ce-886a-339025e7ef72}} is applied to every voxel, which will not occur when a stride {{formula:03627d38-81e5-4655-8974-3d4a3abd477a}} is used for patch extraction. We adopt an alternating minimization strategy to solve REF , which decouples it into two simpler sub-problems corresponding to denoising and inversion steps. We iterate between the two steps until convergence is reached. {{formula:e459d0f4-214b-4afe-8d36-c0546b9f0c4c}} is chosen to be a 3D UNet architecture with four encoder and decoder levels with skip connections. In the denoising step, the network weights are initialized using the weights from the previous iteration. They are updated using an ADAM optimizer with a learning rate of 1e-6. We choose a patch size {{formula:f8e60671-6f70-4008-9ce6-4d57a2ae147b}} and stride {{formula:c34f9efb-b8a2-448f-9df6-8fdac307108b}} . The algorithm was run on a CentOS 7 Linux machine equipped with NVIDIA RTX A6000 GPU.
| m | 7526671b2d030cdf541ffff3747673b0 |
With the advances of deep neural networks, many deep learning-based methods {{cite:8107055ed0889f935d056443a32f0ac22e53a7bc}}, {{cite:bdc75fee01254088fc3cbbcf77461640280c0dbc}}, {{cite:725adac0e3293a56c96cf7e95bc5b61843120824}}, {{cite:d8c6ef0b5c2edb720d5c5c085bca9d8b1dde1ca2}}, {{cite:411f80631cf291a002023e81a1b66f2e2df5a704}}, {{cite:c3b6f52b68f2e6604ddcfa5b5cd5c6f7f9d4b761}}, {{cite:682547e2328896bd864d041425bafa4a37a242e2}}, {{cite:36cf0fb7e0d16c0b893f6eb844a08ffdf215c808}} have been proposed and boosted the performance of LF depth estimation. Recent deep learning-based methods achieve LF depth estimation in a four-step pipeline including feature extraction, cost construction, cost aggregation, and depth regression. To achieve higher accuracy, these methods designed different modules for feature extraction {{cite:c3b6f52b68f2e6604ddcfa5b5cd5c6f7f9d4b761}} and cost aggregation {{cite:682547e2328896bd864d041425bafa4a37a242e2}}, {{cite:36cf0fb7e0d16c0b893f6eb844a08ffdf215c808}}. However, as a key step in LF depth estimation, matching cost construction was rarely studied.
{{figure:e49b9da9-02e6-48cb-b67c-3af6b13d2569}} | i | fce5e2ff3155a77600f36736843fe973 |
We introduced the idea of GPs in surface terminology that are known in statistics and machine learning literature. In contrast to ARMA models, they extend linear processes into continuous domain and, hence, can model a wider range of rough surfaces. In sum, we showed that grinded and honed surfaces can be simulated by this method, like in other studies. In addition, we showed that GPs can model rough surfaces with strong periodic components automatically from data by spectral mixture ACVFs {{cite:9afe1cfdc8072876ff518177313f7eb2d93c3b33}}. Particularly, we found that it can simulate turned profiles and turned surfaces with their properties but the model results better simulations in profiles than in surfaces since short wavelengths have been also added in the simulations. Another drawback of this approach, not discussed in this paper, its simulation is memory and computational inefficient compared to other methods, despite the effort put into recent studies. Nevertheless, we have simulated rough surfaces with up to {{formula:d650669d-3b31-49f9-a6ef-bcc305cb3523}} points (see sec. REF ) in this paper.
| d | 9399a3b94abfab49dc6f4a8a5154fa27 |
Of course, follow-up observations have placed much stronger constraints on
strictly periodic signals. {{cite:1c56faf12b3170a41e681144402676c92df7110b}} completely excludes strict
periodicity for periods less than 14 hours. Going further, {{cite:860b403fb304ea750e0db1876fde33a607193284}}
provides the tightest constraints to date, finding that periods from 0 to
40 hour would have been detected in 99% of their realisations.
| d | 67395d59c791c2d2fabf9f35d7e12d23 |
Cluster initial conditions and {{formula:ff55cc6c-8066-48b8-8a06-c633c86d370d}} -body code.
The initial positions and velocities of the stars were sampled from an isotropic Plummer model{{cite:fee9f07f6cea19bf2b1feba029f7ec5cfc7ad3cb}}, truncated at 20 scale radii. Initial stellar masses were sampled from a Kroupa IMF{{cite:a4742b4a91f8ac966bd244641f88057260e7f04b}} in the range {{formula:9273513f-819b-47f4-b2c6-a0bd7bdb8c73}} and a metallicity of {{formula:ae1fe716-480f-4f96-8537-131fd6bfb741}} was adopted, that is {{formula:3b735398-1ab5-4a76-9f6c-9eba48ed9295}}{{cite:bdb70290958fd69abdac705b8cc1111c53b169b0}}. All simulations were run with the direct (that is, no softening) {{formula:cec313a3-d469-48ab-a32d-d9c1bbba983b}} -body code nbody6++gpu{{cite:42230cab513dc57871ff58091017e173005226d9}}, {{cite:e26817dd871bbffae6568b86a1fc7586587100a5}}, {{cite:3e922b200989b5cd6d96693bc2177a843295adc0}}, which deploys a 4th-order Hermite integrator with an Ahmad-Cohen neighbour scheme{{cite:8b6039d693bc3c8418ea7ab74a1940134d2c59ba}}, {{cite:505db6efa2c7ffaefe68a05789c1123b5e6942bd}}. It has recipes for stellar and binary evolution{{cite:185af89a0312856d5e241356b99c1458178426f8}}, {{cite:8e983ca9f0052c1c181ca059f3651c9f0fc82685}}, with recent updates for BH masses and kicks{{cite:badfa7023834b0dc10ef2e99fed697a240197fdd}} and it deals with close encounters with Kustaanheimo-Stiefel (KS) regularisation. We use the Graphics Processing Unit (GPU)-enabled{{cite:c0dc3c7762817c0e4550c68a02d350fad7cd3fa8}} version and the simulations were run on a server with GeForce RTX 2080 Ti GPUs at ICCUB. A few modifications to the code were made for this project. The singular isothermal halo was replaced by the NFW halo, with the force and force derivatives derived from equation (1). Stars were stripped from the simulation when they reached a distance of 40 times the instantaneous half-mass radius of the bound particles and for each escaper the time, position and velocity in the Galactic frame was stored. The escapers were then integrated as tracer particles in the Galactic potential until 11.5 Gyr with a separate integrator to construct the tidal tails. We did not include the contribution of the cluster to the equation of motion of the tail stars. Near the end of the simulation the fractional contribution of the cluster to the total force is approximately {{formula:29ad5dc5-14fe-47b7-bba9-5e53686b46d3}} for stars that just left the cluster, and smaller for stars at larger distances, justifying this assumption. All models were evolved until complete dissolution, and for the models that dissolved after 11.5 Gyr, a snapshot was saved at exactly 11.5 Gyr (that is, when the cluster is at the position of Pal 5 today).
| m | a3f972c1eaae6dfb5ded0487c88785eb |
This area started with the investigation of Edge Estimation problem by Dell and Lapinskas {{cite:5281b13df2ee397dd1e72c5e4bb5ca212c8e7be0}}, {{cite:63687d933413ff3d835f7eb4f1f4942f3d388457}} and Beame et al. {{cite:ca7aae3d5b46424e098baba83852a343372fdfe1}}, then Bhattacharya et al. {{cite:ded9050d320dc4b377b0c4ebbd718a61978529f9}}, {{cite:0a4de1f50b09980743879b126083d5ac12ae7f7f}} studied {{formula:14e3a9e3-aa34-4875-a674-004d89fe8fa2}} -Hyperedge-Estimation for {{formula:e92e0b81-a0d4-4221-b761-bff9e38c1587}} , and more recently Dell et al. {{cite:04a53d8db4a734201b8ee40f0737a8158d1fc347}} gave algorithms for {{formula:0c6bece6-1087-4b9c-856b-64a3786fe591}} -Hyperedge-Estimation and {{formula:980d2502-ab16-4a18-b065-240ad260fa58}} -Hyperedge-Sample for general {{formula:69862419-59e3-4be5-b39d-47d2137858c9}} . Beame et al. {{cite:ca7aae3d5b46424e098baba83852a343372fdfe1}} showed that Edge Estimation problem can be solved using {{formula:d66a32b6-18ff-4616-9d79-4fad15d40333}} BIS queries. Having estimated the number of edges in a graph using BIS queries, a very natural question was to estimate the number of hyperedges in a hypergraph using an appropriate query oracle. This extension is nontrivial as two edges in a graph can intersect in at most one vertex but the intersection pattern between two hyperedges in a hypergraph is more complicated. As a first step towards resolving this question, Bhattacharya et al. {{cite:ded9050d320dc4b377b0c4ebbd718a61978529f9}}, {{cite:0a4de1f50b09980743879b126083d5ac12ae7f7f}} considered {{formula:c117111d-e163-4d48-aea4-0472a0ce896f}} -Hyperedge-Estimation in 3-uniform hypergraphs using CID queries.
They showed that when co-degree of any pair of vertices in a 3-uniform hypergraph is bounded above by {{formula:583aa163-5544-4c6a-a897-b990430f097e}} , then one can solve {{formula:36b4f45a-313b-4035-8419-3842c4df3c6e}} -Hyperedge-Estimation using {{formula:feb610f9-02de-4e10-b2e6-ea0f51a0d798}} CID queries. Recall that co-degree of two vertices in a hypergraph is the number of hyperedges that contain both vertices.
Dell et al. {{cite:04a53d8db4a734201b8ee40f0737a8158d1fc347}} generalized the results of Beame et al. {{cite:ca7aae3d5b46424e098baba83852a343372fdfe1}} and Bhattacharya et al. {{cite:ded9050d320dc4b377b0c4ebbd718a61978529f9}}, {{cite:0a4de1f50b09980743879b126083d5ac12ae7f7f}}, and obtained a similar (with an improved dependency in terms of {{formula:92a22c82-9725-4793-b366-f79e5f027650}} ) result for the {{formula:836a1918-c808-48b2-a5f7-96446a6e4766}} -Hyperedge-Estimation problem for general {{formula:57f18bf5-6e2a-46cd-87e0-6df8fbae1bed}} . Apart from {{formula:386c382b-5f84-46e7-8c81-36040571560d}} -Hyperedge-Estimation problem, they also considered the problem of {{formula:bb8da599-ad5b-4139-8627-89e11e3ab953}} -Hyperedge-Sample.
The results of Dell et al. {{cite:04a53d8db4a734201b8ee40f0737a8158d1fc347}} are formally stated in the following proposition:
| r | bb3c449bc57fdf94240beb955dd82a4c |
Ref. James:2019gi emphasized the significance of the ridge-crossing process, also observed here, by which the nucleus switches from the {{formula:8b5143f0-544e-4ebf-8eed-8af335cf154d}} channel to the {{formula:c7a8f311-62bf-49cd-913a-f0c57c3fb73f}} channel.
This process is a discontinuous phase transition that occurs in the finite-sized nucleus as it grows. This is termed a “fluctuation phase transition" (FPT) in Ref. James:2019gi
because it is a phase transition that occurs in a transient and spatially localized fluctuation, which in the present case is the nucleus.
The FPT is probable only when {{formula:57356d4b-4a5b-49ae-beb8-48a3e38b7b79}} . If {{formula:b18cd70d-deed-43fb-bbbd-4fd9ce6038b5}} then the FPT occurs as a restructuring of the pre-critical nucleus before it reaches the transition state that represents the exit from the basin of the bulk metastable {{formula:6375f63e-a259-4790-b248-310892152d5b}} phase; see Fig. REF (a). This case may provide a way to understand non-classical effects observed in pre-critical nuclei that otherwise seem to pass through a transition state typical of simple, one-step nucleation {{cite:a0218374d5eab970ec6e240afbbb731ef7a49ec6}}.
Alternatively, when {{formula:a621e66b-f536-413b-902d-61422e45bb4f}} , the nucleus has already passed through the transition state and exited the metastable phase before undergoing the FPT that converts it to a nucleus that contains the stable {{formula:8c43c989-e55f-4a8d-927f-595b53680c1c}} phase; see Fig. REF (c). It is this case that is normally associated with TSN.
In sum, our results show that a FPT is a feature of the FES given by Eq. REF under all conditions studied here and so
may provide a unified explanation of a wide range of non-classical behavior associated with both pre-critical and post-critical nuclei.
| d | 4990f044fdaf4b75490c36960c03f597 |
The effects included in this analysis were purely standard model Physics. More generally one would apply the techniques discussed here to verify the avenues of discovery for new Physics hidden in the GWB. We note that the numerical method utilized in this work can be straightforwardly generalized to non-standard thermal histories that transition from RD to MD and back one or more times, as is the case in a variety of scenarios of beyond the standard model physics {{cite:7f14e3d3999173495f356ee519c217b8ab983b84}}, {{cite:f05b037f6e166bda310a508e6de619b20c8bd782}}, {{cite:1e06379e0efa50dac297724022ce441ea81c1ccc}}. It can also be extended to include the presence of other light, weakly interacting particles, such as axions or axion-like particles in the early universe {{cite:616cda8840282a1fd319c9f1177f84edac5e6756}}. We defer the implementation of this to a future study.
| d | d40e48ed2eb01c230b866a8f4a07d782 |
While the ROC-AUC improvements might seem minor, the immense body of work on oversampling tells a different story. SMOTE is widely used and all major random forest algorithms (Catboost{{cite:bac12c992555b8020f9e93194ac680a9d9f7f6bb}}, lightGBM{{cite:77163c001d0170b5363477b438f8f1083a468268}} and XGBoost{{cite:fc4d72dcd5e75bd5a240b4a44e28d9a47fd41cbf}}) innately support upweighting of the minority class (upweighting is equivalent to ROS) thus implying that the small ROC-AUC benefits they provide are important. Over all scenarios, the ROC-AUC improvements of our best performing oversampler Poly+VAE were 2-10 times larger than the benefits of SMOTE and ROS. Therefore, our improvement over these methods is significant.
| d | a9642f80bb2d039f42bc1c2647de390d |
Ablation Studies.
(a) Spatial Benchmark:
We first present an ablation study on individual queries. The aim of this study
is to measure the error in relative to the variability of query latency. For
initial training of the latency prediction model, we used plans from spatial
benchmark {{cite:1b56c96c387a81de4d38b49600886a5d18d558be}}, {{cite:5810ebaa5988a5f64108724e152c2f72d369862b}}, {{cite:5b879c15457a08d26eea8aeb35c963c9e9f1fb21}} executed on
120 different database configurations. The trained model then predicts query
latency for spatial queries on different database configuration. To prepare our
test datasets, we ran each benchmark 50 times with very different database
configuration settings.
{{table:0eb5d831-bc5b-4f43-a236-6369e9b9103d}} | r | 5d6391c2f69a54862a790aa0ab73fc61 |
paragraph4
.5em plus1ex minus.2ex-.5emReduce training noise in BN.
Apart from reducing train-test inconsistencies, several other normalization methods
attempt to reduce training noise of BatchNorm.
BatchRenorm (BRN) {{cite:86b41205e1432bd56ebbfecbf27d9acb94931be1}} introduces correction terms
to bring the training-time statistics closer to EMA,
to reduce the noise in batch statistics.
Moving Average BatchNorm (MABN) {{cite:47f85b6b21070bbbdbe79a0132aefdd40ecbbf0e}}
reduces training noise by applying EMA to both the batch statistics and
the back-propagated gradients.
Both methods can improve BatchNorm under the small batch regime.
{{cite:d95160ad0928d44868816eda640f8fcdce4f26f4}}, {{cite:62107521461625d83d4d44d0fe44f0fb4e1eb36d}}
also study the noise in batch statistics and propose alternative
normalization scheme in training.
| d | 3c439fa5eb90bf3b9c0e21134f40f0b7 |
Another issue of significant physical interest is the occurrence of invisibility, namely the scattering pattern is identically zero. Generically, it is believed that geometric singularities on the support of a generic medium scatterer prevents the occurrence of the invisibility phenomenon. We refer to {{cite:4a5802861991a8dd11ea5c7e056d82e2f042db63}}, {{cite:f0bf250853d66f142216146a22c9d655da4f678d}}, {{cite:f4004e091c9b1982b435f269cde1473ab80e8641}}, {{cite:1cda77e15b5432d3e06f8a8f3ff9037aa06f0fd1}}, {{cite:6b0c25b4848e0bc0c96f0b1fb05503673d24e183}}, {{cite:053c074b3b319976b2d21c8e3315f09a195bc057}}, {{cite:e7890ea9b76ecb046170847b7bcecaa4487239d1}}, {{cite:bac4c3ea4cd58f0ebb95fb478c3a91bbfefe7b14}}, {{cite:74db1e1315101fcb97aba1d63dcd3c5493b715b0}}, {{cite:9aee92145e4875ade42a65fac885cdc84030bfb0}}, {{cite:f7d6673fd1d20ce33d2a70951b2e85262788a17e}}, {{cite:6266253e9d180df366edbd22f125b6dbb6c734d1}}, {{cite:9a268e06236b119526bc754d0fbaa2cea73e5619}}, {{cite:c873541b9cbbe7f669bbf2e88a6c6dd9a2256152}} for related studies on this intriguing topic in different physical contexts. In {{cite:6b0c25b4848e0bc0c96f0b1fb05503673d24e183}}, a geometrically singular point (say, e.g. a corner point) on the boundary of a shape is treated as with infinite curvature, and it is further shown that a medium scatterer whose smooth shape possesses a sufficiently high curvature point can also prevent the occurrence of invisibility. All of the aforementioned results are qualitative and in {{cite:1cda77e15b5432d3e06f8a8f3ff9037aa06f0fd1}} sharp estimates were established by showing that there exist positive lower bounds of the scattering patterns, which quantify the non-invisibility phenomena due to the presence of the shape singularities. It is noted that the lower scattering bounds have been derived only for the acoustic scattering.
| d | 1b0e374cebe6bca9ec76ab3134467f57 |
In the CAMELYON16 challenge {{cite:e210911cbf9e9ae6d94534666614b178b6b6b6fe}}, hundreds of whole-slide images of sentinel lymph nodes sections with or without nodal metastases verified by standard immunohistochemical staining by expert pathologists are provided to the participants to build algorithms. The PCam data set is composed of patches of 96 x 96 pixels images automatically extracted from the CAMELYON data set {{cite:5f5d586d3b3416c16b006c09a21c5d27d88a5c4e}}. For each image, a positive label indicates that the 32 x 32 pixel center of the image contains at least one pixel annotated as tumor tissue (Figure REF ).
{{figure:8d31eab7-646a-4410-81e3-ee0d727f0880}} | r | 5801330464db2ea15fb28f4ab3b2486f |
1.11. For definitions not cited here, we refer the reader to {{cite:f513b855c8b62e0ae7d25d5e1e6912468340ab09}}, {{cite:11c23d059977056fff334c0a9551e71aec12f5e2}}, {{cite:eb56aa6610d444736d5162a5b5952e51c0b8ab4b}}, {{cite:ab1fbacc191fafb73fd4997c76a9ca50abfb82bd}}, {{cite:a96cde60cfc7288516b8c055c2d75840a166fecf}}, {{cite:aeec9e627c9af9d473fe782c7c3a46e2ec12e2c3}}, {{cite:c6e24a5e1476e33dbf3c48bcbdf08d43409d2068}}, {{cite:936a84c49dc6da4d34abdd8e15cd843d496fb0ea}}.
| r | d25ecd5f385902b93b4fc2343fe4f9b0 |
We compare our method with the original styleGAN {{cite:121ee7b43d460f2e67ffe367d470861f6e2c6a14}} truncation to demonstrate the effectiveness of our approach both qualitatively and quantitatively.
| i | 120de683aae8d4e07d2b19150ef51bdb |
for which the positive singularity could be described by fundamental solution of fractional Laplacian.
As well as for the Laplacian, this method fails for the classification of isolated singularities for the Serrin's critical and supercritical case, i.e. {{formula:20d274b4-e86c-4bfc-bca0-bfb0f567b91d}} .
When {{formula:7715f87d-45c0-451f-9f9e-2320d855e31a}} , {{formula:092f8ca9-a266-4ebc-a7d7-9012922a7c93}} , {{cite:9de0f524c24c9eaf0fffdc7f3d0a3a0ee7206e99}}, {{cite:688d94784f0552b9c4748c35a5e34d1fb54d692a}} build the platform of the isolated singularity for positive solution to
{{formula:a21f0a22-7aa0-4c7a-8ef4-e5478e6eeb31}}
| i | 64e26806ef7bfd1988194e353761a8ef |
Since the objective of this paper is to propose a newer faster baseline, we must focus our scrutiny on three areas primarily, amount of resources used, the time required for the complete training process, and the final error percentage. In all the three fronts we either match the NASH or are better. Table REF gives a comparison of our framework (with Linear Morphisms, Updated Operations & Gradient Stopping with SGDR) with the two NASH models proposed in {{cite:acb97930f1fde4a489eeade6dd2b8d5a663655df}}, the Shake-Shake {{cite:500d4c6a4a35f93805d68ad547635556d9d8bdee}} model, and a reinforcement learning based Neural Architecture Search Scheme {{cite:cc64a2734245bc6adb48d3a272b5639de7a92e49}}. NASH-1 has {{formula:39d37d52-655c-4ae6-b82b-6a410b2dcb79}} , while NASH-2 parameters are given in Table REF . Shake-Shake {{cite:500d4c6a4a35f93805d68ad547635556d9d8bdee}} is a manually crafted state-of-the-art model in CIFAR-10 classification which uses 2 GPUs and gives 2.9% error in 2 days. However, on comparing with a Neural Architecture Search scheme like that of {{cite:cc64a2734245bc6adb48d3a272b5639de7a92e49}}, that although gives a low error of 3.65%, but uses a mammoth 800 GPU system, is quite unrealistic for practical purposes. Our baseline, NASH scheme, uses 1 GPU and one day of training time to give a 5.2% error, against our training time of 19.4 hours to produce better results at 4.96% error. The reported error for our model is the average of three full runs on CIFAR-10 classification which yielded 5.1%, 4.9%, 4.9% errors respectively averaging 19.4 hours of training time. We also note that our method searches for comparatively more of the neural architecture space in less time and produces better accuracy.
| r | 08c3b6cebdf9c0edd6c06440622abcfd |
We then apply our framework in [thm:thm:main]Theorem thm:thm:main to the sliding window model.
To that end, we first recall that given a {{formula:2a93eae1-4a23-41ce-a69f-e3bf7ba6604e}} -approximation algorithm for the insertion-only streaming model, the smooth histogram framework {{cite:bc163818ff33ac6117964f67a8b8e6c94dbd7bca}} provides a transformation that obtains a {{formula:f69e4f9d-e5a7-4129-ab48-b8e0c356e2ce}} -approximation algorithm in the sliding window model for a “smooth” function.
Although there are problems that are known to not be smooth, e.g., {{cite:d9cc361182d3592b9ae7bbbb80a4a21c37b3a907}}, {{cite:6c4ea19e7f4f19e4811da4bfc921bfbc6d78de3e}}, {{cite:e607cd8192f4570e120d6c6977415c5703cedc1b}}, {{cite:a86dee97df11bb62b166e43b1570fa3fde51a4be}}, {{cite:3f84ed29a5c9ec880c42a4b3308f3037be51e862}}, the smooth histogram framework does provide a {{formula:591d8574-75d5-4323-94b2-8466642f0f5e}} -approximation to many important problems, such as counting, longest increasing subsequence, {{formula:7486f7ec-e403-4fc6-ac9f-5cedec4fabee}} norm estimation for {{formula:2d9f8724-39d5-4dfb-9c96-cab83deea45c}} (and also {{formula:fea50f58-4f27-49aa-8afc-57d6b34d024e}} moment estimation for {{formula:b71a24a6-b7a5-4968-8aea-3a1742244546}} ), and distinct elements estimation.
We remark that if we tried to apply the non-private smooth histogram framework to a DP insertion-only streaming algorithm, this might preserve privacy by post-processing, but may significantly increase the error in terms of accuracy.
On the other hand, our framework avoids these issues and achieves private analogs of these algorithms in the sliding window model without compromising utility.
We summarize our results for the sliding window model in [tab:tab:sliding]Table tab:tab:sliding.
{{table:02774516-4f56-46ff-9696-10035e023584}} | r | a7c0f5d3961b3cd9197dcc412bb4a30d |
Transfer learning (TL) based on pre-training and fine-tuning {{cite:bb09984b79fe396bc080aaab61e9f2e41bbef3b9}}, {{cite:4dbbb7864c6709af832c31f57d8a99bad6b5896a}}, {{cite:fddc555dd9c7b688960e6134b91198474db6266c}}, {{cite:d47827d81a9feec5087ac63611c1b3658f031a11}} is widely employed for domain adaptation tasks. Its basic idea is to first pre-train a large neural network model with plenty of source data and then fine-tune it in the target domain where there might be insufficient training data. Fine-tuning has become a core technique for successful TL and been widely studied in computer vision {{cite:8e303fe3351c33db2327a2bc8b22c51a19b36208}} and NLP {{cite:fddc555dd9c7b688960e6134b91198474db6266c}}; however, thus far, it attracted very little attention in the recommendation field. In this paper, we aim to investigate how to
perform fine-tuning for cross-domain recommendations
and encourage practitioners to apply our proposed fine-tuning as a common technique to further improve the performance of their CDR models.
{{figure:e5e8c385-feed-4173-a321-10501d4933df}} | i | 433fc7b1d1fa4fca1b60511f528a754f |
Recent computational approaches have attempted to infer participant beliefs by modeling their behavior {{cite:a33fb0612738cdd8c7b7a5929517b5add56f7a35}}, {{cite:3e2e290ac6d9c1663694597f2cf2ed66346747fe}}, {{cite:1c8026d0f80044e2b89d93cd6293cfd1deba719a}}, {{cite:60279aa9b5db32dfcec5bb5bda34354faf585c4e}}, {{cite:79912c496034d5802be0deb148d6ef8dd758c841}}, {{cite:36a01ecff9e044143e9aca5d36bff7decfe2f2b3}}. For example, Bayesian models of human learning represent participant beliefs as probability distributions, representing how likely events are to occur {{cite:97630a1dacbcf24ca7d98296666158acab21ae8b}}, {{cite:a33fb0612738cdd8c7b7a5929517b5add56f7a35}}, {{cite:3e2e290ac6d9c1663694597f2cf2ed66346747fe}}, {{cite:1c8026d0f80044e2b89d93cd6293cfd1deba719a}}, {{cite:60279aa9b5db32dfcec5bb5bda34354faf585c4e}}, {{cite:d0bd9c43844d394d8dd53496662be05e492ac199}}, {{cite:6a1c42a76f661aabe99e7227d918b1d00f024f5d}}. These distributions are then updated with each new observation, providing a dynamic representation of the way participant beliefs evolve throughout a task.
| i | 6df6945ff7a79e8b4b35c9c5c2098935 |
In this paper, we will conduct a systematic study of the {{formula:b13fc776-3f23-441c-be19-61746eed8a08}} distribution of {{formula:9cbe707c-3f82-4545-b9ff-58a8136616d9}} -meson in jets both in p+p and nucleus-nucleus collisions at the LHC energy. The initial {{formula:a4d121c5-ca49-4d48-ac85-6d599cd8578a}} distribution of {{formula:8d59842b-e28a-427d-b307-ac95bcabdcd0}} -tagged jets is computed by POWHEG+PYTHIA8 {{cite:2eb25c2c75f4747a447af786ddc767165da085b6}}, {{cite:867d5ac1642e4c171b2eecc383e0934a7492b330}}, {{cite:fa211804d3d11bbe6a70cce549739b7ee2e9855f}}, {{cite:db5e4a62fd245a6943cd0969d9ae7b2295654ef1}}. The in-medium evolution of heavy quark jet is implemented by a Langevin transport approach which takes into account the collisional (elastic) and radiative (inelastic) interactions {{cite:11c555e9174b77bc4c0b830a3d24d82d21debb4d}}, {{cite:73583d107bf8503818c1263c8ffb635ccae952cf}}, {{cite:759746fc03d2b452dd446f512e80e03cdec8fbf2}}, {{cite:a547fbefad1d7db81a4dc5e2e42c29f29da859c9}}, {{cite:7f576bd2e94334344396c25d93c2d158af163988}}, {{cite:b919b0a73298ff0f941c2bafe9b751ac61be5d49}}. The modification patterns of the energy fraction of heavy quarks in jets may provide a new perspective to reveal the energy loss mechanism of heavy quarks as interacting with the thermal parton, and would also deep our understanding of the mass effect of jet quenching. For the first time, we present the theoretical predictions for the {{formula:2e39f2af-eb38-4211-b86d-749209adb965}} distributions of {{formula:a52bd152-2b09-4028-a664-03ca7ed4d195}} -tagged jets as well as the medium modifications in central {{formula:c842a95e-a7ad-486b-af41-9cf3033d7adc}} Pb+Pb collisions at {{formula:7eb4f9d4-93f2-4f97-b5ae-f66ff189b333}} = 5.02 TeV. We specifically investigate their dependence on kinematics region, jet cone size and collision centrality. Additionally, the comparisons of the {{formula:b998f07e-7412-4f7c-94a1-67125f8ac00f}} distributions between {{formula:6e88208a-f27b-446b-81c2-b56df4c867ae}} -jet and {{formula:4fb07a55-430a-4aef-876f-186bfc54b477}} -jet are carried out to test the potential mass effect that may be reflected in this observable both in vacuum and in the bulk QGP medium.
| i | 9b21cffe6d71a1f29ce80e44d9267fcb |
In this paper, we show that properly designed and trained CNN codes with iterative decoders, which we call DeepIC, outperform the state-of-the-art by a significant margin on the challenging problem of communicating over two-user AWGN interference channels. While it had been shown in the literature {{cite:27cb2d5d5576b1d7584d06029464dde46e60f171}} that neural network based codes, in particular, feedforward networks, can outperform the time division for a very short block length, such as {{formula:109591af-0d6c-45d8-963e-2210680b5479}} bits, this work is the first to show that such improvement is possible for longer blocklengths, such as {{formula:4b5d165d-9428-4401-8bd0-90b1cfd3d02b}} bits.
| d | 59ba2e217cafcb5314c295745e520ad6 |
In experiments, our dimerized NHQC may be realized in photonic systems.
The uniform part of hopping amplitude and quasiperiodic non-Hermitian
onsite potential could be realized by a frequency-modulated mode-locked
laser with gain medium, phase modulator and low-finesse intracavity
etalon, as proposed in Ref. {{cite:005d77640066b0724d8e9de0d6c1782e069a5ac0}}. The dimerized hopping
amplitude could also be realized by engineering the profile of refractive
index in the model-locked lasers setup {{cite:3cbe841ce345a58ad2112c69774677cc95fce012}}. Therefore, the
model we proposed should be within reach in current or near-term experimental
situations.
| d | 584fc6f52438b3d8f329ce6efd14a3a2 |
For us, the emphasis was to derive the first {{formula:41d16554-6b94-47c0-8190-d51045b4275b}} lower bound for the partially observed setting (Corollary REF ). Thus demonstrating that isotropic output noise does not necessarily help the learner and that such systems can be at least as hard; in fact, partial observability may further hurt the learner if the optimal filter gain is large. Further, we revisited known fundamental limitations in the state-feedback setting due to {{cite:2317d6a47305d48cd6a73e361db0ec01e895be5b}} and were able to improve on them in terms of system-theoretic quantities. In particular, it was shown that systems operating near marginal stability are fundamentally hard to learn and any algorithm operating on them necessarily suffers large regret. Dually, systems with poor observability characteristics may also exhibit a diverging regret lower bound. This opens up an interesting direction for future work: to ascertain the optimal dependency on system-theoretic quantities for regret minimization in LQR and LQG.
| d | 7d2677d1f75dc370f561da3197ce38de |
This result is interesting because central limit theorems for shape parameters of discrete random structures arising from computer science which have a variance which is significantly larger than the mean are rare; the only other example with a similar behavior for mean and variance can be found in Flajolet et al. {{cite:059ecadac8a38cfa8861b86e86923e62a7b1d885}}. Also, in both these examples, most standard methods for proving a central limit theorem do not seem to work (see, e.g., Remark REF in Section ), leaving only the (more technical) method of moments as a feasible approach; see {{cite:059ecadac8a38cfa8861b86e86923e62a7b1d885}} and Section 30 of Billingsley {{cite:71f4f7e6aa4b68585a1b2f1905c6dbd05c810bea}}.
| i | a47bc2e35e5ba309174fa27c991b1731 |
Navigating nets.
In 2004 {{cite:40953bfc31a257b1ea5e0a7fa7666de83645ce96}} claimed that all {{formula:dfda4c8b-919e-43fa-8e27-68ba4634190f}} -nearest neighbors of a query point {{formula:85a05a5c-e1ed-44c7-9f3d-c5e4c1d0ac93}} are found by navigating nets in time {{formula:ee0ef287-93a5-4705-8c39-d83d81d0184f}} , where {{formula:991fa15a-5948-4fc7-ba29-2b0197fe3a4d}} is the expansion rate above. All proofs and pseudocodes were omitted.
The authors didn't reply to our request for details.
| r | 4b0c835f4a3a5d066132f47bf91e7f27 |
The spin models are implemented with a system of two-component bosons in an optical lattice, which is well-described by the Bose-Hubbard model. These two states (lowest and second-lowest hyperfine states of {{formula:1f6681a3-0af2-45d1-b126-0afb29571634}} Li), labelled {{formula:0edc055e-64fb-4f02-a639-e7c2b68165c2}} and {{formula:bb3ce3aa-11cc-48d5-96d3-bfec17f12af4}} , form a spin-{{formula:3e41b6a7-6d07-4b72-be0d-da07fb2e57b2}} system. In the idealized scenario of a Mott insulating regime at unity filling, bosons cannot tunnel and the effective Hamiltonian for the remaining spin degree of freedoms is given by the spin-1/2 Heisenberg XXZ model {{cite:c77e8c8cd01a023c077ce1c297ed80f5fe40463c}}, {{cite:efde7dc284a18647476c36f6a52f270945e7a77d}}, {{cite:25aa18a0a9dd10772d38ac2a8ed58adea4cafb85}}, {{cite:0834648f10f63f880cc78d4e888274a8856643fa}}
{{formula:2ac98655-b8eb-4256-84bc-f3a17451612f}}
| m | bebdc2494775435c3bf205b64cb32451 |
In our CRG setup see Fig. REF A, we use StyleGAN as generator {{formula:def09393-46a3-47b3-879a-c230e08d2f72}} and a two branch Resnet-101 based architecture as encoder {{formula:d39d8548-d278-44fd-8980-dbd0d8b93a90}} . We took inspiration from {{cite:701d25f343ae13467e2bc2f6bad20683670b76f7}} in designing the architecture of {{formula:5dc6aa85-9f5b-4e4b-8d4c-526ddbd7e8a9}} and furthermore used denormalization as suggested in {{cite:7d21e5d5da0ea7f7ccbaf03f7ecfe3b52907d499}} for merging the features from both branches. The high-level architecture of {{formula:b5fe4978-1052-46ba-91b8-399d7c65c6c6}} is depicted in Fig. REF B. In a first step, we train {{formula:642559e0-88c6-465c-ac2d-50ddf19e50aa}} using frontal X-rays from the CheXpert dataset in 128x128 pixel resolution. We then train {{formula:30c6a70e-e6e4-448c-8233-8cf499011a69}} , while keeping the weights of {{formula:fa858b04-57f2-4830-9766-01476c9ad589}} fixed and furthermore using a constant noise realization.
During training, the weights of {{formula:8461165f-066f-479e-99ed-9971a1dbc174}} are updated two times in each iteration as proposed in the original CRG work {{cite:33522b9f64003ac61a49a7c3be0c5a3fea44436a}}. In the first update, following the cyclic path depicted with black lines in Fig. REF A, we back-propagate a loss {{formula:e0fa6d64-e729-4066-9b0d-5546cc6e5753}} designed to minimize the difference between generated synthetic images and their reconstructions.
More specifically, {{formula:81394cdf-01c0-44ad-9e1a-aa644b7894bd}} , where {{formula:6574fd32-66e6-4764-8201-acaa76caae97}} -s and {{formula:53a75c1a-05f4-42f9-94a6-a06864c6f5f3}} -s refer to latent codes and images, respectively, SSIM is the structural similarity metric, and {{formula:faf39a95-d80d-44f8-92c3-f08225b32610}} . Here, {{formula:341f4d4a-eb53-45b0-bccc-561c856d6125}} denotes the features from the {{formula:2c53ba17-cbc4-4855-8994-958c064c58ef}} hidden layer of {{formula:d0a56411-2849-4dd3-a40d-878803182564}} , {{formula:ad92951d-0912-4e7c-ac14-b3981968ef3e}} is the total size of the corresponding feature map, and {{formula:1e48abce-f004-427a-a3e0-6465fb5a1d2c}} is the number of hidden layers in the network.
The second update is designed to optimize the quality of real image reconstructions and follows the loop shown by green lines in Fig. REF A.
Using an analogous notation as above, the loss back-propagated in this cycle is defined as {{formula:1287f4f7-8109-4598-9b45-f22e7efcb3c4}} , where {{formula:99bc5342-e7ca-482b-8c70-4c370bc9c802}} . Note, however, this time content loss is computed using the features of the encoder.
| m | 6a085c79357a4122e7668172777574ef |
It is interesting to compare the Path of Destruction method with image inpainting techniques. For centuries, conservators have studied how to best restore art pieces by inpainting parts that are missing or destroyed due to e.g. deterioration or vandalism. In recent years, a burgeoning subfield of AI poses inpainting as a computational problem and advances machine learning-based methods to solve it {{cite:03912f3586240b13ad1f762f456ad0a4fbccab26}}, {{cite:5d5f7741f1d0ae1c2d2251d167978b760ce5e9fa}}. These methods typically take a set of images and create training data by randomly removing parts of the images. The model is thus tasked to regenerate the missing parts. In that sense, the overall procedure of image inpainting is similar to the Path of Destruction method presented here. However, in our method, each edit action pertains only to a single tile (or pixel) based on a limited neighborhood (of field of view). From this perspective, the Path of Destruction method could be seen as an extreme case of inpainting, where each tile is inpainted separately and the resulting level consists of only inpainting. Furthermore, as the starting state is entirely random, any given pixel could be “inpainted” an arbitrary amount of times.
| d | 242d58cfd6b1d06e934567ff3f030133 |
In the first simulations, we consider the following setup {{formula:5ba58e2a-cc91-4c87-99a3-b05c60698a4d}} , where the cluster of AP serving each user {{formula:5e696ce3-6dd8-4343-8894-932d6849e3a3}} is formed by the {{formula:b29a5d71-f069-4b14-8b1c-a20783e1e021}} AP with the largest values of {{formula:69263e59-d839-486c-a1bf-3f90d4a79054}} , i.e., we adopt a largest-large-scale-based selection {{cite:60e0d37b628f1a9a9b1ab77e31ea0199fdeb2781}}.
This is a legacy solution that does not consider the multiple CPU aspect in the system.
| r | 0ef53af85233ce18bc99b8066a2704b8 |
Another promising line of improvement, though not widely explored, is the use of ensemble methods which combines predictions from multiple learners. Modern deep learning architectures rely on stochastic optimizers for training (e.g. SGD). They are highly sensitive to initialization, choices of hyper-parameters, and data augmentation, and, as a result, tend to converge to different local minimum and thus yield different predictions {{cite:0e714e92a942000e0771fb72e832de4525a3a26e}}. However, by training multiple models separately and averaging their predictions, it is possible to reduce the prediction variance and generate performances that are better than any individual model. While ensemble learning has been extensively applied to classification {{cite:ddaf4d87cf2c4303167767d9eee0417593cabf91}}, {{cite:37b7ef32d059885d3685aa175373e76235a12e2b}}, {{cite:177c44abeba84975a4688b608e5653665c9ac8a7}}, deep metric learning {{cite:ab9793d5988321f9b98ea2572c2f0ce4aa46eec4}}, {{cite:fab0012b49b5d0e266e29c828216127f2c5e3dfa}}, and to some extent to object detection {{cite:d38449d6885cc1417ec695f980afde1e063c3914}}, {{cite:2bcdb14dc2bdb808e2e42e00587e00670fb0c45a}}, its application to semantic segmentation {{cite:70e8f2f1eddd474782108142b2ae44b5c06bc801}}, {{cite:772eb7e034461c663327ecc38d326a0dbcc20872}} is still limited, mainly due to the prohibitive cost of model training.
| i | 4d9bd70ed40793ea8aa5ab094fd06104 |
CIFAR-100.
Similar to the comparison configuration of CIFAR-10, we show the experimental results of CIFAR-100 in Tab. REF .
Compared with the competitors, our lottery jackpots retain better top-1 accuracy under different pruning rates, while charging less pruning cost.
For instance, our method can achieve a top-1 accuracy of 74.63% when pruning VGGNet-19 at 95% sparsity, which surpasses other state-of-the-arts by a large margin (4.86%, 4.20%, and 2.84% higher than SET {{cite:53881532a6044f9aece9bd5c8f12f2d45348f618}}, LT {{cite:f29dba5bf1a92eb549817c63ff60beb3bc984d34}}, and SNIP {{cite:fbb75035f5567049bc6a77bc1d724bd84ed5458e}}, respectively).
Note that it even exceeds the origin dense network by 0.47%.
Compared with OBD {{cite:ad6490ee0ab36bdeab6d03f2771f8ef33efecd79}} that conducts fine-tuning after pruning the pre-trained ResNet-32, lottery jackpots can achieve better accuracy under all sparsity levels even without weight tuning process.
Such results show that, instead of conducting time-consuming fine-tuning, the key part of network pruning falls in directly locating the lottery jackpots.
| m | bbf15d788f698aa45e9dce376600d148 |
Obtaining Community K-Shell (CKS):
Community K-Shell concept incorporates knowledge of information flow in a network. Obtaining CKSs comprises the following steps: identifying community structures using Louvain’s algorithm {{cite:3aac60f2c7369ad954fea656a0344820e15ec5db}}; isolating communities by removing connections between different communities; and passing isolated communities through K-Shell algorithm {{cite:5dfbc6834de45b4f45b7f7a7c9a780751f8c81fa}} to obtain K-Shell scores particular to the community of each node (i.e., Community K-shell score). The higher the Community K-shell score of a node, the closer it is to the core of the given community.
| m | 84c1a73618e4d270c9d86ad2e42512e6 |
The modular Hamiltonian has been used to derive the holographic entanglement entropy in the AdS/CFT correspondence {{cite:38845888b481dacb65857fc26589963d10937540}}. Another importance of the modular Hamiltonian is in the derivation of the first law of entanglement {{cite:63d7b4200774c66b49008ce1e91889bda6df62db}}. Given importance of this Hamiltonian in AdS/CFT correspondence, we would like to study its role in non-AdS holography. So far the vacuum modular flow generator and the corresponding modular Hamiltonian have been determined in a specific class of non-AdS holographies. In the {{formula:98472842-8536-4627-97c0-cb63010ab6b4}} holography as a case of holography beyond AdS/CFT, it is considered that gravity in asymptotically flat three-dimensional spacetimes is dual to a BMS-invariant field theory (BMSFT) {{cite:2d4c3ff54fac3c08f226bbdda58f215e70fd384a}}, {{cite:6f52c3328cf7842aeb33dd703b66a92c972b6aab}}. In this class of the holography, the flow generated by modular Hamiltonian differs from the modular flow in AdS/CFT {{cite:6867fc286570d173b2f9ba317c6dcad86d3f43aa}}, {{cite:e655bc9009d3a601fae995576cfd1681f3f9e0d3}}.
| i | f45de7803b4a4f5f034ea1e28cbb2724 |
There are several limitations to our current study. First, our models could benefit from being trained on more data as shown in the training curve from {{cite:eac2c8a25125d255f4df0f619e621f7c144debd2}} (Figure 1.c). Second, our models should be validated on larger cohorts, encompassing different patient populations, treatments (neoadjuvant chemotherapy can impact cell morphology), scanner manufacturer and sample types (resections, biopsies). Third, SSL techniques are evolving rapidly using new architectures such as Vision Transformers [{{cite:d703e0fe76c9410ff29659a6b49b0a6640190d06}}] and more experiments are required to find how to apply them in histology, including taking into account the spatial arrangement of the tiles. However, such experiments require access to extensive computational resources, which limits reproducibility. Finally, in contrast to several concurrent works [{{cite:eac2c8a25125d255f4df0f619e621f7c144debd2}}, {{cite:9843eb17ed4938a0ef628ca8d96826e40255e743}}, {{cite:0112d242dce26fc6dff07c1b8087ac12acec9de9}}] that fine-tuned the backbones, while our study kept them entirely frozen.
| d | 16b1231ba8a36b10f112a617f727bc3f |
We compare ZORB to BP with Adam {{cite:eff9738584d6b853feb8a985b46652af1c0379f4}} and Multi-layered Extreme Learning Machines (ML-ELM) {{cite:1f1b5767c99f4926e423038384a505b1cf2cd8a9}}.
For consistency in the optimization process across algorithms, we train feed-forward NNs to reduce the sum of squared error.
To compare training times, all algorithms were implemented using NumPy {{cite:d4dc4b0b96d77ed7ae91452396142735a5cdd2fc}} and Autograd {{cite:f10216e3a13b1d156a637895cc4d649c6b10c6b5}}.
Table from figure REF displays the results from benchmark experiments used to verify the working of NNs.
To test ZORB on a large dataset, we trained 3 NNs with varying number of layers on the MNIST dataset {{cite:f32994d72130663804af8f9d33f0e752d494a7c0}}, displaying results in figure REF .
ZORB is compared against baseline training algorithms on 3 metrics: Mean squared error, classification accuracy and wall-clock time.
The time displayed in tables for the Adam optimizer is minimum between the time taken to reach ZORB's error rate and time taken to reach a maximum iteration count.
Dataset statistics, network architectures and hyperparameter values have been provided in section of the appendix.
Codes are publicly available at https://github.com/varunranga/zorb-numpy.
{{figure:5bb4950a-ebf6-4a5c-9489-48d77ba6b4d1}} | r | a421f1e02f78110eb11c4ecb43ec1c09 |
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