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which empirically matches
{{formula:9a6ab932-2f17-4fd6-8a2a-074dafa0cc39}} closely {{cite:166a8acfe4cb4eb6a7f9199fa6b6d3e52593df2b}}.
This is shown as a function of {{formula:0ffbf52f-0238-4670-8cbd-5a24e8520652}} in Fig. REF and of inverse
coupling {{formula:37cda92b-a2fa-43ac-987e-b329d4f8524a}} at fixed {{formula:79f9f40c-9435-4e81-8d1f-9700e08d2bc1}} in Fig. REF .
{{figure:491ca9b3-f4d0-4ccf-8a66-2646f395e554}} | r | 08ae6dfad48e1b5eeabe7f8401dd3032 |
In this paper, our objective is to design a neural ODE such that the features extracted are within a neighborhood of the Lyapunov-stable equilibrium points of the ODE. We first develop a diversity promoting technique applied in the final fully connected (FC) layer to improve the ODE's stability and analyze the reasons why. We then propose a stable neural ODE with Lyapunov-stable equilibrium points to eliminate the effects of perturbations in the input. From linear control theory {{cite:f4e4410f246f02862b961d43b603572526c80274}}, a linear time-invariant system {{formula:6073a76c-270d-4012-94c6-af5a10e3ca1b}} , where {{formula:74dd2fe6-47ce-4833-b3b6-bb173751e1f6}} is a constant matrix, is exponentially stable if all eigenvalues of {{formula:69868e19-b047-4f8a-a36e-9b09f1c1a50d}} have negative real parts. Specifically, we propose to force the Jacobian matrix of the ODE used in the neural ODE to have eigenvalues with negative real parts. Instead of directly imposing constraints on the eigenvalues of the matrix, which lead to high computational complexity when the Jacobian matrix is large, we instead add constraints to the matrix elements to implicitly force the real parts of its eigenvalues to be negative.
| i | ae13ff8752932adc8120e06bffe5a1a9 |
We are sincerely grateful to the referee who provided a number of insightful and constructive suggestions that helped to clarify parts of our work that were initially vague. We thank Warren Brown, Margaret Geller and Scott Kenyon for stimulating discussions on the topic of hypervelocity stars, and for constructive comments on the manuscript. SSC was supported by the grant “The Milky Way and Dwarf Weights with Space Scales” funded by University of Torino and Compagnia di S. Paolo (UniTO-CSP), by the grant no. IDROL 70541 IDRF 2020.0756 funded by Fondazione CRT, by INFN, and by the Departments of Excellence grant L.232/2016 of the Italian Ministry of Education, University and Research (MIUR).
This last grant fully supported the PhD fellowship of AG. We acknowledge partial support from the INFN grant InDark. The work of SE included here was part of his Master Thesis project at the University of Torino.
This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
This research has made use of NASA’s Astrophysics Data System Bibliographic Services. This work has made use of Topcat {{cite:924573fad417d28c8da41802c60b248d458ed3a2}} and the following Python modules: Matplotlib {{cite:e2003e757370901ad334d603161f57103f504874}}, NumPy {{cite:142a0de1a11a49b0bd81b7c11c506a6dff7e4f54}}, SciPy {{cite:04114a0e862543c9388b19edf3a21fc96eaad4e7}}, AstroPy {{cite:50f3ea122852784f1e705cf5f73482365d77e63f}}, {{cite:b9e0945699b2e1f340dfc1acc719ec814fcd474f}} GalPy {{cite:9ce0b95b40164d72b76e1f12153c3c801e503185}}.
| d | 30f3e408998e7b824fc507934756083d |
Table REF contains the aggregate results for each task and demonstrates the efficacy of using the proposed multi-objective approach. While the median population-level accuracy falls slightly compared to accuracy-only NAS, there is a substantial increase in hypervolume across experiments. Note that the best accuracy of XNAS on ImageNet-16-120 is on par with the best-performing methods as evaluated in {{cite:c4ab5c457fb1ccc9c280ffb433f121e107bef21f}}.
We plot the Pareto front of every search result and shade in the hypervolume in Figure REF . The visualizations make clear where the multi-objective approach makes up hypervolume over single-objective (accuracy). Across all tasks, multi-objective covers a larger range of introspectability values. As one would expect, focusing on accuracy has the tendency of clustering the majority of non-dominated solutions in the upper-left of the front. The hypervolume of random guessing illustrates why we set the hypervolume reference point to {{formula:6a930c58-bbbc-4933-acc9-fe1940fec49f}} : some solutions manage to achieve high introspectability but are effectively useless since their predictions are no better than random.
| r | 2bd78849f63ed41a74eb183d44bece21 |
Gaussian processes (GPs) cross-fertilize merits of kernel methods and Bayesian models to benefit several learning tasks, including regression, classification, ranking, and dimensionality reduction {{cite:e3cfe618be9971da9ffb9fc675f00e255d75e129}}. In GP-based approaches, a Gaussian prior is assumed over a learning function {{formula:d497939d-3adb-4f3a-8579-2d90af3f8382}} with covariance (kernel) capturing similarities among {{formula:80f941bf-087f-4469-b090-ca7e90e894d9}} dependent on inputs {{formula:bb078eca-b134-4ddb-8b13-467e42c5514c}} . Given observed outputs {{formula:90ba9003-9055-467a-b703-c19c53b38e60}} linked to the latent function {{formula:f0e7c2bf-2e14-45d5-8fc5-4cfcc40ab62c}} via the conditionally independent per-datum likelihood {{formula:195a0ce4-ae2c-4fc4-8669-5c9ed2c3548c}} , Bayes rule produces the posterior distribution of {{formula:89620afd-e49d-4db5-b1e0-7e91c1407097}} , based on which task-specific inference can be effected on the unseen data. Besides learning functions with rich expressiveness, the Bayesian framework of GP-based approaches further quantifies uncertainty of the function estimate, which is of utmost importance in safety-critical applications. For instance in medical diagnosis {{cite:983fa5a42d6f2f00937cd82e6e69ee58bbb9bac3}}, human intervention would be called for when machine operated decisions are accompanied by high uncertainty.
| i | ce37551b43b75d8dd74ab623f4e3a92d |
Lung cancer is the most commonly diagnosed cancer worldwide, which accounts for 18.4% of global cancer-related mortality in 2018 {{cite:d830e4fd9953035e8200731c4b6f952291a51dfa}}. Remarkable success has been achieved in deep learning for lung nodule detection {{cite:8b10c3f93a583c79f9ae944e9ff55fec18d54141}}, {{cite:4313a51faff73a292e70a42fd254dfca0a73d7c6}}, {{cite:4c929a7e0547972203a936429c80b06794aa01b1}} and diagnosis {{cite:ba460abbc09a7d757f03fde96cca46cb3cc47663}}, {{cite:f2bc00deb7ce65b520747b704be58ea2bad1bec2}}, {{cite:0d70190772fff4d31deabb3e032e0ec2f3432cbf}}, thanks to medical datasets, e.g., LIDC-IDRI {{cite:d16f7d83a588a10e27ed8fb861853b78335aa790}}. However, the radiological diagnosis of lung cancer suffers from ambiguous labels {{cite:3e985feb07ff099ea5b5c7dd9683443a5b4599f1}}. For instance, 4 expert annotators make diverse diagnosis in LIDC-IDRI dataset {{cite:d16f7d83a588a10e27ed8fb861853b78335aa790}}. A possible solution to reduce label ambiguity is to leverage clinical golden standard. For lung cancer diagnosis, invasive pathological analysis serves as the golden standard. To this end, we build a large-scale radio-pathomics dataset, consisting of 5,134 radiological CT images with pathologically confirmed labels. Once a deep learning system is well trained on this dataset, it could predict invasive pathological labels via non-invasive procedures, i.e., radiological CT scans. The in-house dataset, named Pulmonary-RadPath, is collected retrospectively from a single clinical center. It covers most diseases in lung cancer-related diagnosis, including cancer (e.g., invasive / non-invaisve adenocarcinoma, squamous carcinoma) and non-cancer diseases (e.g., tuberculosis, hamartoma).
| i | 8059aa0deca82c488f6e3a7c1c6b1287 |
Various new physics scenarios try to explain the muon
{{formula:c6213a76-6204-40f2-907e-a245b794f35f}} excess, for recent reviews, see e.g.
Refs. {{cite:4d57ded4fee92ea085c9bd70e5ee556f42655fac}}, {{cite:3ccb5624fc3c269e3bd7243798db546b2edc6de3}}, {{cite:effa9d81f466c1bcedaa64549bcb1682df454cf4}}, {{cite:66f7e2c44ffa1050bfc410409edb8705f1a6db39}}, {{cite:0977cd2fa951090d668e6ace19627c5f5561d4af}}.
Among these new physics models, the left-right twin Higgs model may also accommodate
the possibilities for the muon {{formula:9ee5bf98-206f-4064-bc79-5df5402d9b76}} anomaly{{cite:e0b60718f3dea947c04b7d406598b63437e267ce}}, in which the extra scalars
can give positive contributions to muon {{formula:97197964-52ce-4bf6-b1a0-4538b3ca618d}} via the two-loop Barr-Zee diagrams.
| i | aae5e7e6aa67f728ab8cfa92863b581f |
The goal is to enhance the performance metrics of the best baseline model, Visual Bert COCO in Kiela {{cite:7da569be9bc2f36c96e601c82a4685af47e0ac41}} to approach the human's test accuracy of 84.7% on hateful memes classification. We leveraged Memotion Dataset 7K {{cite:e4a8cfcbb9f58487e58972e54faded71321aac54}} to increment the original training metadata from Facebook AI via semi-supervised learning. There are 3 experiments upon 3 stages of incremental training metadata and the data characteristic analysis. The major performance metrics are accuracy and AUROC. AUROC is the area under the receiver operating characteristic curve based on the integration of the product of true positive rate and inverted false positive rate between 0 and 1.
| r | 14e79ac8e30d92137e0424bdfc757eac |
To further evaluate the generality, we validate the proposed method on an office-home dataset and compare the performance with 19 SOTA methods as reported in Tables REF and REF , including adversarial-based methods, difference-based methods, and mixed methods. It can be seen that the four domains in Office-Home form 12 different UDA tasks, and the proposed TVT+SAFF achieves the best performance on all tasks, with an average accuracy of 84.86{{formula:79bed07e-81f8-4ebc-a789-54bec228928a}} , which outperforms other UDA methods significantly.
As shown in Table REF , DANN {{cite:40a3e34090856d64b118069d6caf54018693fe25}} consistently underperforms, and other adversarial-based methods such as TAT {{cite:b0995a3a4529bea3621be3fc5f34467be0be9912}}, CDAN+E {{cite:cbffa0f95ad64aa3c91cc87a304e9954f5826b78}} and CVB-GD {{cite:67c7709c6500c28a420a59fae535f9457c5c653a}} perform slightly better, but still unsatisfactory. JAN {{cite:971df6a3c8ba1e91ac368141e456d241aee95478}} is one of the early attempts of difference-based methods, which learn a transfer network by aligning the joint distributions of multiple domain-specific layers across domains based on a joint maximum mean discrepancy (JMMD) criterion. Similarly, TransDA {{cite:a7619f8c5a718c217f4b84b5dd77b25297601ae9}}, TPN {{cite:895f92f316a02e29dc0c85c1ff6ba9dde513b08f}}, SHOT {{cite:09483c3d46c7ec50f878c177fe43d10214fd88ac}}, DeiT-S {{cite:32843b1bb10bd0a225c07a91bc332ea3df07a031}}, Liu et al {{cite:8b14578c128d733993acda442c750a943a357dc1}}, GVB-GD+SPCL {{cite:dfe962f0e7f95586af1b3f9c6f9740a3d59187c4}}, ATDOC-NA {{cite:f0f2ff2aae126ae56a7379c61381c7ba8aae5480}}, SFDA-DE {{cite:030014599c98297ae45275e654ed6e79fb0e9d1e}}, and WinTR-S {{cite:8e1a11a625049aff1b172c148cc1c8a333ea31c2}} utilize strategies such as optimal transport theory, pseudo-labels, etc. to align domain features. Although these methods achieve better performance than adversarial-based methods, they ignore styles between different domain features. In contrast, our proposed SAFF can make full use of multiple-style information to enrich the latent feature space and greatly improves the classification accuracy.
| r | 4740b69f6d564b9478c034718524501a |
As shown in Table REF , TVT+SAFF achieves the best performance, which proves the effectiveness of the proposed SAFF. DANN {{cite:40a3e34090856d64b118069d6caf54018693fe25}} achieves the worst results since it uses a gradient reversal layer to learn invariant features between domains for adversarial adaptation, which may weaken the difference between categories, resulting in lower recognition ability. MCD {{cite:aeb928147540119484036431ce4ce35444e0ec63}} and CDAN+E {{cite:cbffa0f95ad64aa3c91cc87a304e9954f5826b78}} further exploit discriminative information conveyed in the classifier predictions to assist adversarial adaptation, improving classification accuracy by 25.3{{formula:e6aef520-71f9-42dd-ac17-b000655b669f}} and 28.7{{formula:b0d2a2a5-c440-467e-a353-27d2b9f72d1c}} respectively.
| r | 0c2c73d1abd3b01d852a2bd868da27e7 |
Solutions based on fiber transmission have been aiming for suppressing the fiber-induced phase noise to retrieve precise frequency information at remote locations. To achieve this aim, active compensation schemes as first demonstrated in 1994 by Ma et al. have been proposed to cancel the fiber-induced phase drift and implement highly stable optical frequency distribution {{cite:66df08d99ceaf31c370b667e8f69a351f2edab71}}, {{cite:e7c3b8d6836b693ae89791d4bd762df1ea8d6d24}}, {{cite:3ad43287d24d9634c8a399613bfbd9acb1212fa1}}, {{cite:44c941a98b6cffb04eb2696a5a698752cef9999a}}. It generally utilizes the phase error from a round-trip probe signal to achieve the feedback control of compensators. The compensators mainly include variable delay lines {{cite:d19596fb5ede5a10031ae43371886ba96dc98cbd}} and phase-locked loops (PLL) {{cite:66df08d99ceaf31c370b667e8f69a351f2edab71}}. Although this scheme can accomplish very high phase stability, the response speed and phase recovery time are restricted by the compensators' parameters and optimization. Moreover, much attention has paid into the relative long-term frequency instability and accuracy, while little into high spectral purity of the transferred light. The possibility of transferring the spectral purity of an ultrastable laser across different locations is beneficial to the increasing requirement of high frequency stability lasers for optical atomic clocks and high-resolution spectroscopy {{cite:24d2349405885621a8169c83bc0deab9830c9724}}, {{cite:3fa1c6d203dd11fff9818fd1dde92533a5438767}}. Optical frequency transfer with high spectral purity enables such performances to be copied to any laser in any locations, with a simplification of the experimental setup. This is especially relevant when several ultrastable lasers at different locations are needed, but only one ultrastable cavity or clock exists.
| i | 4a31566a4b614ed96ea0dca2fcf7079e |
In this section, the spectral projected gradient (SPG) method is applied to the nonlinear programming problem (REF ). One main feature of SPG is the spectral choice of step length (also called BB stepsize) along the search direction, originally proposed by Barzilai and Borwein {{cite:4db300a3d7e9bb9301e5eb21f277e4804a5f20bf}}. The Barzilai-Borwein method performs much better than the steepest descent gradient method or projected gradient method in practice {{cite:7a94d25811926fec241ec402aae081d7c9ae8a25}}, {{cite:ccd599398d4a3e9fbe63eaeb6dac2e8b4c7a14f3}}, {{cite:6061fa13ddbd971ab1e68bfb97b767bd0ecbd44d}}. Especially, when the objective function is a convex quadratic function and {{formula:9bba7018-8e98-47cc-9033-a9569d43c2d8}} , a sequence generated by the BB method converges {{formula:3c2da65d-3834-451b-a8e6-7fc07e2e324a}} -superlinearly to the global minimizer {{cite:4db300a3d7e9bb9301e5eb21f277e4804a5f20bf}}. For any dimension convex quadratic function, it is still globally convergent {{cite:eff4973a7575c74ff8631292d6148bf0c565efa8}} but the convergence is {{formula:2ba08f68-66e0-4d70-90f1-d79a85530e1b}} -linear {{cite:86c674331d27e24cad4e751f09e5530d24a35ffe}}.
| m | 225419d9a5730816593aec0273c0ec7b |
Our results provide a feasible test for multipartite entanglement in quantum networks
and bridges the two well known cases of multipartite entanglement and multipartite Bell nonlocality. Moreover the scenario considered is a natural generalization of bipartite quantum steering {{cite:1ff730f198a02ba7931b8d3274b0199384ad6491}} (see {{cite:38ebfca1ef40f233f70f6ce1f453d3d0f37f807b}}, {{cite:babb9a2f43ba2fbd21988d9dea37bb310636879b}} for alternative definitions) . Since steering has found applications in cryptographic protocols {{cite:d4f0fa00deb1da925b89db41ff70a4a350512e2c}}, {{cite:3a3d08a2a367d6cfc2d624e9ed4eb2ead085bbb3}}, we believe that our results can be used as a starting point to define semi-device-independent cryptographic applications in future quantum networks.
| d | 795fe15c5a46147cc6adaeb179f38be6 |
In the previous work {{cite:03bb2e586faeb8978675b9de2035d1c020616580}} the monoT5 ranker is still fine-tuned by a text generation loss.
The generation loss for each token is defined on a softmax function over the entire vocabulary, and two separate target tokens “{{formula:8e6c76c2-656c-4100-aec8-1b0184a19cf8}} ” and “{{formula:8965f84a-d4b6-44f6-a8b4-34b8fa9fb95f}} ” are used during the fine-tuning.
Hence only using the logits of single target token “{{formula:25c02ebe-3358-45de-b4d5-9ce6e3c3d21c}} ” as ranking scores does not align with the fine-tuning set up and cannot achieves reasonable results.
If they apply the constraints during fine-tuning that the logits for the “{{formula:10fd13b7-881e-4c33-8575-71ac74607667}} ” target token are always 0 and all the other tokens are excluded,
they should be able to only use the logits of “{{formula:79a9613e-b63f-4b65-90b6-74c6052dd018}} ” as ranking scores.
When there are abundant training data, it should be practically equivalent to our RankT5 with the encoder-decoder structure fine-tuned with the PointCE loss.
With these commonalities, we expect our RankT5-EncDec model performs no worse than monoT5 when fine-tuned with the PointCE loss.
| d | 662d5dccf6cc976e87740cf1749690db |
With this formulation, we can express many popular architectures for registration (such as FCGF {{cite:c9de91d36058c09da087f59c15d1448601ddd01d}} or D3Feat {{cite:ced33c90e4eaf6e492f13879a42ff5ed03903a04}}).
Then, finding the right output descriptors is a problem of metric learning.
We attempt to compute descriptors with minimal distance between positive matches and maximum distance between negatives matches.
For each pair of point clouds {{formula:8b3b6eba-79b8-4cbd-9453-5697d99f4c34}} , we minimize the hard negative contrastive loss:
{{formula:a19ba161-77e6-417b-934c-5d42114dba84}}
| m | f517f104a94e26ecea89cc7bc4542b11 |
An approximate SOSP means the gradient norm at the point is small and the least eigenvalue of the Hessian at the point is lower bounded by a small negative constant {{cite:d025f82ae27bef7a08ebf1d4b20c722a1b56ca98}}.
| d | 918c25f6eadf82e2c9022133d6e1a741 |
Although primarily serving for graph OOD generalization
problem, our theory complements the identifiability study on graphs
through contrastive learning, and aligns with the discoveries
in the image domain that contrastive learning learns to isolate
the content ({{formula:a9759352-6c3d-44d1-82bd-7cfa558b01e2}} ) and style ({{formula:a04d9558-4668-4fa1-86ed-6615d0d56888}} ) {{cite:106fde157d1d205a84268b2debef99e3b6bbf58d}}, {{cite:86b566742b27565415c3906c639485a73fd33ca7}}.
Moreover, our theoretical analysis also partially explains the empirical success of
graph contrastive learning {{cite:8acaf7fed57fa301a7b3faf45a322ecfc8142506}}, {{cite:9cc537add2706dbf636fa4cc1c5e964f993bbcd2}}, {{cite:2f16e9b21490218421d21fc3ecf7a7f25e6cc4f3}},
where the GNN may implicitly learn to identify the underlying invariant subgraph.
Besides, the framework of {{formula:9fee7c33-43b1-4ad8-a153-0114da3ded58}} can also be applied to
other tasks involving relational information such as node classification.
While we sample positive samples according to the labels,
the previous contrastive learning with augmentations can also be applied
to Eq. REF for reducing the sample complexity.
supervised contrastive loss in image domain {{cite:e76c4b0219398fd137de6f67b5b05f360d21afb2}}.
| d | ca49de46f4c89c13280925064dba73e7 |
We have shown in {{cite:cbca072c1dc5e89fadc372b1b0ca44c68987931f}} the initial application of the optimal fitting approach to in situ spacecraft measurements by the Freidberg solution. The merit of the results was justified by the criteria such that the minimum reduced {{formula:2a270d04-a60e-4c83-a4ec-e283f2be6b76}} and {{formula:fd59f654-7c51-4910-aeb7-971f6bdc39c7}} , based on {{formula:b11c3c63-0d62-4e58-9502-36c8b4b6d076}} statistics {{cite:4af1978cbacf47fc96bf554992ea8d418c71e53d}}. To further validate the approach for practical applications, we present an additional case study here by using in situ measurements from two spacecraft with an appropriate separation distance. This is a rare occurrence during the early stage of the twin Solar and TErrestrial RElations Observatory
(STEREO) spacecraft mission. On 22 May 2007, the two STEREO spacecraft, Ahead and Behind (hereafter STA and STB, respectively), were separated from Earth by {{formula:ac21e475-a5c6-4e23-9c8e-7cb510a08fa2}} and {{formula:e27db3b6-7932-459c-8009-d07026f3252f}} , respectively, in the ecliptic plane, with STA leading Earth to the west and STB lagging behind to the east. Both STB and the Advanced Composition Explorer (ACE; at Earth) spacecraft observed an MC event with distinct and similar signatures, based on in situ measurements, while the signatures at STA for an encounter of the same MC structure are much less clear. This event has been studied extensively, by a number of prior studies, employing multiple spacecraft measurements {{cite:89a25e0c6e558a13042e1f903e329b82c996c5a9}}, {{cite:d25f450fd44d9b702448bfda6d1e246d1b7aeca7}}, {{cite:97aa2f74ebd84bc1869c7d5aff9c7ee8f33311a0}}, {{cite:7a192307e39ed2742cc2c330acad1ff23a18eec7}}, inter-relating the observations of the same event at different locations and to the solar sources. In particular, {{cite:d25f450fd44d9b702448bfda6d1e246d1b7aeca7}} performed a comprehensive study of this event and reconstructed a 2D configuration by combining the GS reconstruction results from both STB and Wind spacecraft measurements {{cite:da8ea1bc16bda67019a4c53a16bd3db58fc469d0}}. We compare a selected number of parameters characterizing the magnetic field configurations between our results and those from {{cite:d25f450fd44d9b702448bfda6d1e246d1b7aeca7}}, as listed in Table REF .
{{figure:e8007cde-b234-48a6-9bf9-2461cb3e11f0}}{{figure:56e9458e-2984-43ee-a28b-602c2c4a932a}}{{figure:c3756d53-d203-42cf-8eec-d7c992d6717f}}{{figure:fbefb827-4bb8-4141-bc37-78a44a4a6489}} | m | 43809a64e14b9aa5c701c5ff090bf939 |
Aligning the marginals may be insufficient. Our method seeks to restore the full joint feature distribution by aligning (approximations of) the marginals. While we found that this is often sufficient, it cannot be guaranteed unless the features are independent. One potential remedy is to encourage feature independence in the source domain using “disentanglement” methods {{cite:88e78663879a33dd1cbc069cc9df6b2a8652a77b}}, {{cite:228c6119cd2e8f647bb6b4ed253b421ab12ae43d}}, allowing the marginals to better capture the joint.
| d | a447ee083e03a99d05ab11be8ef37718 |
One of the simplest updates in GraphSage {{cite:2fc7ee6a2a4e7ce7bbc9356601dca3fa747fb139}} for skip connection uses a concatenation vector to contain more node-level information during a messages passage process:
{{formula:5f4988b4-760d-46ed-8f52-a790b7e8c831}}
| m | 11b90e4cda788158d1c70e98f25f619d |
The dispersion of the probe pulse is encoded in the spectral phase
information, which can be retrieved using the methods discussed in
§ REF . Figure REF (d & e) show the real and imaginary parts
of the phase-rate variable {{formula:53b42ed6-066c-4460-8454-45b68b439fe5}} for the transmitted pulse as
well as the initial pulse. We see that
{{formula:9493aaf3-c95c-42a9-b3ef-1f6e4a8ba6b1}} increases as {{formula:6f4a6ccc-4328-4aeb-8ad2-68e51821cd53}}
approaches the cutoff near the initial plasma frequency (vertical
dotted line), which is expected as the group velocity decreases for
frequencies closer to the plasma frequency. Note that the flat initial
value of {{formula:b7c529a4-cbeb-4430-af6a-2cdc5dfb98b2}} is due to the choice of initial pulse shape;
see § REF for a short discussion on the effects of
the initial pulse shape. From {{formula:71c438ea-340a-44d3-a5d9-1770dca31836}} , we reconstruct the phase
variation {{formula:3e3dd67d-9f90-4986-bda4-afb6d937bdf6}} (fig. REF d) that is
proportional to the group delay, which is what would be measured with
the RABBIT {{cite:53ec3bbf868f2b935a03b272f52faa6906ab57f9}} or attosecond streak-camera
{{cite:d510e783cadc440dcef2387c842332fec31abb0b}} methods in an experiment.
| r | c0cbb3ffee5715e1c9c4269778908771 |
The late-time gravitational waves signal from compact sources is prominently dominated by characteristic ringdown phase. This phase is described by a so-called quasinormal modes (QNMs). In principle, one can determine the nature of the source by measuring damping time of gravitational waves amplitude. Moreover, linear stabilities of compact objects can also be verified by the QNMs. An exponentially decay of perturbation mode indicates that a perturbed object is stable under a linear perturbation. The studies of black hole quasinormal modes can be traced back to 1970, where Vishveshwara calculates an oscillation of a gaussian wavepacket around the Schwarzschild black hole {{cite:b7f7ada7ce39f74e0f4114e5b578f68985134692}}. It turns out that, the frequency and damping of these oscillations are solely characterized by its mass. Since then, numerous of a similar study have been explored with various types of black holes and fields (see {{cite:f129922c05fe7f2a57f9912f68e15b98d228076d}}, {{cite:99146af2d31c7b5cbf485be32a8a03c3506b7da2}}, {{cite:3c04cd1adec6db5f6a58d4d27842f8530898452f}} for a nice review on this subject). Beyond general relativity, QNMs of black holes in modified gravity are studied in great numbers. For instance, extended analyses for black hole/string in massive gravity and generalized spherical symmetric background {{cite:1997cf97b9e4004334e70f165bf472bd7cf0f367}}, {{cite:86ace080e6d72ecd6744197b32a943caff36774a}}, {{cite:5115d2c3be784bf1df59af99e813b281334914b5}}, {{cite:6b91bec4c843ca78b26c3631df2303a95233ac0e}}, {{cite:927c1d941d4a23df593bc5f30be66b3d629fdb22}} demonstrate rich structure of the black hole QNMs and remarkable connections to the Strong Cosmic Censorship.
| i | e62047b4b1558a1437d6cc02cd61082b |
Now we come back to the general CG method as introduced in {{cite:8a77f4a1870ef9ed8cda6ed887c8b773a38b7b0a}}. The method is already formulated in Algorithm REF ; we may notice the Fletcher-Reeves Conjugate Gradient method (Algorithm REF ) is just the same as the Practical Conjugate Gradient method (Algorithm REF ) when the loss function is strongly convex quadratic and the learning rate {{formula:cf2cd91d-de14-45ef-b46b-08be254393cd}} is selected to be exact line search.
| m | 462eb6d4407a79c5827daf668d7e0c9b |
We propose a nonparametric bivariate time-varying coefficient model for longitudinal data and a kernel estimating method based on complete cases analysis, i.e. using data when terminal events are available, which is shown to be a valid approach. In contrast, {{cite:dbd54b11abc4a65c3cb74a319c2e07f70c3a8cac}} considered a parametric model and likelihood based estimating method that uses all observations, including both censored and uncensored observations. Clearly parametric models suffer from model misspecification, but {{cite:dbd54b11abc4a65c3cb74a319c2e07f70c3a8cac}} showed that including censored observations improves efficiency over the complete case analysis. We find the likelihood based inference approach is difficult to apply for models involving time-varying covariates for two reasons: (1) It requires estimating the survival function {{formula:3a3b76a7-0e48-4f6b-aec4-59ec1e5e55d9}} beyond censoring time, i.e. {{formula:99d29e0f-d021-4236-ab83-c171f492571f}} , if one wants to include censored individuals, where {{formula:bc9e11cd-d89f-482f-89b2-fb1367ea0986}} is the history of the time-dependent covariates {{formula:d288f0c3-dad9-459a-b292-ac55dd5754d5}} up to time {{formula:88fd5d40-26c7-4835-856f-7b271806a160}} . This means that the covariate history has to be extrapolated beyond {{formula:b199b82a-54f4-4e5c-bb7a-c9b6196978d3}} as {{cite:dbd54b11abc4a65c3cb74a319c2e07f70c3a8cac}} also pointed out, which is extremely difficult and introduces measurement errors even when it is doable. (2) Oftentimes in longitudinal studies, the time-varying covariates are internal covariates {{cite:04096f3010e68f18510afa3ffa21f5751d5eae93}} that make the conditional survival function undefined, leading to invalid likelihood based inference. Hence we argue that the complete case analysis is most appropriate for longitudinal data with time-varying covariates, as in our analysis of the USRDS data where the indicator variable of Medicare as secondary payer is time-varying. Additionally, efficiency loss should not be a concern in our analysis of the USRDS data because of the very low censoring rate. It is worth pointing out that even under scenarios where efficiency loss could be a serious concern, our proposed method can be used as an exploratory tool for finding an appropriate parametric model.
| d | 0010913626911ada2edf3515aa51d0e2 |
For large sample sizes, performing EKPCA amounts to a significant computational burden, motivating many approximation schemes. We explore the popular Nyström approximation {{cite:638be780d85d3e9e4e6e9b95a1365f18055ee6bd}}, {{cite:1e6e47939c708bdce3daf7e94edf167120073209}}, {{cite:36add20428dc398680779b6368edd174b43d717b}} to speed up EKPCA and study the trade-offs between computational gains and statistical accuracy.
The general idea in Nyström method is to obtain a low-rank approximation to the Gram matrix {{formula:7ffe7821-4923-4979-bfb1-d67ada7e375b}} , and replace {{formula:b20d2de4-7a92-4625-9269-8e83c6c86d2e}} by this approximation in kernel algorithms, resulting in computational speedup. Since the eigenspace of {{formula:38559db4-4d8d-43a1-a63f-c7274362e6d1}} is related to that of {{formula:1553dc46-1a34-4821-a189-27a25326569a}} (as noted in Proposition REF ), Nyström method also yields a low rank approximation to {{formula:e53fd6e5-72d8-4d62-b33a-39dde1c07b95}} , which is what we exploit in developing Nyström approximate KPCA. It follows from Proposition REF that the eigenfunctions of {{formula:933d348e-d94a-448d-be44-ea3eb7fa0e55}} lie in the following space,
{{formula:19f93c23-b625-40b6-b92c-c6971a1edb8d}}
| m | 8def993662370f6062a777cdd43f1ea9 |
Another line of work, inspired by the deep image prior {{cite:d89931242c62022d23732e247d11d168b9102b2f}} focuses on using the inductive bias of convolutional networks to perform reconstruction without any training data {{cite:90100a8b33d13a076a5631cbe54c30c14fb9f302}}, {{cite:ba361282d960f0768cd2411ea1e8e6664f4e21c7}}, {{cite:389adcee8c7b936f2181792e22367cb681dd8e4e}}, {{cite:05e1a48e9f100baa13552fb3c5f48ccdafe6abd4}}, {{cite:52dedf9b74c724dba8f03739ad0d23fdeb2859d1}}. Those methods do perform significantly better than classical un-trained networks, but do not perform as well as neural networks trained on large sets of training data.
| m | 2c0380430b95c27970558f2063639e10 |
To investigate the presence of a spontaneous magnetic field in the sample, we have collected ZF-{{formula:1eb3a4d2-f500-4f3c-8b08-4594c185e3a0}} SR spectra at temperatures above and below the superconducting transition temperature. The asymmetry spectra were best fitted by static Kubo-Toyabe function multiplied by an exponential decay component {{cite:4f36eb9a16ec83921cb3715a65a43fea97d8fc80}} is given by
{{formula:3bcc7d2a-8e1f-4304-8281-514f9bf70be3}}
| r | 43e4666ae131c2b676b0753a9a87a1c0 |
In this work, we consider a universal line-based OCR pipeline that can extract dense printed or handwritten text as well as sparse scene-text with the goal of determining the optimal text-line recognition (TLR) model in this scenario. In such a pipeline, a separate the text detection model is responsible for
detecting and rectifying all lines of text in the image. As this step is outside the scope of this paper, we exclude from the analysis here public datasets with irregular scene text where detection and rectification are the main focus, such as {{cite:231a425883f129659e11ec9511c2fa8a3bc8ce47}}.
In a line-based OCR system, the recognizer needs to handle arbitrarily long text-lines effectively and efficiently. This challenge has been overlooked by previous state-of-the-art word-based models. Public datasets (mostly word level) have relatively narrow image width and sequence length distributions (see Figure REF ). At the same time, the design, performance and speed of TLR models depends on these variables. To understand these issues, we study TLR models trained on an internal dataset containing examples within a wide range of lengths and with a much larger symbol coverage (675 classes containing most of the symbols in Latin script and special characters, compared to alphanumeric characters used in majority of the public datasets). We found that techniques such as image chunking substantially alleviate the challenges posed by examples of wildly different sizes.
| i | 851d5da2c1521e5bdf6ab53eb50f301c |
Previous works on synthetic segmentation can be classified into two categories, including two-stage method {{cite:ed6827560576cb0d020b61382b3890171f71b0c5}} and end-to-end methods {{cite:9eb617ba19ab5f81cdad306bf7dcfd1d4851d3c5}}, {{cite:ffda47592501f5d14e6d0eb48ec4c57a60b67250}}. Zhang et al. {{cite:ed6827560576cb0d020b61382b3890171f71b0c5}} developed a two-step strategy, called TD-GAN, for chest x-ray segmentation, where they first use a CycleGAN {{cite:d15e34763aecdc013f03f464affab8181aea666b}} to adapt the target domain image to the domain with a well-trained segmenter, and then predict the segmentation on the adapted image. However, the segmentation performance relies on the image adaptation performance, thus the two-step process may prone to error aggregation. On the other hand, Kamnitsas et al. {{cite:9eb617ba19ab5f81cdad306bf7dcfd1d4851d3c5}} developed an end-to-end unsupervised domain adaptation for MRI brain lesion segmentation. However, they only used overlapping MRI modalities (e.g., FLAIR, T2, PD, MPRAGE) in both source and target imaging modalities to ensure performance. Later, Huo et al. {{cite:ffda47592501f5d14e6d0eb48ec4c57a60b67250}} proposed to directly concatenate CycleGAN and segmenter as an end-to-end network, called SynSeg-Net, and performed studies on two independent imaging modalities (e.g., MRI and CT). While SynSeg-Net achieved reasonable performance, there are still several issues. First, the training image of the segmentation network relies on high-quality adapted images from the CycleGAN part of SynSeg-Net. Without preserving anatomy structures and contents during the adaptation, the image could be adapted to a target domain image with incorrect structure/content, and negatively impact the subsequent segmentation network's training. Second, SynSeg-Net is a heavy design that relies on training 5 different networks simultaneously which requires careful hyper-parameter tuning, long training time, and high GPU memory consumption.
| i | 225ee22b3ec1002424d893cfac8c02a8 |
Solutions with degenerate metric were a subject of a long-standing
discussions starting probably with the paper by Einstein and
Rosen{{cite:67759aedb97dd390ea1ffdde345be1589561248a}}. In spite of some difficulty interpreting
solutions with degenerate metric in classical theory of
gravitation, the prevailing view was that they have physical
meaning and must be included in the path
integral{{cite:8841726636da549d2c4b1b058bcd329e86e96993}},{{cite:2166e10a9d1cc20041b1991c8eb71f0f151a129f}},{{cite:32fcc4aec8f42bd5aef9c4bb0e6b2cb0f0247161}}.
As it was shown in Refs.{{cite:8841726636da549d2c4b1b058bcd329e86e96993}},{{cite:0dcfd098209c354b0278d5ff5a44067f533779f9}}, in the
first order formulation of an appropriately extended general
relativity, solutions with {{formula:4e83f089-cbfb-4750-84f4-6734b1709328}} can
describe changes of the space-time topology. Similar idea is
realized also in the Ashtekar's
variables{{cite:cab0dd0b56e788f00eccf6cacf91df188ffb23b3}},{{cite:c63a78726aa31748f39fc0a586fdf2cc5bfd27f2}}.
There are known also classical
solutions{{cite:c325a0eb513812dd212f8e0d8b8b6bf8134c15bc}}-{{cite:9461be806402630d56b82f473c99282cc8499cb2}} with change of the
signature of the metric tensor.
| i | 7474d6f53af26c14caf0d0f3c642f3fc |
We can then proceed with an analysis exactly along the lines of our discussion of Mrk 421 in {{cite:c4b40fff0e09ed1f81dcf4bcaf269f5d9380c22d}}, and specifically refer the reader to equations (17)–(21) in that paper and to the discussion around Eq. (5) of {{cite:9a433f99bbf9752583d9d729d9f3300514686e0d}}. In summary, we use the synchrotron cooling timescale for an electron of Lorentz factor {{formula:4be52bdf-1c7f-471f-8e5c-5ae6cc190e92}}
{{cite:37e39ddd57bc261b63450a5cff66ed695b3e4606}}
and combine it with the critical synchrotron emission frequency in the Sukaku energy range we consider here (0.8 – 8.0 KeV) and the shortest weighted variability timescale for PKS 2155{{formula:41aa71d4-7775-4e94-9293-35c5e212015b}} 304, or 18.5 ks, for which {{formula:e5578f88-e9bc-47a5-b6d7-21ef30cfa7cf}} %. By requiring the cooling timescale to not be shorter than the minimum variability timescale one obtains a constraint on the minimum value of the magnetic field of
{{formula:4b59724f-ddb0-4848-a282-fafd1dbfb3c1}}
| d | 1216e242d160bb5194bb55b40fa76092 |
It is often desirable to study statistics on barcodes and much work has been done in this area (see, for instance, {{cite:86aa2c95204b9427e91d2169c2ded46ba68dcb36}}).
Recently, researchers have begun studying combinatorial invariants of barcodes. In particular, Kanari, Garin, and Hess discovered a natural mapping between the space associated to barcodes with {{formula:86fb81e3-638f-4361-b840-c171f9db8d31}} bars and the symmetric group {{formula:09fd5921-2a7a-4f28-a471-9b177be89680}} in {{cite:cbdeda9ffae88ee9f9ca88e567d6aed34d244c00}}. In a follow-up work, Brück and Garin refine this mapping in order to stratify the space of barcodes into regions with the same average and standard deviation in each endpoint and the same permutation types {{cite:c7dd16e1b372d3d0b124346461845aa29815ccaa}}. The coordinates obtained through this mapping are an elegant blend of continuous and discrete invariants.
| i | 1b6f70755c55ea18b4ebc84ac1c4d42c |
The H{{formula:06d238fe-cdc2-4e02-832c-927641a613a4}} emission at the position of AB Aur b has been detected by Subaru/VAMPIRES {{cite:497301211fd4e9677236627a7839fdffe614a4de}} and HST/WFC3 (this work). However, it is unclear whether the VAMPIRES detection is physically associated with AB Aur b due to uncertainties in the instrument's astrometric calibration {{cite:497301211fd4e9677236627a7839fdffe614a4de}}. The astrometry of the WFC3 detection is well-calibrated and consistent with measurements in other bands. Therefore, we only adopt the WFC3 measurement for this discussion. The WFC3 band-averaged H{{formula:3c19661c-eea1-4bae-8391-f8db74e4d039}} flux density of {{formula:2fd306d1-237a-455d-b616-51d03fda701a}} mJy is higher than the optical continuum measured by HST/STIS ({{formula:15830cc1-c647-4591-90ed-280c45115374}} mJy; {{formula:a440db64-8d93-4a67-9ea4-260751ca4ab9}} m, {{formula:9b5605a5-c54a-4955-803f-8f12b9617203}} m) and Subaru/VAMPIRES ({{formula:23ff6eaa-7439-4b93-b16d-54a2d385b4fb}} mJy; {{formula:d9eabcf3-29df-46cb-8ed1-f1f102cd03a4}} m), but the difference is moderate to marginal, respectively. The line-to-continuum flux ratio (defined as the band-averaged F656N flux divided by the continuum flux) is {{formula:977aaec7-582d-414a-af50-65c291adb93f}} or {{formula:c7621cb1-b7f4-4696-ae29-fbce3bb42dad}} , depending on whether the STIS or the VAMPIRES flux is adopted for the continuum, much lower than the flux ratios {{formula:194d20f8-015d-4351-8864-584d4b3d33f5}} estimated for the PDS 70 planets, as well as several accreting planetary mass companions {{cite:a96a1cbaf63543beec69c46d5399febe28500b54}}, {{cite:28d9f9a605000fb821ac6ae65ba88f211cfd741f}}, {{cite:96bc7889469fffb496babeb6996852aa85223b57}}. AB Aur b's low line-to-continuum flux ratio is inconsistent with the accretion shock models that explains the observations of PDS 70 b and c {{cite:af6a97da4a2bf6839d691873677ad03f7ec707f2}}, which produce pronounced H{{formula:5603e6e6-6875-4c96-a562-09c9d7bd1f7a}} lines. As a result, the H{{formula:f27896b1-28f1-498c-9b09-07455dd9c3e4}} detection does not strengthen the interpretation that AB Aur b is an accreting protoplanet.
| d | a9ea637e16823d6b6611cf16b1b301ae |
The twistorial formalism we have presented here firmly establishes the geometric foundations of the Newman-Penrose map. In particular, for any Kerr-Schild spacetime with an expanding SNGC, we have defined a coordinate-independent construction for both the operator {{formula:23e4f26c-0daa-429e-b734-71629193a5f5}} and the complex scalar {{formula:bdb4e648-f033-4932-af00-0671c875cd2c}} in terms of twistor variables. These quantities are then used to define the self-dual gauge field in the Newman-Penrose map, {{formula:edc0f533-6f26-4df0-9483-13651a5439b7}} , which we showed in previous work {{cite:4f5d89c3f44dc0aaf0862b7636505f9878cd22f0}} coincides with other double copy prescriptions.
The close relationship between twistor theory and the geometry of SNGCs is at the heart of this construction, and given the distinguished role that shear-free rays play in several of the approaches to the classical double copy, it is no wonder that twistors are increasingly being recognized as a useful tool in this setting. The work we presented here was partially motivated by applications of twistor theory to the Weyl double copy {{cite:8194bc8b486995c1442bc514b84d65ea1d1d4503}}, {{cite:be6f6200ed20dbd0b441e6294d8b1b201961e7f0}}, where the Penrose transform was of central importance; however our investigations seem to run somewhat orthogonal to those references, and it would be very desirable to understand more clearly the relationship between the two approaches.
| d | 84df7947f59fcc0f57d244f3c6a1e76f |
Whether the improved performance and superiority of the non-adiabatic operations extend to larger problem size is an important question for future study. However, the scope for classical simulation is limited due to the typical explosion of Hilbert space size with problem size. Analytic insights would be extremely valuable, though have often proved challenging beyond small-p. One possible approach is to investigate the locality of QAOA with the RQED-mixer. For standard QAOA with X-mixer, the locality was studied {{cite:80f9fee29f9bc7cca03b575429d991c59bcdb822}} to prove the performance of QAOA on the independent set problem, another famous NP-complete problem on graph. Last but not least, it would be desirable to implement the algorithm on near-term quantum computers, as these devices begin to eclipse classical simulation {{cite:5c3c9d0b5681293b8d1260490b9c08cf54008191}}.
| d | f12f0de68aa0377efdb98674f497dacc |
This section briefly describes the details of training and presents the experimental results on the compared PDDL benchmark domains: Sokoban, Maze-with-Teleports, and Floor-Tile. A* algorithms with learnt heuristic functions realized by the proposed convolution-attention-position networks (further denoted as A*-CoAt) are compared to A* with learned heuristic function realized by convolutional networks as proposed in {{cite:a96c17eb571ea82663f7e815b16c1276b23b06ca}} (denoted as A*-CNN), and to the state of the art planners LAMA {{cite:5acc94040c5b8a8a82e6cb5e7520381b06145ac9}}, SymBA* {{cite:9f426e54afa8fa20740c558aaae607f50bd454b0}}, and Mercury {{cite:d5a1c27d5f59e08f5026e6258e584eda045b914e}}. We emphasize that A*-CNN and A*-CoAt uses vanilla A* search algorithm {{cite:af5ea8593910dbf1afc16a44710bac807fd5406c}} without any additional tweaks. In case of Sokoban, we also compare our planner to a solution based on Reinforcement Learning {{cite:cfe10123fee4807065afbf3c74f28d57395e53fc}}.
| r | 73ad408bc197cb341bddd94b4d8a3eb9 |
Due to the more complicated integrable structures of Pfaffian point processes, it is not surprising that the local universality classes (i.e. scaling limits of all eigenvalue correlation functions) were first investigated in the complex symmetry class.
Indeed, the bulk scaling limit of the complex Ginibre ensemble was already introduced in the work {{cite:b628726035cac4918a1b33cc3e6e16a38f5c6698}} of Ginibre.
On the other hand, the edge scaling limit of the complex Ginibre ensemble was discovered in {{cite:fe10e444b1a0426fab5fd794e2b47b7ffeb1cc0c}}.
For the real symmetry class, the bulk and edge scaling limits of the Ginibre ensemble were investigated in {{cite:477bc7caecfb4a01bc69c3c15fa5e46fffe20d2e}}, {{cite:10ab1f9b9e74413d28b67cc72ae8768f24d0e5d1}}, {{cite:5d85fe5dce427b3647ff7a44407465e8106500e6}}.
Finally, for the quaternion case, the bulk scaling limit was first introduced in the second edition of Mehta's book {{cite:b967a745d8cfc4b6a47e2af309f34a7ec5155741}} and later rediscovered by Kanzieper {{cite:173459d63914408884667efcae40167f3d7293df}}.
In contrast, the edge scaling limit in this symmetry class was discovered only recently in {{cite:4a006695ec42c0265c0057e6a5da1db44203d89d}}.
(See also {{cite:a53b9151fea65951000f4bf9a6b16fde09f0e7de}} for an alternative derivation for the 1-point function.)
| i | 272cc3a75755d68555d72f324a057baf |
In this study, we assumed that the body and inertial forces are negligible. It would be interesting to include such effects in future works and investigate how they impact the model's accuracy. Moreover, for all the cases studied here, we have used feedforward neural networks. However, one can use more advanced architectures such as long short-term memory (LSTM), gated recurrent unit (GRU), or temporal convolutional network (TCN), which are deep sequence learning model. Such architectures are very useful for cases that are history-dependent such as plasticity and viscoplasticity {{cite:a7940dc41cffccc34fc1d6ab544c21827b05b7dc}}, {{cite:63156157d148550ab1b09f5af3e132c69a6eee31}}. Therefore, it would be intriguing to employ such sequence learning models within the DCM to solve path-dependent problems. Additionally, in future works, other geometries, including irregular geometries, need to be considered and study the DCM's accuracy for more complex geometries. It is also worth mentioning that the penalty method has been used to satisfy the constraints (boundary conditions). One can reformulate the loss function, so the constraints (boundary conditions) are satisfied using Lagrange multipliers. The displacement field and Lagrange multipliers can be inferenced by the DNN, and then one can check if a reasonable accuracy can be obtained. Solving partial differential equations using deep learning methods is an active research area, and this study is far from being the last word on the topic.
| d | 0432d8e30bcd99017fd5adc4ef1dcf84 |
Many recent works have used adversarial attacks on CNNs to demonstrate the susceptibility of the networks to simple methods that could lead the network to make completely wrong predictions{{cite:0a2cec41e2f6d9238ad1a79e9d17e26a032141a0}}. Different adversarial attacks on the network can be used to interpret its behaviour{{cite:5ef1ef252acc24ab9ae13bb03279b438f8bea9b0}}. Sample images that produce adversarial results give hints about the behaviour of the network{{cite:db89ef89da099b1448eb36d5edcb9d1d99f4f8e3}}, {{cite:496139504c2284f94203a9dad71ef50bdd61d4bd}}. For example, the one-pixel attack proposed by Su et al.{{cite:8be58ac11a03a345f61208c16264ca566ebc072f}}, showed that the network can have a completely wrong prediction by changing just one pixel in input image. Studying these adversarial attacks we can interpret the regions of the image that the network focuses on to make a decision.
| m | c5da451b9eab5d10b3020b61f13ca555 |
Two trivial solutions exist: (a) recomputing low-discrepancy signings
on the active set of vectors after every update operation incurs optimal offline discrepancy guarantees with a recourse of {{formula:69af7cce-a791-449f-aacb-65c185404d8b}} per
update, and (b) an independent and uniformly random signing of every
new vector maintains at any time {{formula:94e75df0-ef0a-456a-a960-b10fc10beb48}} a signing of discrepancy
{{formula:995ab60a-9c8c-451f-9ad7-e7a6c4601d01}} w.h.p., while performing no recourse
whatsoever.
Since {{formula:8aa4dfc9-26fa-4161-b693-ac59d9006eed}} , this is much larger than the
optimal offline discrepancy bounds of {{formula:96c8ef1e-e62f-43d4-abb7-a53f818f9f62}} for any collection of {{formula:fe7b7d62-8222-4e1e-be90-598ba9af5283}} vectors in
{{formula:e6f1915d-1b35-4d10-9b74-8e4507ab8907}} {{cite:d6a8b2a02904e229f788e9c8c59a63d251bbf979}}, {{cite:e05617bd74c861fa8cce92bd0c1b38cff1de7cbf}}, {{cite:8ecdcfc4d9a7192c3dc7cc2e31c30c3e1f187e77}}.
We ask: can we get near-optimalIn this paper, we use “near-optimal” to mean optimal up to poly-logarithmic factors. discrepancy bounds with a small amount of
recourse?
| i | 2ad27370a9fa4e89c9c95b174c25b892 |
The ideal prototypical representation should be expressive and encompass enough intra-class variance, while being distinguishable between different classes. In the literature {{cite:27cedc2cc7ec21b456dd83b295ff7af4ba3ba475}}, {{cite:764e14db0fed727c33b69b7de568032bd2d75a52}}, however, the prototypes are commonly modeled by a single or multiple deterministic vectors obtained by average pooling of only a few samples or clustering. Hence, they are not sufficiently representative of object categories. Moreover, uncertainty is inevitable due to the scarcity of data, which should also be encoded into the prototypical representations. In this paper, we derive a probabilistic latent variable model by modeling prototypes as distributions, which are learned by variational inference.
| m | 4c8aefef138b2249866de66c2e67f465 |
We evaluate the pixel-level anomaly detection performance in Table REF , and illustrate the model outputs in Figure REF of both texture and object classes. In all cases we use a vanilla AE with {{formula:6f09cbdb-78d2-4ce4-a18b-ff437f7b43b4}} , {{formula:047ace8a-b874-445f-9167-44ffaa31fbc7}} and {{formula:7baba782-b156-4d41-b4da-dc63452a4a98}} . It is clear that the NLN-enabled AE demonstrates performance increases in the object classes of MVTec-AD. However, this is not the case for the texture classes. We suspect that this is due to our NLN-enabled AE not being able to distinguish between different texture-patches. This behaviour is similarly demonstrated in {{cite:51f73ac8e6b276655c08cddb5afc9fb3dcd6e182}}, and we believe that this is an inherent weakness of standard autoencoding architectures.
{{figure:de227dfe-dfb8-41de-a94b-a486f2ff8a4e}} | r | 0632b810aee2e9ddfded4be8301af818 |
Results on ScanNet: Table REF shows the segmentation results in mIoU(%) in ScanNet{{cite:494f90358f7a6ce39a596452c48ae9733e5c0fbf}} validation set. Our method outperforms the previous method MPRM{{cite:7b8153b3d0e6c0db5a892dd7273a71540ad444fc}} by a large margin. However, with 10% points labeled, the baseline results is already very close to the fully supervised results. We argue that ScanNet is a very large scale dataset, 10% of the label can already provide strong supervision. Our method is effective with only 1% labeled points, where we outperform the baseline method by 1.9% mIoU. In practice, it is not easy to collect a large scale dataset like ScanNet, we believe our method is meaningful in real-world applications.
{{table:5ff708cf-b9eb-4bf7-ac57-5d8942fcc308}} | r | b10b41338ff03f08429f1329a9f280b2 |
The resulting quotiented structure ({{formula:c7485c1b-0f8b-4a11-84d0-2c7cd0abded8}} ) (which is isomorphic to ({{formula:abdee107-8726-4826-a6d7-3bd3ad1b90e6}} )) is in some sense, a richer object than the orders considered in this paper. Every countable poset is embeddable in ({{formula:ac538e29-a21f-40ed-b0ee-f21b0e47c034}} ) {{cite:f28b674cd001608daa0de160a579d738fbf40f67}}; this is clearly not the case with {{formula:6c671622-2fdd-419d-a1e7-5dbabf9d3291}} and {{formula:c60cd422-4b45-41d4-bd7e-23b44a25b94a}} each of which is well-founded and thus does not contain an infinite descending chain. Given the undecidability result of Hatami {{cite:3e302608218618acd1462f1471698249c21609a9}}, one expects the first order theory of this structure to be undecidable. In fact, we expect:
The first order theory of ({{formula:c91f0f95-3433-4379-be0f-673ea784be06}} ) (where {{formula:6d7aba63-4044-4431-8d0e-4c2ab0172634}} are predicate versions of {{formula:046a2f50-fef0-49d8-8dbf-628ea30d8a55}} and {{formula:fb8e34ee-5846-4356-987c-86103b8ad53e}} ) is definable in ({{formula:9a14ac19-2912-4f94-ab6e-908da86bc78a}} ).
| d | 835a87c68ad7fdbdd79487c3f38fbd09 |
When the weight distribution of a linear code is known, it is possible to obtain the weight distribution of its corresponding dual code using the Krawtchouck polynomials. Through the following, we recall such an important mathematical tool (see, for example, {{cite:ae1f5b94be391d53d066aea7ed6bc532850f00c6}}).
| r | 9c16e9b202004b9a992a147c77ab2f14 |
Beyond this, there were several notable theoretical works considering the cavity statistics of lasers with embedded nonlinear absorbers {{cite:f00cb811b72480ece4c481148279d75e53a26bc8}}, {{cite:b4464d56eefb1424f615f608669b56cfbe372b1e}}, {{cite:550d3f60edc115b271676364f5b0d677602d71d2}} (e.g., saturable absorption, two-photon, and three-photon absorption). This is reasonable, as all of these effects lead to “negative feedback” which was long-known to lead to noise reduction (a recent proposal in superconducting qubits, which explains the idea, is presented in Ref. {{cite:225fc8162655af32be4919aa39c1993c6607e237}}). For low-order absorbers (second- and third-), the achievable noise reductions are modest ({{formula:20494454-c88b-4522-b7bf-d53a1323ec2f}} 50%). High-order nonlinearities (larger than third) could in principle achieve further noise reductions {{cite:83aa63feccbb385035c513e275662a2bd0b7955f}}, {{cite:441855f71d030a2c35d8ca0608f5016f96202ad2}}. Perhaps mostly closely related to our work, Yariv and Vahala noted that frequency-dependent losses could could lead to linewidth and amplitude noise suppression in the presence of amplitude-phase coupling (specific to semiconductor lasers {{cite:ac9b09f797ddc28f803eee9db0c152197d4b0809}}, {{cite:20771e8f8b24a04d3093c362501cd7ca9edd9bd0}}). In all cases, these concepts would enrich the idea we present here: higher-order nonlinearities, as well as “quiet pumping”, would likely bring the achievable noise reduction very close to 100%, probably even in macroscopic cases. We would be remiss to not mention squeezing. The noise condensation effect shown here can be considered as an extreme-form of number squeezing (as opposed to the quadrature-squeezing of squeezed-vacuum achieved by {{formula:6e811794-2d4d-4595-b7a9-8e28ee6e3040}} and {{formula:04b92d72-292f-4681-87fc-a4cd2a6d80f8}} media). Number squeezing is also achievable through low-order nonlinearities by means of displacing a squeezed state. That said, a Fock state is fundamentally different from an amplitude-squeezed state {{cite:03a5418807d371d181c4ae101bf43071313b0ff3}}: a Fock state is not squeezed (it has large uncertainties in phase, and phase space volume {{formula:582ac023-8061-43a6-a8f6-3df560812ba0}} ). In a way, one of the important results of this work is that we have identified a nonlinearity that naturally produces Fock and other number-squeezed states of light (as well as suggested mechanisms to realize it).
| d | c29ebb7b49ff64087f6532a5da970f80 |
Example 1.7 (Thurston {{cite:85575ddbff68b56c8a3922098adfa12d02d013e5}})
Let {{formula:01beb6fc-479f-4223-90d9-eefe76c46b24}} be a cusped hyperbolic 3-manifold. By Dehn filling {{formula:909976cc-06a5-41f0-b6c1-6ddba6c60d39}} , one can get non-isomoprhic hyperbolic 3-manifolds {{formula:c26b9754-d20b-4848-8d28-95a61e1b2396}} with {{formula:80362269-ee2f-4ee0-a65c-f67822f4328f}} . Since {{formula:7c88a156-0567-4944-8f77-47f7ace2c4ab}} are non-isomorphic, by Mostow Rigidity {{cite:f71cd3bfb15106be3bbae1c7743b039cef739e84}} they have non-isomorphic fundamental groups {{formula:44dd38d5-f920-4af2-923a-47cc034d8ead}} , which thus have arbitrarily large {{formula:2ce26f1f-781c-4ac9-8cc6-a6d667da40e2}} and {{formula:2c1cb184-3f77-4f4a-8e24-27542c84e178}} .
| r | 56854c996bae42ab634a4b95810d133d |
In order to give full play to the role of ultra-wideband, we develop a JMMSE-based distance estimation method which is able to exploit the low-rankness structure of the covariance matrix in the frequency domain{{cite:a4669c3fd9734572d191b6a35c85bb416dc873bf}}.
When {{formula:5d7a9bf9-2735-46a0-949c-b30c315ea962}} is in the active state with a proper codeword selected, we estimate the corresponding RUS-UE distance with the JMMSE channel estimation of all sub-bands.
| m | 7e38f7900f037bf0db3855b797a6596e |
where {{formula:bb827e24-bca6-4714-af90-c511090516b1}} is the modified Bessel function
{{cite:52b83e05e350a25ed23f227f1979385f7a826fc3}}.
In Appendix A we evaluate the right hand side of Eq. (REF )
as a Taylor expansion in powers of {{formula:cb38fa32-28f6-420d-8765-f439eb16388f}} .
We obtain
{{formula:34494aaa-525a-4d05-a86a-74f05ce1b993}}
| d | aa220cc548193fe37a3081e9ab648199 |
In this paper we solve the above two challenges using three techniques.
First, our model extracts a spatial temporal feature sequence from the observed video using inflated 3D convolutional networks {{cite:355819ac06afb55a76c47e6f7356839da5c6350f}}.
Then we propose a novel encoder decoder architecture to forecast future actions for future unobserved frames.
Our temporal recurrent encoder consists of a GRU model and a self-attention-based model to weight the most relevant temporal feature dimensions of observed video sequence. This allows us to better model the temporal information. GRU model captures the temporal evolution of features while the feature-based self-attention identifies the relevant feature dimensions of the signal that are important for action understanding and forecasting.
Typically, self-attention modules are applied in the temporal axis to identify the most relevant features of the sequence.
In our case, we use the self-attention mechanism in an orthogonal direction to identify the most relevant feature dimensions of the temporal signal.
Experimentally, we demonstrate the impact of this design choice.
| i | 9e462fbca4bf602c29772e64fadc688e |
Given the diversity of the downstream tasks, we do not see a single clear winner.
However, our Ladder-BYOL maintain a balance of downstream performances at a high level by being the best in ImageNet-1k (IN) linear classification, the best in COCO (CC) box-based detection, and the second best in instance segmentation.
For example, LEWEL-BYOL {{cite:04f032aeb5e4af1fba74a6d39f916c90120962d2}} performed well and similarly in classification and detection to ours, but was found to be less generalizable to segmentation.
In contrast, DenseCL {{cite:fd38d7b1a1b4d5a75f45f6721238520ad9899a9e}} was the best in VOC segmentation but at the cost of classification accuracy.
Our Ladder-DenseBYOL is the second best in VOC semantic segmentation, while it has similar but slightly worse performances in the other tasks than Ladder-BYOL. Thus, it can be regarded as a still versatile but somewhat segmentation-oriented backbone.
| r | d285cc076f1d4673dc72a227ea6c6a8e |
One dimensional disordered electronic systems are always localized. Following the scaling theory
{{cite:b50aba340ef13f86fe8ba50ce33783d8bca7091a}} this implies that by increasing the length {{formula:00f88c76-98e6-459d-a01f-ba2e844960e2}} of the wire for a fixed
amplitude of disorder, its typical conductance ultimately reaches vanishingly small values. The
localization length {{formula:f0e52088-ab35-4b1b-ba78-8a8a887f1218}} separates metallic regime for small length {{formula:69c75a33-9222-4ede-b237-38bd606b8c8e}} from the
asymptotic insulating regime. In the present paper, we focus on several universal properties of
both metallic and insulating regime of these wires in the simultaneous presence of two kinds of
disorder.
The first type corresponds to scalar potentials induced by the impurities, for which the system
has time reversal symmetry (TRS) and spin rotation degeneracy. In this class the Hamiltonian
belongs to the so-called Gaussian Orthogonal Ensemble (GOE) of the Random Matrix Theory
classification {{cite:23f3f9b757a7ae098a8b1c139f42cc7e07a11d7c}} (RMT), corresponding to the class AI in the modern classification of Anderson universality classes
(see e.g. {{cite:e5a105fb865b474afe655e94e5f362fa5562a0ce}}).
If impurities do have a spin, the TRS is broken as well as spin rotation invariance. The Hamiltonian
is then a unitary matrix, which corresponds in RMT to the Gaussian Unitary Ensemble (GUE) with
the breaking of Kramers degeneracy {{cite:a889b5e4bfeb9fc44b307bbae8389e8ac8fa3c45}}, and to the Anderson class A {{cite:e5a105fb865b474afe655e94e5f362fa5562a0ce}}.
However, for the experimentally relevant
case of a magnetic potential weaker than the scalar potential, the system is neither described by the
GUE class, nor by the GOE class, but extrapolates in between. This intermediate regime, of particular relevance experimentally,
is the main object of study of the present paper. Moreover the present work
paved the way towards a numerical study of the correlation of conductances in the cross over regime {{cite:7bb7261b4f453590649df68cff102bfd52e92978}}.
| i | 3a638881c8c30b68a8b23c0606b0866b |
One of the key aspects of the CERN LHC physics program is the search for new resonances predicted in theories beyond the standard model (SM). Given the fairly stringent limits already set on masses of such resonances in fermionic decay channels (e.g., via dilepton or dijet searches), it is particularly interesting to explore bosonic decay channels, which can dominate if the couplings of a new resonance to fermions are suppressed. Examples of such signatures are decays into a pair of massive bosons: VV and VH, where V represents either a {{formula:f4132c3f-037b-496c-8dc8-fceffdb193a3}} or a {{formula:a36bd0a3-3aa3-4c19-a1d7-01c964c5120d}} boson, and H refers to the recently discovered Higgs boson {{cite:ced4514ad5d637449fca7a956ca4e35669dcde10}}, {{cite:ac95eaa230a1ba9fe0e079e97e210e4f7976eafd}}, {{cite:b4450a90c525d55ab3ea785cfb0dbdbbfc31e864}}. The latest results from these searches at the LHC are described in Refs. {{cite:332a0aba4f8798f0768cfa8ad207816bdf22b040}}, {{cite:fca0c7689f2cb2a3d19252d74f7358ae29962d5d}}, {{cite:1ceeacbb11ce6352761d29de181eb2160c238198}}, {{cite:f4ccc6c873d2aee40fc43f0c79e9b45b1628b005}}, {{cite:ea997d0510575655610131a95003b4a9730c7603}}, {{cite:32fe7419aeffe6c55d549f90d0b07a8f8497bc09}}, {{cite:e0f82b87072f89d9bf16bc73998af32af3b5cb9c}}, {{cite:aff48f8ff3ce78f27ec938951871e528e3900f2a}}, {{cite:610312cf495439c26099422a53f8f38e5df752c3}}, {{cite:0792b20d8a07df87944b7358c570f0856095cf57}}, {{cite:bb84374a1ed14ca6cb3ee08a42fb6109dbfaf801}}, {{cite:a7fcbb785a93b3102dd0078a0a41d805ef65e7ea}} for the VV channels and in Refs. {{cite:e0f82b87072f89d9bf16bc73998af32af3b5cb9c}}, {{cite:262296b7c57af6e7c28d10c4a5f20d66c4fe08e8}}, {{cite:a45f98e3e215c4a8532f5f5654b384734490a42e}}, {{cite:799caeaaf582fc42afceb1f3aff5d5409682e1ce}}, {{cite:0524ce87c0ef9d1c3947b01a3d7d60b9eceb3675}}, {{cite:e05c88eea7874818d5450de32a53521097bdceba}}, {{cite:3f33939dd9eac1cc232bb09043799a9f657caf73}} for the VH channels.
| i | 0fe2fabc91ac09efd8a720deb4aa466c |
In order for baryogenesis to take place, the following three Sakharov requirements {{cite:229de645cea441bf623e1878dd3ebf2bb0ea924d}} must be met:
(i) non-conservation of baryon number ({{formula:9354381f-3eec-4db1-bb06-77f89b896e5f}} ), (ii) {{formula:b1e86fbe-a90f-4f5d-b9e0-d591242c3917}} and {{formula:4e969e2c-2820-4937-8de8-c3538cf7f188}} violations
({{formula:bfd9ce5b-4dd8-477d-be6a-d5fe0985078b}} , {{formula:26e83960-b08c-4c93-a2a3-7793704a2b06}} ) and (iii) departure from thermal equilibrium.
Electroweak baryogenesis (EWBG) is one of the most attractive mechanisms to explain the BAU. It has been widely studied in the literature {{cite:a8fcf7d306cfba907fb4c38268bd2c14514ba08d}}, {{cite:1220bb580b5dd81aa039c4429fe442024e7fb03b}}, {{cite:65bf22472cf4f0c7fd8f8ffd9b0a1bcf56bd6942}}, {{cite:bbfd46adfd5ebc9322b5cb51d397839e93dbdd5f}} and it requires an FOPT in the electroweak Higgs sector. FOPT fulfils the third criterion of Sakharov's conditions, i.e., the system has to go out of thermal equilibrium. In addition, the phase transition has to be strongly first-order to avoid a wash-out of the created baryons inside the broken EW phase {{cite:67776ef2455105b9c5e65cdf78e8b016e84fc4c5}}.
| i | 748ade91b52e5b6dbb05a4e7bde43936 |
No other data on the W diffusion activation energy in EUROFER could be found in the literature, but there is some data for the activation energy for W diffusion in Fe available.
All of the reported experiments are done at considerably higher temperatures (>1000K) and analysed either by electron probe micro analysis (EPMA) or by measuring radioactive tracer isotope diffusion.
In these studies activation energies of 2.47eV {{cite:165bf96924a70606565510c85c54fd0595938254}}, 2.97eV {{cite:90b0e30eebab55fce0757dc1c9b2c1566124d217}}, and 2.61eV {{cite:aea2f3566ae54a62cadad72bcad4e75eee64b3ff}} are obtained.
Compared to the present results, these are significantly larger values.
There are various factors which might contribute to the different behaviour.
On the one hand, EUROFER is a more complex alloy with multiple constituents.
On the other hand, the microstructure may play a decisive role.
The EUROFER samples have small grains in the m range as is shown in figure REF .
The Fe samples investigated in the referred diffusion studies are carefully annealed and have a different structure with larger grains.
An enhanced grain boundary diffusion in EUROFER could be responsible for the observed much lower diffusion activation energy
| r | f4dac7a4030b96488e3fa95ea4866452 |
Since the transverse electric field is applied in the plane of metal atoms, its effect is added to the diagonal elements of the Hamiltonian matrix as a potential term. The mentioned term is calculated by multiplying the strength of the field to the y-coordinate of each atom while the lower (upper) edge of the nanoribbon is considered as the reference line. In addition, the bias voltage between leads changes the Fermi distribution function at left (right) lead equal to {{formula:b65f7710-c710-4e7b-a851-688a0e392240}} where {{formula:87594632-a301-4891-a637-4bd900436b4d}} is bias voltage. The difference between these two distributions i.e., {{formula:b1c01a19-4168-45ba-bd18-048ea84715d9}} should be considered in calculating the transmission probability {{cite:4becde873d5c824a7937ef2dfe0b809886fb61c8}}. It should be noted, both the bias voltage and shedding light, place the system in the non-equilibrium condition. Thus, the self-consistent method should be used for calculating the transmission probability and spin polarization {{cite:4becde873d5c824a7937ef2dfe0b809886fb61c8}}. It is important to note that we used the optimal values for energy of photons, intensity of light, and the intensity of {{formula:32328871-2f93-495e-a8af-f58ff4cee9e6}} which are 0.12 eV, {{formula:b2224c46-755c-43ab-a246-465d8d10105b}} , and 0.2 eV, respectively in our mentioned numerical calculations. In other words, we found that, by altering the mentioned parameters, the spin polarization could be changed. Therefore, first, we calculated the optimum values for them aimed at getting the maximum spin polarization, and then the optimal values were exploited in our calculations.
| m | cfebbef81cf90a4986b8a260d3e25ce5 |
This section provides a connection between LDU (section 3.2) and kernel ridge regression.
Let us consider the generic training of a kernel ridge regressor model {{cite:58d0c35cef2e91bcfa1ef12172bb9f2a2f42cec6}} {{formula:232fe487-aea6-4f3c-a67f-5e74389d6f53}} on the training set {{formula:2e19e1d7-cb64-4dff-bfff-ea636e93d6ce}} , where {{formula:f660137c-40d6-42c1-b906-e9fa44eef95c}} is the number of training samples. Let us denote by {{formula:6c6dc66f-caa2-464a-b29f-16303e42cd72}} the kernel.
The Representer Theorem {{cite:58d0c35cef2e91bcfa1ef12172bb9f2a2f42cec6}} states that the solution to this problem is of the form {{formula:77679f40-25ed-403f-b37b-e7454dcd3386}} , where {{formula:5f14521f-3715-4681-b6aa-94d4eec4fc2c}} are the parameters to optimize.
| m | 23799c270eccfe740e451968a7471072 |
Brownian dynamics simulation.
We implemented a basic bead-spring algorithm{{cite:74702a57afa5a4825e9574f6e623f14603c403a1}}, {{cite:850fe759c6dbe8d1de76f54a919f86695b9c7dd6}} to simulate the Brownian dynamics of polymer chains in an entangled solution, using standard interactions as discussed previously{{cite:5db9d9316c1dc320b9685700d60e4c170eaddcb3}}, {{cite:52b1e2fcc0ec5fb6cd7c27e1438bdd2723e7cba8}}, {{cite:08434328ab9e58f2995da14f2b9fd342846f5add}}, {{cite:c01c0df88d75c6395f28a700fa9ee9c5af25c477}}, and explained in detail below.
Our simulations comprise {{formula:3c6c4339-484a-43c7-a4a7-d2f7bd730efd}} polymer chains with {{formula:78f4c964-042f-41a4-8089-3bbcccdf86f9}} in a cubic simulation volume with edge length {{formula:dd28796d-eeb3-4a84-9c0e-be3ef15cd827}} , and periodic boundary conditions. Each polymer is represented by a linear sequence of {{formula:0da23e1d-01a9-4f7d-8b2c-4e2163128e28}} beads connected by springs.
For low densities we used {{formula:66ef18a8-79e3-4492-88f9-cb008df0ff64}} , while for densities above {{formula:4be7afa9-e817-468b-96e7-3f2255227b8c}} we used a finer discretisation with {{formula:429bfcda-6c12-49dd-890f-f9937e527dff}} ; this ensures that the polymers are thin enough such that the density of the entangled solution is sufficiently below the threshold to the nematic phase{{cite:066436f34dcb6d2e4ae8e59c7d9e7b401ef61ffa}}, {{cite:fc9288475e3977fafc26ad0bf789cbde3d2a4b4c}}, {{cite:de0bd1bc43b5cfb2fcc7322541946f2ac290dd30}}.
| m | 6d8f69bbf6fe83c49469c0c82164121e |
Tabular {{formula:b520e42c-b689-404a-a141-e0478de655fb}} (with importance sampling) is one of the widely used methods for off-policy evaluation in reinforcement learning (RL), whose goal is to estimate the value function of a given target policy via the data that is generated from a behavior policy.
Due to the high-dimensional state space, instead of tabular learning, a standard approach is to estimate the value function with a linear function {{cite:1c74908e33a0301b940f1197a16ffd427d6c7609}}.
There is very little literature to study {{formula:f5e71328-aab0-4674-8bf1-8fae25d16ba6}} with function approximation for off-policy learning.
To our best knowledge, Sutton and Barto sutton2018reinforcement (section 12.9) firstly extend off-line estimate (multi-step bootstrapping) to {{formula:90463a9b-bb16-457f-bd37-51d974e0be1a}} with linear function approximation.
| i | 09ba01a8eeb30e3338e52ee867932858 |
AutoKeras {{cite:d36413913d89d9d6988f47b197a3f7470f2f5a9d}} based on Keras package {{cite:eaa9ed4466dc64238b85c2558816055b60aa3f7f}} searches deep neural networks and hyper-parameters. For each dataset, we set number of max_trials as 20 and number of epochs as 20. It tries 20 different Keras models and trains each model for 20 epochs. We choose the best model based on the highest AUC score on validation set.
| m | 097b9eec3276d48053c6b0d54579bffa |
The last decade witnessed a spectacular progress in the astrophysical black hole observations. The Event Horizon Telescope (EHT) collaboration unraveled the first-ever image of the supermassive black hole M87* at the center of the nearby galaxy Messier 87 {{cite:d18a38ff20de1af078d5831d66b51fec6a445826}}, {{cite:cad4d25eb22db1be259f9bffcaa8d03017e6e60b}}, {{cite:677a2e6c9381bd054d59c6213ca387945a18dbed}}, {{cite:239b1d910ba9d2ef447481a40778bf5b4a69135a}}, {{cite:aa8a68c314742f12cbb80bb380f2e419d4e47a25}}, {{cite:642cc284a9db6d88cb0fa807c27713aba9f62405}}. The M87* shadow results offer a fascinating probe of the strong gravitational fields and place the theories of gravity on the testing grounds. Although the primary studies suggested that the observed shadow is consistent with the expected image of the Kerr black hole as predicted by the general relativity {{cite:d18a38ff20de1af078d5831d66b51fec6a445826}}. However, the current uncertainty in the measurement of spin angular momentum and the deviation parameters does not wholly exclude the possibilities of the non-Kerr black holes in general relativity as well as in modified theories of gravity {{cite:72b0aebb8b1f643138604ed8791023f3f7e9f3da}}, {{cite:4d9aeb7c15694029991e50093f8fd9ed166d6c75}}. Moreover, considering the parametric non-Kerr metrics, stringent constraints are placed on the second post-Newtonian metric coefficient using the M87* shadow angular size {{cite:a47939423f8df0cae6e93842bb8ae9d5bac8ad1d}}. Thus, the non-Kerr black holes which predict significant departure from the Kerr black hole could be ruled out {{cite:a47939423f8df0cae6e93842bb8ae9d5bac8ad1d}}.
| i | c85651cce18484fb881c302012066730 |
Reaching results similar to the state-of-the-art architectures in generic tasks, with reasonable hardware and GPU time investment, is crucial for applying NAS in the industry.
POPNASv3 goal is to provide fast neural architecture prototyping, optimizing the computation time without any significant accuracy drop compared to more costly NAS methods.
To do so, we extended the POPNASv2 {{cite:3e9d7294a258c17d44af20627d33a8f411eac410}} method, which was inspired by the original POPNAS {{cite:5d8749b86cc8f6fa919fd94617307271f9db7883}} and PNAS {{cite:a8bdd02d620e444c20b5771259d0bf709c1819aa}} ones.
The algorithm proposed is characterized by a sequential model-based optimization (SMBO) strategy, which is enriched by the presence of accuracy and time predictors to estimate respectively the accuracy and training time of candidate architectures.
Thus, our work addresses NAS as a time-accuracy optimization problem, selecting only the architectures which belong to the Pareto front computed on the estimates made by the predictors, since these models achieve the best tradeoff between the two metrics.
Pareto optimization can reduce the number of networks to sample in each step, while preserving a set of time-efficient diversified architectures.
Training structurally different architectures helps the predictors in finding the key aspects which contribute to the gaps in training time and accuracy, progressively improving the Pareto front accuracy at each iteration.
In this section, we provide a comprehensive explanation of how POPNASv3 implements the three main NAS traits, namely the search space, search strategy and performance estimation strategy, in order to achieve the intended goal.
| m | 86b0e695f0ad661c4755860efa4190ed |
A substantial body of work has investigated contemporary language models (LMs) by assessing whether their behavior is consistent with the rules of syntax {{cite:ae4b26e8e40b066d89dff63c36dfa0cbac15043a}}, {{cite:9a8ce73c99e76132cbb8f4de59bb7fac3ab7ddb2}}, {{cite:56a7e8a4fe94970afed80a9c952c3775b9fd0ec2}}.Data and code for this paper can be found online at https://github.com/wilcoxeg/targeted-assessment-imaze Among other structures, these studies have investigated agreement {{cite:62f3784cb36c531cd5cb22d937ba62b8e020e4d2}}, {{cite:530cad25ca912a242106bf067b4ddf2020b884af}} long distance dependencies {{cite:d4b6caf1833d406be5d4148474e59acfdd0baf64}}, pronominal and particle licensing {{cite:6aad93ce84eb4c7c9c751bd030438bf26e3bff98}}, {{cite:267418d9b8246e5c8f6f353106126df8acd4af9d}}, and expectations for phrase-level constituents {{cite:0d4aa9f8f9c46079982b35670df6953159069c20}}. Many of the studies which report aggregate behavior across a broad number of phenomena focus on accuracy scores, or the proportion of time LMs or human subjects in an online experiment prefer a grammatical variant in matching grammatical / ungrammatical sentence pairs. While these investigations provide much insight, they collapse a crucial dimension of comparison, namely the difference in magnitude between the grammatical and ungrammatical conditions. As long as the direction of their predictions are the same, an LM which finds grammatical conditions only marginally worse than their corresponding ungrammatical counterpart will receive the same score as a model that displays large differences between the two conditions.
| i | 4e59d7a2ae2391af3c6bda28c75602d3 |
For our proposed deep network, we provide a more direct and efficient strategy to generate arbitrary resolution of the enhanced image (see Figure REF ) compared to bilateral learning methods.
In addition, for HDRNet {{cite:eb14b06deb551a9a4d53a533b7f320a4c75c5c53}}, we replace the additive operator with a convolutional operator in the slicing process, and the PSNR value is increased on the FIVEK dataset. More discussions are described in the supplementary materials.
| d | e8fa153ac6a893ece3b9fdf59a974af4 |
Lemma 10 (From RDP to {{formula:a4312795-6fc1-4176-89f2-85ea5b374e43}} -DP {{cite:8fe991dba7c07441d39891b2ccec74725c751562}})
If a randomized mechanism {{formula:f8f96537-9656-40da-9a6f-dedc2268a740}} satisfies {{formula:2de39913-e0f9-46bd-b5a0-7e7e22fc4d84}} -RDP, then {{formula:9563bb20-023a-4020-be56-967bedb621d4}} satisfies {{formula:3bfb65be-1dfd-48d7-b432-1fe6d6ed8ad6}} -DP for all {{formula:6c0dae77-2ee6-43f6-87d0-99dc3ab1b18a}} .
| r | 07074b76dceb05658c61e6115f16bc6c |
Localised contrasting methods form pretext tasks by pulling the representation of a node closer to its augmented counterpart or close neighbours to distil the localised contextual information {{cite:eeae4b09db79e8450dbce4180342221377c43c3d}}, {{cite:6f7317a19e5f803ada0f2392b8a803c86a7b4bd8}}, {{cite:559179d387e1e4e33e9292e643f1390494b956ba}}. These methods can be considered as UGCL with a tiny {{formula:2b8b47e8-f6c0-4a11-8734-95824fe94984}} for the power of {{formula:5c313116-9435-400e-8bb1-f355433eaa53}} when building the contextual view. To illustrate this point, we present GRACE {{cite:eeae4b09db79e8450dbce4180342221377c43c3d}} and GMI {{cite:6f7317a19e5f803ada0f2392b8a803c86a7b4bd8}} (i.e., two typical localised methods) with the unified framework in Figure REF .
| m | 8817e207041da7b02f1fece9f82f81e0 |
Moreover, we did not allow for the production of scalar particles in
the cascade. In section REF we argued that we may
safely leave out the SM Higgs doublet in our analysis, but this may be
different in models with extended Higgs sectors (with more degrees of
freedom, and often also enhanced couplings to some fermions). Scalars,
and Majorana gauginos, will certainly be important if one wishes to
analyze a supersymmetric cascade. Results for medium induced
scalar–scalar–gauge boson splittings have been published in the
literature {{cite:44b189e7d2553be9cf759f7aae38e3d6ff1c6dc6}}; these would need to be augmented with
splitting functions involving Yukawa interactions.
| d | be27994b7fdd31ad20b8b452e2eec449 |
Some improvements over interpolated Kneser-Ney have been suggested over the years, with limited acceptance.
Modified Kneser-Ney smoothing {{cite:362013f565585925f00360c7c0da92d3a3657678}}, {{cite:d2d856a5f144f6d1089cd658421b7c5e76e60969}}, {{cite:5742bfa29f75c30e9cf20c01a75b69ee6eacb4d3}}, {{cite:f4aad55d36016f95c03d74cbbc43fb2181c10f96}} replaces the discount for each order with
three different discounts for counts 1, 2 and 3+, optimized together on held-out data for perplexity
{{cite:362013f565585925f00360c7c0da92d3a3657678}}, {{cite:d2d856a5f144f6d1089cd658421b7c5e76e60969}}. For both interpolated
and modified Kneser-Ney, the discount parameters can be estimated on held-out data, or approximated with heuristics such
as the discussed discount estimate {{formula:24fbcce5-13d1-4bfd-a005-de9b68fa532f}} .
Power-law discounting LM {{cite:6c9274f6b3c4d90bb9ec8eaffed22facf757644f}} replaces the
absolute discounting in interpolated Kneser-Ney with Pitman-Yor Process smoothing.
| m | 115b2ad5fa6a5db6009d8964caaf3fad |
A possibility we have in mind is that the current time value {{formula:17ec6f95-29da-4b40-94f1-ebec23d51bd9}} derived from the data fitted with the standard model {{cite:c2d80be17563125ed5120100412348ba319546b3}}, i.e. assuming Einstein's equation, might be biased due to the fact that this equation implicitly prefers a Euclidean topology, in the sense that its NR limit is only possible in this type of topology. Therefore, starting from a theory without such a preference, e.g. the present bi-metric theory, might lead to another value of {{formula:b6da9c1b-d4b1-4a8d-97ec-d48dcf708808}} . If this is the case, the hope is that other parameters might also be changed and some tensions of the current model solved. As an example, let us consider the recent study performed by {{cite:e1d8f0ef33caa5f807ced3aed80b9e5fbff607e3}} (see also e.g. {{cite:2c0b409c83d4d512907fc93e95ce01418ffb1d3e}}, ) who showed that the best fit of the CMB power spectrum at all scales seems to prefer a value at current time of {{formula:09a6af8e-d14c-471e-85b9-a0e1c37ab708}} (equivalently in their case {{formula:8c2c972b-1daf-4ee1-815d-d34af2b65efe}} , with {{formula:8fea397e-d92c-47ee-b386-bbb867ba8da1}} ). The main issue with this analysis is that it changes the Hubble constant {{formula:909972ef-9246-4624-a529-dd27e049cc1d}} inferred from the CMB, increasing too much the tension with the local supernovae measurement {{formula:78f77ef7-71c0-4b50-8d77-0a2efd1203ed}} : from {{formula:3d686e88-1870-42f9-88aa-45bfc2323dd2}} km/s/Mpc to {{formula:07b83ea3-0a3f-4e71-9fe9-23af09f2b16a}} km/s/Mpc. If their evaluation of the curvature is solely based on the CMB data and does not depend on the expansion model between the CMB time and current time, their value of curvature {{formula:943afbb6-0d04-455e-892e-d9e252ddc202}} might still be obtain in our cosmological model from the analysis of the CMB power spectrum alone. However, because in that model curvature does not affect anymore directly the expansion, then from the same initial conditions in terms of matter density {{formula:41a3eb33-bab8-4d32-89dd-47a900bba868}} , redshift {{formula:3ee41e0f-2566-4365-b755-5b0f7ed4780e}} and expansion rate {{formula:8929f82b-7f6c-4ed8-aec9-fc8ae7d25f05}} at CMB time, the Hubble constant at current time is unchanged, keeping the tension at around 5 km/s/Mpc. A hope with the second question is that, on top of providing a best fit of the CMB power spectrum as in the analysis of {{cite:e1d8f0ef33caa5f807ced3aed80b9e5fbff607e3}} with {{formula:bb93935b-5d8e-4644-a2fd-6e934a83ccef}} while not increasing the Hubble tension, our model would solve it. For this, other cosmological parameters, such as the sound horizon distanceHowever, changing only {{formula:16789a19-883f-4e5b-9390-6e5006237f23}} is unlikely to solve the Hubble tension as pointed out by ., calculated from the CMB must be changed compared to what is obtained with the standard model.
However, the analysis of the CMB is subtle as pointed out by who performed a similar study as {{cite:e1d8f0ef33caa5f807ced3aed80b9e5fbff607e3}} of the CMB power spectrum without finding an evidence for a positive spatial curvature. This shows that a complete thorough reevaluation of the cosmological parameters, within the context of our model, using Planck's data (as in {{cite:e1d8f0ef33caa5f807ced3aed80b9e5fbff607e3}}) and/or catalogues of galaxies (as in {{cite:4b7a11586f20632d899cbf1f5bb5114a1f082ccc}}) is required to assess whether or not the blind expansion law (REF ) and the weak field equations in Table REF , which were derived for this purpose, can provide a better fit of the data than the standard model. Such a better fit would only be possible if {{formula:dc40ef16-4bbd-4bb4-b561-85171fb07455}} is found non-negligible within our model, otherwise, it is equivalent to the standard model.
| d | f1fab70d5f4283bc0858292d2e8e871f |
Figure REF shows the qualitative results of FSCN on the KITTI Eigen validation set, while comparing with two leading algorithms BTS{{cite:862409ef291c1a2316f8c9b6833b5168ff2d6177}} and DenseDepth{{cite:7b2953f515ec2fafa32d5c2211dafed0d1f3b8f9}}. From this figure, we can observe that FSCN method shows more details in the contents like cars structure, traffic signs, sketch of human and so on, comparing with the other two counterpart methods, which may convey the evidence that our method with full skip connection mechanism is able to preserve and propagate more feature information along the deep network.
| r | 1ac9d10f63277b2e9e2cd6fc1c31cf3b |
Our results indicate that all machine learning methods substantially outperformed the traditional AFT and Cox proportional hazards models in estimating TEH. This is not surprising given that the traditional models often encode strong parametric and linearity assumptions, which are prone to bias when model assumptions fail to hold. Among the class of machine learning methods, the nonparametric version of the AFT-BART model {{cite:4fd5dade8c8daa7b523319fed5d6241957c12a85}} generally outperformed the other methods, both from the traditional prediction perspective (bias and RMSE) and the decision perspective (expected regret). The advantage of AFT-BART-NP becomes more pronounced with a larger sample size and increased data complexity. On the other hand, AFT-BART-NP also conveniently enables posterior inference by providing credible intervals for ISTE and the associated subgroup-specific treatment effects. In particular, we demonstrated that when there is strong or moderate overlap, AFT-BART-NP could provide close to nominal frequentist coverage for almost all average causal effect among subpopulations defined by propensity score strata. Under weak overlap, AFT-BART-NP still provides satisfactory frequentist coverage for the subpopulation near the centroid of the propensity score distribution. While the overall population may exhibit weak overlap, the central region of the propensity score distribution may still present satisfying local overlap and in fact admits valid inference for the causal effects. However, AFT-BART-NP could understate the uncertainty of ISTE estimates in regions with lack of overlap. This observation was also discussed in an invited Commentary to Hahn et al.{{cite:6d382bdbb7de943c5c8872dbc503c0822152a37a}} by Papadogeorgou and Li,{{cite:2dfd2be1d39fc7e1370a60163732a876413fc40d}} who illustrated that BART for continuous outcomes produced overly narrow confidence band in the region of poor overlap. As a potential improvement, we found that including a non-parametrically estimated propensity score in the AFT-BART-NP model formulation leads to more accurate estimation and inference for ISTE, evidenced by less variable subgroup-specific performance measures, as well as higher frequentist coverage under weak overlap.
Because previous simulations for TEH rarely considered the effect of overlap, our results offer new insights. Importantly, our findings can provide new perspectives into the estimation of ISTE relative to average treatment effects. At the minimum, we noticed that even though it is challenging to estimate ISTE for units at the tails of the propensity score distribution, it remains practically feasible to make accurate inference for ISTE within the centroid of the propensity score distribution. In fact, the centroid region of the propensity score distribution includes individuals at clinical equipoise (and for whom the treatment decisions are mostly unclear) and resemble those recruited in a randomized controlled trial. In the propensity score literature, this subpopulation is sometimes referred to as the overlap population, for which there exists an efficient weighting estimator for the average causal effect. {{cite:853cecfe4bad909c9369822c5980292a8c7fd299}}, {{cite:9e00478a35efb4b82352df1c562e475dc8a5ce1e}}, {{cite:434531bd91cc70f8ce475f7a2388c8d8bf277b6b}}, {{cite:709756be239178636c85320c7bbd7ca1e2f9135b}}
| d | 59b32f0ce8d7cfdb4e8a3dea2fa86554 |
The learning rate {{formula:7007ff1a-ff01-405a-ab62-5152fb450d78}} should decrease with iteration number {{formula:3b2fb787-a83c-413e-8d3d-4c473568c449}} , such
that the conditions {{cite:b1cb489854ac386509f1e4e89ddd4573c7a12af6}}, {{cite:db5e71668c75b21bc9a4189bf113484876be6846}}
{{formula:229bc47b-d6dc-4f0c-a9be-d9e6cac112db}}
| m | 34494f9f250945a437bcd95d579b6f0b |
Base: Each client uses local data to train its local models without federated learning.
FedAvg {{cite:45ef48e112ff92f0f41ffec393adf81707d2df53}}: The server aggregates all client models without any particular operations for non-iid data.
FedProx {{cite:1cbf345cf4452bbd1d3c1f0c4ebe7ba628d35d38}}: Allow partial information aggregation and add a proximal term to FedAvg.
FedPer {{cite:981de02573af284c7f835a226b963fbec569681c}}: Each client preserves some local layers.
FedBN {{cite:9f4cc4f4da50eb15b847101d3bc551d8ca058abd}}: Each client preserves the local batch normalization.
| m | d345fd1159b59a6a3f166a66517b51cc |
where {{formula:a95c89e0-c12f-47f4-9a0e-ed0e412bcdff}} and {{formula:d35e8ad2-6a45-4fdc-94b2-bf498ccb470a}} are the momenta in the
{{formula:beb8ee57-3e7e-40bc-982b-e6eb0d1d512b}} and {{formula:efec70b5-8fbc-4890-bef4-15bed2d9824b}} center of mass systems respectively, evaluated at
the energy in the {{formula:672029f4-1803-4adc-a1fb-e4fc442c1629}} center of mass system.
{{formula:cc61c4ca-abfe-47d5-99ad-e353454d28cc}}
is the fine structure constant. {{formula:60a66b81-3248-4eb4-8588-2a7e43f632d0}} is related to the
photon coupling to {{formula:94b4cc6d-843f-4fdc-9885-5a3f2bc611b1}} meson {{cite:86bfe680b2048387d4351451ff891c754f8ceca5}}, which is extracted from
the measured {{formula:2b2ae31b-6903-4e43-a767-7dabd0260972}} decay width {{cite:9266035cc6c0b8c0eb5f26280c448a3a98789776}} using the expression
{{formula:dc81bab6-c1ac-416a-abb3-e210527955b3}} = {{formula:e0e28b7b-4aed-440e-8f95-39b7442b798b}} {{cite:86bfe680b2048387d4351451ff891c754f8ceca5}}.
The
energy dependent values of {{formula:beaf2a8f-5019-45b7-b1ff-e9799de3ab4a}} have been evaluated using
the experimentally determined values of
{{formula:314fcacc-e0e7-46d0-abf5-59f45cf9edc9}} {{cite:1187a88993dce3f47671127e5ef574336fd0103a}}, {{cite:61d494df77a7d9af17d3c594d7789e05c6057094}} and
{{formula:a82ffc70-e2f8-4399-afd8-d3b3155bec34}} {{cite:5426f8653a58d0934f416e0f2d089d2c6238a3a8}} in the above equation.
| d | d58e7109256f6cb1ac6d9cb0b84c9ed0 |
We compare our model with the following non-autoregressive methods.
NAT with fertility {{cite:b945c96f48dc6646d619a7498a7572e8d07b9efe}} is the first to propose non-autoregressive neural machine translation, which predicts input token
fertilities as a latent variable.
Latent Transformer (LT) {{cite:2fef44f6fda96a6a259999ac8f814f9d9ad67d2e}} incorporates an autoregressive module into NAT to predict a sequence of discrete latent variables.
Iterative Refinement {{cite:ea422bcc6f96349502f16aba1a0cd8390b30d0b5}} trains extra decoders to iteratively refine the translation output with multiple iterations.
CTC {{cite:a00648a75ad1b8a4589c5bace430b763f34eede4}} uses connectionist temporal classification.
Auxiliary Regularization {{cite:2830c743c83e8282865560c88db7880d551e00b1}} adds two auxiliary regularization terms on the decoder representations.
FlowSeq {{cite:f8f9b4435d4a0236e97eaadb6778986ef6b5a726}} introduces a method based on generative flow.
Bag-of-ngrams Loss {{cite:aaa9dc9556f147b55b4e778542d6729a508d75d5}} minimizes the bag-of-ngrams difference between the model output and the reference sentence.
FCL-NAT {{cite:b51ab4344eda953ac369099bd450f1477829e3e0}} introduces curriculum learning into fine-tuning of NAT.
We also compare with strong autoregressive methods that are based on LSTM {{cite:361ca964a116bc4fa29854dfa86706506d1b0865}}, CNN {{cite:6565996a6f909b8e2b8a7183108efb69227aa1c3}} and self-attention {{cite:35fbab1ec6fdbd0eaee66c0d0051f2257645923a}}.
The inference latency is the average per-sentence decoding latency over the newstest2014 test set, and is conducted on a single Tesla V100 GPU.
The speedup relative to the autoregressive Transformer is also reported.
Results are shown in Table REF .
| r | ce7fad9ee4c6dc36f73680da43034f5d |
Generation of Oracle-Invariant examples: While the strongest Oracle-Invariant examples are generated using the gradient-free attacks Square {{cite:c981532167c322a73778264969e18b7a56b1e396}} and Ray-S {{cite:03235df7056ae1b4d425f42d0621b636aea5e900}}, they require a large number of queries (5000 to 10000), which is computationally expensive for use in adversarial training. Furthermore, reducing the number of queries weakens the attack significantly. The most efficient attack that is widely used for adversarial training is the PGD 10-step attack. However, it cannot be used for the generation of Oracle-Invariant samples as gradient-based attacks generated from adversarially trained models produce Oracle-Sensitive samples.
We propose to use the Learned Perceptual Image Patch Similarity (LPIPS) measure for the generation of Oracle-Invariant attacks, as it is known to match well with perceptual similarity based on a study involving human annotators {{cite:c2275520608392c195bbbfcceeade921cb355a86}}, {{cite:a59c1fd34cff126459ad0dcbc9f9de9ea2f85bd3}}. Further, we observe that while the standard AlexNet model used in prior work {{cite:a59c1fd34cff126459ad0dcbc9f9de9ea2f85bd3}} fails to distinguish between Oracle-Invariant and Oracle-Sensitive samples, an adversarially trained model is able to distinguish between the two effectively as shown in Fig.REF . We therefore propose to minimize the LPIPS distance between natural and perturbed images, in addition to the maximization of Cross-Entropy loss for attack generation: {{formula:5bf45fd6-1011-47fb-ae1c-66ae2a35abcb}} . The ideal setting of {{formula:3327cfd9-7923-47ea-9c1b-3530b765f509}} is the minimum value that transforms attacks from Oracle-Sensitive to Oracle-Invariant (OI) for majority of the images. This results in the generation of strong Oracle-Invariant (OI) attacks. We present several Oracle-Invariant examples for visual inspection in Fig.REF .
[tb]
Oracle-Aligned Adversarial Training
| m | 23a009cd5483af66d1c105b2fa8faf30 |
Filtering Test Datasets.
Following prior practices {{cite:9aacec59d159f933bd5894f915d70a0ecc56986e}}, {{cite:f649e016608c6ebc598221b149f0d68d4dbe8826}} and our criterion mentioned above, we filter and refrain to report potentially contaminated datasets' evaluation results.
For LAMBADA and CLUE, we find minimal overlap under the 13-gram setting.
Pile, MMLU, and BIG-bench are either held-out or released later than the crawling of corpora.
| r | d881b8420277d018f4e5279abb9b41bc |
The mass modelling of Q2138-431 turned out to be straightforward. This
was not unexpected, as the lensing galaxy lies close to the line of
centres of the quasar images, and roughly in the position one would expect
given their brightness ratio. This contrasts strongly with for example the
asymmetric Q0957+561 {{cite:958661cd5b1767afe2e0202b11b9ecdd381d8ec6}}, and more closely resembles HE1104-1805
{{cite:88a8f57082b32a0d0f4c29809fde323495fb0436}}, another wide separation binary. This simplicity of modelling
is important if Q2138-431 is to be used for measuring the Hubble constant,
where the accuracy with which light travel time to the two images can be
modelled is the most important factor limiting the accuracy of the result.
| d | 160385feafaf533b945bd81acf7489e2 |
To evaluate quantitative results, we use precision, recall, F1 score and accuracy. As a test set, we use a COVIDx introduced by Wang et al. {{cite:40d716e7b598452a6af3dd7bfc9440d71dedbb7c}}. It consists of 300 images equally distributed into three classes. A globally trained model’s inference results in a single classification per image, while inference of a locally trained one requires majority voting before making the final decision. When we train Oh's patch-based learning model, we follow the same pre-processing and augmentations as the author and the only differences are the model used for lungs segmentation and our masks filtration algorithm. We compare the performance of four models that are trained on the COVIDx dataset. The results presented in Table REF are comparable in terms of accuracy, which oscillates around 90%. However, COVID-Net's accuracy, as well as its precision of COVID-19 classification, stands out. Our method achieves the highest F1 score of 0.974 for the COVID-19 class. Oh's model performs similarly to the results reported in their work, where it scored an accuracy of 0.889 on their dataset.
{{table:0171f73c-4f73-4ee7-ac41-8f6663600cbe}} | r | f3f60620d5e135b8084ff4f218dfd5f8 |
As shown in Table 1 in the experiments section, without RL, training under MLE already produces high-quality candidate captions with the upper bound reaching a CIDEr-D score of {{formula:4be5c5e1-0ddf-47aa-bfd4-8cd421f64448}} points. We suggest that one possible future work is training a stronger image-text selector, taking the progress of cross-modal representations beyond the task of image captioning, such as visual question answering, visual reasoning, and image-text retrieval {{cite:e7ec2595efaa5539d5dd32a4cba5260653e5af21}}. In this way, we may quickly train a generator without RL and fine-tune an image-text selector based on pre-trained cross-modal embedding networks. This paradigm may also bridge the gap between text generation and image/text understanding tasks.
| d | c2eb846143e730666e6f146cb1c922c4 |
There has been a long-standing interest in electrical breakdown in
liquid helium (LHe), motivated by practical applications as well as
fundamental interest. LHe may be used as electric insulator and
thermal conductor at cryogenic temperatures, which may simplify the
design of superconducting magnets{{cite:e8539b05b7cf69c6a17de41eb68c41bee48f1c91}}. Studying the behavior of
LHe under a strong electric field may be of interest in
understanding electronic properties of condensed helium{{cite:2d5779331293341a3c1cfa042d36bcbb5b4ebc10}}.
More recently, the study of electrical breakdown of LHe is motivated
by the importance of superfluid LHe as a medium in which experiments
in nuclear, particle, and astroparticle physics are performed, along
with other noble liquids, in particular LAr and LXe.{{cite:ea6917b0c411cc7cf4006d93a65192217119725d}} For some experiments, the
application of a high electric field is necessary. These include
experiments to search for the electric dipole
moment of the neutron{{cite:f1b061f9b46dfe314db350285267a75220bb4718}}, {{cite:1902c1c212a39dd5ed868fb4d2d03a31b2d002e3}}, {{cite:d18c910c52ba9e44ceac783f2af28c4e20cf54e9}}, {{cite:e67d9b607decc498330faeb72f6e65a72cc62df6}}, {{cite:fbb2e3fbe7d5f5000e06be089f2faca198a335c0}} and experiments to look for
light dark matter particles.{{cite:3e7e366c55e9aa37068d59e61987aa8a077c630d}}, {{cite:bacc6721b8fb9912b9e8cef8868b04145179e899}}, {{cite:d7cc64c869c57a4b5789bb08d7c4349598e41a6c}}, {{cite:9abb891d0fe1341ee891fbfcbeef48804f2fe0e7}} For these
experiments, breakdown of LHe in response to DC electric fields (as
opposed to AC or pulsed electric fields) is particularly relevant. For
a new method to generate a large electric potential ({{formula:6077d8c8-35cc-4841-b5eb-70a358124541}} 1 MV) inside LHe, see
Ref. CLA18.
| i | cce77ae11e7322b3f16473c9dabb69fb |
The augmented Lagrangian (in its “scaled form” – see {{cite:bdc182574fa17d286af40eb1607c220e11c56cee}}) associated with this problem is given by
{{formula:6ea81b07-167f-4c1b-8661-5148eac90c39}}
| m | ef33febc1793cf4ec015925b80249ca4 |
The heterogeneous network model described in this
paper facilitates characterization of the dynamics of complex,
biochemical systems by abstracting the dynamics of their composite
motifs such as the yeast cell cycle based upon {{cite:974ee8232c089d76f348196e4388dd94fd4bf624}}. We note that the proposed heterogeneous network model is deterministic once the initial values of all the switches and oscillator frequencies have been specified. However, many intracellular reactions (e.g., {{cite:18bac515bc1ade6d8b638a0687c7387412c198f6}}) and neuronal systems (reviewed in {{cite:e2a9ae67a6e75a1467dec7ea252ed203063ef93d}}, {{cite:9437cf2c3b4c3b875067b8606ac407f45e7c6310}}) evolve stochastically. In these cases, the Hopfield networks used to model the switches could be replaced with probabilistic Boolean networks {{cite:f96c00a23b68e2324cc1a89d80aa8b96bb046ea9}} and the oscillators evolved with stochastic solvers such as the stochastic simulation algorithm (reviewed in {{cite:98bcca19aa0d7caa96758d41b5f5d93b91f2d919}}), integrated with the methodology developed in {{cite:45684bd14134ff3ebcd418c01149ab0f301a6783}}. Similar modifications could also extend the heterogeneous model to incorporate coupling with components of additional dynamics pertinent to biochemical systems, such as those of the network motifs enumerated in {{cite:b67d8fd9fc07ea2949e6ee2c855ef0a479197482}}, {{cite:5128392e109f6317d1fdfa1a2190d7421d7b9087}}, {{cite:42804861cc98e5ea43c86d5b3763e8d175c58daa}}. These studies would also ideally consider the dynamics of the heterogeneous network model in additional small-world and random network topologies, as well as the topologies defined by neuronal systems and gene regulatory networks.
| d | 52ddbf86e55a77d4ab48d35456ce97d3 |
Problem (REF ) is arguably the most basic optimization problem, which nevertheless arises in many applications in machine learning and statistics {{cite:9d46c730e85936d3229cf4822a6ca74983ea9d00}}, {{cite:3d9c2af25bfdbb569b10057af01a0562e4b05dfe}}, {{cite:c37f298c19ed3dd1f8bb4517cc60462ed8cab493}}, {{cite:5d3e7dbcec7a7b2a45833a6899e04586fd9eb61f}}. There is a plethora of methods for solving (REF ), and each (type of) method has its own benefits under favorable settings. This paper particularly focuses on solving (REF ) via second-order methods, where a (approximated) Hessian matrix is involved in the scheme. Consider vanilla Newton's iteration of the form
{{formula:8b0ac231-9f13-4140-bf4c-5c90a62a45fe}}
| i | f6e5d6504cb5919a982d895be785a0e4 |
Multimodal encoding
Given the input features {{formula:0944a6d1-1357-4459-813b-a9aa0595cddc}} , {{formula:08893b3a-69ee-4051-8771-b90dfa4f429a}} , as shown in fig:model, we use two encoders to compute their representation respectively. For each multimodal encoder, a learned [cls] token {{cite:35f780dda6d7ad8fb462e213c54b628729a94225}} is concatenated to the beginning of the input feature, which is used to produce the final output representation of the transformer. We denote the output of the Query Encoder as {{formula:215fb905-d199-4e29-b56e-4aa44d8e4c88}} for the question {{formula:fd0f31dc-ad67-4d8a-9ec0-4602e152afe9}} , and the output of the Video Encoder as {{formula:7cc4ca4e-1844-4462-949b-90f08c6b6032}} for the video segment {{formula:b8ce1f44-da5f-4e78-b2d5-0daa6fd51e34}} .
| m | 9e2ed1e046b0d1f01257bc3364dc3beb |
Regarding the center-of-mass energy of the hadron collisions, we use by default {{formula:ea21f2df-ce31-44fc-9e46-743e4a498035}} , although we also explored the TeV region accessible by LHC, setting {{formula:c12bdeb7-291d-4ab3-9e02-de917e286c2a}} . We are interested in studying the improvements associated to new and up-to-date PDF sets (for instance, the one developed by NNPDF collaboration {{cite:d91c5b731c662f6ec6025651effbface840a6e97}}) w.r.t. the predictions obtained with older distributions {{cite:41a7cf024449ab7eea7f81d3512487ee21859864}}. Likewise, we have suppressed, directly from the MC code, the interpolator of the distribution functions and we have carried out the interpolation through the LHAPDF framework{{cite:75000207e1c17c1e48a5991081b0ebaed83bd73f}}. Besides, we implemented the updated set of FFs, DSS2014 {{cite:0b5ddede8fc89ea62580c2ce1618502c541e5777}}.
| r | 83195ecdac3f98ce0e204ddd70a8cf05 |
NOMA is considered as one of the key technologies for fifth-generation (5G) and beyond 5G cellular networks {{cite:b0194ef65cad0e200538c2dbff6bd2cdf1191036}}. In NOMA, the users are multiplexed across the power domain and the SIC is employed at the receiver side to decode the data. The capacity improvement with the multiplexing of users in NOMA is significantly dependent on the channel conditions of the users {{cite:03c855f7cf403f595b6d22b6d5f9f07e2f45fe28}}. Hence, to achieve higher data rates, the BS must optimally choose the number of users to be clustered and allocate the available power to all the users in each cluster. Most of the existing works like {{cite:03c855f7cf403f595b6d22b6d5f9f07e2f45fe28}}, {{cite:94253a789927081a3cc04fb30fcde479d83f7a53}} discuss the user clustering algorithms considering 2 to 3 fixed number of users in each cluster. Limited analysis has been performed towards user clustering and power allocation for a generalized number of users in each cluster {{cite:e8536a55766b73a11e40d889f708a3e28137f0c9}}.
| i | e49dd992e9170fbad291e42efea07065 |
The ECG original samples, {{formula:43f298f5-eb31-4527-be73-e25da6eea076}} are perturbed through the FGSM attack by calculating the gradients of the Discriminator model, {{formula:039686f7-485c-484f-a035-a056690c6f6b}} . So it calculates the gradients of the loss, {{formula:6f6749ef-c6be-4eb0-a752-b00cb9e202bc}} based on the input signal, {{formula:e27b4056-589f-4bab-8f04-65e37d2f8cd9}} to create new adversarial signals, {{formula:e16dc222-4057-4bdd-8c5e-59d102d7cd50}} that maximize the loss{{cite:f5bdacbd74d38cffc4643d95e7bb25baf79f9c5b}}.
{{formula:c570ad88-e94c-4c2f-9edb-5413f338a871}}
| m | 94ea7b2e23fb5aa92b870c260617ddf9 |
At the pressures required to stabilize many of the superconducting polyhydrides, the chemical intuition developed from living at atmospheric pressure breaks down. Seemingly bizarre stoichiometries such as NaCl{{formula:63b29bca-532c-4728-9dff-fe87f32bc9f2}} {{cite:a4ba6c61f67310cee5f9f7fea7fa4f7312710f34}} and FeH{{formula:8f7ea652-866e-4a74-a7be-2cc321ca51a4}} {{cite:d7b592d424ed6876473cddff393e57a7c93e6efb}} have been synthesized in diamond anvil cell experiments. Meanwhile, geometrical motifs that are not observed at 1 atm such as the pentagraphene units in ScH{{formula:6590daf8-7b01-490f-b792-af1deeda3a86}} {{cite:3894da8119695be3b8d2fe04ed28f66df9698b70}} and HfH{{formula:8f4171ca-6586-4f54-8ff3-beeb4f8cf0e1}} {{cite:ce79a9b38d74eae7081d3ed7f99b24ff7187665a}}, as well as the hydrogenic clathrate cages in CaH{{formula:4a988f76-de88-4502-94fb-8b9772aa01cf}} {{cite:fad8fd9890fd704dcc73d6aab77cff0e639955ff}} and LaH{{formula:5df89fe4-118e-4694-9a4d-8d9330c8b1d2}} {{cite:74c42982948ea07f294813327d062827412af675}}, {{cite:ce68415d05a677f4b67521e8267cd183b7be6ee0}} have been predicted. Pressure also influences the electronic structure and physical properties of matter. For example, in a behavior reversal, whereas hydrogen is expected to become metallic and superconducting, {{cite:d398524c9e5ab79335d5e70eccbeba5e836404d4}}, {{cite:c6ab4802ebe8d9d792f2cda761ad3e95b09d4564}}, {{cite:b061cadde74e02fd795a27b8de72bf35ad670e78}} sodium undergoes a metal-to-insulator transition under pressure. {{cite:cfcb2d23c261f504c71ee56a202dc18b6c424738}}
| m | 631e1798c046c70aaa50bd4c4c68455d |
Since the CosmoGrid simulation is a dark matter-only simulation, we do
not account for the effect of baryons. Because the formation of the
large-scale environment is dominated by dark matter, the lack of
baryons has little influence on the formation of the haloes. Star
clusters however likely contain little or no dark matter
{{cite:bbd5f50aee754b5e80485e73981dbc51a66fac8f}}, {{cite:fec0cf872e8bd94d1b250b83f050ce4416c7aa72}}.
| d | 25ce9fc34e66622bd2ddbcb8e9a45303 |
The frame potential function {{cite:8874fa212fc4099ca3c162e98b59df66b3b128b3}} takes a frame as input and returns its “frame potential value”. This value reveals important information about the properties of the input frame.
The concept was first studied in {{cite:d6b041ddb0331833ae8aa6547f8c40c6d2b30377}} where the question of minimizing the frame potential was initially answered - the potential is minimized when the input frame has specific geometry. Further results in this direction can be found in {{cite:07680e5942bcb1d90e9df1693a81f6f5e6cce55b}}, where alternative definitions and generalizations of the notion are also pursued. For a study of the frame potential in finite-dimensional Banach spaces see {{cite:9b1480b697d4310800d8614fbcca09bea054478e}}.
| i | 38dad0c5a51b3f96496ea35e1dd7a0d6 |
where {{formula:690c0662-47dc-41b2-b90f-e6fc8af30d94}} is the number of base learners used to build the ensemble. A necessary condition for Eq. (REF ) to be valid is that all base learners need to produce quality estimates of the same perceptual scale, which is nontrivial to satisfy when formulating BIQA as a ranking problem {{cite:129e988cea0bf425610cfa1dce1aa9724f249bf2}}. We will give a detailed treatment of this scale alignment in Sec. REF .
| m | 147d75fcee8c6f4b387790d44ef6efeb |
The gradient reversal layer requires additional tuning {{cite:a6588f4230b46c5de5a41a8f11d019c589c86178}}.
Specifically, like {{cite:a6588f4230b46c5de5a41a8f11d019c589c86178}}, we gradually introduce gradient reversal in our training using a warm-up schedule.
For the first 10 epochs of training, the {{formula:ac8ba6af-7064-4863-a50f-44b79b3bcdc8}} hyperparameter is set to {{formula:6fb465a9-4de0-4a88-aea5-08e5192d1cb1}} ,
while from epoch 10 to 60 we linearly increase {{formula:5abe79a5-ec63-4f90-ba36-afa6ca15c681}} to 1.
| m | bcc4321498632b2654a818fde409618f |
1.) The weighting function in distance correlation is selected in such a way that the dependence measure can be expressed in terms of covariances of data-dependent distances. However this convenience comes with the price, since weighting function may remove some important information from {{formula:236416ad-490b-4b0b-b8c7-c42f079ff258}} . In addition the distance correlation, {{cite:71bd005d26e2d998ecab2a73e8a60aea079c0471}} ({{formula:eabe7011-b800-44fc-b849-3fcb26b2725a}} ) in high dimensions is affected by the curse of dimensionality ( {{cite:7c6c82d8e1c53fc9f66d6dad21d11a787cfeaf51}}). These drawbacks serve as our main motivation to focus on regular (non-weighted) {{formula:1797b764-e6c6-4d2b-9bbb-6b225022b794}} spaces.
| m | a477004e59cd7c67390a3a92ce982bb9 |
Probability distribution: The total simulation volume containing the field value {{formula:d77ba26c-caf5-4ad1-bdc8-27c582befd86}} at a given time {{formula:b0d0e799-ecb4-40e8-975a-1f407b48a008}} is displayed in Fig. REF . This probability distribution is initially peaked at {{formula:b19b5c69-30ed-4c1a-91fa-8710923d2f59}} , with a dispersion relation given by {{formula:b35a4968-2108-4a80-9e78-98683d885e97}} . As time passes by, the distribution evolves towards the effective minima of the potential at large field values, eventually splitting in two. Contrary to other symmetry breaking scenarios {{cite:0fa9d6cc83df9e88f5a02217d7d2573b97296296}}, {{cite:1de0765c74316baef9f04e7932d71dc8d5bcf63f}}, {{cite:196d319767bf6164f794cad3991e3fd9dad57d4f}}, {{cite:9d9e026ac6f24f9ad7112226d9ccfedb9d7a1782}}, the time-dependent character of the minima prevents the stabilization around them, giving rise to an oscillatory bi-modal pattern that survives for quite a number of oscillations.
{{figure:ee0bf3e4-268d-4e71-8a7f-96e334261322}}
Time-dependent dispersion: The root mean-square perturbation {{formula:1bcbe817-d284-4e1c-a84c-e2bb55813499}} is displayed in Fig. REF as a function of the dimensionless conformal time {{formula:6b302219-fdd2-4166-9828-f84cb109f642}} and the number of {{formula:0809a089-28cd-4a04-a495-a1c7f4c743ce}} -folds of kination, {{formula:dc8f3658-f486-44f2-aead-7ed581e8c79a}} . Note that, as argued in Refs. {{cite:0fa9d6cc83df9e88f5a02217d7d2573b97296296}}, {{cite:1de0765c74316baef9f04e7932d71dc8d5bcf63f}}, {{cite:8cc472ca88483053b39582d85c710f79fcd22fca}}, the picture of a homogeneously oscillating scalar field is incorrect when applied to spontaneous symmetry breaking. Indeed, when the initial value of the homogeneous component is close to zero, the classical rolling of the field is dominated by its quantum fluctuations, in agreement with the analytical result (REF ).
{{figure:ab5acbc1-bee8-4369-8daf-4493701cff44}}
Spectral distributions:
The evolution of the occupation numbers (REF ) is shown in Fig. REF . We observe a rapid growth of infrared fluctuations at the early stages of symmetry breaking followed by a slower motion towards the UV due to the potential interactions. Note that the displayed behaviour is far from thermal. Indeed, thermal equilibrium can be only achieved once the occupation numbers in the infrared have significantly decreased to {{formula:f8c9e503-ee43-489d-8368-b3070bdc8778}} ; a limit that notably exceeds our simulation time. On top of that, it is well known that classical lattice simulations cannot completely describe the approach to equilibrium due to the Rayleigh-Jeans divergenceIn the continuum temperature goes to zero; on the lattice it is cut-off dependent. {{cite:c2c58fac0d7b013404bc368586b125768651f22d}}.
A simple characterization of the UV cascade can be obtained by computing the average wavenumber {{cite:7590e76ef3398a594d8f44d8f2a58ac8bfd2eda0}}
{{formula:9a21328d-a865-4f80-a124-b74568fcbdf7}}
where we have intentionally excluded the infrared modes filled at the onset of the simulation, namely those below {{formula:ac206430-6484-4e06-9b57-5cc5828b52b1}} .
As shown in Fig. REF , the momentum scale {{formula:67e5ea18-2093-4876-8fd9-43f15ca438e7}} is always smaller than the UV lattice cutoff, confirming that all relevant scales are well resolved throughout the entire simulation time.
{{figure:607b4fe0-e937-4328-834d-bd1057301bd6}}{{figure:d354d1f5-c608-407c-a0e4-7a7aea8a7cc6}}
Energy budget: The evolution of the kinetic, gradient, potential and interaction contributions to the total spectator energy density is displayed in Fig. REF . After a rapid growth at early times and a violent oscillatory regime completely dominated by the interaction term, the system approaches an asymptotic state characterized by a large kinetic energy density. The smooth UV cascade in Fig. REF translates then into a steady flow of energy from the interaction and potential terms to a slowly growing gradient component. As time passes by, the system relaxes towards a virialized state with {{formula:0e8a8a9b-a44c-4a4a-83a7-2b0acce88f1f}} , in agreement with the expectation for a quartic potential {{cite:519e532eaa5dca4fc5dc86ca567053699992f896}}, {{cite:7590e76ef3398a594d8f44d8f2a58ac8bfd2eda0}}.
{{figure:7f5a1902-f210-4b68-9c30-f5ac2a44ea2a}}
Equation-of-state parameter:
The behaviour of the different energy density contributions is reflected also on the evolution of the associated equation-of-state parameter
{{formula:7f3d183f-bb0e-4614-b45c-ed3bbebd3ab2}}
which we display in Fig. REF .
Since this quantity is rapidly oscillating as compared to the characteristic expansion rate, we perform here an additional coarse-graining in time, along the lines of Eq. (REF ). As shown in the left panel of the figure, and in agreement with the analytical estimate in Appendix , the averaged equation of state is initially negative, becoming positive only during the tachyonic-to-oscillatory transition. The small discrepancy between the lattice and the analytical estimate can be traced back to the fact that the latter assumes exact homogeneity and complete irrelevance of the non-linear potential terms while, albeit small initially, gradients are always present in the simulation and the potential terms can contribute. As shown in the right panel, {{formula:0762a4c7-7060-4638-9632-368cd9dfdba8}} approaches a value rather close to that of a radiation fluid ({{formula:ae1d351c-6e61-4a26-9b6a-00d184c38d61}} ) at late times. This behaviour is intrinsically related to the virialization process displayed in Fig. REF and completely independent of whether the system is already thermalized or not.
{{figure:de7dea76-bbf6-4958-ad05-4d7d0c61a0ee}}
Non-Gaussianities: To characterize the level of non-gaussianity in our scenario, we consider the so-called excess kurtosis, customarily defined as
{{formula:c4957252-9721-4842-997c-6c438dc08246}}
{{figure:6299ed9f-4d2f-4f4a-ad39-fc24664ad852}}
| r | 5faa03bf6b85cf4d56dc9dc53b3e0fc8 |
The existing approaches to segmenting unknown objects can be divided into two depending on whether they use supervision for unknown objects or not. In either case, the model has access to known classes during training, i.e. inlier or in-distribution, and the goal is to identify the pixels belonging to an unknown class, i.e. anomalous, outlier, or out-of-distribution (OoD). Earlier approaches resort to an ensemble of models {{cite:9b3f91567a576ba4dae416b75cc762b6d60a6367}} or Monte Carlo dropout {{cite:82ee32a1c63ac14519e92c6498339f424e0ca3df}} which require multiple forward passes, therefore costly in practice. More recent approaches use the maximum class probability {{cite:755f6845b0237ff490a9bc08498d1c329a5b2318}} predicted by the model as a measure of its confidence. However, this approach requires the probability predictions to be calibrated, which is not guaranteed {{cite:6836200a02ea26a4b91854100f32008432ae40cf}}, {{cite:99fdffda6850cb9ea4361a7a9cdf35f8ba5ce2e7}}, {{cite:6e0542e389c147554e008d6043102dea5b9c5e14}}, {{cite:bbc7caa2463e3087107cd7dc74955cf4020aa27c}}, {{cite:62b99f27889794f00b0ce2592cb6350d51294176}}. In the supervised case, the model can utilize outlier data to learn a discriminative representation, however, outlier data is limited. Typically, another dataset from a different domain is used for this purpose {{cite:3c7ffb494ade223b1109667115501bbe78a861a0}}, or outlier objects are artificially added to driving images {{cite:4fb289523a81494ed853b2af4b1d40305ade06d7}}, {{cite:56cc0a30af2d5ab3f961238817965ebbd2c6a81c}}. Despite the better performance {{cite:56cc0a30af2d5ab3f961238817965ebbd2c6a81c}}, outlier supervision can bias the model to a particular distribution of outliers.
{{figure:f8f13645-413c-4479-8999-b6c1ac5f1817}} | i | 7227f5e251d6f2db3db6fdf2b687c2f6 |
There are other possibilities for implementing full
unitarity and analyticity in the one-loop results. In particular a well-known alternative that we also consider here is the
N/D method {{cite:d965746a7ea772d84de3de6917c1c361362a0beb}}. There are many ways for applying it depending on the problem at hand. Here we will follow an approach
which is particularly suited to perturbation theory. To start with we will consider first the elastic {{formula:2bca8eff-d809-4992-b8fb-eb6fdea2fd7a}} scattering.
The main assumption of the N/D method is that the corresponding partial waves can be written as
{{formula:1ac7c51e-0dd6-4301-a29c-93612ef67f94}}
| m | 3cd8db28cc8f9f93a06a60d9451fae4b |
In this paper, we show that despite the general consensus that textual adversarial attacks should preserve semantics, striving for ever-higher success rates seems to be more important when implementing them. We combine a human evaluation with a simple probabilistic analysis to show that between 96% and 99% of the adversarial examples on BERT {{cite:54a988e13368ec563a8f1a7e8558630215ecbb86}} created by four different attacks do not preserve semantics. Additionally, we propose a two-step procedure consisting of data augmentation and post-processing for defending against adversarial examplesWe will release the code with the official publication of this paper.. While this sounds contradictive at first, the results show that we can eliminate a large portion of the successful attacks by simply including data similar to the adversarial examples and further detect many of the remaining adversarial examples in a post-processing step. Compared to traditional adversarial training strategies, our method is much more efficient and can be used as a baseline defense for researchers looking into new and better attacks.
| i | 75a9fdbd72efed4848dda4e4421aa888 |
The H30{{formula:f320ff67-ad0f-4958-b1ff-cf68148fab41}} results can be compared to some of the published {{formula:1b0fa3d8-f972-4486-aec3-be24cff191f8}} based on other radio data analyses. To start with, two papers have published analyses based on radio recombination lines. {{cite:c7bcb7036d21d7c422e3e2062580c8201ef47d07}} published multiple values of {{formula:570c5969-549f-4a19-8dea-5d4103e15bf2}} based on different models applied to H92{{formula:e4bd09d0-0538-4eb7-89fa-5b10d4f0442a}} (8.31 GHz) data; these {{formula:786f6ed9-6976-493c-b9f0-984f7acc36ae}} values range from 0.9{{formula:42c1c598-35b7-4165-a4ea-368279b937bb}}{{formula:344d901d-8e14-4819-aee0-e13c2b51cb61}} to 2{{formula:cd467f93-9119-4be0-b958-be156171f280}}{{formula:3f3ed6d2-3343-4f01-aba1-df2ccb770af7}} s{{formula:0871f7e1-37a3-4d68-9630-8984539109d3}} when rescaled for a distance of 3.15 Mpc. {{cite:a3e54d9f99233fdf28b220cbfd6b5ca461b31b1c}} using H53{{formula:c8735c5c-9327-4d33-a535-b89d43ccb980}} (42.95 GHz) data obtained a {{formula:6e4a70b9-9aa4-41f4-bf14-8caeea523120}} of 1.2{{formula:c8ed0751-ed5c-4bc1-962c-96910c97c6b8}}{{formula:d6fb87ba-23c9-4f4d-bb9a-086634adbc28}} s{{formula:fee10e91-1623-48da-83f6-64b8d6257871}} . Most of these measurements are lower than the value of (1.9{{formula:829e203f-f23f-488c-938d-26c33695d6f0}} 0.3){{formula:356a9d7e-a482-4978-af97-9d8ea539ba6f}}{{formula:cc5d2102-9528-4139-868c-cd5d629af1fc}} s{{formula:706c169d-1a7a-46b4-9f26-756f871e2f9a}} from the H30{{formula:35a12af1-ee3e-4df3-93ca-12548658f840}} data, although Model IV from {{cite:c7bcb7036d21d7c422e3e2062580c8201ef47d07}} produced a slightly higher {{formula:40fc61b8-fc0e-423c-b887-ea4f9fd612c4}} , and most other results differ by less than 2{{formula:cdc2bb69-08f2-4bc8-a19a-77f95e81c653}} . Both the {{cite:c7bcb7036d21d7c422e3e2062580c8201ef47d07}} and {{cite:a3e54d9f99233fdf28b220cbfd6b5ca461b31b1c}} {{formula:82ce6133-1d57-48aa-ad9d-75e8aba18348}} values are based on models that have attempted to account for masing and gas opacity effects, but it is possible that they were not always able to correct for these effects accurately. Nonetheless, some fine-tuning of the models of the lower frequency recombination line emission may yield more accurate {{formula:f642f709-0dca-4759-a66e-2c6fbcf610fe}} and SFR values from the higher order recombination lines.
| r | 70ca0b7608558229b696481828651d91 |
Current methods for detecting interference include conditional randomization tests {{cite:16b031303c668d2fd47f0e3e3d95d9802b43856a}}, {{cite:4a023663629c4b48fad07107a9815f6016444a5f}} (as outlined in Section ) and carefully designed experiments performed with the intention to detect interference {{cite:6d24e2f4a0f0674a495e0931fd2201196494fa50}}, {{cite:2207bffc4a8223f42219291b711b204a9387df7a}}.
We now provide a summary of these methods for testing for interference.
For randomization tests, we focus on the choice of test statistic used.
For experimental design methods, we describe both experimental setup and the test statistic.
| m | 8423b6d0e51fe075ffc8f94d7405d09a |
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