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This paper is organised in the following way: In Section , we define extended affine Jacobi group {{formula:e384e115-a411-4e07-8b39-d00558f8bf6a}} and we prove some results related with its ring of invariant functions. In Section , we construct a Dubrovin–Frobenius structure on the orbit spaces of {{formula:ca576f6b-c1f7-40a2-91b9-dade1ed07196}} and compute its free-energy. Furthermore, we show that the orbit space of the group {{formula:8c9ae08f-1f73-4bc5-956b-3f1d1535289a}} is isomorphic, as a Dubrovin–Frobenius manifold, to the Hurwitz–Frobenius manifold {{formula:460df691-b25d-4d4d-9048-150c9ea7a3b0}} {{cite:f290143c80c1284b1667ef091ccc483e5b0874d0}}, {{cite:1eeb2ee730b68ae22999159b99f79bce100ec395}}. See Theorem REF for details.
| r | a8512d1585929718da2e08791abc7b9a |
Now that we have defined our model, we assess its validity through extensive experiments on a diverse set of 46 publicly available time series classification datasets.
These 46 datasets are used in {{cite:ef87bab1d3b70de72e063dca0190e9303c085ea6}} who, fortunately, also report classification accuracy and earliness of compared approaches.
They are made available on the UCR repository {{cite:80d2cea1a35015d34be5ddc3178e2fffa48141f4}}, {{cite:3f6b73994bb34fdede274bfa514b9b45652c721a}} and cover a wide range of data modalities, ranging from motion capture through audio to Electrocardiography (ECG) sensor data.
The competitors considered here are the best method from {{cite:ef87bab1d3b70de72e063dca0190e9303c085ea6}} (denoted SR2-CF2), the pioneering work of {{cite:7a067d08d84a1142150e72b17dc334d295d4a754}} (ECTS), as well as EDSC {{cite:54aee6da8968738a3d734630da3f1195896ce6ee}}, and RelClass {{cite:8ad8b32bbca4e47d4cc24b88dac74e2e186c6bfc}} methods.
{{figure:d2ec5745-5c4c-4f5f-b0e0-4abc6c87efd4}}{{figure:6d525639-44fa-4649-b8d5-574df643955e}} | r | 5b71f0658b9a10bdd95c50748a062430 |
In nonequilibrium steady state, the quantity {{formula:f33c72ec-5c6e-44b8-a86b-f04dad2a0778}} might play an important role. Under the existence of the non-potential force, the entropy production rate is generally decomposed into two non-negative parts, the Wasserstein part {{formula:3b348700-612d-4e56-9cf6-af8fdd513d0f}} and the excess part {{formula:85664ee9-127f-467f-895a-3126f2ed222d}} . This fact is very similar to the case of the steady state thermodynamics {{cite:3e18bbab6c98910648740a2b9f2f9f428e6dc46d}}, where the entropy production is decomposed into the excess entropy production and the house keeping heat.
| d | a93ffb39e0384370373b0ebbf13a1fd6 |
It is difficult to compare our results with related works, since there are, to our best knowledge, no studies regarding automatic spinal metastases segmentation in MR imaging. Thus, comparison is indirect and refers to CNN-based segmentation approaches for instance of liver and brain lesions, as well as a recently published work by Chmelik et al. {{cite:03867aeb4b738f4c4714f1a58509a2460b9934f2}} for spinal CT data.
Depending on the used data sets, CNN-based brain tumor segmentations in MR images achieved Dice scores up to {{formula:f46a23a5-c4b0-433f-926a-c439193784af}} {{cite:19f0da4a82d21567fc01f0293af9419f61458e55}} (brain tumor segmentation challenge 2013) or {{formula:b2c45e6b-b056-40b8-9e08-0450a3693ae7}} {{cite:f77c4c0181d145f6d436093584deeb24c1be7e38}} (brain tumor segmentation challenge 2015). Segmentation of liver lesions in MR images achieved Dice coefficients of {{formula:5d0d2b91-6545-4a3b-a4e9-f361a8f0d1ab}} {{cite:22fe0d50ebd5e9aecd1b1c86dbd2e3468922c1b2}}, in CT images up to {{formula:dbea688c-db9c-43ea-b025-c0ff4373536f}} {{cite:38c0a7bd9a57df9f31815c7718a3dd19d3835e81}}. Overall, our results are comparable with the segmentation accuracies of liver lesions, although our data base was comparatively small (40 patient cases vs. 200 cases in {{cite:38c0a7bd9a57df9f31815c7718a3dd19d3835e81}}), which is also reflected in the fairly high standard deviation of our results.
Chmelik et al. {{cite:03867aeb4b738f4c4714f1a58509a2460b9934f2}} were one of the first to adapt a CNN to vertebral metastases segmentation in CT images. They achieved a voxel-wise sensitivity rate of {{formula:6c8253c8-fef7-4eb9-a308-3919731db6bd}} for sclerotic and {{formula:4bd7df0f-18b1-4753-a91d-99fcdc7747e6}} for lytic lesions as well as a specificity rate of {{formula:1643b390-1711-43b4-982d-07cd23ce4195}} (sclerotic) and {{formula:9bbc454a-817b-404f-832d-eec06251ec31}} (lytic).
In comparison, our results including {{formula:991cd74f-ab45-4075-9ae4-dd134a1c4a55}} -weighted images are somewhat better (mean sensitivity of {{formula:1b0186f5-5565-4d59-bdef-b36eb99e4382}} ), though the experiments only with {{formula:9482bc3e-7b20-41f3-9b66-24979be662c4}} -weighted MR data clearly lack accuracy. Additionally, it is important to account for the differences in spatial resolution (slice thickness of {{formula:8ea37987-655e-46e5-8d40-dbfd4f43f18f}} vs. our average {{formula:8802be12-81cd-45fc-90e5-4e1c6a82961c}} ) and the effects of high spatial anisotropy and therefore, partial volume effects, which could hamper automatic segmentation approaches.
| d | 23b55d10b8d18aa75a0ba006711ddcd2 |
The proposed edge ensembles framework facilitates the operation of deep learning on edge devices by accounting for their unique properties and requirements. In particular, Algorithms REF -REF are tailored to account for the limited hardware and computation capabilities of such devices, combined with their mobile dynamic nature and ability to collaborate in a decentralized manner. In fact, edge ensembles treat ai-empowered mobile devices as a crowd of diverse intelligent individuals: each agent is capable of inferring on its own, and can thus operate solely without any connectivity. However, a group of users can infer more reliably in a collaborative manner as a form of (artificial) wisdom of crowds {{cite:bed5ec070aa26ca532ff6883895b602311aa8679}}. Specifically, this collaboration boils down to an equivalent deep ensemble, which is an established concept in the deep learning literature {{cite:497b5dde9125c16bd01f06dff8313c3b6ad07d4c}} known to improve accuracy and robustness.
| d | cc4697a0b8318a7dd8f741c8d6647622 |
A QD-microdisk resonator system is not limited to acting as a source of quantum light states, but can also be used for their control or processing. As an example, this system can act as a Bell-state analyzer, a key element of a quantum optical network {{cite:6082be0f4285b4110dd185d9c899161fbeac4c03}}, either in a standard cavity-QED configuration {{cite:6c493646e1d762fd8087f17cb8287942626929de}} or as a passive, nonlinear scatterer {{cite:8f440b75b1c485fb6988568122f78a7baa61705b}}. For cavity-QED, the Purcell factor can be re-expressed in terms of the QD-cavity coupling strength {{formula:5f3dd71c-230f-4691-a5aa-15f805f0fad4}} ,. The resulting {{formula:26dfe084-6a75-4476-a1f8-b0b90ef9a4cc}} GHz, which can be used to write the cooperativity of the system {{cite:cc645abb51d5c889ab895e7218b40aae287f4d63}} {{formula:08a364d2-612f-4c43-95a1-ab6da5314c3e}} . Given the success rate of a cavity-QED based analyzer of {{formula:3854abdb-9a70-4d32-85b6-b2c781a946bf}} , we expect our modest {{formula:20080773-6498-4aae-bc49-3f20ec865621}} device to succeed {{formula:175d2207-e8ef-47e3-9f2b-289dbd96d2ec}} of the time.
| d | c97e34798162466d3c4de52059d33217 |
Finally, to show the benefits brought by multi-antenna UAV data harvesting in terms of energy saving, we consider the trade-off between the average transmit power limit of SNs and the energy consumption of the UAV. In general, the energy consumption of the UAV consists of two parts for our considered problem. The first part is the propulsion energy, while the second part is the communication-related energy, which is much smaller than the former for practical UAVs and thus is ignored for simplicity. Specifically, based on {{cite:f408a7f2327ebfba631a6b85e24a2ea8eed12d00}}, the propulsion power of the UAV can be modelled as
{{formula:87823d1b-bbb2-401b-a239-7f1c5b5d9f10}}
| r | 6011f5357397f14e0b3175b07edf3ee2 |
The above effects depend on the typical electron density and temperature of the plasma surrounding a BH, so in the following it might be useful to estimate the typical scales involved in astrophysical environments. We shall consider BHs in a wide range of masses from stellar-origin to supermassive (in practice assuming simply that {{formula:f04cdaf9-5656-4088-a5e7-91127883afc3}} ) and an arbitrary dimensionless spin parameter {{formula:3b1949db-bd82-47fa-abc0-b131acf5dbff}} (such that {{formula:b0f1b518-888a-4df7-aef1-86af8e1e8dec}} ). The typical temperature of a thin accretion disk at a distance {{formula:1b5e2e1c-ca99-4289-8c45-7a923d5bf53f}} from the BH is approximately {{cite:249306a74837fc4828dba5063b28bedf0a899957}}
{{formula:01a8e810-1d05-442c-baba-9a8f16a81e8c}}
| i | 09085284d82bec085218c3a49f27608a |
Can we determine the location of a scene given a single ground-level RGB image? For famous and characteristic scenes, such as the Eiffel Tower, it is trivial because the landmark is so distinctive of Paris. Moreover, there is a lot of images captured in such prominent locations under different viewing angles, at different times of the day, and even in different weather or lighting conditions. However, some scenes, especially places outside cities and tourist attractions, may not have characteristic landmarks and it is not so obvious to locate where they were snapped. This is the case for the vast majority of the places in the world. Moreover, such places are less popular and are less photographed. As a result, there are very few images from such locations and the existing ones do not capture a diversity of viewing angles, time of the day, or weather conditions, making it much harder to geo-locate. Because of the complexity of this problem, most existing geo-localization approaches have been constrained to small parts of the world {{cite:14296c81a3b5650d9741b88c6775b116b122976e}}, {{cite:336bdb857c923ff7e66c9beef4616a89eb41337c}}, {{cite:bd79ff869538a8c3fc09fda8f55f5730e8081fd1}}, {{cite:19dcca97eaca2916c861d7dcecc28fffd60f2e1e}}. Recently, convolutional neural networks (CNNs) trained with large datasets have significantly improved the performance of geo-localization methods and enabled extending the task to the scale of the entire world {{cite:bb8e19bc0497042a8a08e29837c2fbfc0668a22a}}, {{cite:9f0adad2df481400329007f3e4d042269b89ac38}}, {{cite:6f1ad16e39d052e571a2a0ebc762c4d85e6f3391}}, {{cite:09d2ec74ed19336ff307d5580732012c89e55df5}}. However, planet-scale unconstrained geo-localization is still a very challenging problem and existing state-of-the-art methods struggle to geo-locate images taken anywhere in the world.
| i | f29ab2369c62e958381986eda83c284d |
The study of moderately exponential algorithms for NP-Complete problems is extensive.
In fact, exponential yet better-than-naive algorithms for NP-Complete problems were known for some problems, for example The Travelling Salesman Problem, long before the definition of NP.
A survey of Woeginger {{cite:0f23c52b7856815e4e33c0d1d6399c00e9109a6f}} covers and refers to dozens of papers exploring such algorithms for many problems including satisfiability, graph coloring, knapsack, TSP, maximum independent sets and more.
Subsequent review article of Fomin and Kaski {{cite:e3f83a0a19d51671eb6bd1894e22a5af8e938ea3}} and book of Fomin and Kratsch {{cite:60e4b3ba374419629b2a799968b8c52d6b9c57f5}} further cover the topic of exact exponential-time algorithms.
| i | cd24e86afb0c5a711899c640ce598b2b |
We introduce an interaction potential {{formula:8e2e1a15-3bad-4c24-b6aa-c25f32d1a18b}} and consider equilibrium states to be Gibbs measures built with the DLR framework, see e.g. {{cite:7553dd26da52d8b293f409f61391f48e2b216ab7}}: they are the probability measures {{formula:e9b1a9e4-a2af-4ba9-bfde-2ad2e015dc12}} consistent with the Gibbsian specification {{formula:cea9e60f-2eff-491f-9de7-f89d17cc8c9d}} in the sense that a version of their conditional probabilities w.r.t. the outside of any finite set {{formula:679cf800-7e79-4eb7-8f92-f3ae57a4ad4b}} of the tree is given by the corresponding element of the Gibbs specification {{formula:fecef4a8-d7a2-4d11-b17c-c046a3272e7f}} , that is
{{formula:e783457c-1db7-4c75-88ff-7ffe5fee8547}}
| r | 099d69eb41cd01d9f42bdcb878a4bf56 |
In Section , we propose LEATHER, our novel theory for computational learning of dialogue generation. We use the GuessWhat?! visual dialogue game {{cite:11b4f1da2d463ea49927348879c2d5ddb0684f20}} as an example to ground abstract terminology in practice. We conclude Section by applying our theory to analyze a cooperative learning algorithm for GuessWhat?!. Our theory unveils harmful shifts in data-distribution that occur during training.
In Section , we use LEATHER to study the general problem of data-shift in text-generation. We provide new theoretical study that characterizes statistical energy as an effective empirical tool for quantifying the impact of data-shift. Aptly, to conclude Section , we use energy to motivate an improved learning algorithm for our running example – the GuessWhat?! game.
In Section , empirically, we demonstrate the benefits of our LEATHER-inspired algorithm compared to common baselines. Importantly, we also show our proposed statistic (energy) is predictive of the quality of generated dialogue; i.e., we exhibit a linear relationship. This suggests LEATHER is useful, not only as a theoretical tool for algorithm design, but also as an empirical tool for model-selection.
| i | db8ab1299f9112d3c5b98c158e53b705 |
Robust Estimation.
For RANSAC-based robust pose estimation, we solve our minimal problem by first running gP4Pc and then using Umeyama's method {{cite:7d33344305424280d4a35a11b981b9623b5e4bf5}} for 3D point-to-point alignment in order to estimate the similarity transformation. We refer to that method as gP4Pc+s to differentiate it from another variant gP4Pc+a which we have experimented with. gP4Pc+a uses a linear method to compute an affine transformation from the four 3D point pairs instead of a similarity. During RANSAC, gP4Pc+a retains the best affine hypothesis , the one with the most inliers and uses Umeyama's method at the end to compute the similarity transformation from all the inliers. However, we found that gP4Pc+s consistently outperforms gP4Pc+a.
| r | 991b11de4748371a06b660377fad8e00 |
On the other hand, several GNN models were developed in {{cite:9fa17e0e07518df82bb654376c0483084d0b30e3}}, {{cite:6576f98534c54723059f934ce737ffbb3985224e}} to learn vector representations of nodes in signed (unipartite) graphs with both positive and negative edges based on the structural balance theory {{cite:3e224475c06e8066caa44f751695c24cc84f2d93}}. However, it is worth noting that the balance theory does not hold in recommender systems due to the fact that users' preferences cannot be dichotomous, i.e., a behavior of users disliking similar items does not always imply the same degree of user preferences about items. Therefore, adopting such GNN methods designed for signed graphs would not be desirable to capture different levels of user preferences.
{{figure:22733347-1d23-4daf-a374-f3edff447347}} | d | 8730cf146d63aaff0f9adfa2f3f17106 |
Stochastic geometry is a mathematical tool that characterizes the spatial distributions of base stations' and users' locations in wireless networks {{cite:c6816afb4577df31dca03c37170c4103e1a1573b}}, {{cite:2ba219656c4f6cf728cdb307bdedf41d19a64285}}, {{cite:504a7ed0c7f0df93ce76eee5ec6c36a05a702dd7}}. Significant progress has been made in recent years on characterizing wireless networks' coverage and rate performances using stochastic geometry. By modeling the placements of base stations and users according to Poisson point processes (PPPs), analytically tractable expressions for coverage and rates, which produce useful insights on network design guidance, have been found for ad-hoc {{cite:2ba219656c4f6cf728cdb307bdedf41d19a64285}}, {{cite:07067fb7b0fbb1250a4aad412c34124e5a18cfdd}}, {{cite:504a7ed0c7f0df93ce76eee5ec6c36a05a702dd7}}, {{cite:9c5bec2a73830c702ac312200db32c9123f58e26}}, {{cite:aa2a5aff5fd2b1a160c212e29f8d0907c7585b47}}, cellular {{cite:3a31024022bde597f0d5b68ad754247e461a1e18}}, {{cite:b48780749ac279f26e301267285a8aa67f24eff3}}, {{cite:2c329ab8d060d4a5bbccc8d83c1bd57d08e54c3a}}, {{cite:f99b00027d84ab103b581e5cdf0c0f22e7915abb}}, multi-antenna {{cite:a600829e59234af7b7f5223b6395febcde668e4e}}, {{cite:6a9d165442222b92639ecfdc4ea59e4e8d1fd3dc}}, {{cite:3fc22d28f5233d4ebb1ad9d9b9230ba861b713e2}}, mmWave {{cite:b66d9f3340a2c2dbca6f48e64e6476690a57f46d}}, {{cite:f8a7f8abbca95e5ab1568466204dd818cd116afb}}, {{cite:0d199219b6185f56103469ad8b255b0c4e099df5}}, {{cite:4dc88a65c509a5bd250f6da12e437b36eca63341}}, and UAVs {{cite:944d75b540ae6dd646e8630444f2ec271bd7893a}}, {{cite:58efae5da065cdaa53e366a6c2096e4fb9028b2c}} networks. Continuing in the same spirit, in this work, we develop a tractable model for satellite downlink networks and characterize the coverage probability to illuminate the design principle of satellite downlink networks in terms of relevant network parameters.
| i | bb979fa4314effe4e97eeee15ab46241 |
Existing literature covers how to learn a reward function in cases of
unclear tasks or how to make efficient use of it in cases where it exists
and can be evaluated frequently.
In contrast to that, in many other tasks the reward function is clearly
defined but costly to evaluate.
Providing these kinds of rewards to an agent during training thus can become
prohibitively expensive even with off-policy learning with experience replay
as one may fail to gather enough examples to learn from.
In the following we describe our proposed ACRL framework to alleviate this
issue.
We use a standard MDP formulation as found in {{cite:ea40981de991a57a72ff3adbfaac750224a77fa7}}.
| m | d66b4cc3b8bf2338790236ab7b31012c |
Enumeration of Conjunctive Query. Conjunctive queries are built upon natural join ({{formula:59fa4023-e0f3-4e3e-821b-690fca36eb5a}} ), which is a special case of similarity join with {{formula:a7470859-4271-47c2-9dd5-de4f6c03b4db}} , i.e., two tuples can be joined if and only if they have the same value on the join attributes.
Enumeration of conjunctive queries has been extensively studied in the static settings {{cite:c65b6ff546bdf326e361508704f6b368767a87f5}}, {{cite:c91dcb7951e920f9a4a8e9f2da9f10813e4c1639}}, {{cite:7a04b4884a4e8a6e1dd073a59d91d7e8728a5b8b}} for a long time.
In 2017, two simultaneous papers {{cite:bebb5640707240fdb3f13104309a081d9dc96782}}, {{cite:6235871706bcad7e8c354e37730aae2bc6461b2b}} started to study dynamic enumeration of conjunctive query. Both obtained a dichotomy that a linear-size data structure that can be updated in {{formula:75db7be0-b068-4824-a042-991aa9033381}} time while supporting {{formula:28ef4477-e282-482f-977d-c107aed0d339}} -delay enumeration, exists for a conjunctive query if and only if it is q-hierarchical (e.g., the degenerated natural join over two tables is q-hierarchical).
However, for non-q-hierarchical queries with input size {{formula:5cf91223-26fd-422b-a4b4-ee2501dd3cd6}} , they showed a lower bound {{formula:cf769b76-5342-48fa-b8e9-66392ea55765}} on the update time for any small constant {{formula:3ba81613-f576-48ed-9619-26bb27d1c164}} , if aiming at {{formula:22149dd2-ada4-4369-802b-6690dcee9dda}} delay. This result is very negative since q-hierarchical queries are a very restricted class; for example, the matrix multiplication query {{formula:c7a22a8f-0e14-416c-a954-51a1b50f1b73}} , where {{formula:fac86304-1ffe-4095-b7ca-b70cec0be0ea}} denotes the projection on attributes {{formula:34da47ea-54cb-4b98-af17-c2685000f084}} , and the triangle join {{formula:56b20262-b8fb-40a7-9049-b6e053711816}} are already non-q-hierarchical.
Later, Kara et al. {{cite:efd3e95afbec3978789af3fb4a064adcd528b53a}} designed optimal data structures supporting {{formula:e0ce8190-68b1-44de-95d5-9d5f6f7fb99d}} -time maintenance for some selected non-q-hierarchical queries like the triangle query etc.
However, it is still unclear if a data structure of {{formula:47bb4f81-2105-41a9-9029-1e91086cb6f2}} -time maintenance can be obtained for a large class of queries. Some additional trade-off results have been obtained in {{cite:a2d2260dc3110bd710d5c9ebd6332e583a8b9f75}}, {{cite:861b594c7b56c3e212a058e375c8117d64aa32cc}}.
| r | c8e57c68ea7cf57da4b593c5e816ce55 |
where {{formula:382ea421-41d9-4a48-b68e-f6c51fb1890d}} and {{formula:44c9d1b6-8c79-46a2-a716-8157141502b8}} denote the deviance of the proposed model and the null model respectively. The value of {{formula:7298898d-6c82-4b2d-9099-9f1beb008c77}} shows the ratio of the deviance explained by the proposed model that the null model fails to explain. This measure does not attempt to account for over-fitting, and tends to be higher for larger models. Therefore, we also consider a cross-validated version of {{formula:453e593d-e5fb-40b5-b19d-9a93e2fddc1a}} , denoted by {{formula:b626a973-2246-4672-b3f5-5995345f8874}} , which can directly be used to assess the prediction power of the fitted models. A statistical comparison between different models based on their deviances requires taking into account the effective degrees of freedom (d.o.f.) of each model as well. Among various measures introduced for the effective d.o.f., we use the approach that to our knowledge is the most prevalent. This approach defines the effective d.o.f to be the trace of the hat matrix {{formula:9e301f31-f6cb-4a27-9d5d-6bf3cf3796c9}} , which is satisfying {{formula:964ddd5e-fdb1-4a9c-9304-72a4f1b67321}} where {{formula:c9096686-a0bb-4158-844a-f347d0b9e8ca}} denotes the estimate of the response vector {{cite:5241add8658720c3b023c1b7326bde99eee4821e}}. In order to make the comparison easier, we divide the effective d.o.f. for each method by that for Standard IRLS, and call it effective d.o.f. ratio. Additionally, we compare the different methods based on the computational resources they require. To do so, we compute the relative run time and the relative peak memory of each method with respect to standard IRLS on the same system. All models have been fit 10 times, each using a different pair of trials from the training set, and mean values are computed.
| m | 4b4d6c5c3792298ef54aa68955187240 |
A popular modeling framework to study methods of influencing selfish behavior in engineered systems is the nonatomic congestion game, which is often used to model urban transportation networks {{cite:4ca0edf98c4b06f8662019a297cd1715315d0add}}.
This model was one of the first to admit straightforward characterizations of the price of anarchy, a popular measure of the social cost of selfish behavior {{cite:6d1fb050ae6e39b8b4b15e6c3aabd98a4c9323f6}}.
It is also a natural setting to study various modified models of human decision-making; examples include altruism {{cite:38f835e23ce505b067d55e8bc41c8e2158d546b6}}, pessimism {{cite:0adce11f5403380dcd4ba4028719f891fb0e101f}}, risk-aversion {{cite:667468e84e2116efd0693ef95d71d323baed559d}}, and various generalizations {{cite:9eb2cbaae9ee54ebcfe22317bdb85dcf0e18b35d}}.
More relevant to this paper, it has proved fertile ground for the study of various methods of influencing user behavior: taxation {{cite:f53112016e8e6605c95552773412d22986b53988}}, {{cite:a594a934e4ed3e9ad0e7710ec7780641bfc97abe}}, {{cite:d22ed37e737743afb34ba391fc7c39832be451e9}}, {{cite:e59773517313d330b8d969753fca4a1e15d3bf7e}}, autonomously-controlled traffic {{cite:51a8259abd05400fae1055a5e2429d8ec8787311}}, {{cite:499fdbf569cfc914027b88d8f3ef0cad22f78d93}}, and traffic information systems {{cite:5bd72706680eda8f2d36f7f9582a9f74215e37c4}}, {{cite:c3258e4006767de73629a00dd7da82a0612ceb23}}, {{cite:c454d1fa17019b1ef0572cb2c7b7d36658519034}} have all been investigated in this context.
The majority of this literature depends on the usual game-theoretic assumption that users are expected utility maximizers.
| i | fb48dcd8a9913fccd8e739fd65cbd054 |
Most recommendation models extract users' and items' latent representations implicitly or explicitly and then calculate the relevance between them via inner-product or other neural network methods, e.g., MLP. Traditional models, such as Collaborative Filtering {{cite:ad37997a466f3333549ad8ac85f04e6b04b6ba25}} and Matrix Factorization {{cite:3822d52f1e7fd08a11bd29aa75355380436cdec9}}, {{cite:4de307ea82662ee216614924e427a256b78edf47}}, exploit the interactions between users and items in-depth to learn representations. However, modeling the observed interactions is insufficient to make suitable recommendations as the informative attributes of users and items are ignored. In the past decade, deep learning has achieved great success in the areas of computer vision {{cite:8ffe5b26903ca55029d71e0006897d3a3833704f}}, natural language processing {{cite:9f4f9479ee88ec3af29bc1777211d4ab93a77c64}}, and natural science {{cite:5d5c899b8d2d0140fafdefc6d7cd3d48451abd38}} with its powerful representation learning ability. Therefore, it becomes increasingly ubiquitous in modern recommendation systems to exploit arbitrary continuous and categorical attribute features with deep neural networks {{cite:4f76751fa9ed35c799e6d74b07a169e8adf46fe2}}. These models usually compare favorably to the aforementioned traditional models because they could leverage items and users' attribute features. Besides, these models could remedy the problem of inadequate labeled interaction data.
| i | fa54a08fd04e7fe32f02045c730658df |
Mathematical cancer models have provided a deeper understanding of this immensely complex disease by unveiling the underlying mechanisms and offering quantitative insights {{cite:2882421b736f234d3951a6e18833f631792a0db6}}, {{cite:c608943dee13d9434e3cbaa6e9073e471b4a1ed2}}, {{cite:7ce8e4974fb4a273b30ab47591c156b050caa640}}, {{cite:2248854679eeda36b73a86c213cb6ccef7f0b7d1}}. Such models have entered all areas of GBM research, ranging from the classification and detection of brain tumours to therapy {{cite:a82727b28e441656e9204f61fd3fdce393d2c4ad}}, {{cite:08a9ea837eba7df477c77cf74928ce42cadda66c}}.
| i | 1aa277f2ba810b0eba40a4f7c83f4b19 |
An interaction of topological SMs with a continuous-wave laser provides the studies of
topological materials with another avenue from the perspective of the quantum control of
underlying topological properties by means of built-in laser parameters — intensity, frequency
{{formula:e4e1d211-4591-4769-94f6-73912ecba5d1}} , and polarization — and the exploration of topological phases
that are in non-equilibrium.
{{cite:b8e5bc3eac6fced3a079eb37b172ca23cf54934f}}, {{cite:e104985d1158f181e8cc0c767cab632395d016f0}}, {{cite:7408f1def65d984f2e60d79daf23eb988c183950}}, {{cite:799e86dca3cd9b12371e6cb2c0d21ea14cd2a106}}, {{cite:898f57ea258b1e0bcb2a1b5259dd7ab0f479e537}}, {{cite:bc31982333849512ea1c65579275d180d0a9c2e7}}, {{cite:f9600d20feb333474bcd05f849d74abc7fb55350}}, {{cite:62d69a623aa9a14295d303679c024c7786339198}}, {{cite:dcab64274bf94b1e3f1c71fd3a11b15528c21b3c}}, {{cite:4880ffafb0a6da92c5ecd6d092d2278f4bd63c16}}, {{cite:59bd5056b8061a4fc2ad2bceb4ad531806b2e8f4}}, {{cite:74f64aff32f2ab2a7bbc616d26a355492c49feee}}
Here, the total Hamiltonian {{formula:c88d8a4d-55e1-49b2-9ce2-a516dde1b777}} of concern at time {{formula:46c0d445-6f6c-479e-b582-15b8198f4832}} has temporal periodicity
{{formula:7f69801e-a8a7-4d95-848c-c11de1302c9c}} to ensure the Floquet theorem, with {{formula:f75f8ebd-ff35-4f8d-adfb-55ba803ea175}} .
{{cite:8224e40ca4de0e3e4e030bb664a437778e5162b2}}
By the drive with a circularly polarized laser — in place of the application of a static intrinsic Zeeman field —,
the T-symmetry in the DSMs and NLSMs is broken to form the WSMs, and these are termed as Floquet WSMs (FWSMs).
This scenario for creating FWSMs is applied to the DSMs of alkali pnictides such as NaBi{{formula:1ee0d779-5bae-4279-ba23-afbd41b5bd2f}} and II{{formula:cbd538a5-20ea-4293-b804-f9fb89935f96}} -V{{formula:59600948-0d06-4975-831a-3307da579751}} -type narrow gap semiconductors such as Bi{{formula:a50fb757-5dfc-4246-b30f-277e94db14e4}} As{{formula:01339f0d-ec6d-493e-ad8b-61c82caf9630}} , {{cite:7408f1def65d984f2e60d79daf23eb988c183950}} and
3D stacked graphene systems.{{cite:799e86dca3cd9b12371e6cb2c0d21ea14cd2a106}}
Here, the former DSMs are realized
by the band-inversion mechanism due to
the presence of a {{formula:8c336b52-43fe-4baa-b0bf-07504a4ef578}} -fold uniaxial rotational
symmetry along a symmetry line,
hosting edge modes known as double Fermi arcs at the surfaces.
{{cite:7acf9c76fde0926f8c5a2dd3b3b875a65007a275}}, {{cite:524b94d9bc3d85802c3c9a5e96db37b301d22109}}, {{cite:fd45fd49d1d86ea6ce08a5bbcd678d4d3494f99d}}, {{cite:f691ef772eea9248134f16923ce74f1dca5d878a}}, {{cite:ac6f5cf038e90edd77964fbfb8955de0bf795f2d}}
Further, NLSMs are driven to result in FWSMs, revealing a photovoltaic anomalous Hall effect
associated with the Weyl point nodes.{{cite:e104985d1158f181e8cc0c767cab632395d016f0}}
Very recently, frequency-independent magnetization mechanisms in response to
circularly polarized light are studied in WSMs.
{{cite:bc31982333849512ea1c65579275d180d0a9c2e7}}, {{cite:62d69a623aa9a14295d303679c024c7786339198}}
| i | 7eb9f0e915a4be9aa8108a47053762fd |
We have performed the semantic segmentation experiments on the Stanford large-scale 3D Indoor Spaces Dataset (S3DIS) {{cite:f467b4fa76fe6c606b8d2732339da238d2f5336a}}, which contains 3D point clouds of 271 rooms from 6 different areas. Each point in a point cloud is annotated with one of the following 13 semantic labels representing different categories: {chair, table, sofa, bookcase, board, window, door, column, beam, floor, wall, ceiling and clutter}. To prepare the training and testing data, we split each room into blocks of {{formula:61a70d3c-c54b-418e-b193-8103cafae83c}} , where {{formula:6678e79e-4266-4a57-9c8a-19be732dd85b}} is the height of the room, and 4096 points are sampled from each block. Each point in a block has the following features: the 3D coordinates ({{formula:68754a8c-c57e-4c96-80ab-d4a49837e528}} ,{{formula:20956a18-4ca3-475f-95aa-55d79e374971}} ,{{formula:7fb91898-cdae-4785-a970-93220236da72}} ), RGB color ({{formula:a1ce3d54-47c7-4d99-b09d-292e67e3b93a}} ,{{formula:39b69a83-85f5-435c-84bd-cd986b7bd4fc}} ,{{formula:60b8e8b5-c420-4b03-9f2a-221e3aa1028b}} ) and the normalized (according to the block origin) coordinates ({{formula:275c8a68-7ea6-41c6-b3d3-e2e1fca02226}} ,{{formula:1d28da1a-797f-48dc-9e8d-bb007606f03c}} ,{{formula:c6d2be07-c0b0-46bc-8db5-86d5d30c8a3f}} ). Thus, the input point cloud for each block becomes {{formula:a3bdef3c-4a5c-4046-8b15-faecc37089f8}} .
| r | 5e4ab1de6ed01d8609a1be6744e9ce59 |
Here we only considered stabilizing SGD with momentum. Adaptive optimizers such as Adam could form a further stable alternative to rewinding or large-batch training, as they typically employ much lower learning rates. Though a full discussion is beyond the scope, {{cite:f7fec14b4ad8ffa57bb53e3eb79bdacc174aef53}} evaluate the LTH on an Adam-optimized BERT and find winning tickets without rewinding.
| d | 6af59b2417c3f361b7c8bb0c1b6a7c48 |
We may extend this work along several directions: The first one is the background independent formulation of closed string field theory. As proposed in {{cite:063f229f244c6ef6357bcef9c297ae5d32e00be9}}, {{cite:2c817ed0a937a124e9daf1d25b2b0ce163490966}}, {{cite:77f5c1f35424009bd82fd9469242f37c65f9e92e}}, this cubic closed string field theory may be obtained from pure cubic field theory as we expand the pure cubic string field action around a classical solution. With the explicit expression of the {{formula:8a425322-498a-4aa2-a58a-80ff6c37a5d3}} operation between closed string fields, we may be able to make their arguments more concrete. It is also interesting to compare this cubic closed string field theory with closed string field theory {{cite:8bde444e872e1fb20c389caf69d2b8cb1d72c565}}, {{cite:9d3a3578bec35c0e38fd11b1a51ee0bb1fbb9afa}}, {{cite:77e9fa438bf97e2a143c115becb08149005df324}}, {{cite:4bf058078ad6391cb63e94b1f6436d4c482e6912}}, {{cite:a94c2c6d14c78bc136a1a828043cf6cbb766f439}}, {{cite:0cd5b9feafc2246a4bcb71ebbbf4257dafe81281}} based on the Batalin-Vilkovisky formulation {{cite:6715c3901848f2cb556df58851a9b783da510f70}}, {{cite:32cb018d9ac18d7e17ffa9780b4a3d28390dd60e}}, {{cite:d3649aecf087441c9695b150e14dc61e218ba532}}, {{cite:83fac80624f9932c1ad83e7ac1d89202474e0dc6}}, {{cite:97186eecbceaf5ff5faeed04a64027a327b9e202}}. We need to clarify the relationship between these two approaches in future works.
| d | a761bd71424e0dc4001e8b39cb2de538 |
An interesting example of an indeterminate moment problem on the real line is the moment problem corresponding to continuous {{formula:346cdf2c-5e76-41e3-ab82-076734b31a10}} -Hermite polynomials {{cite:1426ef8c92f4514970cd28ee29ada12d742c4a94}} for {{formula:16701243-a6ad-4bad-9ff4-0966787158bd}} . Askey was the first to give an explicit weight function for continuous {{formula:d7ec26a6-1643-4e1d-83ce-e1caba5f52be}} -Hermite polynomials when {{formula:5ee51485-680c-453d-8535-1dacdca59fb1}} (cf. {{cite:a74ee58d4d22f52506837bd5b99487c608f247c8}}). The name {{formula:1bce2d08-ac41-4ce9-8e17-175be3f9c3fb}} -Hermite polynomials was introduced by Ismail and Masson in {{cite:dc631e2349fa891b295e0e23e813e84854c0b214}} who studied these polynomials extensively. In {{cite:9b570a73dc966e72a1094bedbc75f226dbc091e6}}, Christiansen and Ismail give more solutions for the {{formula:218378d1-0ff0-459a-9bc6-9965c9cc93f4}} -Hermite moment problem and also discuss the moment problem for a symmetric case of the Al-Salam-Chihara polynomials. Christiansen and Koelink (cf. {{cite:9d026f1d61380775bf17f356b2ee3180a85568ce}}) provide an alternative derivation of the N-extremal measures for the continuous {{formula:63cf9f27-f82b-4d41-8add-843fb26a2556}} -Hermite and Al-Salam-Chihara polynomials. More recent contributions to the indeterminate Hamburger moment problem associated with Al-Salam-Chihara polynomials are due to Groenevelt (cf. {{cite:474996c7e40f33830f4ac99927e167b8360092f2}}) and Ismail (cf. {{cite:cf9f324473a487c89b8f29f2b9d93aec0d0c5777}}). In {{cite:cf9f324473a487c89b8f29f2b9d93aec0d0c5777}}, new infinite families of orthogonality measures are also provided for {{formula:b93134cd-bc8d-4b8a-98fa-c49fded9b938}} -Hermite polynomials, {{formula:72d304ca-9d66-4b87-8848-88ac824b3a93}} -Laguerre polynomials and Stieltjes-Wigert polynomials.
| i | 185733f8552832c28d5f7c4b31e96d16 |
Depth, width, and resolution change in an exponential order. They have different values of their change rates among scaling stages. Depth and resolution change similarly, while that of width is slightly smaller, which is similar to EfficientNet {{cite:a8035f5b0e602f2d9b2647352bf85962f745706d}}.
| d | f7461b9e6671022d53596501e1dffc18 |
This year, the RBC/UKQCD has published the first ab-initio calculation of the the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon, at the physical pion mass, with a continuum extrapolation and an estimate of finite-size effects corrections {{cite:974fa7ff9dc7465bce23cf2f65b6dde48e3af1df}}. The study is based on Domain-Wall fermions at the physical point using two sets of ensembles generated with different gauge actions. Simulations include the fully connected contribution for the light quark as well as the leading {{formula:2fccd1fd-494b-4790-b735-177ff600c5f5}} quark disconnected contribution with both the light and the strange quarks. The latter contributes only at the level of 5% of the disconnected contribution.
| r | 3bc9323ba7f9adcc7f1fe8ec2844b825 |
In this section, we seek to compare the performance of the transformer heads we have analyzed in this work to baseline convex optimization methods. This comparison allows us to illustrate the implicit biases imposed by these novel heads in a practical example. In particular, we consider the task of training a single new block of these convex heads for performing an image classification task. This is essentially the task of transfer learning without fine-tuning existing weights of the backbone network, which may be essential in computation and memory-constrained settings at the edge. For few-shot fine-tuning transformer tasks, non-convex optimization has observed to be unstable under different random initializations {{cite:4dee9388b29b1654bb97e9746b8af786d2b161f0}}. Furthermore, fine-tuning only the final layer a network is a common practice, which performs very well in spurious correlation benchmarks {{cite:02cbad099d77d2cd1cf381c7b5d8928e364c42b2}}.
| r | 59abd5cbeb9887b3547454018092a5d0 |
where {{formula:f1eb0713-93db-4b1c-89b9-3e7bd68d0495}} is the degradation model parameterized by noise parameters {{formula:3b50d023-2997-4e54-aad0-40067122840a}} . The training set doesn't have the clean images {{formula:89cf83f6-1df1-424e-95e1-5ee7710e166e}} and only contains one noisy instance of the corrupt image {{formula:d247beb0-2e13-4a88-85a3-24d5037f6070}} for each {{formula:42ad0c0d-278d-4300-9973-960f3a4688ab}} , contrary to the work of {{cite:c526342af3a9d6f7ebcdedc4db0c6ba6bbe17f4d}} which contained 2 realizations of the corrupted images. With this, we come to the description of our manifold.
| m | 8f233b621ec9145869e048023df60423 |
Such correlations between the two gas phases can be interpreted as the manifestation of a common origin, like the condensation of low-entropy ICM gas through thermal instabilities. The ICM surrounding the {{formula:88aa0527-8170-44a0-a01b-349ca927ec7d}} tail has the
lowest entropy according to {{cite:ee1cdd0e4886533a53b181758f26fdd32da9ffb4}}, therefore, being a prime candidate for the reservoir of gas that cools to become star-forming molecular gas. Moreover, the recovered values for the gas phase metallicity in the BCG are consistent to the ones recovered by {{cite:ee1cdd0e4886533a53b181758f26fdd32da9ffb4}} for the ICM, within the errors. These findings support the scenario, that the warm gas has condensed from the ICM, without being further polluted by the stars in the system.
| d | 7c8fdd0c1e220d5a1b90380ec36d3a82 |
This is a new situation that did not exist in classical physics, where the procedure for obtaining theoretical predictions was not very complicated. In any case, the complexity there has almost always been within the reach of classical supercomputers, which are created mainly to cover processes from the point of view of classical physics - by the number of particles in the system under consideration. In quantum mechanics, the complexity increases exponentially with the number of particles, and the classical way of computing becomes unacceptable. This was strictly proved by the discovery of theoretically possible (from the point of view of the standard - Copenhagen quantum theory) processes that cannot be modeled on any classical supercomputers - the so-called fast quantum algorithms ({{cite:38c987aad71356fc47cf98fe7b9259a46d6b94e5}}, {{cite:54fefd16740a59b2364ffab4248941338c088584}}).
| i | 2a171857978e0e5ba8c2fefbf3da8402 |
When applying such procedure to the photon gas problem, it has been long known that one detects non-trivial modifications of the equation of state parameter {{cite:0ba1701176a817ec8713f08343cca2010aeaeeb8}} proportional to the ratio between the temperature of the fluid and Planck temperature. On the other hand, it has been found by Kiselev a solution of the general relativity field equations {{cite:f3f1632064ea40b2b8cffd14e82e6a253db168e4}} that is able to modify the static black hole metric in a way that depends on an averaged equation of state parameter of the fluid that surrounds the black hole. In particular, the Reissner-Nordström solution has been shown to correspond to the special case in which the average equation of state parameter corresponds to that of a photon gas. Planck-scale corrections of the Reissner-Nordström metric induced by the above mentioned modified thermodynamics have been recently analyzed by some of the authors in {{cite:378fb7730fa99c86da208609037af0e131e20c64}}. Besides that, the impact of the trans-Planckian regime and the novel notion of thermal dimension {{cite:6b663b5ba2040c35a2fad3187ed869a32d996dbd}}, {{cite:af3fc38a4808dedd336ad77465fdfcb2503df9b2}}, {{cite:fb61d4b3902bbcc84d95c6e03c80032e806f87f5}} on the evaporation of charged black holes have been studied in {{cite:823d35b595fe20c67ec70247237ce97af13f607f}}.
| i | 3ec22dea99aef6e5b1abd2d4b7d775c5 |
Memory Networks. Memory networks can cache sequential inputs in memory slots, and explicitly utilize even far early information. Memory especially receives attentions in long story understanding, such as movie and TV, which not only requires to understand the content of shot video clips, but also to infer more abstract and high-level knowledge.
{{cite:935a5c08a63bc6a9bde425028f739b3fb60515ff}}
first incorporate and modify memory network {{cite:a90d5cc33949d0e5759e24337ff504e8a1e82520}} into VideoQA, to store video and subtitle features into memory slots. To enable memory read and write operations with high capacity and flexibility, {{cite:12e7bca50884276295cb79cdf1b99e50a08eb02d}} design memory network with multiple convolution layers. Considering dual modal information in movie story, {{cite:347c91e340758cbf82420d4c8323cb6f0d43afaa}} introduce a progressive attention mechanism to progressively prune out irrelevant temporal parts in memory for each modality, and adaptively integrate outputs of each memory.
Memory has also been explored in VideoQA. {{cite:f3fe3eeb57e71eba6969a6a0ed713fe311814f9d}} propose a two-stream framework (CoMem) deal with motion and appearance information with a co-memory attention module, introducing multi-level contextual information and producing dynamic fact ensemble for diverse questions. Considering that CoMem synchronizes the attentions detected by appearance and motion features, thus could generate incorrect attentions, {{cite:5caba635a93ac720fc2f3086fa506567e3bfe15c}} further introduce a heterogeneous external memory module (HME) with attentional read and write operations to intergrate the motion and appearance features and learn spatio-temporal attention simultaneously.
| m | 67e795fd9d875ce4cfa10dd0641f2df0 |
To study the bipartite entanglement we will use the concept of negativity {{cite:7ccc8717bbb07c31499fab6a73d48f8af1eed481}}, {{cite:b3787c97608868df3bc0a44cb2cb7fcb3b1a582b}}, {{cite:c26dac10f2c1a544362fc6ef011c7bd4613affe7}}, which is defined in terms of negative eigenvalues {{formula:d83ee34d-1e2f-42d8-9f11-1457b564cb3e}} of the partially transposed density matrix {{formula:40636ee1-8d6b-46d7-bf55-4ecf4cf5fb81}} ,
{{formula:2e78823a-611f-475d-b7ca-ab4cd733e038}} .
The zero value of the negativity corresponds to separable (disentangled) states, whereas its non-zero value corresponds to inseparable (entangled) ones. For MSHD, the negativity of the maximally entangled state equals to one-half ({{formula:3285d506-b507-4fe7-89c4-43f14dcbd4b9}} ). Detailed derivations of the negativity of MSHD can readers find in Ref. {{cite:72eecbb4d00c20e7afca6277bd30f94b4158262d}}.
| m | 789a09443866bed169bc8b4b6cacb571 |
We use density functional theory (DFT) with lattice flexible boundary conditions (FBC) to optimize the core structures of {{formula:de9b41ca-e039-4c7b-b155-242dc791742d}} edge,
{{formula:c9f1e8da-49a9-434b-a0ba-527de1e695b3}} edge, {{formula:1fab65fd-2ad0-4693-a51b-d6f2c1031fab}} edge, and {{formula:b18653ce-c044-49ee-a699-ad5cd440b455}} {{formula:9f2927ed-9e37-4e42-a5d2-067bd3758866}} mixed dislocations in bcc Fe. The FBC
approach couples the highly-distorted dislocation core which is treated with DFT to an infinite harmonic lattice via the lattice Green function
(LGF), which allows the dislocation to effectively relax as an isolated defect. In contrast to most previous first-principles FBC calculations of
dislocation cores that use the bulk LGF to relax the harmonic region outside the core, we use LGFs specifically computed for each dislocation
geometry. The simple bulk-like approximation we used for generating the force constants and corresponding LGFs for the {{formula:4eaba407-4990-42a3-8469-421a2fff7f8d}} edge,
{{formula:e70d8af2-5e24-41f2-9618-1fa2d52b4442}} edge, and {{formula:ec8ac3c4-221f-43d3-9eba-1adf96087203}} {{formula:f4d8c4ab-4745-445f-8548-480a32744ac6}} mixed dislocations fails to produce an adequate LGF for the
{{formula:4999e3e4-f2f0-40b2-ba03-2e396f469f5c}} edge dislocation. For this case, we found that a Gaussian approximation potential (GAP) for bcc Fe produces
accurate force constants under strain which lead to a dislocation LGF capable of optimizing the core geometry. We find that the cores of all the
dislocations in this study are compact and the magnetic moments on the atoms in the cores increase in the tensile region below the slip planes and
decrease in the compressive region above the slip planes. Except for highly distorted sites nearest to the cores, the strain response of the magnetic
moments on the atoms in the dislocated geometries closely follows the volumetric-strain response of the magnetic moment in bulk bcc Fe. We find that
the initial ferromagnetic ordering we impose on the magnetic moments in each geometry remains after relaxation, showing that ferromagnetic ordering
in the cores is at least metastable. Future studies could investigate the impact of different initial magnetic configurations in the dislocation
cores on their relaxed magnetic states and geometries. We find that most of the core structures computed using the GAP, MEAM, and EAM interatomic
potentials compare well with the DFT core structures, with a few notable exceptions where the cores relax to different structures. While none of the
potentials is able to produce core geometries similar to DFT for all of the dislocations, the EAM potential from Ref.{{cite:a422675e0fd436957669d26503d4e85c2c2d0608}} has the best
overall performance. All of the core geometries optimized with this potential using a conjugate gradient method are similar to DFT, and they all
remain stable under annealing except for the {{formula:a7abc21e-0a9a-4255-bee4-29cff5a46db7}} edge dislocation which remains compact but becomes asymmetric along the slip direction.
Additionally, this EAM potential produces a compact and symmetric core structure for {{formula:c1293c42-6a6c-46f8-8945-ad9470732cc1}} screw dislocations similar to
DFT{{cite:b186ac10ff549cfc11605feb85b223909ab2662e}}. Relaxed dislocation core structures are of fundamental importance for understanding plasticity in bcc Fe, provide the geometries
required for first principles-based studies of solid-solution strengthening{{cite:46bd5e55b2c20f52a0c9fa9e7dd07f5b3be00896}} and solute diffusion near dislocations{{cite:2d9eba72c0323d40778f74741b57d2bd4b8de933}},
provide data for parameterizing and benchmarking more computationally efficient models such as classical interatomic potentials, and serve as a
comparison point for future experimental measurement of edge and mixed dislocation core structures in bcc Fe.
| d | 646855bc6edd6fc945b2d7a7b39af806 |
This gives that {{formula:b8634273-166a-4b7e-b206-8dc4caf9a12e}} is the singular value decomposition of the compact operator {{formula:8d7b7ee8-6b96-4dee-a20c-1d2863498eb8}} . Now just as in {{cite:d94b66e2beb2316752bcd1b0c3c2759cbb1d4f66}} we can define the regularized solution of {{formula:54b1aa87-7622-4a25-90fe-ce463dad15ec}} to be {{formula:fdaa7d01-eb5e-47eb-ab36-15f14794d045}} which is given by
x= (n ; )n xn,XX* xn.
The real-valued function {{formula:b29601f1-09b0-470e-9792-f1ed49f2dfad}} denotes the filter associated with a given regularization technique. Here we will assume that {{formula:736c6b5c-e371-433d-a21f-ee3804cae6c6}} satisfies that for all {{formula:c0fab7ae-8e56-4717-9b3d-f3851780adaf}}
{{formula:27326973-f37a-43f7-b3f1-ca3475bca657}}
| m | a470b407be443047abf371616be9342d |
A new opportunity arrives thanks to the Gaia mission {{cite:94968d840111b9a78cf8ffe7c68567734a38f9a8}}.
For the first time, the recent Gaia Data Release {{cite:c3c029dc4d0b477e61220b73e14a50912f6a9dbc}} has provided stellar parameters and chemical abundances estimated from the spectra taken with the Radial Velocity Spectrometer {{cite:59f9da0a3af26ace65250cad31a0c9b6d96a3fb7}} instrument.
The spectra cover the Ca triplet region ({{formula:e7033393-1db7-4317-a3f4-58df83d689e2}} ) with a resolution of {{formula:55a3bd6a-f0a8-42e9-b94a-bd63a017e38e}} , and are analyzed through the General Stellar Parametriser-spectroscopy, GSP-Spec module {{cite:f34af933c5437d26b5b5f75519af606d8cc72eed}}.
The current GSP-Spec catalog contains 5.6 million stars analyzed and is already one of the largest catalogs of stellar parameters derived from spectra; moreover, the number is expected to increase in future releases.
By filtering out stars with suspicious solutions, {{cite:ccccb34731abe60699147163300a1f0812cc170b}} demonstrate that the estimated astrophysical quantities have excellent quality.
| i | 40a04224f94b4e072630e338be37688d |
Optimization of Miller-Abrahams resistor network {{cite:0c680d22552535886ff79f1db724148ad8a4cc6e}} of all available pairs of droplets of two adjacent puddles leads to the new H-mechanism conductivity:
{{formula:44cae24f-61ef-43df-86d5-59ea4f244bbb}}
| r | 212e56f3d929dea711bb7c1d794aa0fe |
Simply minimizing the standard cross-entropy loss for highly non-convex and non-linear models such as (deep) neural networks is not guaranteed to obtain solutions that generalize well, especially for today's overparamatrized networks. The key underlying issue is that these models have many different local minima which can have wildly different generalization properties despite having nearly the same performance on training and validation data. Naturally, there is a rich literature that studies the properties of well-behaving local minima, as well as the design choices that improve our chances of finding them {{cite:39e01826d869f7bbce5ed8b0de7fca5d785a58d3}}. The notion of flatness which measure how quickly the loss changes in a neighbourhood around a given local minimum has been empirically shown to correlate with generalization among a variety of different measures {{cite:2a27b77aeb7e9f052e54cd5da42e4c372a9ad9eb}}. In addition, generalization bounds based on the PAC-Bayes framework {{cite:5d67b92e041f86f54b88f5fb58d21ba4e5f2eda5}}, {{cite:a93c41bcbefabe56595ac0107670f7899b24af9b}} provide theoretical insights that corroborate the mounting empirical data.
Since the evidence implies that flatter minima tend to generalize better, the obvious question is how to efficiently find them.
| i | a8e0dbe73e2aa9a2c3ef7164fa3c5182 |
respectively, with {{formula:13eaaea7-7b4c-4be1-a11b-a7ead682ffc3}} for {{formula:fa8fca42-bb84-4a45-a9db-7ad4365336f4}} odd (even). Here, one has {{formula:91064381-fcde-4359-b191-fab3e9a84073}} in the absence of the NF contributions. In the numerical calculations, the Wolfenstein parametrization is used for the CKM matrix elements in the SM, taken to be {{cite:29a377256035c2e3aba2863d170071e25923b9be}}
{{formula:10233d3d-9a9c-4d94-a949-23436426923c}}
| r | 29617cc40acda35cff5d375f661da97d |
The magnetic transitions (M1) can probe the internal charge structure of hadrons, and therefore they will likely play an important role in determining the hadronic structures of {{formula:4ed4edd0-82b4-4dd6-8c58-3976c1bc8bdd}} meson. The present M1 transitions widths of {{formula:1f75ea76-867f-4e59-98b4-325382cbee46}} meson states as listed in Table REF are in accordance with the model prediction of {{cite:e0276b347de9aa15ad3b697633feb67f351b6ddf}} while the upper bound provided by PDG {{cite:0146d4298bbae2cdfb20d5c19fc70fa15cd74c76}} is very wide. We do not find any theoretical predictions for M1 transition width of excited states for comparison. Thus we only look forward to see future experimental support to our predictions.
| r | beefe3f2042ebfe90cbc2ca50c3e7140 |
Our calculation in the gauge theory demonstrate the power of the methods introduced in {{cite:12c74e5ae8629d8c4360648a37fa8d91164efb4a}}, {{cite:f74570508ffcc143e21356fb659295620aa8cef1}} for computing correlators of fully-symmetric Schur polynomials. Our methods are in many respects more streamlined when compared to the approach introduced in {{cite:ccdaad2dd9e4604d521fa4244c0e20df4c088b98}} for dealing with symmetric Schur functions. In principle our computation gives an exact integral representation for half-BPS correlators, without having to deal with a divergent generating series. Since we can express this generating function as a sum of residues with only one residue providing an exponentially large contribution, it is natural to expect that the saddle-point approximation gives the exact answer up to a simple one-loop determinant coming from the remaining residues. In fact the holographic computations of non-extremal correlators seem to agree with the exact computations obtained from explicit computations with the Schur basis {{cite:b0dd2f94f837693be184ccb538831fd62b628ab0}}. It would be nice to check whether this expectation holds by embedding the correlator into a supersymmetric observable where supersymmetric localization techniques can be used {{cite:274a8e4fecbd01dee67eb9d38f3cd67657f14425}}. For example, the connection between the coadjoint orbit integrals and Wilson loops via geometric quantization is well known {{cite:a4001aecc920b684b5470ac007836fdab81c6f12}}.
| d | f3ad1a56288eae2c04b3595779078415 |
Therefore, one of our technical contributions is to accurately solve the MDP in (REF ). We summarize the high-level idea of solving (REF ): First, in Lemma REF , we show the optimal policy among the extended policy space {{formula:44cb49cb-2208-4951-a5c2-89519b30a8bd}} with universally measurable stochastic kernel {{cite:582ccd85871297ee217483e3593121cace0652ef}} satisfies the Bellman equation. Then, in Lemma REF , we provide an exact value function that is the solution to (REF ). Finally, under Assumption REF , Lemma REF guarantees the uniqueness of the Bellman equation.
{{figure:11a784f7-8b92-48b6-9db6-37d849475243}}{{figure:b1ad9a21-9c3f-4d66-97b2-ab9f74322829}}{{figure:92631fc2-4a3e-43d6-951c-75f9a457f01a}} | d | fd3a995ec31f220431c1efa71b12184b |
The second AC multi-agent extension, called Independent Actor Critic
(IAC) {{cite:5a5ed7543eb30b3e3b7b2f46353de3e788ee421a}}, {{cite:6180c17a1b772c69c039662572223085586b2956}}, learns a
decentralized policy and critic {{formula:c0347617-6842-42f0-a23a-71897bf8ab59}} for each of the agents locally.
At every timestep {{formula:6e31e7ed-9fa8-42e2-b24e-a148544ea8d2}} , a local experience {{formula:a7dfaa4b-9c05-442c-bb1d-aef848ca4a7f}} is generated for agent {{formula:b4d9d9b1-0001-467b-8383-60977757be81}} .
The policy gradient learning for agent {{formula:d1d3c609-f1c6-4505-95a8-b21819728912}} is defined as
{{formula:1e783859-d0f2-45e4-9cf7-0d5994b148c1}}
| m | c6e259edf2a108a413b30fee8a823920 |
We then develop a Relationship Feature Propagation (RFP) module that explores the connections between heterophilic relationships. Two challenges emerge in the design of RFP: the effectiveness of feature propagation and heterophily modeling. To reduce computational complexity, we only require each relationship to contact neighboring relationships that share the subject or object. Moreover, the contextual coefficients obtained from ART are adopted to represent the correlations between relationships. To propagate heterophilic features between relationships, we extend the PageRank-based GNN {{cite:0157a2ae3f0e814a1984a1c5bc4ba7ec0347018d}} to a high-pass graph filter. This approach enables the RFP module to learn the relationship correlation of disparate classes by passing relevant high-frequency graph signals (, heterophily).
| i | b5a63afed2754f5255f188ed42eba869 |
DNN
watermarks {{cite:3a542d81507bf3ae9fd95b16484ec6a764fc53be}}, {{cite:7f2c54ba34e5057004440e947044530f70ac4de3}}, {{cite:9125086e4671869d75d85dc78ceae58dc6cf7a66}}
are designed to address the need for proof of model ownership. A robust
watermark should provide a persistent and unforgeable link between the model
and its owner or trainer. Such a watermark would require three properties. First,
it needs to provide a strongly verifiable link between an owner and the
watermark (authentication). Second, a watermark needs to be
persistent, so that it cannot be corrupted, removed or manipulated by an
attacker (persistence). Finally, it should be unforgeable, such
that an attacker cannot add additional watermarks of their own to a model in
order to dispute ownership (piracy-resistance).
| i | c333af4aa1692b65b9c26cab55aea19b |
In addition to the models discussed above, certain
variants of {{cite:85c522f3e4b25ccbfd7c389f5d65a96da87106dc}} and sparse attention patterns (local-to-global attention; {{cite:1524422a4d00b9f907f50705ffa34bdd6b4fa399}}, {{cite:89642547e7cd8bcde956c0d03a2a02bb5354d8a7}}, {{cite:8a69ea6b3a570f33a56edc7ff3f3d50d99309647}})
can also be seen as instances of Abc (Appendix ).
| d | b266f9220a0ab39f456c13424cf1f54a |
However, the attention mechanism substantially improves the fitting and prediction ability of NP, its computational complexity also limits the length of the input sequence. In Figure 1, ANP only takes 32×32 image pixels as input, and the pixel sequence of each image is about 1000. However, when facing higher resolution images (e.g., 600×600, 800×800), it is difficult for ANP to effectively cope with the excessively long pixel sequences if it continues to use the image pixels as input elements. Facing the limitation of attention mechanism in image processing, Wang et al. designed the structure of the non-local neural network {{cite:1ab871d22287b69660e602821d73c944ae74dc0a}}, using the feature map of a convolutional neural network as the input of attention module, which is more convenient for processing compared with the original image; Ramachandram proposed isolated attention and Huiyu Wang et al. proposed axial attention {{cite:d0a1a2ceab0aa667b3a0300f37dc3f4d50014d76}} to solving the higher computational complexity, but the above two schemes use specialized attention, which is difficult to scale effectively on hardware.
| i | 4805bdea4945445217fb82739932e849 |
The vast majority ({{formula:9b2c7c6a-b8c5-4f2d-8397-b5c6c0b29c58}} ) of our dataset requires contextual commonsense reasoning, in contrast with existing machine comprehension (MRC) datasets such as SQuAD {{cite:7283fc078178e34e0b1df4339b1223fbf5b70e92}}, RACE {{cite:3c39430578b66b3f9ffcd84f59ede6cb5b6704a7}}, Narrative QA {{cite:7f90b951fd65c25960cf87594afe7093f17cee45}}, and MCScript {{cite:52551e7dd31ab0c5651eed75e16c4d03b3f6257a}}, where only a relatively smaller portion of the questions (e.g., {{formula:bea308c0-78a7-4933-9294-87f3be83c0b2}} in MCScript) require commonsense inference.
In addition, the correct answer cannot be found in the context paragraph as a text span, thus we formulate the task as multiple-choice questions for easy and robust evaluation.
However, our dataset can also be used for generative evaluation, as will be demonstrated in our empirical study.
| i | 5bf1993e11c1034019883430e4f030e1 |
In the context of a digital twin, calibrating the simulation element of the twin with current data is essential for ensuring that the simulation is representing reality as closely as possible. Manual calibration is time consuming and not suitable when parameter values are changing. This study explores the suitability of a particle filter approach for calibration and compares it against static Bayesian calibration following the {{cite:06ac4587cf9089ad58cbcfe64c35e58b4dd7e09d}} approach, and also uses the KOH approach sequentially as a further comparison.
| d | 99a758abacd56921b430ba2289f0eef0 |
In this environment, we ran experiments on 7 different Atari games to test and compare the fitness-based approach, Sugar Search, and its generalization - Pixel Novelty to other techniques like Novelty Search {{cite:36927aaeaf4f075d27c0bc03447f9bff673434f0}} or DQN {{cite:7335b42f12f07035d099ab02a173cf643408c96d}}. The results in Table REF show that Sugar Search does not always lead to a higher score compared to the fitness-based approach, but it performs comparably well with Novelty Search consistently across different games, as shown in Table REF . The scores achieved with Pixel Novelty are also competitive or comparable to other approaches, meaning that Pixel Novelty is a valid generalization of Sugar Search.
| r | 7452acf1b32a74cce14912b968a79680 |
It is known that for the diagnosis of certain diseases by ECG, a small number of features is enough. For example, for a myocardial infarction, this number can be reduced to seven {{cite:e2b1a9532ec98c76ae260261e3ec76825951205a}}. This indirectly indicates the presence of a low-dimensional structure in ECGs. But our experiments have demonstrated that basic convolutional autoencoders fail to learn interpretable parametrisation of the ECG-s manifold in the space of all signals of predefined length. Experiments indicate that common regularization techniques (like batch normalization{{cite:c4bb85deb6cbfdf3fb8bf114488af7336315eb0c}}) do not help to eliminate the negative effects from sec.. Probably, some other regularization must be developed for this situation.
| d | 0a9a6ce007dbdddec955070c3a128f55 |
One theoretical challenge is the proper pre-processing of the problem Hamiltonian by scaling and shifting the coefficients of the objective function, such that we optimally make use of the parameter space {{formula:804e715f-a3fc-4a01-9ae3-d6fdc75d2fce}} (most of the problems in the dataset did not suffer from this issue, as we found the default scaling to work well already). However, scaling the problem way beyond necessity also creates issues as the energy landscape is periodic in nature {{cite:81b86cc8d6340044f699d8cd8f4682e3a76415b2}}. Thus, one possible way is to use scaling as a heuristic within the QAOA process, and treat it as a hyperparameter to optimize over.
| d | 453ad40dab9b01872611009a434721a1 |
Vision transformer:
We validated the applicability of our proposed integer training on the original vision transformer model, notably ViT-B-16-224 {{cite:40ca0903f819c6de1715dd9fa7d729d2100225b7}}. We took the floating point checkpoint pretrained on ImageNet21KRefer to: https://huggingface.co/google/vit-base-patch16-224. We used Huggingface {{cite:7db57f2aa501a5199e9db7e44dd229e71c23b4f9}} to fine-tune the model on CIFAR10. In this experiment, we used int8 linear layer, int8 matrix multiplication, int8 convolutional layer, and int8 layer-norm for our integer training pipeline. The result is reported in Table REF demonstrating negligible loss of accuracy ({{formula:8945d508-9af2-464f-8923-af3b93964eb4}} ).
| r | d07d387126f50bdfe25625458b74b823 |
Since the phenomenon we are considering is a resonant effect, even a higher multipole moment would also induce transition, if it is sufficiently large and the resonant frequency is hit earlier. As mentioned in Ref. {{cite:6790243429f25cf48e6320dad15575cfb60ad222}}, considering the octupolar tidal perturbation, the cloud also depletes when {{formula:5e149a76-36df-40e7-aa0d-ae809d372fc5}} mode is the fastest and the orbit is counter-rotating. However, it is not clear that how higher multipole moments affect the transition network especially in the region where the non-trivial transition occurs. In addition, when the cloud is in the relativistic regime, the configuration is largely different from the one of the hydrogen atom. Hence, the overlap between mode functions will change and whether the adiabatic condition is satisfied or not is non-trivial. Therefore, we should solve the transition network taking into account the higher multipole moments and evaluate the transition rate appropriately for each transition in order to get a conclusive answer to the consequence of perturbative tidal effects. Our work is the first step in the investigation of cloud depletion in a wide parameter region.
| d | 1ba89fe09f71bcda384efa7615fa10fc |
However, these existing methods suffer from three problems. (1) Both the heuristic compression policy and lightweight module design require domain expertise to explore the architecture space. However, the space is so large that such hand-crafted methods cannot afford the architecture search cost. Due to the limitations imposed on the search space, the resulting neural networks are usually sub-optimal. Moreover, these methods have to take the constraint of hardware resources into account. Unfortunately, the computational complexity makes it prohibitive to produce application and hardware specific models. (2) Previous NAS methods exploit reinforcement learning and evolutionary optimisation algorithms to automatically explore the discrete search space, thus achieving the state-of-the-art recognition performance. However, such methods generate a large number of candidate neural architectures, more than 20,000 candidate neural networks across 500GPUs over 4 days in {{cite:097bb5a01f908910343da83ea2d0c23b459ea25e}}. It is time-consuming to train and evaluate them so as to guide the neural net architecture search. (3) The existing DNAS methods relax the problem to search discrete neural architectures to optimize the probability of stochastic supernets, and allow us to explore continuous search spaces by using gradient-based methods. However, some DNAS methods still require a few candidate neural architectures to identify the best candidate by sampling based on the probability distribution of learned architecture parameters {{cite:5e722b4453b0688ed433d0a65f86ec272484bbd5}}.
| i | 9decac30b96a7cca13e8ec6a1d1fe855 |
Our empirical examples have used VB.
The approach has potential value in Bayesian
optimization {{cite:7ab55841573f6e77d6dc7aebbff9a1ee39eb733f}}
and optimal transport {{cite:69d9e28c6fa5491f6aa0569fd3d0e3497031037f}}, {{cite:c3bc6eec7f08122338bd9540403d412b0e266110}}
as well.
| d | a7fdef4042dc4adbf31c0e71116e6ad4 |
For comparison, two baseline algorithms are included in the results as specified and measured in {{cite:ca17ebe00ae169c522f3b318b4e8955048c52476}}, note that these algorithms too included beat-synchronized features. Firstly, the method of {{cite:2b862df9b9a96eeb472d800b062822efac083733}} is included as it most closely mirrors the algorithm of Section . Secondly, the algorithm of {{cite:97a618171f4512f05bc70ddf175b9b535cb7b005}} is widely evaluated as having the best performance with respect to unsupervised boundary detection in music segmentation. CQT features have been evaluated to provide superior performance in {{cite:ca17ebe00ae169c522f3b318b4e8955048c52476}}, and are used at the input to all algorithms, proposed and benchmark, in the results presented here. For the proposed algorithms, three methods are investigated, "Unsynchronized", employing a constant hop size of 3.6 ms between successive CQT windows; "Beat-Synchronized", employing 128 CQT windows centered at times linearly interpolated between successive beat markers (estimated during training and inference by an algorithm similar to {{cite:df4a8b4c1e2391c8209d91a4de04b7e6dddc210a}}); and "Biased", employing the same features as the "Beat-Synchronized" approach, but using the 2D Fourier Transform comparison sampling described in Section . The CQT features use a minimum frequency of 40 Hz, 12 bins per octave and 6 octaves.
{{figure:92b8a6c8-9e9e-45bf-be26-b57facecfa76}} | r | e8e761f8565a810f2f5342875935da2c |
In this paper we consider linear-time temporal domains.
LTL limits its set of expressible properties to the
First-Order Logic (FOL) definable fragment of regular languages. This
is quite restrictive when compared with the most popular abstract
models of procedural programs, such as Pushdown Systems, Boolean
Programs {{cite:aaa19624acef078380d488c3a142d19e6be85a9d}}, and Recursive State Machines {{cite:93a7ffeee7955c4f1dd10e4bb5d1e47e222832a4}}.
All such stack-based formalisms show behaviors which are
expressible by means of Context-Free Languages (CFLs), rather than regular ones.
State and configuration reachability, fair
computation problems, and model checking of regular specifications
have been thoroughly studied for such formalisms
{{cite:ac8f767cd2336911abc5ebec791c45513146c787}}, {{cite:8c38305d76677c26f9f3b557910186fd3473fedd}}, {{cite:2c8f3e6ffc971b8babb91df450e1499d7cf8cc0b}}, {{cite:136a4034d5c7efe8fb144f27bb883897c468b8b2}}, {{cite:b90c851701482932526cf2f007fbcca0d1358301}}, {{cite:98b058d24700f72fd90487162e15971fad32664c}}, {{cite:55f29a6bd7bc0733fd729918134f8bd66d9ee898}}, {{cite:93a7ffeee7955c4f1dd10e4bb5d1e47e222832a4}}, {{cite:5604bea7d09d3e0a6cfeb00b4b1db66425243d18}}, {{cite:4c97c0b73bcbd1b6e560871d4f8479ad3a0eeef0}}.
To expand the expressive power of specification languages too,
{{cite:c94942e3bebe4e740bcd90bb84b242da4ea1fa89}}, {{cite:7f0e9fb21365360921425d8327373f3e851623de}} augmented LTL with
Presburger arithmetic constraints on the occurrences of states,
obtaining a logic capable of even some context-sensitive
specifications, but with only restricted decidable fragments.
{{cite:598f6039207cf9bd9403c341d4f11f238f5600c9}} introduced model checking of pushdown tree automata
specifications on regular systems, and Dynamic Logic was extended
to some limited classes of CFLs {{cite:dcb0a19aba8aa59f33ed61923b0861053564debd}}.
Decision procedures for different kinds of regular constraints on
stack contents have been given in {{cite:1e5a7e9c03abeaad38eaf59eb2752898c0005015}}, {{cite:9da848eb37bf93843682bd20c11c7f86caf9b21e}}, {{cite:8ee174895a6ae627ab6fa016458f15e3c55af56e}}.
| i | 39b8290477cb289d0be90c0670ef7bcb |
Our algorithm is implemented with an adaptive gradient described by the proximal terms {{formula:79fea5f2-9727-4b65-8be1-d7b0d03e5d85}} , {{formula:0d2a4294-2642-4ca4-9286-b8af8c8d9dfa}} (line 6 - 9). The proximal term is motivated by its use in online learning to reduce the regret, where the term aggregates the historical information to combat the online setting {{cite:07e1b078b9d1e2bd7b40912e2254f1d05dc0f194}}. Such a term in our algorithm helps the step size to be robust to its initial value for a more stable learning process in practice. A similar utilization of the proximal term could be found in AdaGrad {{cite:5053163f2eab6dbb3d78ce7b2b834f07ffb22a3b}} for more general cases in optimization. While past applications were limited to convex functions and i.i.d. sampling, we take the use of proximal function further to primal-dual optimization with nonconvex-nonconcave objective function and under Markovian sampling. Our algorithm implicitly optimizes the objective with a proximal term with Mahalanobis norm (e.g. {{formula:f81a66b0-95a3-44a7-8821-05c9c7b2b03e}} ) and does so in a data-driven way. Notice that {{formula:669ea6ed-95ae-4033-b2e0-aff35f3150c1}} , {{formula:d91d8e74-2d43-4153-ac95-82799a6bed62}} are chosen to be diagonal matrices for ease of computation (line 10 - 15).
| m | 121bbb8c5c3b913656321de2f7bfe832 |
Here (and from hereon) we define the `Galactic Plane' as {{formula:9069c618-9761-49dc-bdf3-6e94a560dcc2}} (19 sightlines), including Rosette, Mon OB1 and NGC 2264; the `Gemini region' as {{formula:6f8d87b1-0bad-4759-9f2b-334f3d9232f4}} 5{{formula:cea2859b-81e3-4ba1-846c-c30275f5b7ae}} (23 sightlines), including minimal molecular gas; and the `Taurus region', including both Taurus and California, as {{formula:98437653-e0cb-499a-9d8b-30c17825311e}} {{formula:fea142c3-52d5-4403-94d0-d3cf9bd1c9b7}} 5{{formula:4b01c787-ca8e-4aa5-80e0-ce95267e60c4}} (35 sightlines) (as illustrated in Figure REF ). These latitude divisions (basically based on the distribution of {{formula:1fa3a8fb-c9e5-4d8e-9919-e69d59c8f5d4}} from {{cite:17a7be2f30e7a44448a06180de8da7a1e75b026c}}) roughly divide our sample into three characteristic physical regimes – in-Plane, out-of-Plane with mostly diffuse sightlines (Gemini) and out-of-Plane with many dense/molecular sightlines (Taurus). The colors in the absorption spectra in the plots indicate the HI spin temperature of each CNM component. In general, we detect strong absorption and emission in a wide range of VLSR from {{formula:2ac35cab-b751-4793-bd17-5cee85dff252}} 10 to 50 km s{{formula:fc3c4a0e-a517-4fa2-ab62-2688267f0507}} for sightlines in Gemini, from {{formula:7484326e-3683-4a93-ba86-048dcf9496e7}} 20 to 20 km s{{formula:9265d76a-d7c9-48b9-b3f5-9a82e7506ca7}} for those in Taurus and {{formula:1397f3ad-f596-4f70-9572-2ae68c347de6}} 50 to 50 km s{{formula:51a432ff-bfd2-4052-b71a-539a334c767f}} near the Galactic plane. The strongest absorption/emission is located at {{formula:db2a3c41-6ebe-485e-80dd-7d7de7b3d0cc}} 0 km s{{formula:702f6ac4-9270-4701-b00d-c6c7d58639d6}} , and the closer to the Galactic plane, the more complex the profile shapes.
| r | 2cd8181dbd20faf834f184c63819544e |
blackMethods for the interpretation of machine learning models can be broadly classified into post-hoc interpretation methods and self-explanatory methods. The former typically aims to establish the relationship between the changes in the prediction output and the changes in the input of a machine learning model in order to identify features important for model decision. blackFor example,
{{cite:1ec7fe8c3a0d9e0321e3a1d75957ab1b032c0954}} used probing to examine BERT intermediate layers. {{cite:2cd77a6734bbea9c596f4a50422de05c5a4f72a3}} modified input text by linguistic perturbations. {{cite:440aaf8df1402320c626cb2462e70e2af3a80f37}} tracked the impact from gradient changes. {{cite:829254c7b4a800b35ada947e4beeeefda4dbd26e}} erased word tokens from input text by marginalising out the tokens. The self-explanatory models are able to generate explanations during model training by `twinning' black-box ML model with transparent modules.
For example, in parallel to model learning, an addition module is trained to interpret model behaviour and is used to regularise the model for interpretability {{cite:841e1a29c1c1ba15f20eeb7fdec0c04555db2f69}}, {{cite:e803e63a96da60e3127a5c6d28dc895ac1fe0d3e}}. Such models however usually require expert prior knowledge or annotated data to guide the learning of interpretability modules. {{cite:8402011cf5ff17cfe9f0010f2cc36ba73b828ea5}} proposed to improve the interpretability of neural text classifiers by inserting variational word masks into the classifier after the word embedding layer in order to filter out noisy word-level features. The interpretations generated by their model are only at the word-level and blackignore hierarchical semantic compositions in text.
| i | 67d7f8cd1099fda8e7665a13af29524e |
Expectation-Maximization (EM) algorithm has been frequently adopted in deep learning in recent works {{cite:c3bb3a8c0c90b1b24c4e699c5c5672e7a4724abb}}, {{cite:6e48d0d281dacda55d9f6027f77342056fa62f83}}, {{cite:9c1f33b5f4f141b424d44837577061de6843db86}}, {{cite:c457a88f24cb6fa91d2a647ba37dd2410f6bdd19}}, {{cite:71ef622c975f633650cb00b9d7c2dbae2bfaf7f7}}, {{cite:5d86a29f309d5ad85fed325772b2183848954cb4}}. Hinton et al. {{cite:c3bb3a8c0c90b1b24c4e699c5c5672e7a4724abb}} introduced EM routing to group capsules for part-whole relationship construction. Yang et al. {{cite:6e48d0d281dacda55d9f6027f77342056fa62f83}} designed prototype mixture models for few-shot segmentation. They applied EM algorithm to estimate the models' mean vectors for query images. Biggs et al. {{cite:71ef622c975f633650cb00b9d7c2dbae2bfaf7f7}} used EM algorithm to learn a 3D shape prior for animal reconstruction. Most prior works jointly optimized the parameters in the EM algorithm and the network's parameters during training. In comparison, we derive an EM based algorithm during inference as an unsupervised soft-clustering mechanism for foreground-background separation.
| m | 9188c6431289c76b759e371f0c0048a7 |
The proof of Theorem REF used the
compactification technique of Section to
show there is R-tipping in the nonautonomous system (REF ) by computing codimension-one
heteroclinic connections in the compactified system ().
A similar approach has previously been used on a case-by-case basis to compute critical rates in specific examples of R-tipping {{cite:42db0a1db8fa9ae3440d4957627ebc5b9117f652}}, {{cite:0f8fd3620e5055e7564f1dd51d28770ac5a33a99}}, {{cite:9b80e0b2227f129509b48a3a0801a1b645e0e1cc}}, {{cite:9d4a521632eee6f8fae6e562abef58d41c6f1538}}, {{cite:706078950e64d67c9b52936c22cbc01a147c864a}}. We show here that connecting (heteroclinic) orbits of () can be used to:
| m | b7f9f0e615402442ccd446e0e66fda8d |
Figure REF presents the results of fitting a PINN model, as described above, to Burgers' equation {{cite:e51f9900cc589717cffb82b1522dca7b9f2c7e5b}} using the L-BFGS-B optimizer. This version of the BFGS model extends L-BFGS to take into account the box constraints needed to solve Burgers' equation. The results obtained are identical to that obtained previously {{cite:e51f9900cc589717cffb82b1522dca7b9f2c7e5b}}. Figure REF presents the results obtained using the LM optimizser and are identical to the results obtained using L-BFGS-B. Finally, Figure REF shows the MSE loss curve for the LM optimiser over 50 epochs, with the MSE value approaching 1e-7, several orders of magnitude lower than previously reported MSE values, with the potential for further improvement. The application of the LM model required no hyperparameter tuning.
| r | 8449d79d72793b9143c11fcc087ca3ae |
fig:lada illustrates the pipeline architecture of LADA, where the generator {{formula:5c41bac6-8b98-4fb5-8375-1068670188d3}} targets to generate mask images that will fail the lithography modeling network {{formula:7d000a3d-17c8-49ef-accd-41d39eb36343}} .
For the best of LADA performance, we select StyleGAN-2 {{cite:57860f0b6662f3ff79a0b1f696bfcb96d145db26}} as our generator backbone and DOINN {{cite:6e0379da31b288a90a1f957d604177631f4ae954}} to be the machine learning-based lithography model.
However, their limitations require litho-dedicated design to make the whole framework feasible.
| m | 0ed880da1bde03bc8a4317f684e243ba |
Henceforth we
use the following notation. For a real matrix {{formula:c4951170-d2f5-4cef-893a-19c8d8dbbbb2}} , denote by {{formula:37bf1d1c-ba81-4354-a1a7-75d8f3cd5700}}
the transpose matrix to {{formula:96a50d81-15f6-429f-9e5e-72e34fc38678}} . The identity matrix is denoted by {{formula:5148c765-83a4-4fda-94a8-d73b80b23b32}}
and the all ones row vector is denoted by {{formula:cf27d1f6-caca-466a-947e-fd17a96acadb}} . The
determinant of the matrix {{formula:e8da46fc-af2f-481f-a6b0-fcef74cdea04}} is denoted by {{formula:e4d6aa71-d5d5-48e4-92ef-fa7c7beca295}} , or {{formula:e70f49b8-bac6-49eb-8e2d-7900eea8fbfc}} for
simplify. We refer to D. Cvetkovi{{formula:b9b3c009-0714-4b0f-b8ff-208dcf1f02cc}} , M. Doob and H. Sachs
{{cite:b192fe50225d94b581aa7287dfa0b784b37aaf24}} for more terminology and notation not defined here.
| r | 39b2dc4f9712964c802bfc6b6261aa0c |
Ablation Study.
To analyse the settings of sRender, we build two model variants by removing the stroke loss {{formula:180825b9-31a0-4fca-b84b-923379173862}} (denoted by sRender w/o {{formula:9a3c9bd9-fe98-4a82-a302-2be508e388b1}} ) and replacing sRender by Pix2Pix {{cite:d7139f2266c48ac77f4d2c71f3b9995d4caa413e}} (denoted by sRender{{formula:1f1ccd4b-e1db-43fd-8b50-4683346160c8}} ), respectively. We evaluate these models on the testing sketches.
| r | c5b88819289441f6d44382fb79981511 |
We demonstrate the application of our framework for boundary layer flows. Boundary layer phenomenon is one of the most important flows and is of engineering concern in many scientific and industrial applications {{cite:493a43c02cd7bf98af899dfe82d9abb73af8cba0}}. The behavior of flow in the boundary layer has implications on the drag force in ship hulls and aircraft, the energy required to move oil through pipes, and the distribution of heat in the atmosphere, and therefore boundary layer flows are extensively studied in the literature {{cite:ce1888938874afdc1dcdd267d37a656e80ec1b85}}, {{cite:307be36b68fd04be410e02b3b3275db82f38e24a}}, {{cite:f9beedfcf6fac212e81efc212453f8091a6bc7c9}}. Given that boundary layer flows are prevalent in engineering applications, building a computationally efficient and accurate surrogate model is of paramount importance for online tasks like boundary layer control to achieve lift enhancement, noise mitigation, drag reduction, and wall cooling. Additionally, boundary layer flows can be described using models that have different levels of fidelity spanning analytical models to direct numerical simulations and hence represent an interesting test case for illustrating the effectiveness of concatenated neural networks. As we will detail in Methods section, our multi-fidelity data-fusion framework approach consists of a concatenated neural network architecture where the self-similarity solution is a low-fidelity model and the Reynolds-Averaged Navier-Stokes Equations (RANSE) solver is a high-fidelity model. This framework can be easily scaled to large problems such as wake behind bluff bodies with information from many models fused to predict the high-fidelity data. While in this work we consider only two levels of fidelity, the proposed framework can be applied for blending information from various levels of fidelity. Moreover, the neural architecture search tools can be utilized to discover more complex and optimal architectures automatically {{cite:c26dc5a362b8d653623eeefdd2a26f1451b52cae}}.
| i | 24e133047261b8b21d64bc287f192d7f |
In deriving stellar radii, we use the Gaia EDR3 results {{cite:1e4547b8603ee9d44c97d57e4cb9940c84190152}} for the LB-1 parallax of {{formula:93808bab-afab-4197-a174-e7f9f082bf62}} mas, notably corrected as recommended by the recipe from {{cite:f3394c23fd7bcfe0aa9f4d9e14b7f2ee965eb439}}, which depends on magnitude, color, and ecliptic distance, and that for our target yields a zero point of {{formula:898257d8-1a11-4e78-ba82-c43a1b09eb6a}} 0.0511 mas. Such a correction does not include the effect of the covariance for small angular distances seen in the LMC data of {{cite:29966e901bbf6a03db832258444c2511083bb9b4}}, namely, the checkered pattern, and to account for it, we add 0.0260 mas in quadrature to the parallax uncertaintyThis is a conservative estimate based on the measurements for quasars of {{cite:29966e901bbf6a03db832258444c2511083bb9b4}}. It may be possible to refine it in the future using further analysis (Maíz Apellániz et al. in preparation)., resulting in {{formula:43012975-89f7-4668-b57d-d73477b56717}} mas.
Using the OB star prior of {{cite:24312abf8884ed83e74bc6651928b0d999fa3b42}}, {{cite:e8623a364b979c90d48ec1d79c698ed229ce350e}} this leads to a distance of {{formula:cf181a7e-e456-42e9-8de5-8c29efef15ea}} kpc, consistent with {{formula:c8b06104-46ac-430c-abe6-97aa63d93431}} kpc estimated in {{cite:49d367cd6cc9ce8797450c4dccb0e898554d9fa9}} using {{formula:f47068e1-e7b0-4306-8ae0-221ebf2a63df}} DR2 data, though with a smaller uncertainty.
The EDR3 data for LB-1 are now based on 26 transits, compared to 14 in DR2, and following the discussion in Appendix D of {{cite:49d367cd6cc9ce8797450c4dccb0e898554d9fa9}}, these new data also do not display evidence for orbital motion of the B-star {{cite:f8fb3ab2b38fef400aa6055291259aac020c9fe5}}.
The ruwe parameter of 1.22 still indicates a clean astrometric fit, while the image parameter determination quality flags, ipd_multi_peak and ipd_odd_win, are both 0, which is consistent with the PSF from the WFC3/IR image. However, while the goodness of fit parameter ipd_gof_harmonic_amplitude is on the high side at 0.09, this is not reflected in the WFC3/IR images mentioned in Section 2, which have negligible ellipticity. As discussed in detail in Appendix D of {{cite:49d367cd6cc9ce8797450c4dccb0e898554d9fa9}}, we attribute the puzzling lack of evidence for the orbital motion of the system to it being aligned almost edge-on and the particular circumstances of its orientation with respect to the sun and its proper motion vector.
| d | c57fa9f09b87a2d08a1b803e293bef0c |
Baselines: Baselines include one contrastive, two non-contrastive, one geometrical, and two whitening (redundancy reduction) baselines, namely, SimCLR {{cite:a6b58e45bafcde8104f570b977583c7dfdccd6ed}}, BYOL {{cite:e586b2d871de8aecb5b3cbc18db3bd36b35e42ad}}, SimSiam {{cite:b58e5ce0842700886fba935ca3d0d275d916bbec}}, SwAV {{cite:e02bcbebddced00f8d3fee43a390a27454bd0bcb}}, Whitening-MSE ({{formula:298fe773-db44-4d5d-9bad-0370939e0f6d}} ) {{cite:dd0686dfd925b9f3b657dd6670d8c099777029f4}} and Barlow Twins {{cite:1f986831bc80205e587ad4e77d4d7b4acfff7ff8}}.
For SimCLR as a contrastive baseline we followed the original formulation {{cite:a6b58e45bafcde8104f570b977583c7dfdccd6ed}} with {{formula:22f3386d-d03c-4114-ba23-def661a9841e}} . Following the original implementation of B-Twins, we set {{formula:79c52715-bbd5-4441-ac02-d4483d9d16fb}} . SwAV is a clustering based method representing very robust results in a number of settings. Similar to prior work such as {{cite:dd0686dfd925b9f3b657dd6670d8c099777029f4}} we nort-2 normalize the latent space in all baselines.
| r | 956fbfdec85b1f614757528a128bb58c |
Multi Task Learning. As shown in Figure 1, our model consists of VAE and geometric transformation predictor.
Inspired by {{cite:68f8df54e2f01cbdfd146670971b381d223e3fe3}}, {{cite:9c6225750bfbeb83754394f88f37f83f1a70c96c}}, the self-supervised learning based on pretext from geometric transformation is used in our method.
For training geometric transformation predictor, the labels {{formula:d402b69f-51b8-49b2-b427-566d4900d890}} are generated by rotation the sample in {{formula:17a58950-b56c-4fb0-8f6b-483ab443f9bf}} ] at random or translating the image by {{formula:88158bbd-4e3e-4330-ae00-76ec5cb1919e}} th of the image size in vertical or horizontal. The number of permutations of rotations and translation combinations gives the number of neurons at the output of the fully connected layer. The rotation and translation help in learning the global geometric features of in-distribution healthy scans. The geometric transformation predictor is trained by
{{formula:e1caa314-b6cb-42fa-9ab1-9c467c63dd0c}}
| m | 5ef64287f86a421c9e6cbfa438b42b4a |
From the results in the first group (the upper part) of Table REF , we have the following observations: 1) with the same model architecture, the full-sized MCAN{{formula:d52456c7-2762-4588-88a7-ae29d14dadbd}} model outperforms the reference MCAN model and another Transformer-based model MUAN without the DST training (Line #7 vs. Line #5 and #6). This improvement benefits from the synergistic effect of the weight-sharing submodel architectures and KD-based training strategy; 2) with only 0.38{{formula:4030243a-4c20-45dc-8dbf-dc01e91705db}} model size and 0.27{{formula:a79d1d4b-fb8b-4faa-b06a-96f06c4c046f}} FLOPs, MCAN{{formula:b51b1515-507f-40e5-b9a8-1b0c96f00c86}} is still competitive with the reference MCAN model (Line #8 vs. Line #6), showing the potential of width slimming; 3) by slimming depth to {{formula:0a0d9beb-4809-4468-b269-22df22925951}} (Line #9), its corresponding model size and FLOPs are respectively reduced to 0.6{{formula:8e74cde5-664b-499a-b384-49a1ff8389ea}} and 0.4{{formula:473e7237-009a-427b-8c87-fd580e870799}} of its counterpart in Line #8, at the expense of 1-point accuracy drop. Compared with MFB {{cite:a48cc3e9b973d726219946e690e6d40e718e712f}}, MFH {{cite:0711daac611800b39c4943bda344c69e50233648}}, and BAN {{cite:c3ed93d034474ffb54a7a34d51fb48db952d33b7}}, MCAN{{formula:af44a698-4386-423a-9075-a6bd10d2c44f}} achieves superior or comparable performance with up to 0.125{{formula:189b88fc-2a6e-478c-beb6-d701faf74e18}} model size and 0.05{{formula:c14e9204-3858-4a10-9a56-27f971f1f753}} FLOPs; and 4) MCAN{{formula:7f88f152-383c-48e5-b72b-1e8e63c7bf26}} still outperforms UpDn {{cite:04019ea46f4c3d9f8951b1c927d27ef4682a3c71}} by 2.1 points with an extremely small model size of 10M. This model size is close to the lower bound of MCAN, which includes 7.8M uncompressible model parameters in the embedders and classifier.
| r | e96229a81df71ab9d19ff0bd2bade786 |
Notice that as a consequence, the expected objective function {{formula:df29ec6e-5537-4ae6-bb79-a8a46d1a94b4}} and gradient {{formula:0539c78e-22d4-4914-b061-6918d9d85bf6}} are {{formula:9beb8725-a4e2-44f7-b453-46f4001a324b}} -strongly convex in {{formula:2f2492cd-930b-4713-a46b-5eb7e770e49c}} , and {{formula:90fa801f-f736-4296-891e-7255d75cc0ab}} -Lipschitz in {{formula:56f5d311-909b-4420-a6b1-004a9664e5ad}} , respectively. These are standard assumptions in the optimization literature. As indicated by {{cite:99e80b9fbd45a670b3c265984af57ac9b01d7c43}}, these conditions are necessary for finding a performative stable solution in ().
| r | 26f0ad98867cc0fb50559b5abf5dffcd |
Previous methods of OOD detection can be generally classified into two types: supervised and unsupervised OOD detection. Supervised OOD detection {{cite:bba6aa9964cb4d3edc8c5f214297c2fe472567eb}}, {{cite:7c7a70f57c27e133675d716d6cc34dea57117a51}}, {{cite:7fac1450b7411b28de039b278540d0435a62f58a}}, {{cite:b9c68509bfdd732fa42616f287f684628f4d0e85}}, {{cite:f277ebf3ef020d9067b4e48d2e63723481aa615e}}, {{cite:8e3fae45c807e3878d08cb77cd10304f979750f1}} represents that there are extensive labeled OOD samples in the training data. In contrast, unsupervised OOD detection {{cite:dd20a04d5280226252704ba786c34fd3e861c195}}, {{cite:0cafe5578d02036a06f721c04854d471a3bc2078}}, {{cite:feccf5c4e233a2d8ee70111a050e879466c40b4a}}, {{cite:c0e2db38419d89a6c2ec18cc2a0c6f936c4ea23d}}, {{cite:fe24284c8b83214211b67b1d2c06d01e01d3d86b}}, {{cite:e6568aab5e01ad9ec78ed92f3571c9c138edda5d}}, {{cite:2ae774c036c0d6ab369764877531fcacc5383094}}, {{cite:3d1395b5979bb48a676fd9bd5e434f9c2fec2724}} means no labeled OOD samples except for labeled in-domain data. Specifically, for supervised OOD detection, Fei2016BreakingTC,larson-etal-2019-evaluation, form a {{formula:c33be2f6-1d66-4b08-8adb-265646d701c9}} -class classification problem where the {{formula:f96f6095-7bcc-4ec6-80b9-e5463490c52f}} -th class represents the unseen intents.
Further, Zheng2020OutofDomainDF uses labeled OOD data to generate an entropy regularization term to enforce the predicted distribution of OOD inputs closer to the uniform distribution.
However, these methods heavily rely on large-scale time-consuming labeled OOD data. Compared to these supervised methods, unsupervised OOD detection first learns discriminative intent representations via in-domain (IND) data, then employs detecting algorithms, such as Maximum Softmax Probability (MSP) {{cite:0cafe5578d02036a06f721c04854d471a3bc2078}}, Local Outlier Factor (LOF) {{cite:e6568aab5e01ad9ec78ed92f3571c9c138edda5d}}, Gaussian Discriminant Analysis (GDA) {{cite:2ae774c036c0d6ab369764877531fcacc5383094}} to compute the similarity of features between OOD samples and IND samples.
In this paper, we focus on the unsupervised OOD detection.
{{figure:1c466731-944b-4df5-9963-80a0f26c0fad}} | i | 33f30eea8fbe0546ce6d08a36895556c |
A massive scalar field around a BH can be bound by gravitational interaction, and
it can extract the rotation energy from a spinning BH through the superradiance {{cite:01b06b4dd1b327aecc12ce602e05a16f7f9cd5f7}}.
When the Compton wavelength of the scalar field is comparable to the radius of the BH, this energy extraction mechanism works most
efficiently, and thus the field forms a macroscopic condensate around
the BH.
For astrophysical BHs, a scalar field with the mass in the range {{formula:223a6086-41c4-4057-abfb-37e67feb0909}} has an appropriate Compton wavelength to form this condensate {{cite:9e17a9c84136cfa8e173d2c6e608cd3e841f0c90}}, {{cite:807ef5686163a458a697bc1ac7000ff14d1ebdf7}}.
In the following, we refer to such a scalar field simply as an axion,
and its condensate formed around a BH as an axion cloud.
| i | 59720e4fe90faa75bc234244875dc4ed |
Since {{formula:9b8fbbd3-3a40-4299-aa41-93ab640bd334}} is effectively coupled to charged leptons, the muon and electron anomalous magnetic moments can be used to set constraints, which are presented in Fig. REF , being labelled as {{formula:7c514fb8-7267-4ee7-891e-6447167f3c2c}} and {{formula:4c98f219-f88d-45ca-afb8-c5f742b48f45}} , respectively. These curves are obtained by setting {{formula:661ebe45-4539-4955-a9b9-2c568b060251}} (5{{formula:d3d2f750-9201-4db1-87e0-97252c669909}} ) {{cite:6eff8451e76b40685dab6d6ad7f68d08f3376c4e}}
and {{formula:5c0dcabd-c606-4371-b14d-cf4e3b08573b}} (3{{formula:14ec5e60-600b-4da4-8800-549b5fe351ad}} ) {{cite:5d9c460fe0c1bcb844fd06afbe199468d01890b1}}
where {{formula:579a9382-344c-46f4-98a5-46e867fe5432}} ({{formula:b1955816-68cc-45ec-8b0c-79a5d9ba2bce}} , {{formula:3a2487e5-1d9f-4592-908e-fc4bfda00245}} ) is computed by {{cite:b61cb1a41113138468c885cc3b7163227b761675}}, {{cite:4f0c01793389d0219c0408c2d5028951d1f29e30}}
{{formula:f0076032-fa65-41bd-91f1-74de033fd91b}}
| r | d44f32757262395d63de052e83c15f82 |
We present in this section a variety of numerical results about the accuracy of Nyström discretizations of the elastodynamic BIE solvers discussed in this text. Specifically, we show far field accuracy results of solvers based on CFIE formulations as well as Helmholtz decomposition formulations (REF ) and (REF ). In addition, we study the iterative behavior of solvers based on the aforementioned formulations using GMRES {{cite:7cf80d6bb71011663b9779ec8de15774829cffbc}} iterative solvers for the solution of the linear systems ensuing from Nyström discretizations. While the size of the linear systems we considered allows for application of direct solvers, the iterative behavior of BIE formulations does shed light on the iterative properties of their three dimensional counterparts. Finally, we present numerical results concerning BIE based CQ solutions of time dependent elasticity scattering problems.
| r | 3df660bf765d7971072a15da74d984aa |
For some definitions and notation, we refer to the monograph {{cite:509aa0d5181e1964a547a5e1c26bda68d78af4de}}.
Given an ordered {{formula:f7db0daa-3904-45f2-a225-fd478348d4f4}} -subset {{formula:9627af2e-1798-4504-99b3-c608492931a0}} of {{formula:7c8b0dff-775e-45e9-ab4e-43b919853360}} , let {{formula:9615ac60-f1ee-4ac9-91fc-301087ca1249}} denote the step-function on {{formula:99bd13a2-3a02-47c1-9494-a1ee9c4a1ace}} with uniform steps of length {{formula:479c34e1-bf74-468a-8320-1d6cb420f436}} in each variable, and values given by {{formula:ed21ca41-70ff-431b-a69f-1a03b27e0d1c}} , and 0 on the main diagonal (this latter is in order to avoid having to use values concentrated on a null-set). Throughout this paper we shall assume that {{formula:57ab7d9b-fd62-40fc-9560-6c1dad681c87}} is obtained by sampling {{formula:7bb12058-ab7a-4b2e-9b4c-ee67d8fc995b}} independent and identically distributed points uniformly from {{formula:3ab99316-296c-4755-af8b-0547c10b6602}} , and then rearranging them in increasing order.
| r | cad333ecab1521794131ed1670207c55 |
Circular milling in this system has not previously been studied using the kinds of methods now common
in the study of active matter {{cite:1f82d6f1769a160e18478c0e3dfd96730c562814}}. There are open experimental questions at various levels of organisation in
this setup that mirror those that have been successfully answered for bacterial, algal and other microswimmer systems,
including measurements of flow fields around individual swimmers, pairwise interactions between them, the temporal dynamics of
mill formation from individuals, the flow fields around the mills and the dynamics of the mills themselves within
their confining containers. Here our focus experimentally is on the latter; the drift of a mill centre within a Petri
dish and the formation of binary mill systems.
| m | cbe72f5eee4768a0edb4e3094731e588 |
Finally, we can ask what theory saturates the stress tensor correlator bootstrap bound with less than maximal supersymmetry. In 3d, the {{formula:bb3fc401-b526-4e4d-b86c-d558b9219878}} bootstrap bounds were found in {{cite:91c30fb358abede3f264405dc13964d8cf7e4c44}}, {{cite:f3e83a54717c17adb303fa00b948485cdb06990f}} to be saturated by {{formula:e0247bcc-9683-4f24-915c-06fff48acbb1}} ABJ theory {{cite:c167551e451e4bd5f8b1361731416dc5fa97bba6}} for all {{formula:031e47bb-699f-4893-9344-95f3e9b62262}} , which has a vector-like large {{formula:aab51ce5-75ef-4cd3-950e-607ca5cf4303}} limit dual to supersymmetric higher spin gravity {{cite:f0db0147ebe1b460769a209f87c70b6238c40e86}}, {{cite:85eab6e69ff276de4f3f43f93057773d60e3f038}}, {{cite:02312dac7c403a456c7f3e1d7d57e1a389eb000a}}. With no supersymmetry, it was observed in {{cite:7b3be13d8a59fbb4b91431075a4573d55a3e502a}}, {{cite:6dcedef89126955f36c76ebf98ae1c3ba95bd82c}}, {{cite:dacef83a85ce8386b9394409b88cd2dbadb23b48}} that critical {{formula:00730164-c3f1-40be-a80b-6e53031e85c3}} vector models saturate the bound on {{formula:89469727-f29c-4bc3-a9c5-9a6e020f2673}} See {{cite:7942e2ab76b4394756fb6fc08e3eca26de8b89a3}}, {{cite:6b3d26399dc74c466e3c58094b7478eb152b343f}} for similar results on {{formula:ab716c8a-73b0-41f4-8101-b8cdab126e46}} critical {{formula:467a4a08-af00-4210-947d-058d6d7f5114}} vector models., so it is likely that the 3d stress tensor correlator bounds in general are saturated by interacting vector model CFTs. In higher dimensions, however, there are no interacting unitary vector models The critical {{formula:696adf49-0d6a-4da2-aaf7-4db72f0154b1}} vector model can be defined also in {{formula:45025c21-5761-4bc1-8556-c60488ffb962}} {{cite:49c0b633e4d15ad66e25ed6f56f8273e05c39cce}}, but it is non-unitary {{cite:5354971c0daa26301521ad1c420e96f8c95318db}}. Nonetheless, it can be non-rigorously bootstrapped with some success {{cite:aa6591b5441f5407aad7e49e0cfaa3eab9878955}}, {{cite:204741f22fb45fcd18ccfafe965bc10dcda50d3c}}, {{cite:4f3d9d53d179a827d04bc4dc85ebe187189d6900}}., so it is possible that the most general non-supersymmetric stress tensor bounds could be saturated by pure AdS{{formula:7487f0a1-b2b0-4182-b8b9-65857439f1fe}} Einstein gravity with {{formula:aa5fea19-3feb-4761-8d8c-a4908cba0a2f}} . It would be fascinating to check this by generalizing the non-supersymmetric stress tensor bootstrap in 3d {{cite:7b2cd500f0fa499fffa29d3fc3b889691cca5870}} to higher {{formula:30ca4b7b-c25c-401d-97e0-db722704d9a6}} . If such non-supersymmetric pure AdS{{formula:3bc2a953-6155-483c-aff0-703c5c7921e6}} theories exist for any {{formula:d2532c0b-a371-4776-a1af-0db5778e86b1}} , then they suggest that unitary interacting CFTs can be constructed for any {{formula:72ee1bfb-c875-4827-a469-caf5cf7bffc0}} , unlike supersymmetric CFTs which only exist for {{formula:e30849f4-d5ac-4c55-8ef1-109435201e27}} .
| d | b50d0bf94c0f03501ad201b3b41153f3 |
The goal of our experiments is to display the effect of our proposed pipeline and model correction method. We demonstrate our work on one toy dataset, decoy *mnist {{cite:7fb95d88d462f6ec8ed719b9deab7e397df813e6}} and two real-world datasets, Dogs vs. Cats {{cite:f1facfcd75a9178dd53114d5b963489897cc63d2}} and *isic skin cancer {{cite:48a18d6cc9587f5f5091c664c9b61af63edaea67}}.
| r | a8798819441272fc8d3be204da2aad0d |
To verify the performance of the proposed method, we consider a simulation scenario that the mBS is located at the origin, {{formula:d8400b69-86d8-4c05-bf8b-7abe58edea01}} IRSs are located at {{formula:e126914f-dc7d-4ffa-98c5-8bc26704fd19}} , {{formula:dc32592b-4b86-47e7-9d42-4d3563578208}} , {{formula:4ea8a323-523a-40e7-8bce-9b527fe64e71}} , {{formula:67eb3428-dc96-4426-98d6-097e5b607bcb}} , {{formula:a18749d1-5a15-499a-916c-8994b6ac2cc4}} and {{formula:a09dbfd2-9de3-4d35-b604-7ebb0d69f8f2}} , respectively. The users are randomly distributed in a circle at {{formula:8c5f8db4-7c96-48cb-9999-32488507238b}} with a radius of {{formula:0ce1a0e5-9c9d-4089-9ce1-1b26945f5621}} . The number of antenna at mBS {{formula:a25325ec-1d1e-4288-a19b-d972ed249de5}} . According to {{cite:84d9aa4ae09e0aa2aa1efe4986e482c53ff20228}} and {{cite:0711587ec0062408babf5e0a4a4f8c3d633016e4}}, the channel gain is generated as {{formula:99e43ca8-b8f3-4ee9-a3e3-f34b03ae7d4c}} and {{formula:cc74aca2-6cec-4648-b04e-e48e11802865}} , where {{formula:ec516ac4-a7f1-4b74-a4fe-197bf5d84734}} . For LOS path, the values of {{formula:7755e474-fbaa-48cd-af22-39f71e5c897f}} , {{formula:90ada5aa-e422-41d2-a6b2-eb21d93ac264}} and {{formula:181d4045-d7fa-4eed-93a9-b50fb4f45752}} are respectively setting as {{formula:a3592972-c2c8-404b-ac7c-5f2fa91182a8}} , {{formula:50d2db55-58fe-4c8c-8ee1-5fb416661eae}} and {{formula:585792f0-d93a-4cda-9633-9014e6be3323}} dB. For NLOS path, the values of {{formula:56a58060-54fd-4f85-8c37-7f94c279b928}} , {{formula:f5131688-45c8-4308-aa7f-84f0cc3f43bf}} and {{formula:41fc7a38-bac0-4f1f-a7d4-95acd053bf12}} are setting as {{formula:5c5ec11d-d591-4c42-979d-7eb3f6b4fc03}} , {{formula:3004ad7a-73d1-415b-84e1-679a45df8be3}} and {{formula:42f8951e-32cc-4d49-a1a8-0413b390b4d4}} dB, respectively. The generation of channel complex gains {{formula:de6da7f8-a27d-438b-807a-8b6b807d0d34}} and {{formula:59f9cda9-9967-4abd-a6ac-53ace4f2970a}} are similar to {{formula:5dfb402f-11a9-47d1-9f69-5ff299bedd0a}} . And other parameters are set as follows: {{formula:d775a77a-58aa-48f2-9a8b-cc95028ca82f}} , {{formula:3f209cfd-8759-452f-9751-f16755dec3ff}} , {{formula:ed2dc388-e773-41e9-aeef-4fc60e3b4160}} dBm, {{formula:5f314783-d704-4ecf-97a3-03205607db1f}} dB and {{formula:6d7c1f81-5a06-45c4-9f2a-5dbd17817523}} dBm.
{{figure:f330b273-cb50-43cc-af57-d801337e3fb3}}{{figure:27536fc6-05d2-4268-a715-cde789a2c058}} | d | adc299ec53a4c86b8a118678850ff14c |
To demonstrate the effectiveness of the two-stage training strategy, Table. REF illustrates the overall classification performance of VGG {{cite:ab46048021689ce2ee7447742f4679872fc14d67}}, LSTM{{cite:b131ea01d67d2cf7c8a5a274aa5271f97080c114}}, ResNet{{cite:ab46048021689ce2ee7447742f4679872fc14d67}}, and MSNet. The first row shows the models without the two-step training, which means that these models are trained with the joint supervision only, and in the second row these models are optimized further with the second stage training (with the softmax loss). These models achieve a gain of {{formula:cedcf47d-03c2-422c-b984-2e37c8137222}} %, which demonstrates the obvious superiority under the optimized results of the first stage training. It can be seen that the well performed models such as ResNet and our proposed MSNet only achieve less than 1% boost in accuracy. This is because the softmax loss in the second training step (S2) mainly focuses on learning separable features. For the well-designed models, they are more capable to learn separable features (as MSNet shown in Fig. REF (c)), and then, during the first training step (S1) with the joint supervision, the features are already both separable and discriminative. Consequently, the two-stage training strategy may not help much for the well-designed models with a high accuracy.
Moreover, for the complexity of the training processing, the two-stage training can be treated as a process of training (the first stage) and fine-tuning (the second stage).
In the first stage, a constant learning rate is utilized to learn both discriminative and separable features by using the combined loss of the center loss and the softmax loss.
Then, in the second stage, the softmax loss is used to further improve the performance.
The second stage of the training process often overs within 5 epochs, which is equal to the required epochs in the process of reducing the learning rate and fine-tuning the trained model.
Thus, the two-stage training strategy cannot increase the complexity of the training.
{{table:4adebb13-b9fa-41ce-83f6-243a93b144a3}} | r | 58e51ba17e7f3959ce606cc79e7fbd11 |
Transformers {{cite:eb692d7862be17664d006f99d232c4d674de28a7}} have become the state-of-the-art model for sequence processing tasks, solving many challenging problems in natural language processing and computer vision
{{cite:7e0731b9842aafbf4371c1b22cc7193360352837}}, {{cite:458b91a9d74ecf2e0547b21f7b3feb00530846a6}}, {{cite:743703202e9b1f9c34130c1dbe8adf1c8748638e}}, {{cite:5be7416923652ea629dd5903b8b05c8ebcab4466}}, {{cite:c422afe03fc4fcbce993b97b93065f67c1597f67}}, {{cite:7668bad589690973e57aea214fbb4e02f8ab86a9}}, {{cite:a5912dcc5746488e58e29450303aa67249bcdf42}}, {{cite:a9d9ff33ce74585625c20db639301393a3a54f92}}, {{cite:f6f89afc2bd20f65662719bf50ce80bf2e53391c}}, {{cite:615b200fa3349e75755c5d24fc7dac3275634a1e}}, {{cite:53142a551a0aea4373e15490b5447ddce1de64d6}}. These models can also transfer the learned knowledge from a pre-trained model to task that involves different data modalities and has limited supervision {{cite:b2c0ce164f7a78c26974aaffae5fbe7652d1c9fc}}, {{cite:1b71db701c38eb73c60c1c8f69c69c454ab233dd}}, {{cite:5be7416923652ea629dd5903b8b05c8ebcab4466}}, {{cite:24d84fd9cf10fd862a212bd2c6494a99db6475a3}}, {{cite:a22c86f4d7b328747ca4630ef1e6c8d6da349d1d}}. The success of transformers is rooted in the self-attention mechanism as their fundamental building blocks for modeling {{cite:e494f4c30bdbade45319605811244e1180c64752}}, {{cite:70d3733505b9321f8c86158bcb6b2c2c7304c934}}, {{cite:7b2b9573e05d356b0f6f40c499763a54b415bd5e}}. For each token, self-attention computes a weighted average of the feature representations of other tokens where the weight is proportional to a similarity score between each pair of tokens. This mechanism allows a token to pay attention to other tokens in the sequence and attain a contextual representation {{cite:f83469e59ae40d736a23a35081e5df30227ae0c0}}, {{cite:eb692d7862be17664d006f99d232c4d674de28a7}}, {{cite:0995ad5f49f2caf99a0156e908be3bccaf4ab080}}. It has been shown that the representation capacity of the attention mechanism {{cite:7b19be426079b09cef457ddc5d750913ddeb88d8}} and its capability of capturing diverse syntactic and semantic relationships {{cite:7b19be426079b09cef457ddc5d750913ddeb88d8}}, {{cite:f4f3b702ce08ce8cdf9381dbc6c93b1f3a7bf9d8}}, {{cite:9f5bf02c0c4aae6382228b867f5a7e806355fef6}}, {{cite:7266692af1d994bf400467ea79e4b79e7accf459}}, {{cite:ce9052fd6b212acd55e743d7bcf7f3d2b604c957}} is keyed to the impressive performance of transformers in practice.
| i | 18f549e7dbc8d0e1fe79efeff21161d2 |
The average CIFAR-100 accuracy of NB201 networks is {{formula:9a215a94-f8e6-4c67-af6c-8df924a29894}} , whereas that of the networks in the subset selected by C-BRED is {{formula:ed3504c5-4546-4c84-be7b-951545d5ae95}} .
To validate this preliminary evaluation, we compared C-BRED to two subspace selection alternatives.
The alternatives we chose partition NB201 into five subsets according to the {{formula:b50cc859-d5ca-4a88-b80a-166f52012f35}} quantiles associated with two statistics: the NASWOTv2 statistic and the number of MAC operations.
We then used the NASWOT technique introduced in {{cite:7ea395216c65289ea8809b3570ee172254b8d383}} as the reference search algorithm.
As can be seen in Table REF , C-BRED has superior performance in that not only the average network accuracy is better, but it is also more stable ({{formula:4477c7a6-1a00-40a0-84ed-dc436c75de02}} decrease in standard deviation).
{{table:debb6dc9-6890-45c9-9fef-2306c50cae21}} | r | 3f605080bb413565ac6fe79b0319358c |
In {{cite:73739700678e4c729343db52e06a336399e670ce}}, Montanari introduced the class of incremental approximate message passing (IAMP) algorithms, which are a special form of the well-studied approximate message passing (AMP) algorithms. We review these algorithms in subsection REF . The work {{cite:5b7d3e2f06a8a9c4c191a9c8d76029bef573eb7a}} showed that the maximum possible value of {{formula:a84dfa59-ba69-4b66-8ec9-e866b0b4f777}} achievable by IAMP algorithms is given by the Parisi variational problem minimized over a larger class of non-monotone functions. This larger class is:
{{formula:c06dd737-7873-4ab1-8420-e7bd7e7d7d2b}}
| r | 6b8feeada103401cda1b9f9e5616bb70 |
In {{cite:5075b91e8887f1ef6b17668629f059e4ebda576d}} 39 different high-pass filters are proposed,
which work on the grayscale version of the original image obtained by standard conversion.
All such filters are extremely simple,
since their goal is to highlight minor variations w.r.t. to typical behaviors.
Typical example are the first order horizontal linear and symmetric nonlinear filters defined by
{{formula:0a4d44c4-772f-43cf-91d9-6be816f6f22f}}
| m | 855b8bcc5f7e6ed9089f898a7e3245ef |
Interaction with a squeezed thermal bath is not the only generalized process
that goes beyond the typical settings in classical thermodynamics. Our findings demonstrate how to utilize the squeezing effect of bath as a
resource to control the irreversibility, where the use of nonthermal bath
offers more degrees of control and manipulation, such as the amount of
squeezing. Note that quantum bath engineering techniques has become powerful
tools that enable the realization of arbitrary thermal and nonthermal bath,
for instance, experimental realizations of squeezed thermal states
range from superconducting circuit QED {{cite:1faeac65874ad5f546d41b40bda5d72b0849ab2b}}, {{cite:a08a660adddfd9c7c7bc994e9a26a82cfdf78e43}}, {{cite:12cd676b8ee58b93b169c91d2ee0ae06eca4c1ca}} to optomechanical
mechanical oscillators {{cite:b3540abf9d7b4187d1f94e913915363c02a5e343}}, {{cite:06608f49d3145a69c75d7c873272aa08eabb5ba2}}. The key parameters considered in
our numerical simulation, such as the inverse temperature {{formula:015de397-c667-4c60-a321-f350af9a4b01}} and the
degree of squeezing {{formula:6d7545b1-75cc-4057-8cb8-fc2beaeac2ee}} , could be experimentally controlled using the
current technologies demonstrated in the above-mentioned experiments.
Additionally, there have been many experiments focus on the assessment of
nonequilibrium thermodynamics irreversibility using the technology of
quantum trajectories of stochastic dynamics in nuclear magnetic resonance
setups {{cite:61ba0c24f78e486dfe8b58919a2ffd2b8f0c50ab}}, superconducting qubit {{cite:53f1e7c9520600bc6e2eefa89d972cb05c7e1aca}}, and mechanical resonator
{{cite:6e548fdabd55c3b7385ee0be5f8195c7f762a347}}, respectively. Our results reveal more detailed properties of
thermodynamic irreversibility that are stronger than the conventional SLT,
for given a restricted class of irreversible processes. Along with
other studies addressing squeezing effects in quantum thermodynamics, we
hope that our analyses help to unveil the role of squeezing effects in
quantum thermodynamics devices.
| d | 28e6893fe21b31024466e85c408f371f |
As with classical community structure, there are many possible
definitions of a quantum community. We restricted ourselves to two broad
classes based on transport and fidelity under coherent evolution, both
based on dynamics, though in the limits considered in this paper the
closenesses and thus quantum community structure can be expressed purely
in terms of static properties. We end by briefly discussing some other
possible definitions based on statics (the earliest classical community
definitions were based on statics {{cite:68b80735836d5c750e575535092b2dae18b5d2d9}}).
The first type is based on some quantum state {{formula:cfa70dc6-9aac-422e-beda-13215dad45d5}} , e.g. the ground state
of {{formula:44dbdbf4-b2b4-42ba-8803-e814446e8441}} . We might wish to partition the network by repeatedly diving the
network in two based on minimally entangled bipartitions. This could be
viewed as identifying optimum communities for some cluster-based
mean-field-like simulation {{cite:4adc261144a312db3c7145d070d7562273682341}} whose entanglement
structure is expected to be similar to {{formula:8b6929b0-eee8-431b-81ef-0597512433f5}} .
The second type is based directly on the spectrum of the Hamiltonian {{formula:e52613b0-6a14-46e9-a0e0-b75cfe9004f1}} .
We might partition the Hilbert space into unions of the eigenspaces of {{formula:323d1a75-4461-4c2d-83c4-d04b8e9ce6e6}}
by treating the corresponding eigenvalues as 1D coordinates
and applying a traditional agglomerative or divisive clustering
algorithm on them.
Note that the resulting partitioning would normally not be in the position basis.
| d | 56ec801f5181812a491e50f83fe3bc30 |
Most existing multi-person pose estimation methods follow top-down pipeline {{cite:50319b2831530690fecf418819929b2b5a00a07b}}, {{cite:6daa9d138a8459690d11013fde8a5c8218db29f1}}, {{cite:5e6027b5cd1ff779afb82849be33a07b4fd21137}}, {{cite:701cd4e30337caf6cc27d63b317d73922253e5c9}}, {{cite:294c62d9e1c241ec3c4459261d21ff08f6389d5d}} and bottom-up pipeline {{cite:6aa950cc770814412b7ff9eebf84ea42c8355267}}, {{cite:89a1419a133aa48eea02451c8ed3a9bef0dc6d0f}}, {{cite:8bd3679b3bb8ce7548592708eea9d8ee2305cbde}}, {{cite:0afbe0410846b4446c8e94393dd9e5334810c22a}}, {{cite:c228472f591e9f0b6246d71a7eb7d62fa88e00a4}}. The top-down methods firstly detect the region of person instance via object detector {{cite:32d05b0c77b8da03d855a2ad0fd88ac70e67dd95}}, {{cite:669cf026a22bd8d04a9fb904f496e3ab39e4c93f}}, {{cite:1c69f4257872e119fe914a10beec8c6db8778a5c}}, then perform single person pose estimation on the cropped human body regions. Generally, the top-down pipeline is limited by the detection-first paradigm which leads to high computation and memory cost. The bottom-up methods firstly locate the keypoints of all persons in an image simultaneously and then assign the keypoints to individuals via a grouping process. However, the additional grouping process is computationally complex.
| i | 98bfd70ac0fb74d5c54c9ba22928d4c0 |
In this work we proposed a new image-to-image translation network that is able to synthesise CT images from input MR images by gradually reducing the error using a separate boosting network. We validated the advantages of the recursive boosting model using a four-fold random bootstrapped validation with a 80:20 split that showed that the average difference between synthesised CT and ground-truth CT images was 68.6HU {{formula:f5550c69-b76a-410d-8062-e21d9c8f83ff}} 15HU, compared to Burgos et al.'s method that achieved a MAE of 131.4HU {{formula:3a663223-5f9c-47c2-b081-5e810880bc17}} 60HU. Other deep learning approaches reported a MAE of 92.5HU {{formula:5df7a327-7cec-4520-8371-e75fe5d9c76c}} 13.9HU {{cite:2ba003c7b7cd173d379776ba4fc904b13e0f3954}} and 84.8HU {{formula:d80e9821-8f25-49bf-9b11-8cf2a6b79d50}} 17.3HU {{cite:8d3a55f89e60efca4b2019d2ffee6b642c416abe}}. However, while results are not directly comparable due to differing data, DBR reports state-of-the-art results on MAE among other deep learning approaches.
| d | 8947344db8f9ab17e38b0aab9b8433f3 |
3. Related works.
The possibility of reducing the MFG system to the matrix Riccati equations has been known for other models (e.g. {{cite:cbb4e6bbd45963603cb1bc78b691ee5c08e89a41}}, {{cite:4085bbbea26712ef8262c8baf3bacf5834eb5dc5}}, {{cite:dcf795283034d1a3f1c014e200005d1e4cb04c20}}, {{cite:2dbbe53468c5b9782eed2ecad8a8f17e52887dfa}}). In {{cite:cdc52c2d799fa9699e685de6dfee968d64c5f947}} the authors obtain the equation for the mathematical expectation and use it for the analysis of a model of trading. This equation also is a second order ODE with constant coefficients. In {{cite:aae17e9a20e7022d6f8e2a8f7aef645fc8d015af}}, {{cite:7a53f04b1fdd41d32cf1af95bea95c8e506ee445}}, {{cite:e92155fbfcf247482b9b05a0de5dad6737e7b5dd}} models with underlying jump-diffusion were considered.
| d | 9982af4848bf5b002ef8bc744d8956dd |
Diffusion-weighted (DW) nuclear magnetic resonance (NMR) methods are highly sensitive to {{formula:3c80c741-bcf4-4eb9-8339-82070b31ecc9}} {{cite:c3949e1b4a6cb196492675b048ab343b57a84642}}, {{cite:c7b21e9ab14ee06453c408f7ae7b2b79f0076e90}}, {{cite:d54eecacd68a83822da12411d758caf019345142}}, {{cite:b91db018b887484614b6f619ff09b20241187815}}, {{cite:78256e8dc856a9f77947ea6a8b2bddb4eca872ae}}, {{cite:020223108fffff006f95dc08bb1f84bb63be606a}}, {{cite:e4f6c3b69ec7ed88f20192e1cf31177c3607eccd}}, and provide a powerful means to probe rich {{formula:6ae7aeb0-af3a-4218-b8c2-a1266a2a9366}} behaviors and infer distinct microsctructural features. DW-NMR experiments have been used to study the short- and long-time {{formula:30a1f5f5-f999-4552-bc2b-c25aac81b00e}} in porous media ranging from sedimentary rock to skeletal muscle. {{cite:ac586783cdfc3a80d6274730d0c3170636236d97}}, {{cite:d98a81dc16b5b2f76d90f4f3acf7aa6e1acc5930}}, {{cite:9b30083c2d3f4c7735ca588d5ea5c5082d5767ac}}, {{cite:9e5fc4e23c4998a68c6a2ca7d736d3519be3322f}}, {{cite:a0948776601f7d4a0ed235f7de4c11dbf59fe050}}, {{cite:54d147d86ee3bef00e6242a20627954e995d84e4}}, {{cite:6f73c1dbe6aa5f340dcacb0ab805a38f5658c445}}, {{cite:b10279de2ea544fcf21c98d26bbb4092240d4ab1}}
| i | fe713131667f4eac8c226af702d2dd42 |
We use the Levenberg-Marquardt algorithm in {{cite:dd46c29d5345e8c4b312e79e02a2d8da46dd5d57}} to solve problem (REF ), which takes advantage of the steepest descent and Gauss-Newton method. Let {{formula:55ca56fa-4a52-4bae-bcb4-56f0ab8e01d8}} and {{formula:06219248-79dc-43ff-b86a-f27adf0e8805}} , where residual {{formula:176b495c-8d6d-4cb4-a83b-b9b554721718}} .
The LM algorithm iteratively updates the value of the estimation of {{formula:028c4ad9-64c1-4d41-b11a-844f98a38e3d}} by solving
{{formula:d9a181ad-f929-4dc3-916a-e659c12ab7f5}}
| m | 7ac368a18dc9424c41ab202c50b81bcd |
The set of parameters {{cite:f3cd306c5e52cffd11da36e4fb8c196c7b158f32}}, {{cite:6459c3c19c8df2929e863ecb9141d24a79d07f7c}} are varied in the range of ;
| d | 5e2ef631da2f542b254bda2420cab1f1 |
The seminal work by Bennet and Brassard{{cite:1db30661977bb78fa0a054ff9f614f6664800625}} single handedly pioneered the study on quantum key distribution protocols. In {{cite:1db30661977bb78fa0a054ff9f614f6664800625}}, the authors designed a bipartite key distribution protocol where one of the parties(Alice) prepares a qubit in one of two conjugate bases{{cite:23170f0ba5d974886daa5f0d0da8a44eb5312b05}} and sends it over a public quantum channel to her counterpart(Bob) who then measures the qubit intercepted. After repeating the preparation and measurement procedures sufficiently many times, the parties reconcile their measurement bases publicly and retain results corresponding to only matching bases(i.e., outputs obtained when they choose the same basis) for further processing. Since, the communication is made over a public quantum channel, any third party (Eve) can intercept, measure the qubits(sent by Alice) and then send some new qubits to Bob thereby posing a threat to secure key generation. Presence of eavesdroppers can be detected by Alice and Bob who who then abort the protocol. Detection of eavesdroppers and successful key generation between Alice and Bob at the end of BB84 protocol mainly rests on quantum laws such as no-cloning theory, measurement induced disturbance in quantum systems{{cite:bc9485e179b9ac0d011987cbfa0cd9f8325888f3}}, etc.It is important to note that the modus operandi of the BB84 protocol depends on preparation and measurement scheme. Several key generation protocols{{cite:325d48cb42416ddbebab34e720679793444bc25d}}, {{cite:f4dc2d62868f6bfe29be9a6fbf9e71c2c2dec28f}}, {{cite:33e82c58b6b9e2190a5c2a494844e8103525efcd}}, {{cite:5086be4e5de9cdcf4f472d06eb672975f4dbffbd}}, {{cite:24dba60b94f2db48d051da6f0206c25e02457df7}}, {{cite:ec63f74151fa96dd461dc7900742b09a55bf6a74}}, {{cite:4d155916b0f42d0c7736c96430e690c351d222aa}} based on this scheme have been designed since the BB84 protocol.
| i | 03a4580331f039ebd3160387f987d80f |
In this work we simulate very scarce data scenarios. We train binary VAE and RBM using all the available samples. Details
on these models can be found at
{{cite:4d040e32b00121a773afd332388d57b66afb4b0b}}, {{cite:22c9e5673958f18fdf8a1af88c1ac79eb7f0c5f2}}, {{cite:98a6b4b954f8e7dd6f0982246aff0f8b6b258797}}. Once these
models are trained, we perform a sample generation following a MCMC procedure.
| m | 25fa6391847af4cc7ae72124d99ada42 |
In the field of image hashing, many direct discrete optimization methods, such as DCC {{cite:12f87282adbfcd5e3163ac7d8a5767ccfdbe0e50}}, SADH {{cite:684a45f8612f331a3f4d7cc2c3e9faa6aeb195e9}}, ARE {{cite:79b551fa2fc708c4a8dd4bd8c3e561bc8160da42}}, ITQ {{cite:aa8b179d0be99a9f29014c280cd481129ef25ccc}} and FastHash {{cite:c5613bb155a501330e575b1e268ba81eb2b89dd5}}, have been proposed, which aim to optimize binary variables directly (SGM can also be seen as a discrete optimization method). For example, the Coordinate Descent (CD) method {{cite:13f66e5a2b16ac1c08b03456cafbb9f66627b144}} is widely used for solving optimization problems with smooth and convex constraints. Motivated by this method, several discrete cyclic coordinate descent (DCC) methods (e.g., RDCM {{cite:9ab1ffe8ea9af6fd04d4ca7324dd38c9be647a8c}}, FSDH {{cite:dc0cea3890e23454812fb4c7d784bdec4ae71b07}}, and SDH {{cite:12f87282adbfcd5e3163ac7d8a5767ccfdbe0e50}}) have been proposed to handle the binary constraint directly. The main idea is that, at each iteration, a subproblem with most entries of the binary variables fixed is considered, and the loss function is minimized with respect to the remaining entries.
Although such methods can work well for specific loss functions, most of them are usually difficult to be extended to handle general binary optimization problems. Furthermore, they often suffer from expensive computational costs.
| m | b152e1152711a3427ec6e4ac901092f0 |
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