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We applied the proposed scheme to the Flickr8K
{{cite:493e1a1971484e169c4b71b6699c67aeac5073e4}} dataset, which was split to 1000 images (and
corresponding captions) for test, 1000 images for validation, and 6000 images
for training, following Karpathy and Fei-Fei {{cite:bd2fdc63c82c4123fef0a5be184fc9b4daf1f3ff}}. We used a
batch size of 128, and applied the proposed semantic embedding to two
backbones: the one in Tables REF , REF , and the one
based on the VSRN {{cite:78ff59fa18d27f8698c67ad4ae6bcdf72bdac4c5}} approach. The retrieval results are reported in
Table REF , where we separately compare the results of CNN
trained with different backbones. It follows that the proposed approach
outperforms all previous schemes in general, and improves over the
VSRN{{cite:78ff59fa18d27f8698c67ad4ae6bcdf72bdac4c5}} and other backbones by an average of 0.6% and 4.5% ,
respectively. As for the number of centers, we tested several configurations
and the `sweet spot' of 100 centers performs best, on both validation and test
sets. Qualitative examples are shown in Figs. REF and
REF , where an image annotation failure is shown in Fig.
REF . We note that although the caption retrieved
first in Fig. REF is incorrect, it seems to adhere to
the caption.
{{figure:7a6ab9bd-8227-4d93-ac3d-308432379e15}}{{figure:61ef009a-c7c5-4467-9fed-d59973c06927}}{{figure:0722c30d-dd0b-463a-8b13-f683264c44a5}} | r | 7944296b25e8c79dc6c895b31aafa5a9 |
Similar to the previous reports in other systems {{cite:f4102c41115694a5ce6954c9838b8327ea1f9e76}}, {{cite:b85f0da5ebf236758101002315deb86b965ca71c}}, {{cite:4b7e4da77a53e5766657b4e48dd1092760939fb2}}, {{cite:b7d07c7c07bc889c6deb2a1acda5fd5702ec723a}},
the {{formula:de1c64e4-2c28-43ec-a24e-23b821461a83}} -{{formula:a323ca96-5acd-404d-800d-d999256ca66f}} data in Fig. 2(b) in each small temperature intervals can be analyzed using the conventional power-law scaling
{{formula:795e84e9-b581-4dda-b702-187f5751c2ed}}
| r | 678d19cb9eb7ef2a96f2cbf66ac96d18 |
Lemma 5 (Convergence of an approximate entropy-regularized NPG, Theorem 2 in {{cite:22afd7451b0a0f8cbec1fb223da2347088b71b21}})
For any learning rate {{formula:2c4cbd37-10a7-4383-b247-72b9e2f40860}} and any {{formula:0e88468e-aa0f-4778-87d6-8a7a6ba93f9e}} , if {{formula:a9473131-4ccf-4115-9be5-cbfe05e1baf7}} the entropy-regularized NPG updates satisfy
{{formula:59f3b796-c32a-47ba-b2b8-fa6c50694fbd}}
| r | c87c82efcc3fd4ce62aa378bf7709464 |
One common approach is determining a single metric in controlled experiments. Researchers put significant effort into the operationalizing the metric that can capture the “success” of explorative tasks (e.g., false discovery rate {{cite:7fb1486d28047d451376a10428ec77acda892b3f}}, interaction rates {{cite:c4f720898ebe529f9226432591a4c3ec3a4374aa}}), yet consensus has not been made. Plaisant argue that relying solely on controlled experiments may not allow builders to fully capture the degree to which a particular system can support users in a natural environment {{cite:85ad8e10e109d93f43103422947302cb622750e9}}. Another concern with controlled studies is that tasks to be examined can be artificial and coverage of possible use cases can be narrow when conditions are rigorously controlled. Doshi-Velez and Kim explain that when humans are involved in the evaluation, the tasks used for the evaluation can become “simplified” {{cite:1640e1735d5f6c6a1e76fb421496a163b778b497}} and may not reflect the complexity of ML-related tasks in real scenarios. Ren et al. discuss the difficulties of deterministically arguing one's treatment in a control experiment is always useful in realistic use context, as their findings suggest that useful information and information in investigating ML models is highy context-dependent {{cite:01ed89e49667ac45496d3bc749a491df1d8cc7c6}}. Another methodological approach is using a case study or some usability metrics that are heuristically developed, such as NASA TLX {{cite:53fc5e44946deb6763ae0e44ecb0f04f15beee48}} and System Usability Scale (SUS) {{cite:b82b654f196fbb1d0e49ed076bdb0b5e0ab669f6}}. However, the general consensus in HCI community is that the insights drawn using such evaluation methodology can be often not specific enough for drawing insights for improving the design {{cite:d697301eb69cccdbb4482c881ce48212bd1b049c}}. To fill the gap, researchers have dedicated effort into creating visualizations that can better measure the behavior of users engaged in exploratory tasks or empirically understanding how professionals such as data scientists perform ML-related tasks. For example, Battle and Heer discuss the importance of considering “interaction sequences” and especially “behavior graphs” {{cite:468691ab439a826c12b417b77e3f8331d63be23d}} in analyzing the quality of using a system in the domain of Exploratory Visual Analysis (EVA). InfoVis workshop related to visualizing user interaction logs identified a series of visualization approaches as well as open challenges {{cite:e2079591ec4c7fd96e90f2a4f6b3fa78c899e33e}}.
| m | d5b94c64ed685343b3389df7f1ac2d48 |
Second, the epistemic equity of the models used to guide clinical care – our concern here – is obviously not the only kind of equity healthcare must consider. Unwarranted variation in clinical outcomes may arise from a wide diversity of procedural, cultural, social, economic, political, and regulatory factors that operate outside the realm of evidence-guided practice and need to be addressed independently from it {{cite:3d510bbffd1f29f1ed204c9704a93c6817220de6}}, {{cite:3fc2f999d77fb691808ee033f3e47a8cb8311229}}, {{cite:0210a18a7b353fb05690d0fccddeaff0a7e87c8b}}, {{cite:c7f4e61419acb0db242ead5e54cec30e41305573}}, {{cite:794256c48edfb02dfe06cf11f9bac2089934b1e0}}, {{cite:27132302dfc30a784f4953688cb30c79ac16b882}}, {{cite:cc86bea59a03bfb47d51affde00e1a928b011c99}}, {{cite:e2822cc4c7101f86ffb9c9060d63c63f01ab295e}}, {{cite:93b0795fc2abf8fd916803bf8338b323b3076fb0}}, {{cite:8a69bbb5736c2210ac7e636c351a895939d2521c}}, {{cite:53397dd6ff5edf7afcc387999e04d994853fd1bd}}, {{cite:506fc93f479476dcf4bce820f8e8d87b8ba04437}}, {{cite:3fc2f999d77fb691808ee033f3e47a8cb8311229}}, {{cite:29928fb6d13294bcd0cc78bbcafb5e9f05dace58}}. In focusing on epistemic equity we are not denying the importance of other kinds. But since action proceeds from belief, and belief in medicine strives to be objectively evidential, detecting and quantifying epistemic equity will always be a fundamental concern.
| d | 4fb8bf3046e8e51e4f2777938f4ed420 |
“Graph” is a derived discrete data structure consisting of vertices and edges, which can be leveraged to model and solve various general problems. Benefitting from the embedding of human knowledge, graphs are semantically dense data. In contrast, native data structures, such as images and videos, are usually semantically sparse data. Therefore, effectively using graphs to model and learn valuable information for downstream tasks is a compelling area of research. The impressive success in Graph Neural Networks (GNNs) {{cite:7d5402bff2356bbfc136ccbbb3aa9c141c9674a2}}, {{cite:9b5410119a414cb43def2bd5d7292bfafde6543d}}, {{cite:291712c1ee3d530a58e43dfddcb46d0ee6728812}} provokes the exploration to sufficiently learn discriminative representations from graphs.
{{figure:c6b43527-71d6-4c86-851d-331e107c2b19}} | i | 7940937fe0dc71c37957167ffd05c992 |
This section provides numerical results to validate the proposed designs. The parameters are set as follows: {{formula:3cfab7fe-d10d-4d2b-a3bb-b6c6c8f0eaba}} meters, {{formula:b1ff93d8-9576-492c-9035-5fd2355cfa7c}} MHz, path loss exponent {{formula:b8d24367-1b60-4f06-a4c5-a36b5715d238}} , {{formula:9cfef1fe-5b84-401f-a3c1-fb972ee62994}} dBm, {{formula:3dfcb303-c8c6-4a59-a2ad-b2a09e151e1e}} W, Rician factor G = 15 dB, UAV's coverage area is 400 m x 400 m, UAV ground station is located at (1.5m, 398m). On a more general level, we perform 1000 independent trials of Monte-Carlo simulations. In details, for each iteration, we deploy a random GUs topology distributed in the considered area, the RT constraints are uniformly ranging between {{formula:9348d947-d155-4a4a-987b-8b8be6412c58}} and {{formula:d40a15e7-85c4-486f-876e-ecaa1dfafb7d}} . Moreover, the channel coefficient {{formula:a9a78ddf-47e1-45f4-910b-a1ec7d21ff45}} is also regenerated for each iteration. The proposed solutions are compared with a solution in {{cite:c1122c43345c8db416c4edafc66966969e2e6c4b}}, {{cite:d960ed2e756ec5c0bdaa49dde13c09393e86490e}}, which is based on the TSP. Specifically, since the heuristic and DP algorithms can find maximally 1 and {{formula:b543d5ca-3fdd-4d76-807b-d09afe18fc78}} feasible paths, respectively. In order to guarantee that the exhaustive method is always an upper bound, this algorithm takes {{formula:254a277f-a8d1-4b7a-b0ac-c8c4ae00fb61}} ({{formula:bf2e7a6c-0954-4364-8955-235a95195b23}} ) shortest feasible paths while the heuristic and DP algorithms take all feasible paths into consideration.
| r | 09fa52dc0e7c01d8e4669d3a3c9ef636 |
For the sake of completeness, let us briefly discuss the case {{formula:4f7d709a-4ee7-4c45-8d86-eeae6f92e6ae}} when freely falling observers have “orbits” constrained by the finite radius {{formula:0487e574-97d1-4983-823f-db3131b7853f}} . The problem here is that our formula for the Noether charges (REF ) relies on taking the asymptotic limit and hence it is not possible to straightforwardly apply it to this case where we have the maximum radius. It is formaly possible to do an analytic continuation to {{formula:43ec27fb-356d-45ee-9b99-08333d3a37ea}} , leading to complex quantities {{formula:4abaab3d-af45-43f9-abaf-05f11af96948}} and {{formula:07c8b111-0adc-4213-9403-bb541e4cda84}} . It turns out that the {{formula:dcd03499-e52f-40fc-b688-81048d19bb2a}} component of the superpotential is real at {{formula:ee5c22a7-8d5d-4427-8fc1-9e4e9f62c50e}} and hence we obtain the real Noether charge {{formula:8797f423-7911-4d64-a4ba-78287b6fd8fa}} . However, despite the fact that one obtains formally acceptable real result in this particular case, the occurrence of complex parameters in intermediate calculations makes the physical interpretation of such results rather unclear {{cite:209384e0fc7f340d0b3443270c6bf2e4358ad77e}}. Note that complex quantities in tetrad calculus do appear in the literature, e.g., in {{cite:5fe6f8f5cb57ddb1b33f1cce3508eeb606deda8f}}, {{cite:209384e0fc7f340d0b3443270c6bf2e4358ad77e}} in the case of cosmological models.
| d | 35963190e0928f4a9de98c42c3e51823 |
From the perspective of quantum modeling, there is a wide range of extensions that would be desirable. This would include the use of larger networks by means of matrix product states {{cite:321bafea5f4affd43d6c37ccabbc1ec3bf817cd3}}, the use of heterogenous network topologies, e.g. with several fully-connected systems sparsely connected among themselves, or the use of non-Markovian open quantum systems allowing for information back-flow into our spin system. However, we believe that the current iteration of the model represents the essential ingredients for a successful representation of numerosity perception while adhering to minimal complexity.
| d | 21987f3ad7e2fade72f520bf11d21bc8 |
The uncertainty principle
investigated here is different from the standard approaches {{cite:b41837d50639aa25650e9116217e357fd18ba41e}}, {{cite:88aea71cfd68c5f5dc96b9daf05ca5d2c606c7a3}}, {{cite:680236a98ef9415f686cf9554b4424ef9c208ad0}}, {{cite:fd7cd70b9e28610a0049562b7b9c9a085d4ca0f9}}. These are
roughly divided into two schools of thoughts.
The text-book
momentum-position uncertainty relation, is a measure
for uncertainty in the state function. To verify it one needs
to perform two sets of measurements obtaining the uncertainty in
{{formula:89e51dbf-faa2-4eb2-b6ca-0536646f3b2a}} and {{formula:33cef09f-da07-4f87-a79b-e74488c17eaf}} independently.
The second is the disturbance approach originating from the
{{formula:fde955ea-d212-4a45-8128-bb6cb407a1f7}} ray thought experiment {{cite:b41837d50639aa25650e9116217e357fd18ba41e}}.
This dichotomy has attracted considerable ongoing research until recently
{{cite:0926aa95472b62dc3b66825d26ac1926c83b73cf}}, {{cite:8298b068728181e1d92d8aa1935efa4d9e1d6b77}}, {{cite:ea2b3ad180296b93abcdb4bd77d83479bde2a50f}}, {{cite:9b049ef3bdef99a0f3364b9ed2933002f84356a2}}, {{cite:dad9c5b6924ce68b37dee6879f9ec2e768e4ee5d}}, {{cite:2eb503f47fc646d51c63b478e258d1eb72183136}}.
Our approach is different from both and this is obviously related to the
fact that we consider repeated measurements which
backfire and modify the unitary
evolution and also to the observable of interest: the detection probability.
The uncertainty relation found here can be extended to other observables.
In {{cite:731498b9abd5d73d4abb7b75f06b6729bae9dc85}} a time-energy relation was discovered for the fluctuations
of the return time, with an interesting dependence on the winding number
of the problem.
| d | f316c6eecadb7031a519535db463c340 |
As a rule, the basis for the understanding of properties of materials relies on their non-interacting, or single particle, properties. The “particle in a box" model for 3D metals, proposed by Sommerfeld {{cite:9414fb4c80e0dac3de843d915a03ffbbf330adc6}} at the beginning of the 20th century, is an example of how an oversimplified model of non-interacting electrons can provide explanations for physical behaviour and make predictions that have been confirmed experimentally innumerable times. It took many decades of study, and serious theoretical work, culminating in the Landau theory of the Fermi liquid {{cite:75c2da4edef2cf213109c8764386446b065751dd}}, to understand why and how charged particles that interact via strong long-range repulsive forces could behave as if they did not “feel" each other. At the same time, Bloch's theorem and the concept of band structure of crystals {{cite:9414fb4c80e0dac3de843d915a03ffbbf330adc6}} for non-interacting electrons have been at the core of virtually all modern technology based on semiconductors.
| i | e7bfe3c427216d0a4b43d744481cf5da |
Zero-shot ImageNet monitor.
SLIP may also serve as a useful framework within which to evaluate new methods for self-supervised learning.
Training loss on the pre-text task is a poor predictor of downstream performance, so a simple external metric like kNN accuracy is important for quickly estimating performance and diagnosing training issues such as overfitting or instability.
However, kNN classification requires encoding and storing every single training image and naive inference requires very expensive matrix multiplications.
The memory bank kNN monitor {{cite:c1ffd0db47d7908b11bc1a86fd520d4bfc61a889}} alleviates this cost but is not feasible when pre-training on unlabeled datasets such as YFCC100M.
Instead, zero-shot evaluations on ImageNet are virtually as fast as evaluating validation accuracy in the supervised setting.
| d | b5ec9bf069288303a9a0ab8bdac61091 |
Federated Learning (FL) is a learning procedure where the aim is to utilize vast amount of data residing in numerous (in millions) edge devices (clients) to train machine learning models without collecting clients' data {{cite:203368a324c86948d2674e1ae67e3b0fb69d9d92}}. Formally, if there are {{formula:f2e18053-b4b0-4272-af57-357576662264}} clients and {{formula:9e2d5a46-e3c9-4ab5-80ac-66511b4a8334}} denotes the local loss function at client {{formula:28a8a008-7df6-4ba4-b40c-6fd852554912}} , then traditional FL learns a single global model by minimizing
{{formula:8b2bf286-f3a8-4a7d-a663-b1c6e87e84af}}
| i | f07e3c0f182028689004fe4f717cbe81 |
Multi-layer perceptron (MLP) {{cite:94583407e622db9f8056d6191aed41318619252a}} is used to measure the ability of the proposed additive neural network, in machine learning problems. MLP consists of a single input and output layer and multiple hidden layers. The size and the number of hidden layers can vary a great deal, depending on the problem domain. In this research, we use one, two and three hidden layers, respectively, in two different classification problems, namely XOR problem and character recognition of MNIST dataset. The input layer receives pattern sample {{formula:2442bcc0-8af3-43a3-9212-ea0d2d7b9731}} to the network.
| r | 21c51591e8c3a15a7ab8c288024e1c56 |
While the Discovery of the Higgs boson at the Large Hadron Collider (LHC) {{cite:c8e2518a2b43cfedd1d7f2c9f5f048284f8461dd}}, {{cite:d42a5e3ed18e251cbce6ac1e0bba59fa58d08428}} completes the particle spectrum of the Standard Model (SM), this spin-zero boson also confirms the mass generation mechanism of the fermions and gauge bosons via spontaneous symmetry breaking. However, an exception of the aforesaid mechanism occurs for the neutrinos owing to the absence of the counterpart of the left-handed neutrinos in SM. On the contrary to this theoretical observation, the flavor oscillations of the neutrinos yield massive active neutrinos with an upper limit of {{formula:a68d352d-d240-450e-90a2-b95067186441}} (0.1 eV) {{cite:fabd4369fc9bbbd00e4e76a12ef3c88a26ffd8c6}} coming from cosmological observations. This tiny neutrino mass can be generated via see-saw mechanism, which requires the extension of SM with additional fermionic or bosonic degrees of freedom. Depending on the nature and representations of the extended sector, various types of see-saw mechanisms like Type-I {{cite:5dfe6473789474763ce2d731febfc056bdf45f25}}, {{cite:6b6f0cc6d280aa27a4c9fe684c6d5f337068fd61}}, {{cite:5d73b52e423d4d099ce276bb84503326af66d2dc}}, {{cite:943b481479110025aad0293d12840b11779a75f4}}, Type-II {{cite:d2ed46463e47b322c9013bc97682e1cc4b7a8842}}, {{cite:3753e0e845b34d54f35073a03ede8bc3e3ce7721}}, {{cite:0518c59b6d200c62acc97a5f3f117c6a4da28398}}, {{cite:6f607ed20c3762cfe075e34ee38f967d8b67adea}}, {{cite:320702a26e343ea345bf4d91c3d58f146bb6e17f}}, {{cite:8e0518f18c99f975768d3e4ccb92f13642af67a7}}, {{cite:84e7ead8e2cd3d16f47fae2fdcd8059449b036d2}}, {{cite:07c1b5a72fdcff3fe1d7b5f476624e92c1a1dc66}}, {{cite:b4c3a24ae93724620974013a871e450321390296}}, {{cite:d970e25b26a3049fd7720a9aafe9f1739999e4cb}}, {{cite:69c137850fee5865e92df9545371aeda5c658745}}, {{cite:7d4b56b66e6911cb68718d1af41b00f2e48acc3e}}, Type-III {{cite:359e714e8ab580897ac3ffbd5ea8d15ceaa284c8}}, {{cite:890bda680b9bdb85fc931cac5784934dbab48737}}, {{cite:669f956c19dc5a73f542e4e0244217d8ffabac56}}, {{cite:59b7cc7a6d1b137af115b3cf2386fe8a5b36e706}}, {{cite:785040242defc453bea78755de33fd3daffe7316}}, have been studied in the literature. The requirement of tiny active neutrino masses pushes the masses of the additional beyond Standard Model (BSM) fields to higher end and also put a lower bound on the masses of the same. In most of the see-saw mechanisms, the BSM fields are too heavy to be produced and analysed in the present and future collider experiments. The inverse see-saw mechanism {{cite:94c49ff6ba91a6c0ce58756feb62a976fc795375}}, {{cite:30d85d6035b96003c138402c68cee18e0d41731a}}, {{cite:748b63f058c00a195975f3eebcc7352fd9f14ce2}}, {{cite:84a052406f124d484ae948eb6f9846f886a661dd}}, {{cite:5b55aae20912939689eba128dde95781be6c93d1}}, {{cite:b0412b9b15b95647a6d8b141a63f23fe7f27609a}}, {{cite:46f4421bc75f881cfcfde737aee4b28eb4fa21d9}}, {{cite:91e854c0358bef93b03110f4284b2c634ab3f359}}, {{cite:79b95ca27dafe9b7386a597f4c864cb828d6356f}}, {{cite:484e2babddbd691d45eceea25b56cce6df8530a9}}, {{cite:6dbced3018d2bdb0d63da6a84e911fc7576b771d}}, {{cite:cf4b7872191f8180ef3c43c61f00e7c6c4827d50}}, {{cite:a36f6351f0b28b27fd4abb2195a7e1911b11d136}}, {{cite:43434aad7b3e48d0fd36ae2f4c822529bf0d7a94}}, {{cite:7f99081fb3b60a4c9a658b373086095d866105b6}}, {{cite:c1977d7d514cf8ccf3358df9359ff9b1301f852e}}, {{cite:861963a47aa77ebaee781cddfbd83f986b2d441d}}, {{cite:0cc1201d5bb1c3717500c21575bf88a1b5fd8e44}}, {{cite:539412d5ef610822d468a30a45c6b920cffaae9c}} turns out to be very effective for addressing this problem as it can produce TeV scale heavy neutrinos which is well within the reach of future collider experiments. In the inverse see-saw framework, SM is extended by gauge singlet right-handed neutrinos and singlet neutral fermions as will be mentioned in detail later.
| i | e76a0172fb026993792a2ec787701d4b |
The total mid-infrared (MIR) luminosities of the source, obtained with the Wide-Field Infrared Survey Explorer (WISE), have been reported in {{cite:aad491e8088f7bf33b96cd619b5fc5e5dcebdef6}}: {{formula:0ccc88e3-d620-479d-a681-72689f97c8a4}} , {{formula:0e129135-8330-4399-9837-05cad474d1da}} and {{formula:ed59559d-c816-4621-af5d-36978b0c59e2}} . The observed luminosity at {{formula:473c3186-8d8b-428b-9b6a-1c7e88e8319a}} is in agreement with the ones estimated using the {{formula:dcc8833f-e009-4b37-a86a-9e3f1d2f6f35}} -L{{formula:2b9f1dc2-8bdd-4936-a749-a37af89c013b}} correlations from {{cite:a37c8ce796cd7f1d367dae00951440f949068ec8}} and {{cite:4b62e690b1a4f917a7d449f332d046bf4cdc9cc5}}, within statistical uncertainties. In the latter work, local AGN ({{formula:df07e43b-06a7-46d8-ac5b-b79bd2d4c182}} ) in the luminosity range {{formula:a076006a-3500-474d-baa9-cb76599b9988}} were considered. The MIR colors can be also used to estimate the amount of obscuration along the line of sight, as discussed in {{cite:b0c6ded009a00ee0696e8ce823ff1a8f0a1a58c3}}. Using their Eq. (3), from the ratio {{formula:10062df5-dcb2-4088-8e2b-d1b21f14f718}} /{{formula:31d73ae1-206e-45d3-b07a-37797aa9adcb}} =1.17 we obtain a column density value which is in agreement with the upper limit found in Sect. 3.2. However, the obscuring column is known to correlate with the {{formula:9ced598d-5a55-4417-9fe9-471e777e51fa}} ratio {{cite:5bc83e77a05126e38ad39e718c261432aff6868f}}, {{cite:e64cfe1634bdc8f36e87553102cbae94f835bf64}}. Eq. (1) in {{cite:b0c6ded009a00ee0696e8ce823ff1a8f0a1a58c3}} allows us to estimate the 2-10 keV luminosity from the inferred upper limit N{{formula:4b0ffee2-7876-4432-bdf3-361eb96abc98}} cm{{formula:795995a1-c97d-4d5c-983e-5190a50bcdd1}} . We find {{formula:a6d69c15-089e-45c8-8663-d2a24d9455f1}} i.e. {{formula:89e8933e-dbf7-4b6e-842a-a419f1b38375}} erg s{{formula:e674fcda-c41e-4268-a8ac-7f3541c7d5d2}} , which supports the scenario in which the intrinsic flux of the source is steadily decreasing throughout the years.
| d | 89cc34b8569e50cd80e031c3c3674008 |
The state-of-the-art approaches {{cite:3de620647aeb8800818d1ec1f7c4115d5ab673d9}}, {{cite:6d0e16c8d738be49286aafd4df0d10def1c2e304}}, {{cite:1a1aac3ae6aad7cb9107c4ed544e45da355f19c6}} pose the problem of detecting the plane of symmetry as an optimization problem. They use the L2-norm as a metric to find the residuals and assume that the set of correspondences between the reflective symmetric points does not contain many outliers correspondences. However, in practice, the set of correspondences between the mirror reflective points may contain many outliers correspondences due to sensor noise, missing parts and non-ideal feature descriptors. Also, the approaches proposed in {{cite:6d0e16c8d738be49286aafd4df0d10def1c2e304}}, {{cite:3de620647aeb8800818d1ec1f7c4115d5ab673d9}}, {{cite:1a1aac3ae6aad7cb9107c4ed544e45da355f19c6}} used iterative closest point (ICP) based approaches where the plane of symmetry and correspondences between symmetric points are found simultaneously using an iterative algorithm. Since the L2-norm is not robust to outliers, the efficiency of these methods degrades in challenging settings.
In this work, we propose a statistical estimator for the plane of reflection symmetry that is robust to outliers and missing parts efficiently. The idea is to use {{formula:e3051091-b688-4c75-8b79-930fcbc3f4af}} estimator proposed in {{cite:71e4f7c77c81817751ff7904fda98313d37c7979}} that has been used ({{cite:f810838ff8fc4e6965553a14a57f2ec826653ea2}}, {{cite:8c7685c9ae23fd235fb83bb5e275b70489515337}}, {{cite:ee43cad311dfd5676b9d2297461da6fb1e892383}}, {{cite:01c274648aa0753629313b2fd737642a7d9cd329}}) to solve many other problems in computer vision and computer graphics. The penalty curve
for the L2 norm is quadratic and assigns high probabilities even for outliers. Hence, its performance is affected by the outliers. Whereas the {{formula:f6a80aa9-476a-4582-8e73-721a52985569}} estimator assigns very low probabilities for many of the residuals that help it be efficient in the presence of outliers. We further decouple the problem of finding the correspondences and the plane of symmetry to make the proposed approach computationally efficient. We first propose an approach to estimate a set of putative correspondences between mirror symmetric points. We then propose an approach to find reflection symmetry invariant descriptors for points and then match them using an approximate nearest neighbor search approach. We use the spectral properties of the geodesic distance matrix on the local neighborhood of each point to describe a point. Since geodesics are invariant to self-isometry {{cite:32c0a52fce5a7c3e21a23cf51cc92c843386fb90}}, the proposed descriptors are reflection symmetry invariant. Then, we pose the problem of finding an estimator for the plane of reflection symmetry as an optimization problem on a unit 2-Sphere. We show that the proposed approach achieves state-of-the-art performance on the benchmark dataset {{cite:4ed113dcbe3632e580442dd720df60280eac2f12}}. In Figure REF , we shown an example result.
| i | e45d2fa56786a3cfa4c158c3cedc92a7 |
Dataset Sub-groups. For debiasing, *UpWt, *gDRO, and *PGI require additional labels for covariates (sub-group labels). Past work has focused on these labels being supplied by an oracle; however, having access to all relevant sub-group labels is often impractical for large datasets. Some recent efforts have attempted to infer these sub-groups. Just train twice (JTT) {{cite:41837f7653186ffa4de1533cde079ec212b2f18a}} uses a bias-prone ERM model by training for a few epochs to identify the difficult groups. Environment inference for invariant learning (EIIL) {{cite:0a808b849b4ae48a7a6ead118ce9202a2e5eaa36}} learns sub-group assignments that maximize the invariant risk minimization objective {{cite:58a982796b3b155eab308850ac9e29c3c3d8fdd2}}. Unfortunately, inferred sub-groups perform worse in general than when they are supplied by an oracle {{cite:fd20a27669703450315f733b80eb41aff678d5f1}}, {{cite:41837f7653186ffa4de1533cde079ec212b2f18a}}. For the methods that require them, which excludes *OccamNets, we use oracle group labels (i.e., for *BiasedMNIST and *COCO). Inferred group labels are used for *BAR, as oracle labels are not available.
| m | 3e13aea582ee31f8eb73dfc6ba19c48e |
While Medicare data limitations necessitate use of ZIP-code aggregate exposures in our analysis, there are various simplifications to Sections and that can be made to accommodate scenarios where certain measurement error sources are absent. If we were provided individual level outcome and error-prone exposure data, then the measurement error would be closer to a Berkson-type rather than classical {{cite:26ab8f358349be30f849e8b344098b6a23a89d91}}. Accounting for Berkson measurement error would require a different EPE model than the one proposed, however, adapting our framework to meet the needs of Berkson measurement error should be straightforward given the adaptability of the Bayesian framework that we outlined {{cite:7fcc4e392ab5cb473e136b92d483d1e121b547de}}. Lastly, our approach assumes non-differential measurement error, which our context means that {{formula:1e795552-e53d-44be-becc-e1f31409210d}} is unaffected by {{formula:aec5fcbe-60be-49af-98a0-844939b14f3a}} given {{formula:ee088896-23c8-4585-993f-d33407040c8d}} . More work is required to generalize this methodology to the differential measurement error space.
| d | 9172ee428f014af5ea03bda101354bf2 |
the best sum-product results over fields have followed from geometric methods.
Elekes' proof of (REF ) was based on the Szemerédi-Trotter incidence bound {{cite:96c4f74306b99c0f3f73ca59b462884fe8b08960}}, {{cite:d05ef7e35f9511b8fa0821e7ba9d16254c4dbd8a}}.
| r | e53cd04948914ea82aaf790f2d6d4eb4 |
Finally, we give outline of the proofs.
In the one dimension case, the energy functional is bounded from below on the product of {{formula:b2da360a-8f78-49ff-9ade-8caeeb23a94c}} -spheres, the constrained minimization method developed by L. Jeanjean {{cite:c2637fa0631e781cd7fb0692f13ed3493f620511}} can be used to obtained a normalized ground state, which is obtained by establishing the compactness of the minimizing sequences. When {{formula:8faf9cb9-6261-44d2-8b83-ca0631a0fd0b}} , the energy functional is always unbounded on the product of {{formula:84ff7500-72a2-4dff-8d1d-f194326821ec}} -spheres. We use the ideas introduced by N. Soave {{cite:cdd7a6b0c3793edf8e4ad8fcc53d5b73ab8a3fca}}, {{cite:eff849af843e19311abf8091bafc739d1611d8e7}} to study the related fiber maps {{formula:c77e8f62-d5be-4ef5-8a27-45b363775ae9}} (see (REF )). It is easy to see that the critical point of {{formula:ed1e3e3c-b7bc-4993-a682-5cf4a3cc4276}} allow to project a function on {{formula:4dbc5840-8b3a-419c-baea-fa71f76abd84}} (see (REF )) and the monotonicity and convexity properties of {{formula:a06b2f6c-8663-4497-bb52-06c01392be41}} has a strongly affect the structure of {{formula:c9083195-9a57-431b-99c4-840c851da43e}} and then intimately related to the minimax structure of {{formula:80f4807f-58eb-4957-8b33-647f787aaab6}} .
| i | ed543c595c31634534cd38c8b646690d |
For any {{formula:8943db9c-f08d-4e62-90f6-6b45438349a7}} and {{formula:9c7c65c2-5011-4a43-b79c-1af2554a760f}} , we define function {{formula:24b6e5a0-d7bc-4897-a33e-e9e179db8862}} on {{formula:0bba205b-cae7-4572-9200-234453f542e9}} as
{{formula:c4b21e32-b1a4-4bf4-b605-b40ef299f9ec}}
and define {{formula:232ec7af-7ca5-4a0a-be25-ca5a163b3bfe}} the class of functions as
{{formula:eebae2cf-968f-4312-aa9c-0c695512c1c7}}
With the fact that {{formula:79f8d70e-3e5e-46fb-9f8a-b70b57123429}} and the exponential function is monotone on {{formula:545a9086-460f-4850-80b3-8eec50638812}} , by {{cite:e8320c6c0b592a42dd8ff8f37cb90aabfd64dd71}}[Proposition 42-(ii)], it is enough to prove the conclusion holds for the class {{formula:31ab3fd5-9ad3-4c3e-88d0-41d0c7545d99}} .
Let {{formula:5c46d542-6ad7-4cbf-a2ba-07a1752f0d94}} be the number of segments given by the refined partition {{formula:956dc64b-a447-4c1f-9f21-f525226807d2}} and {{formula:33955876-9fe3-4bb5-9cf1-e1bc8bbc4b3d}} the resulted segments on {{formula:24c88937-acd4-40bb-b79a-896b7ed28291}} . For any {{formula:d0fd97b4-e3a3-473c-bd9f-dc305a8c2793}} , we can rewrite it as
{{formula:2045f682-ca6c-4944-80c8-117c2b530202}}
and any {{formula:23881153-33bd-43ff-9a9f-22d2da529bef}} ,
{{formula:56e8f571-a672-4466-825b-642d54bba185}}
As an immediate consequence, for any {{formula:712537fd-5d8d-40c6-aa20-95132879fad8}} , it can be rewritten as
{{formula:7c6b2ffe-6c1a-45d3-bdc8-55bb3e1e47b8}}
Therefore, {{formula:5f106fbd-a6a5-4acf-8532-c333fc2203cf}} is contained in a {{formula:f94ad97c-af8e-45f2-8175-14a2fd08d9ab}} -dimensional vector space spanned by {{formula:dbfae380-6dca-43b8-a067-4711d63871d6}} . By Lemma 2.6.15 of {{cite:df354b732077ce940f624c4fb4ef799233cacdf6}}, we conclude {{formula:927933ee-f5fc-433f-be09-8b0293d5dc3e}} is VC-subgraph on {{formula:1d5933eb-6620-48a6-aed6-58109e1b7630}} with dimension not larger than {{formula:eabc9681-61f8-484b-847a-2e6834810a8b}} .
| r | 5b3ba096a2f09ec1f2a9a739dd140c0d |
Recently, deep learning demonstrates superior performance in computer vision{{cite:79fd4b047e097493d2ba139bf8e3c1a69780f532}} {{cite:a3a38467dfe265afc7ab939e105c7d0bbdb875f3}}. A great deal of image Compressed Sensing reconstruction methods have been developed, such as stacked denoising autoencoder (SDA){{cite:532f0ceb9885e7808decc7b95b1b765a114f84dd}}, non-iterative reconstruction using CNN (ReconNet){{cite:e5d57bba536f1e875c5c0f1986da561d342e7dd4}}, and iterative shrinkage-thresholding algorithm based network (ISTA-Net){{cite:93a3ace14c2268fdb3f61d8e8141922a5f2d6f63}}, etc. Most traditional methods exploit some structured sparsity as an image prior and then solve a sparsity-regularized optimization problem in an iterative fashion such as basis pursuit (BP){{cite:12b576bf07621624a2036b59faa122dfe487de60}}, total variation (TV){{cite:f4a39cf84325787c01102b8e250758ea72420f76}}, and group sparse representation (GSR){{cite:b6e4e85e91d25a9e1ae1bc6c73ee3820ce464fa4}}, etc. However, the traditional methods usually suffer highly computational complexity, and they also encounter the challenges of choosing optimal transform and tuning parameters in their solvers. The non-iterative algorithms, with deep learning method as an example, can dramatically reduce time complexity, while achieving impressive reconstruction performance, and outperform optimization-based algorithms, e.g., BP, TV, GSR, etc.
| i | 30bdf41dd3200d78b5733599efee350b |
The nodes {{formula:7502d91d-5c63-446d-93fe-109d653eb40a}} are the zeros of {{formula:0a72122c-c672-41fc-a033-551f67ed980e}} . The weights, sometimes referred to as Christoffel numbers, can be expressed in various ways (see {{cite:c4ef78e00da62f6bf75c06bb0e7c53afd763f137}}, {{cite:22f56da3edb469e6875e2724645f5b4f1aaaace7}}, {{cite:a6f3d722df3b8f08bbc0b53e10969ecd9da43440}}). One useful expression is
{{formula:a6e0e35e-56a2-40d5-bdb8-644d12d9d7ed}}
| r | 2eac7ea0f0618946e88e26dcc5108d50 |
The overall framework is shown in Figure REF . The reference encoder {{formula:725831cf-c036-4f80-8fb7-eb68c54d2df3}} first encodes {{formula:9a599558-3712-4713-b0cd-4d57a40a0994}} into {{formula:2bcfb9a0-e05b-4051-93cc-b2adbd75166c}} -shot reference maps {{formula:a8ca0e2e-9c1c-4792-be88-c8f576779ead}} , where {{formula:c6c674a6-c3d0-45c4-a87e-d75ca7c6eb9c}} is encoded from {{formula:7d8fa4d5-6301-49cf-b3d9-eab56ba083f3}} . The content encoder {{formula:507a030d-f7dc-4e49-8731-26e5f616a1fd}} extracts the content feature map {{formula:057352ec-de6a-41f0-8c47-5a59babf912d}} from the input content image {{formula:504a64de-56d4-4e90-8223-3b354638ada6}} . Our proposed SAM takes {{formula:ca725afb-b0b3-45da-8f99-9ae6c03a20c1}} and {{formula:bda6eaf2-0594-4d4f-affd-90d597c00102}} as inputs, attends to the corresponding spatially local styles in the reference maps {{formula:981d17d7-66da-4c6f-9210-7d20a9c05801}} and aggregates the local styles into the target style map {{formula:a98d95d8-458a-4efd-9cff-ccd5c6c3fb5a}} . In the end, the decoder {{formula:ad52dcb8-d5a2-44c9-ac5f-0f301f673772}} decodes {{formula:e4fedb5e-1ae3-4cd6-8350-6e52f7c20988}} into the generated output image {{formula:314d755d-81b7-47cf-99d0-b73c3b13eac1}} . A multi-task projection discriminator{{cite:aa1d51dc7847864c4d78854b218cd7f64888d1e0}} is employed to discriminate each generated image and real image. The discriminator outputs a binary classification of fake or real for each character's style and content category.
| m | 5742a5ebbf4b38f796731e25a47f4d74 |
Finally, we would like to mention that similar features can be found in the chimera setup suggest by Abrams and Strogatz {{cite:6cb015d5a85967896864eb32fe9598ad5427bf12}}; these results will be reported elsewhere.
This paper was supported by the Russian Science Foundation (Secs. and , Grant No. 22-12-00348), and the Scientific and Education Mathematical Center “Mathematics for Future Technologies” (Sec. , Project No. 075-02-2022-883).
We thank O. Omelchenko, E. Knobloch, and M. Bolotov for fruitful discussions.
| d | 71e6f4560f8da885e7abfbe674181465 |
From (2.8) in {{cite:eb3a7a62c63ecd48583acd28d311cda7af32201f}},
{{formula:5143e1a0-a842-4997-b76f-f59bdd7751e3}}
has limit zero. {{formula:2e5677ec-a806-4fd0-9291-81badf4cba0f}}
Let {{formula:0db524d4-0a91-4855-8d4a-5da8a8c70f5d}} be the set of coordinates with signal larger than the detection limit ({{formula:f5067cf2-098f-4a81-8432-17d60f08981b}} such that {{formula:0b87451f-e393-4551-b1b8-3735fc8f9d53}} ), and let {{formula:241b5714-cee8-4080-b6b9-00bcc80a96d7}} contain the rest of the coordinates ({{formula:c128e547-3c94-41ba-8098-1fe89bbb462a}} such that {{formula:407f1bb6-ce63-4413-8360-3ff05012b39e}} ). By Theorem 1 in {{cite:6181dbe4e2240fcb43ef4b71afe0a2fbeaf42bde}}, the asymptotic power for detecting signals below the detection limit is one, and that for signals below the limit is zero. Hence, for {{formula:de86510c-326f-4bb3-9eb1-671fae4ee767}} ,
{{formula:0ac58d3b-5ce3-4a88-8d0c-87efbb47e1ae}}
and for {{formula:81857dff-5740-4661-8bd5-7d85c7f28c6e}} ,
{{formula:781f1ff1-3bd7-43e9-bb04-dab4ad00ec17}}
As with Theorem 1, we omit the computation of {{formula:58f86991-47f3-43d7-b1e5-685704ac1895}} , as it follows from the discussion in Section REF . {{formula:c8a2fd31-7443-4707-ab59-f3b9f26ca264}}
| m | 2ce5014b730d3f93d40af12b98fe2dcd |
(2) If {{formula:9c7eb3fb-14ed-419f-947e-4a5757148cc4}} , then {{formula:214f6eb9-0f17-43e1-9baa-df7eba1c708a}} is the class of split triangles by Theorem REF . So {{formula:6ad3b918-d774-4f92-afb3-903ad70f93a8}} is an exact category by {{cite:30bf9195fcb8b6908caa781f1a39fd0b7d531c98}}. Conversely, we assume that {{formula:d7e8267f-5c8e-49fd-8a53-a4b9684fa8c5}} is an exact category. Then any triangle {{formula:79b86de7-9c17-4acb-8bd0-7fcf32133ce7}} in {{formula:3f85baed-c1e2-408c-a1a1-9ee9e9d6e3dc}} satisfies that {{formula:fe102e5a-1a59-4054-b8a5-115d4ec0b405}} is monomorphic. Thus the triangle {{formula:48bf5772-d264-4e87-88d2-7d96452dfb59}} is split, and hence {{formula:082992f0-39f9-4c6c-8555-dde7db9f550c}} is the class of split triangles. So {{formula:4cba4b8a-fee3-4a66-a158-2efc82567bbf}} . This completes the proof.{{formula:1a299a61-a06f-445c-bcbc-1735ff78fb1a}}
| r | 9e2303774ccb2a6810f5033f54bf9afa |
Looking ahead, our first goal is to upgrade these upper bounds to islands for every {{formula:780bc666-4277-4944-b134-fbac388a548a}} and {{formula:5e468dab-3dbf-4311-a353-8f1adeb9b540}} . As was the case for the {{formula:b190817b-86ab-4fa0-b071-cc37a84727cd}} model bootstrap {{cite:b39df17cec1a40ccd241a408bf052e7fb0656268}}, {{cite:2270ad3929d54c14de49e11efa5797bcad411563}}, {{cite:8b3a8c6be6341a0cd98bf561420def02256bdedf}}, {{cite:7b919fd5acab9c92bc506ea323ea8a5470ae2aff}}, {{cite:afe696f0c884602afccc1ce11d4156c6753105e2}}, {{cite:1cff15e41d97b0110505c86aca7b973f1ac72b3a}}, we expect that putting a gap to the spacetime dimension (4 in our case) and inserting the number of relevant operators below should give precise islands for the scaling dimensions of these operators. For SYM, weak coupling and large {{formula:78b18cc8-9887-4b08-a965-ebd97521b396}} estimates for {{formula:c049036f-93d5-4317-a349-52448894394f}} suggest that there are at most two relevant operators for any {{formula:53c2342a-7c16-4fb9-8fc0-7e4ca530f070}} and {{formula:99deb63e-ef22-41ca-b9e6-3bf7008efaf0}} . In order to get islands, the bootstrap must be able to accurately restrict the range of {{formula:c4156ad1-5a1f-4d96-aa82-37524db2d228}} to an interval below 4 for all {{formula:4a263ed5-664e-4c8a-a899-304e6aaf4ab8}} , which we have not yet achieved. It is possible (but not likely) that we might accomplish this by simply increasing the parameter {{formula:d6c7ce3f-e765-4f66-bb7a-fdad07259194}} that measures the size of our functionals. Alternatively, we could consider a mixed correlator between {{formula:54e14e6d-77ed-40c6-8813-9b3ee505719b}} and the dimension 3 half-BPS primary {{formula:013c31f9-eea0-409a-b922-6beebb0271ed}} , as was considered without integrated constraints in {{cite:9fcc7f9e155bce6ebc3654361a574e6b9ad691ed}}, {{cite:ad3bc287f713451e320e18e4ee6c49f350781cd1}}. Not only will mixed correlators improve the bootstrap accuracy by allowing us to impose the uniqueness of the relevant operators as they appear in multiple correlators, which proved very effective for the {{formula:c424eef2-9916-4a92-b498-0a8b73e61202}} bootstrap {{cite:7b919fd5acab9c92bc506ea323ea8a5470ae2aff}}, but this setup will also give us access to the integrated constraint on {{formula:0835ab6f-0746-468e-9faa-645e38556dd3}} as derived in {{cite:14f43210a86a4380d20080ea6da4a429969f0484}}, where the localization input could be computed for any {{formula:7f186f74-7028-43d7-b9e1-987a4ccab328}} and {{formula:ca284557-12d9-4526-8012-ba137798e9a4}} following {{cite:fc03e4680590c917496c9b596a5155832bd520a6}}, {{cite:f684e2816524ec82cc8345f5c3c33040db060d32}}, {{cite:32876b086ea64dad2ab9b2f52e01ca1d84947770}}, {{cite:7efd977e4c71c4d599233463d036ecedd1bbc99c}}. In fact, there are infinite possible integrated constraints that we could access by considering {{formula:7eca1128-3532-4568-8c49-c9d3973d4154}} for each integer {{formula:8a599e08-f788-47f5-a5ef-860a3220f34c}} , where {{formula:4f722ee5-76a9-4364-8822-e7e038764edd}} is the dimension {{formula:52ba544b-e83f-4568-9505-748a9b0f317a}} half-BPS operator considered in {{cite:14f43210a86a4380d20080ea6da4a429969f0484}}.
| d | bfaf75547d72e1525ab06b6c3820eaf3 |
Semantic segmentation is a challenging fundamental problem in computer vision with applications to many real-world tasks which require detailed knowledge regarding the surrounding environment. While the introduction of new architectures e.g., Convolutional Neural Networks (CNNs) {{cite:3d9a5e1cfdfe4cf2d8c0fb35cfee81d9f09fad41}}, {{cite:29680fdd4a29b66ce500e19168d46431f06333a8}} and transformers {{cite:18ade9df432e2ec4f4ffe4c9d8db28c51dc9a60a}}, {{cite:6535732ef79380f3e85214a4621e69b72cf70f48}}, as well as large-scale annotated datasets {{cite:1e428ce50cfbd09f6a7c401fd3d79eae0489194a}}, {{cite:32967f56eaf8aa7f6dc2ef78aaf270f63e72eee9}}, has led to significant improvements in semantic segmentation, the models are typically constrained by pre-defined sets of classes.
Thus, if current semantic segmentation methods are to be extended to new classes, retraining of the entire network and availability of both the old and the new training data, fully annotated with all classes, is required.
| i | e4493d916c80ab36587f17a1669b9259 |
For now the most precise calculations for stable top quarks are the total cross
section at NNLO+NNLL {{cite:c3966ea0a5b85568112ce479b1c27501a8802849}} and differential distributions at
NNLO QCD + NLO EW {{cite:3417e8bb7aeb5ab53785eca64133b00e9185c31f}}. However, the top quark is a
highly unstable particle and decays before it hadronizes and can thus be studied
via its decay products. Including the top quark decay in the calculation allows
the precise study of fiducial phase space regions and offers a closer modelling
of the experimentally accessable final states. To this end, the decay has been
incorporated in the narrow width approximation at NLO in
Refs. {{cite:e12a425c8fc676517f10ba91c3aee220408bbc76}}, {{cite:00d8aa1c4117e58ec5c623f1f412491c3fee2160}} and at approximate NNLO in
Ref. {{cite:c5037326045c9a5648bf3677d99aad8de4aa871f}}. Contrary to this approach, in Refs.
{{cite:2df8472a2fb842675ca817aa6db419e4db7ee29e}}, {{cite:e9cc4e97669b6768d447a922fb4ed5aced93644b}}, {{cite:31ca780093cde6236e1229775ad25f22562333ac}}, {{cite:d43c33f1cf7278fa027e061a0d896f5d8ad2aad6}}, {{cite:b586bc2c6383b6a803f6adfbeabc1cc3021a5af7}}, {{cite:351e010a0341ced22a58cad0816ff2f3c5c0f765}}
the on-shell treatment of top quarks has been abandoned and the complete NLO QCD
corrections for the process {{formula:76114b29-c020-482d-b445-ca66541462f6}}
were calculated and are now also consistently matched with parton showers
{{cite:9277997a5a1151bb1de48bd613b201ed8a0148af}}. Recently also the NLO EW corrections have become
available {{cite:cd7af2edae47d236be55dc93befd846ca9f25f82}} as well as the NLO QCD corrections for the
semi-leptonic decay channel {{cite:8bd7fbba1984e818acba354f6f77ac10027da1da}}.
| i | 7687008d6823b141063bdcdcccd51402 |
We applied our method to the well-studied Kuramoto model, reproducing known behaviors in some cases and revealing novel behaviors and related novel order parameters in others. Further, the known behaviors of the canonical Kuramoto model are not thought to transfer immediately to related models such as with excitable oscillators or for different functional forms for oscillator coupling{{cite:033c94c6a8704f278b71bd73215f13fce4d55110}}, {{cite:3142976bfa89fcb0a630003cb9a07c5d8d42e1c0}}, {{cite:530e6a51fb37ea71b2d9a5acec91a063cb962186}}; repeating the years of human effort that went into the canonical equations for these other models would be impractical. Our framework can be used to reveal behaviors for related models that might be of interest as accurate models of natural systems.
| d | b90976724a791fb77269ee4bf06a8f7e |
Trust-region methods have been used in many fields (see the discussion in {{cite:83f72078e53f52650e77e4e76c6c680147d6f197}}, for instance) and the number of variants is remarkable.
In particular, their robustness for complex optimization tasks has shown advantageous in many regards.
For the work at hand, the idea of a TR method is crucial since it enables optimization methods with certified but adaptive surrogate modeling.
In chap:TRRB, we change Step 1 to an error-aware version, where we use a model function that is a surrogate model for the high-fidelity function {{formula:615ed3b8-24e6-4ebf-9df7-ed9e30df0faa}} .
Let us assume that the error of this surrogate model can be efficiently bounded by an a posteriori error estimator {{formula:3d0c7cab-588c-4631-b137-eed6be3d9900}} .
Then, we can replace the norm {{formula:386b5d31-9f20-4f06-ad31-3acc905ffaa0}} by this estimator, which results in a more meaningful trust-region since it is no longer a relatively unrelated metric object (such as a circle in fig:TRvisualization) but is instead associated to the actual error characteristic that the surrogate model produces.
Moreover, since the surrogate model is built progressively based on all iterates {{formula:48fa005c-5e92-4098-9501-10c9f28b9138}} , we note that, different from fig:TRvisualization, the TR contains all iterates (and their respective local regions).
We precisely describe the algorithm in chap:TRRB and present elaborated illustrations of the resulting error-aware trust-regions; cf. sec:proofofconcept.
| m | 8aca0bd8aeabb7ebf0e29e88edc4af20 |
As a recap, some problem of DP mixture models have been brought about when apply them to practical problems. For example, they always produce more components than that the real data should have. The small mixture components are mainly caused by noise. Some approaches have been proposed for solving this problem. In {{cite:05fdaa3ccc81b59983eb87a655f71bf07ca5f574}}, an upper bound of the number of components is fixed in advance to limit the number in modeling. In {{cite:7a68428e5c39da3e0ce87f279b262e4c48002be3}}, components with little data points are simply discarded, and these data points are reassigned to other existing components. However, this two methods based on simple upper bound or thresholds can not be directly used for real world data, because when you choose a larger bound, DP mixture models can still results in small clusters, and choosing the best thresholds is usually difficult. In this thread, we focus on how to shrink small clusters during sampling.
| m | 69351abdde9d269b0d480c99cb54d50a |
Results obtained are summarised in figure REF and Table REF . In Table REF , we compared our method to the ST-GCN model {{cite:db51c656f3cfee275ccc73e2310a07b59cf2fb44}}, on the 22 ROIs and the ICA subject-specific node timeseries at different dimensionalities for sex classification and fluid intelligence prediction, and to results reported in a recent method which models FC dynamics using spatio-temporal attention on graphs {{cite:6921adda980d22a2d67771c795060632b1d80f5d}}.
In figure REF , performance on sex classification is evaluated across different ICA (and group parcellation) dimensionalities, on models trained and optimised for a maximum number of 2000 iterations. Results show that our Brain-MS-G3D model, inspired by {{cite:94f6d4b80098d27b1cc91b985a8817e66d064723}}, outperforms the ST-GCN model {{cite:701692c57672b3d077520e1d2cbd480e8ba7340a}}, used in {{cite:db51c656f3cfee275ccc73e2310a07b59cf2fb44}}, at every dimensionality, with an average increase in performance of {{formula:22b69492-ab13-4aff-953f-46f490df5140}} , and a maximum of {{formula:6aaccadf-39d0-46fe-912e-8c89e49005de}} at dimensionality 100. In Table REF , we report results for optimised trainings with more iterations, using the best time-window lenght obtained from figure REF . Our Brain-MS-G3D notably reached a 94.4% sex classification accuracy at dimensionality 200. We also note in Table REF an increase in classification for both models when moving from the group-average parcellation (22 ROIs) to a similar ICA dimensionality (25 nodes). For sex classification, we experimented the impact of changing the length of time-windows {{formula:28ec9d56-d380-4369-86ef-287b58840ea2}} for three node dimensionalities (15,25,50): with {{formula:61df764e-3a79-4a10-b2fc-e4b9b04a90a1}} , representing respectively 4.2%, 6.3% and 8.3% of the entire time sequence. Range of performance across time windows is reported through the vertical bars in figure REF , where plotted values correspond to the highest accuracy for {{formula:aee83bae-5c19-4c40-b969-e9e143f9c391}} . In the case of Brain-MS-G3D, all experiments suggest an increase in performance with larger time-windows (best results with {{formula:4b29d925-6acf-44f4-a60c-e6bd2d7e27b1}} ), while the gap reduces when spatial resolution increases.
By comparison, the ST-GCN model demonstrates a larger variance in performance, and the 100-time window network always under-performing the others.
As widely reported in the literature {{cite:43fba582ea2a7b5e7324490a2b8d6c17ece40b0c}}, {{cite:c48e84a6aa302841ddc1ac535c1333cf7d2241e4}}, {{cite:2dded615c768cd4182ffb81f0b829ab914ace78d}}, fluid intelligence was a much more difficult task to predict. As detailed in {{cite:a80913ea6e7bf33aac4c1ea5107a3e9910ac52ba}}, performances for fluid intelligence performance are reported as correlation values in Table REF . Our results quantitatively outperform established methodology such as MAGE and HMM on fluid intelligence prediction (see {{cite:2dded615c768cd4182ffb81f0b829ab914ace78d}}, {{cite:27c8f5b422849b8c3a9d5d53bfd85dc1b3a7a98d}}).
{{figure:9985f23b-09f4-4bc9-a741-18322b65d649}}{{table:3912569a-c746-49ee-915d-abb23b8f5412}} | r | 37e06e322beae1e4726217d971831fa0 |
Models and Datasets.
We use a convex model Logistic Regression (LR) {{cite:48b68060e817c15495cc58c8f3d4d1c048bd0b96}}. We conduct our experiments using a public dataset MNIST {{cite:7379826405278a3002ad75a6afae743f01b0a76b}}.
| m | 3f91a9423c6ac2706c19bd8589091727 |
We train the model described in Section REF on the complete training set before submitting to the leaderboard. Our best performing model was placed 7th amongst the 13 teams that submitted results for this task. We present our score on the test set alongside those of comparable teams in Table REF . We note that the task description paper {{cite:9b9a1819db085bb1340ac93426bbf50d7abe4d00}} describes a method of achieving an F1 score of 22.58% on a similar task although, this reported score is not directly comparable to the results on this task.
{{table:624fe585-31b3-4643-9971-ab7b4f629c8e}} | r | f5392002ca5725e22e62ef9bbeca3371 |
With the integration of RES in the modern power grid, forecasting trends are shifting from point to probabilistic in regards to the future demand and generation at disaggregated levels {{cite:3606382921c4eb557221eb021969b78f4b52a18d}}.
Hong et al. presented a review for probabilistic methods and emphasized their importance over point forecasting with ever changing needs of power industry {{cite:8cef0339e9da4e04160ce2a2be9eb2f3d7a490e0}}, {{cite:641a300bfa244caac9da2989bd6b546403bd84dc}}.
This section identifies the existing literature for probabilistic energy forecasting, which is mainly categorized under parametric and non-parametric approaches. The authors in {{cite:9d6e1f2d09d3a279b4c2160c5820f0df270bc666}} provided a brief review of these two approaches for wind generation forecasting.
Dowell et al. proposed a parametric probabilistic scheme based on Bayesian probability and sparse VAR to forecast very short-term wind power generation in Southeastern Australian wind farms with a 5 min interval {{cite:33b98ecf7fb85b8b97e7cbcf07944830a1f4a02f}}. The authors confirmed superior results by their method with least RMSE in comparison to the standard AR and VAR methods.
| m | 554048c5916c2aedd0cf1b6e0f3ea908 |
Theorems REF and REF show the failure of concept removal methods under a simplified setup and max-margin loss. But current deep-learning models are not trained using max-margin objective and might not satisfy the required assumptions (Assumption REF ,REF ,REF ,REF ). Thus, we now verify the failure modes on three real-world and one synthetic datasets, without making any restrictive assumptions. We use RoBERTa {{cite:915a3d7a060ea2f3a8ceda3ac39f81028a5e8205}} as default encoder and fine-tune it over each real-world dataset. For Synthetic-Text dataset we use sum of pre-trained GloVe embeddings {{cite:033b0262ea65d434890c3e0c3abf02974fdfbf7b}} of words in sentence as default encoder. For more details of experimental setup refer Appendix .
| r | cb46c2997ca834efd23db6572fd13f22 |
In order to study the compact approximation problem, we use the identification of space of compact operators as injective tensor product spaces. The monographs by Ryan ({{cite:a5b2d2237624e32cc430143c236a4d8202d7f12e}}), Diestel and Uhl ({{cite:2260d8c30f98054798837fb40cd84746507a5b61}}, Chapter VIII) are standard references.
| r | bd8b255cc09bd1f8e9268a1ef4257499 |
To summarize our work, we propose wav2vec-U 2.0 - an unsupervised ASR framework with an end-to-end style training and an improved objective function.
In our experiments, we validate the effectiveness of the pipeline simplification and the proposed modification of the objective function.
We show that wav2vec-U 2.0 performs better than the existing unsupervised frameworks across different languages from high-resource to low-resource.
We also combine wav2vec-U 2.0 with self-training strategies {{cite:e3454b22db39b15198142464d67dac7db454c155}}, {{cite:60d099963c663b058451d20f6d685ecb24e37a62}} to compare against prior works and supervised systems.
The implementation is based on fairseq {{cite:23d91541977d714d67869dcbd554cdd7108ae69a}} and the code will be released soon.
| i | 4a1b29d8adc5eb435246abb125f11636 |
It would also be interesting to understand whether we can derive a more general discrete-time analysis framework that works under a relaxed condition, e.g. without requiring contraction in continuous time, but only exponential convergence in function value (which is known for ULA and the Langevin dynamics under the log-Sobolev inequality {{cite:16f96faaa97c061e3b58287f4a3a4f4bfbf8511b}}).
| d | af96978ffeeb372f6c56fbe24dd494b6 |
We also display results from the real-world Pixel3D dataset {{cite:e84b58e70fe775a421e3881d5c9e3127b672ddb3}} in Fig. REF . In general, our model is able to detect the dominant mirror symmetry accurately from images unless multiple symmetries are present.
{{figure:0e7c017d-527c-421e-bb95-fcd11436e56e}} | d | b71ca9e46b007d33a2651b54a9807842 |
where {{formula:4c9c8b6c-de0d-4940-a42a-d5a8443655e3}} and {{formula:ac3fa2dd-dcba-4ad0-92ae-bee68b26eba2}} are the gluon and photon actions and {{formula:7be2fcac-4e94-4045-8101-90779fa6338c}} is the Dirac operator associated to the quark of flavor {{formula:74b032ba-85be-436a-9309-c5b8427d9b93}} . The latter includes coupling to photons and it depends on the quark mass {{formula:a336ba17-d375-4c5b-af99-0d8f8cc70cf0}} , the quark electric charge {{formula:31c45c9f-38d5-4d42-8370-e1ba37ebce2b}} and the gluonic coupling {{formula:d859f700-9f7c-4191-850b-97be3aa97352}} . The first step is to regularize the photon action on the lattice and the associated difficulties are discussed in detail in {{cite:b3fa3d89eca26bd1e7afad4e540471f1b7ed636b}}, {{cite:b0be37c0f130ea938cc13f8fcb5a9dee99432084}}. All results for the HVP are obtained using the QED{{formula:e0f28955-75b7-4ef1-a3e6-47f2777289dd}} prescription {{cite:f38ae49b0faca13f0194a0cdfc9ea01596bfc58d}} where the spatial zero modes of the photon field in finite volume are explicitly removed.
| m | 4b9a58504805f070eb5d61f3dc3ed268 |
In this sections we give detailed training curves for the results shown in Figure REF . As can be seen, in the highly non-iid setting at {{formula:70ca32ad-e551-4fb5-bda9-851490c39cf5}} , all methods exhibit convergence issues. This behavior is well known in FL and is described for instance in {{cite:fedbbdb4c85358fb582a71c801102d891f819f8b}}, {{cite:4e6844e7acfa0adc43fac55217f0175c47cbdeaf}}. Notably, the performance of FedAUX after one single communication round exceeds the maximum achieved performance of all other methods over the entire course of training. At higher values of {{formula:f80f912e-b48a-4473-ad67-802bc18a86db}} all methods train smoothly and validation performance asymptotically increases over the curse of training. FedAUX dominates all baseline methods at all communication rounds in the heterogeneous settings. In the mostly iid-setting at {{formula:1a83dde9-006d-455e-a917-0c8f85be62ae}} FedAUX is en par with the pre-trained version of FedDF.
| r | f5bfbccedb5a39400ae37119b613b65d |
Synthesizing realistic virtual environments is one of the most researched topics in computer graphics and computer vision.
An important decision is how 3D shapes should be encoded and stored in memory.
Users usually choose between triangle meshes, voxel grids, implicit functions, and point clouds {{cite:5f287b50127198175894659ff4af793103d5f5e9}}, {{cite:2fd8c9b0470b15264851eb05b37087d462f063e7}}.
Each representation has different advantages and disadvantages.
For efficient rendering of opaque surfaces, triangle meshes are commonly chosen.
Voxel grids are often used in volume rendering while implicit functions can be used to precisely describe nonlinear analytical surfaces.
Point clouds, on the other hand, have the advantage of being easy to use because no topology has to be considered, which makes them a good candidate for intermediate output or as a representation in a scientific context.
In the early 2000s, point cloud rendering, especially with point splatting, has been a well researched field in computer graphics {{cite:b94f0070c90c14378026ada17cc876851f52d082}}.
In parallel, image-based rendering techniques gained increasing interest {{cite:4d6b463d5a460b9ab370c7f7a1d3da1cc2f59f72}}. Based on a coarse, reconstructed 3D model, as well as a registered set of images of an object, novel views are synthesized.
These approaches suffer from imprecision in the input, for example, ghosting artifacts appear if the geometry contain holes or the input images are not perfectly aligned.
Neural image based rendering approaches such as {{cite:b88f31883c1719436abfe3ec18606e3670a93947}} use neural networks to remove these artifacts and can generate photo-realistic novel views of unprecedented quality.
Aliev et al. {{cite:636421c9c87b2478aa69353b4356a1651f6e214d}} show that this is also possible by pairing a traditional point rasterizer with a deep neural network.
This is especially beneficial in the field of 3D reconstruction because dense point clouds are often the initial output.
An unnecessary and potentially erroneous triangulation can therefore be skipped and the reconstructed scene directly visualized.
| i | 83e91177fcee44e47fdceb9f62a473d1 |
For technical reasons {{cite:a7fb9e4130ad38b4eb2fa1468952879d6805eecc}}, {{cite:a1e751b2941b8d93008ee9478a329b5a19bc0066}}, our intractability results are initially
derived relative to decision versions of our problems, i.e., problems whose answers
are either “Yes” or “No”. Problem TeamEnvVer is already phrased as a decision
problem. The decision versions of ContDes:S{{formula:d7dac195-c19d-48ed-a7a4-fc28f09e44cf}} and TeamDesLS{{formula:084b9b6f-2eb4-40cc-b078-323bc6d81cc0}} (denoted
by ContDesLS{{formula:06cc0236-942f-4f5f-997b-7fac49818a2a}} and TeamDesLS{{formula:95c9e5ec-54c8-4e9e-96cc-59a79bebf418}} , respectively) ask if the structures
requested in each problem ({{formula:20e2c973-f055-4f2d-8420-849875d49b40}} and {{formula:3ddbf442-561f-45ff-8ee6-a8f448326adc}} , respectively) exist or not.
The following lemma (based on the observation that any algorithm for non-decision problem
X can be used to solve X{{formula:ee9d7edd-a12f-4089-b9e0-d0db10968895}} ) will be useful
below in transferring results from decision problems to their associated
non-decision problems.
| r | 5206414f007818363a64b3d5f8ae9da5 |
Our work is an algorithm for multi-arm bandit (MAB) problem. On the novelty side, our work automates the exploration in bandit problems.
Such algorithm could be used in recommendation system and clinic trials. On the positive side, our work could balance the exploration and exploitation trade-off in a problem dependently way, which might improve the customer satisfaction or patient's health care. On the negative side,
depending to the deployed application, the recommended contents might be unsuitable for some users. To mitigate this issue, domain knowledge might be required to filter the recommended contents before releasing to users. Regarding the health care application, expert's supervision is essential to avoid any potential hazard.
Appendidx A
This section contains the proof of Lemma redREF .
Suppose {{formula:835a6b5b-81be-4a55-917e-56399e48d62e}} , that is
{{formula:791b2e4b-2c16-40ac-82df-5a3390c2cc1d}}
Rearrange terms gives
{{formula:3fd1a582-7425-42be-b74b-6b4a082f8421}}
Note that {{formula:9b01fb95-51a3-47be-83c4-848dfc8a825e}} . Then,
{{formula:5ac6c972-9a12-4a6b-b1dc-5bdeec528427}}
and
{{formula:31c93173-32eb-4f98-becc-dd5dd037cb60}}
Combine together we have
{{formula:d02c40c2-1028-4aea-af6c-a21533ac5686}}
Recall by definition {{formula:95af1c46-2a95-431c-bec0-4175c3c7e192}} is the arm with largest lower upper bound at round {{formula:67a95f5f-be8e-4304-839a-a2bb1deb976b}} .
Therefore, {{formula:6c856b95-6997-4303-a45e-8e5f5784f652}} . In words, arm {{formula:760e6821-b505-4291-a3b8-08d156b57089}} is suboptimal.
Suppose {{formula:0a44742e-482e-49b9-afd9-db7690e38c1f}}
{{formula:95990580-5dc4-4901-b497-aec8a884f101}}
Recall the definition of {{formula:851c3690-39e2-46d3-8c87-c66d617b2c52}} ,
{{formula:e24438b8-a30d-4cfa-acb9-1e902049c282}}
Thus, at each time {{formula:1678542a-2499-4777-98c5-e5c433122f33}} , {{formula:1a2fc12e-eb1c-401e-ba18-7600674081ae}} . Then,
{{formula:f14967ac-8e89-427c-bdbe-99aa44439936}}
Appendix B
This section contains the proof of Lemma redREF .
{{formula:8667c05a-8b9f-40f3-91b8-36690148a842}}
By definition, {{formula:9240a072-a4fb-4b02-bc9e-fe7f849b3f21}} , {{formula:c31bea51-4315-4d69-86b5-d9ac40439da6}} . Thus,
{{formula:626be134-d9a6-4dd6-a97a-c62b8f1ad01b}}
Then,
{{formula:71f2bc7a-0d3a-4474-8fbe-43baf46ef94f}}
Therefore,
{{formula:7b0e2b5f-fa52-4fc9-ba51-b99b55045d0e}}
For any probability {{formula:d86469c4-45d7-42a7-b4ba-02f6166e1a2c}} , we can find a {{formula:eaf8ffdc-51b1-4151-bc8c-752605318d94}} such that {{formula:d3369dbb-8e78-4a3c-ab19-37ebf4e88f23}} , namely
{{formula:bd900683-5a5d-4df0-8b9c-18d4d1ddce43}}
Rearrange terms gives
{{formula:357f4604-0990-4b0f-b3e7-348db0160b6a}}
Take logarithm on both sides,
{{formula:35c9e532-77c6-4bb7-b5cf-335fb641723a}}
The left side term is LogSumExp which can be approximated by
{{formula:13ce70c6-fb1e-4355-9f13-cf5356fb5b18}}
Denote {{formula:8a79813d-4f1a-4a03-b1b2-e13226940a6c}} and let
{{formula:433f641c-7a89-4f61-a26f-22355f946ea2}}
we have
{{formula:db056441-5130-4823-8d84-24b11d1ec30a}}
Therefore, if {{formula:2012ea7f-8fe2-423d-976a-deabb6a09928}} satisfies Eq. redREF ,
{{formula:6c3c3ff8-5d7f-40e0-9eb0-527c6ad9ed40}}
Clearly, {{formula:c3fed651-8b9f-4c08-bbac-298524257d71}} since {{formula:bd238648-348d-4478-a4cc-d436c43c557d}} .
Appendix C
This section contains the derive of gradients.
{{formula:f5992f0a-8674-4cef-afc2-8d3bb845305a}}
Apply the Lagrange multipliers, the optimization objective is
{{formula:93a6e7f9-2bab-469e-a31d-7b9a7bbf42ed}}
Apply the score function {{formula:b85d48b0-b3a2-481e-8232-e87da9133484}} to {{formula:d3520b23-3544-4e17-b51b-18c6bc027f09}}
{{formula:bc2f2931-0fb9-4322-a12e-47976d73dc7f}}
{{formula:260ecba8-443a-4a3c-91a8-129f142b10b9}}
Then, the gradient {{formula:e22fafad-3d61-4947-ae50-2ae6f7bf01dc}} is
{{formula:25c7dbb8-ba9c-4301-aad7-b035b5c1f952}}
The gradient estimator {{formula:fea0c32f-cc88-4bc3-b9f2-2ebdb09855bc}} is obtained by repalcing {{formula:bd9ac893-03ad-4347-bb25-c36d7de95ffb}} with {{formula:7ac94318-f949-41e1-bb50-cff3ec56afee}} where {{formula:aa322986-18d0-48f1-8610-52034057f17a}} is obtained via least-square estimator.
{{formula:6c41b076-d2de-4b3f-aae8-c94fedfcbcdb}}
Appendix D
This sextion contains the proof of Theorem redREF .
The probability of each arm is defined as
{{formula:a367e7e2-7775-4a62-ae5e-677e7040df5f}}
{{formula:ebaa8d57-0cd5-48fe-aa73-b035821247ed}} is defined as
{{formula:29eeafcf-5d71-431c-a551-33f9164a1db4}}
The cumulative regret to be minimized is defined as
{{formula:04bce7f0-bc47-41db-8c8a-b55bda924a14}}
where we use {{formula:e11315cc-5d9a-459c-870a-61d536c59805}} .
At each time {{formula:68a02aca-6d89-4721-a27d-f9555cd405dd}} , trm set {{formula:e6d43caa-3658-48c4-8265-f6e0b200ced9}} is divided into two subsets {{formula:2c4e250e-bebb-4965-9ee3-f77387c07888}} and {{formula:34d4bc8a-828f-418e-b8d1-244d326b4138}} with {{formula:6d7d2d8f-e84a-40e1-8f24-7770ceeeeba1}} . Arm {{formula:7b48c471-e343-4736-9337-fe0fe4d3b4cd}} if {{formula:de590bff-b1ac-4e37-b21d-5deaf04cb55d}} and arm {{formula:14b18d40-b43f-4bec-b9de-0cf0aad01d86}} if {{formula:4528a394-cfd7-48f1-bd87-384ca748f7f9}} .
{{formula:7983f002-b359-4b4a-bbb3-3e14f2dcdffb}}
Suppose {{formula:1ee595b5-0b0c-4f74-942e-e041d984e535}} follows Lemma redREF , then {{formula:7fe35ad4-a977-4edb-a8ea-7d392a41fd7b}} . Assume {{formula:f3cfe923-90ce-49bd-966b-2d51d9be420b}} . Then,
{{formula:9e3a570f-57d5-41fe-af36-237b5dce0b56}}
By setting {{formula:a99306dc-0e0e-41a6-82fc-1ee389c7c608}} , we have {{formula:0ff6e1a5-ad9b-4602-9dac-53ee0fe6a832}} . It means arms in {{formula:bd23e9a8-dad6-4fd2-846f-9035327ad4cf}} are unlikely to be selected. So, the second term can be dropped. Therefore,
{{formula:707d1018-30be-4560-b0da-5feee6d6d6ee}}
Thus,
{{formula:7e3eea08-a069-4507-be7d-34ab94853410}}
Note that at each time {{formula:dda09647-a814-4542-9588-c8f37c700811}} , {{formula:b64540fc-4a19-4839-a7df-a0b8a5221d8c}} . Then
{{formula:641f09c7-390d-430f-ae2d-748202b3a6c9}}
and
{{formula:57cd43f9-7921-4833-9966-fb28f61737f9}}
Thus,
{{formula:06e974ee-c521-4f5b-94d3-0c71e826f28a}}
Note that {{formula:4097fd56-ff75-46c1-b961-ced46dbaad95}} where {{formula:7b026870-a1f0-4716-9ff6-bf5a8c062891}} . Therefore,
{{formula:a5abae93-faeb-4cc2-a0f4-d44a30f2880a}}
Since {{formula:1efa5c3d-9d11-42c6-bbed-4defa0508504}} , {{formula:bf109223-61f2-4716-9da7-0bb3ca31dc16}} . That is {{formula:828a4e2a-ef56-4b8f-bbb2-a61991627b8c}} . Then,
{{formula:b4834ad2-31c2-41dc-8730-67cfc26e3c0d}}
Define {{formula:062b1e49-6b01-4635-bdf7-c9aab1713575}} . We have
{{formula:36191fbc-e3f7-44ef-9e96-7d171bc38062}}
Plugging this into Eq. redREF gives
{{formula:0083126b-bd17-46b5-a1ed-665424d8a222}}
Since we assume {{formula:776638d2-5e6c-45ee-929a-469f39621d79}} follows Lemma redREF , we have {{formula:b5e0d352-e575-49e7-80bd-bfe7c8ec850f}} . Therefore,
{{formula:f94eed9c-3adb-451b-8aa8-ea7ab8c81d46}}
Thus, the cumulative regret
{{formula:d705857e-4f79-4901-ae26-2bcf707f1590}}
From Lemma redREF (stated below), we have
{{formula:cfecbe73-e61a-44c1-ac3f-9ec2eb25e255}}
Plugging in Eq. redREF ,
{{formula:1db5f25c-bae7-44b6-a994-1b17c4311a73}}
where {{formula:03e7447d-acf9-4b82-b31f-e18241827f13}} is the probability parameter chosen by user.
Lemma 3
(Lemma 11 in lightblue{{cite:2efd426848f6948e9ea383fa2bf53fd9b0e68316}})
{{formula:0202b1f3-d16f-45d5-b51f-714ad986731d}}
Appendix E
This section contains the pseudo code of brownSoftUCB, brownSoftUCB offline and brownSoftUCB online.
[H]
InputInputOutputOutput
Initialization : {{formula:c7dfa64b-8fb4-4bc1-aa48-a92a95fa6ff5}} , {{formula:a86cc1b1-634f-43a7-a6e3-38fbcf22980e}} , {{formula:5aba2a20-9efb-48a3-bf26-de98981ad999}} , {{formula:013cd691-995e-4a58-9660-7bbecf71b410}} .
{{formula:e12392d7-27f0-43eb-bb84-4bb8ee733e4f}}
Find {{formula:7ce2a0d2-e6a8-49fe-8799-446545d5a73e}} via Eq. redREF with {{formula:ccf173f2-c317-4ab1-9097-b5f3541c124b}} .
Find {{formula:4b2ed2e5-879e-48ef-b389-313c0c7dadb7}} via Eq. redREF with {{formula:242b08ab-1cf1-4a69-9b72-a490c9311560}} .
Select arm {{formula:0c04bb39-35d2-43e2-9c9a-6fa452f11cfa}} randomly following {{formula:79f47e40-d1d1-426e-a207-15faad12c26e}} and receive payoff {{formula:92ad8eb3-6436-4d8f-8576-8801cd1b5c59}} .
Update {{formula:b2d368a3-e419-44d0-b6ed-c7f51ae0bbb2}} , {{formula:32ed9dd6-0a8a-41da-9c4c-cc33a3eb8548}} and {{formula:412f8d2c-aea2-45de-a85d-7f07acf877e6}} .
Update {{formula:3cafaf28-14a1-43d0-8560-3495d2d1bd7f}} via Eq. redREF .
brownSoftUCB
[H]
InputInputOutputOutput
Initialization : {{formula:6cef2589-35ca-437e-8f8b-301c6698790d}} , {{formula:81fa9292-269b-4a8f-9cac-57dbdac51850}} .
{{formula:149d619d-5345-494b-856a-aadcb1c57719}}
Run brownSoftUCB on {{formula:56bbdcb9-6c70-4376-93b0-847f25dce33f}} rounds with {{formula:90157414-1ee9-4357-a4c0-125af05ed241}} .
Update {{formula:a4982f94-6fe3-4ca2-9b9c-6a6ed9a6c065}} via Eq. red REF
{{formula:3ff0144e-e07f-40f3-bfce-e911a10a26eb}}
Run brownSoftUCB on {{formula:bb84fdbe-90a3-487b-9135-3cfdd5e07f06}} with {{formula:f7cd274f-f842-44a8-af18-1bcfb6154f01}} .
brownSoftUCB offline
[H]
InputInputOutputOutput
Initialization : {{formula:a14d11cc-f737-463b-8a1d-4a4d82fc8627}} , {{formula:507a4b8d-5b8f-4c26-aa89-87c1e88f21a0}} , {{formula:3d916322-c6bf-4618-9720-ae938c145fd0}} , {{formula:2e7494a0-acbd-48ae-bad4-ad2b5a082fb8}} , {{formula:1085967c-7435-4706-a6bf-b011da68cf38}} .
{{formula:207ede59-5341-414a-b7d7-16a4a172c979}}
Select arm {{formula:2869c6c5-b5cd-46e9-b3af-cdfec3aaaae2}} randomly following {{formula:1a84a532-4679-46e8-bde8-29576a13307f}} and receive payoff {{formula:dd0bc133-e19e-4165-8201-c3f77d17ad06}} .
Update {{formula:95d9469a-4e62-4d47-805c-8ccb233b0235}} , {{formula:462ccae5-e1f9-46fb-8dc2-e315958ed6ea}} and {{formula:1ca28185-29de-4bed-83b5-03b10cf3ef29}} .
Update {{formula:26fafbc1-97fe-4d99-8ae5-4f9f7e974fe3}} via Eq. redREF .
brownSoftUCB online
Appendix F
This section contains the learning curves of brownSoftUCB offline.
{{figure:7088e84c-7ea8-419a-9840-1e9e5d302785}}{{figure:409190fb-2d0b-4930-bd20-1ac76d7a15b8}}
Appendix G
The dataset Jester contains ratings of 40 jokes from 19891 users. We sample {{formula:27ca5aaf-fcf6-4179-a8ac-516b8b78a3d3}} users randomly as arms. Their rating to top 39 jokes are used as feature vector. Then, to reduce the sparsity, we apply principle component analysis algorithm to reduce the dimension {{formula:5048b914-9258-4cd5-8687-0daa3a2d541a}} . Their rating on the 40th jokes are used as rewards. At each round, the algorithm selects on user to recommend the joke and the reward is the rating given by the user. MovieLens contains 6k users and their ratings on 40k movies. Since not every user gives ratings on all movies, there are a large mount of missing ratings. We factorize the rating matrix to fill the missing values. The rest works the same as in Jester.
| d | f52661224553d7521a5cd20545c2e034 |
Hence the late-time entropy is determined by which subsystem can hold the least information, i.e., if the bath entropy {{formula:8fa1562a-8091-4966-a903-772bc1770615}} is smaller, the baths set the bound, or if {{formula:3505c5d2-2c9c-409e-b45c-f2cc44904af7}} is smaller, the defects set the bound. Of course, if the bath is infinite in size (e.g., as in {{cite:2b42e73b7de4e7291f03256343bca9b15086535c}}, {{cite:78098cb492e5284d4e22db2209282878a65d2997}}), it has infinite capacity and the final entropy is always set by the defect. The same reasoning applies in the absence of defects. That is, one could consider a thermofield double state of two CFTs on geometries of finite size. Then dividing each of the boundaries into two regions and examining the entanglement entropy of a pair of regions, one would expect to find an early-time growth phase and a late-time phase where the entropy is saturated. However, the final entropy would be given by the thermal entropies of the smaller of the two boundary pairs.In {{cite:4a214e148afea9cd526da809670018e2f4861fdb}}, the boundary geometry was infinite in size and so these considerations were not needed.
| d | a634607c340e8a130df55f45b00987e3 |
The norms {{formula:c349415f-d49b-4f5e-be99-ad0ffe101004}} and {{formula:4ab23b0e-4826-480c-abef-2d71fc91bc92}} are the injective and the projective tensor norms, respectively. Actually, they are the smallest and the biggest reasonable crossnorms (we refer to {{cite:80fef02b58b30a9aeb4614b67230107ad9cb8fc6}}, {{cite:cba113991b35b0e84b79fa3ad5a29f0afd669568}} for the definitions and basic properties). In {{cite:70fb5abf4f4f44386d0c5d5f20a78ba972edd297}}, a characterization of the convex bodies in {{formula:e989079d-f4a0-4ded-a618-5aad1c567648}} {{formula:3c8ea67b-6ed6-4198-9b85-bc3bc53932c2}} that are closed unit balls of reasonable crossnorms is given. That is, an explicit description of the convex bodies {{formula:9f5845de-460c-43b0-9571-cb8f35540ddd}} for which there exists norms {{formula:3e70eeab-515a-44c8-b83d-c0cca3ff537a}} {{formula:cf4dfa4e-95ef-41c0-a66f-0b75dcea3d32}} (not determined a priori) such that {{formula:9ec6d64c-090c-4fdd-8fe4-f4676804644a}} is the closed unit ball of a reasonable crossnorm on {{formula:a6fdb0d5-6ee9-49c5-832b-b380cde18df6}} is established. With it, the class of tensorial bodies in {{formula:fa9c2a3e-0b94-4c78-88cf-5baa77a44f3f}} is introduced {{cite:70fb5abf4f4f44386d0c5d5f20a78ba972edd297}}. A centrally symmetric (0-symmetric) convex body {{formula:38870584-7fb7-460e-93e1-9a5e03abafaf}} is called tensorial body if there exists 0-symmetric convex bodies {{formula:33ae38ac-6fe2-457f-b81b-120fb4b6827a}} {{formula:f94a1375-d9aa-40cf-8aea-885e707bb1aa}} such that
{{formula:9fc5175a-fe78-4e49-a3ec-a8b881784076}}
| i | 9eb54618b134b641a590cb331bb0195f |
Very recent works {{cite:5045ecce7d2cf06e4f4219976596e2243d0267d4}}, {{cite:4f2ba6b7e1ed05457ec21f28bf9f4aa19b1ce230}} have explored the use of OSM data combined with social media textual information, obtained from Twitter, to perform land use classification. These works use natural language processing techniques (e.g, fastText {{cite:c20892f157650a56a01a5e7e91382b28a29137dd}}) together with neural networks to process geolocalized tweets. The authors in {{cite:44dd35f490e619d799ef0eaa2adf2f7ef4eec48f}} use Long short-term memory (LSTM) for feature extraction of Twitter data for the classification of OSM urban-objects into three categories: residential, non-residential and mixed-use. In contrast to works that use image data for finegrained land use classification {{cite:3c8f9623ebcb3b4305eda78ec20f6830dacb4101}}, these works present results with datasets that contain only a few land use classes, but have the advantage of the massive amounts of data that can be retrieved from social media. Also, working with Twitter, it creates the need of specialized workflows, typically aiming at denoising data, retrieve useful Tweets, or avoiding spourious geolocation due to re-Tweets. We found these issues very exciting and believe that textual data should be used in a multimodal fashion: as suggested in {{cite:5045ecce7d2cf06e4f4219976596e2243d0267d4}}, textual information and remote sensing data could be used together to perform more precise land use classification and this is, in our opinion, one of the avenues that future research could focus on in the next years.
| d | d3146a36d45f58dd466f15f275e4918a |
Several numerical methods have been proposed for accurate solution of this class of problems based on explicit or implicit representation of the interface. Finite element methods rely on explicit meshing of the surface that poses severe challenges {{cite:b46c5c96095ad3722347d13744a27fb02a7b3609}}, {{cite:97bde05bfdd77b8f5c9d284d8357a81466073c2d}}. Implicit methods include the Immersed Interface Method (IIM) {{cite:04033aff0007b49e192373fb50be96e0a6b8c0eb}} and its variants {{cite:da7c2d78e3fe868e6a78dd40f7babee3e24ea9da}}, {{cite:38e60d1bbd946fc9950ec3590a13bfd44471abdc}}, {{cite:ba57f92986d61a52be871fcc16ab871f0f58b30f}}, {{cite:a1d0e3bba7b4a9cc7e08a7fed871d87c53c6fd09}} that rely on Taylor expansions of the solution on both sides of the interface and modifying the local stencils to impose the jump conditions. The main challenge is evaluating high order jump conditions and surface derivatives along interface. Another method is the Ghost Fluid Method (GFM) {{cite:97e5b71fa0ee07d766e7337066584a1090c012ac}} that was originally introduced to approximate two-phase compressible flows and later applied to the Poisson problem with jump conditions {{cite:4587f8d2c782afafcadf6056fe35f7af40153664}}. The basic idea is to define fictitious fluid regions across the discontinuities by adding jump conditions to the true fluid. While GFM captures the normal jump in solution accurately, the tangential jump is smeared. This was solved by the Voronoi Interface Method (VIM) {{cite:eec251a0c1a992e3eca377c442598cc1496999df}} by applying the GFM treatment on a local Voronoi mesh by adapting a local Cartesian mesh which introduces numerical challenges. Several other approaches include the cut-cell method {{cite:9590e032d8b57cd1b96fc535d1f3dac4a3aaa08d}}, discontinuous Galerkin and eXtended Finite Element Method (XFEM) {{cite:fde025d217aa2190f82f32b59665c0d6c775eea0}}, {{cite:8c4b691241c7e3264c8b076c220146e29738eef0}}, {{cite:b9197c20ef91242464fcd0ddfb369ffc37612efa}} among others.
| m | 5ae02e263ff5830318a699197035735c |
Since implicit feedback such as click is redundant, most methods use the click feedback of users as the prediction target.
They formulate the news recommendation task as a click prediction task.
Some methods simply classify whether a candidate news will be clicked by a target user {{cite:23409dc9bb8dad649bc5faf9918f2b9f3c29b707}}, {{cite:61fca73635745b05746b0db413e589c0e3975548}}, {{cite:36ea8da70f191bc377b44bb3655a0908f2184368}}.
However, these methods cannot exploit the relatedness between clicked and nonclicked samples.
Thus, a few methods use contrastive training techniques to maximize the margin between the predicted click scores of clicked and nonclicked news.
For example, PP-Rec {{cite:9bdc9d70a8a3feef8695703641eac37b130969c0}} uses the Bayesian Personalized Ranking (BPR) loss for model training by comparing each clicked sample with an nonclicked one.
However, the BPR loss can only exploit a small part of nonclicked samples.
NPA {{cite:5957037ea7ee2ebaec97ad4ff4289448bb06b06c}} uses the InfoNCE {{cite:20e7b06be0e5fb1a08bda9b241d42362670e073c}} loss for model training.
For each clicked sample (regarded as a positive sample), it randomly samples a certain number of nonclicked ones (regarded as negative samples) and jointly predicts their click scores.
These click scores are further normalized by the softmax function to compute the posterior click probabilities, and the model aims to maximize the negative log-likelihood of the posterior click probability of positive samples.
In this way, the model can exploit the information of more negative samples.
| m | cfcbae9722de22c7886ae0b7bbfa956b |
It would be very interesting if one would consider other topological defects, like strings and monopoles, which can appear in nonlocal models characterized by continuous-symmetry breaking. In fact, global string might play important roles like axion emissions in an expanding universe. In the local case, the topological defects that are formed from global-symmetry breaking should be unstable because of Derrick's theorem {{cite:c63f45b0cecd6b8962f93a9533e6e14c666b78e6}} which excludes the existence of stationary stable configurations in dimensions greater than one. Then, they can exist only dynamically e.g. in an expanding universe. However, Derrick's theorem might not apply to a nonlocal case thanks to the nonlocality. It would be also interesting to investigate whether such stationary stable configurations could exist in a nonlocal case or not.
| d | 7c9c02a84fc6f0b717ef3864b1c9b9dc |
In the experiments, the action selection algorithm that uses Dropout for action exploration is more effective than the action selection algorithm that does not use Dropout. This is because the action sampling using Dropout can be approximated as Thompson Sampling {{cite:3b6168d36d4172f319eb8b2ddf8fc4b2c32cf97e}}, which helps the model converge to a better local optimal solution, increasing the AAR of 18.6%. In comparison experiments with the Dropout ratio of {{formula:ea895e40-b51a-4686-bd25-44f46c8a8b39}} , {{formula:2a5afbf0-3138-43a5-aa0b-55b3acd1819d}} , {{formula:b6b9b4cc-5d4d-4460-b836-d10d44267742}} , and {{formula:ba944f9c-22f5-48af-90cb-99d279231192}} , we observe that as the Dropout ratio increases, the performance of the model first improves and then decreases. This may be because when the Dropout ratio is low, the model adopts a conservative exploration strategy, which is more likely to converge to a relatively poor local optimal solution; and when the dropout ratio is high, the model frequently explores the action space, which cannot make full use of the learned knowledge, resulting in performance degradation. From Figure REF , it can be seen that in the initial stage of the interaction, the accumulated adoption rate may decrease, which may be caused by the large uncertainty of the model in the initial training stage. After analyzing the real-time accumulated expected regret and accumulated adoption rate during the experiments, we find that when the accumulated adoption rate decreases, the accumulated expected regret's growth speed decreases significantly at the same time, indicating that exploration can make the model better learn the advertisers’ demands.
| r | 0102c3712cc0b33a39eeec35bd66c3d4 |
Channel budget We study here the pruning efficacy of ChipNet coupled with channel constraint on PreResNet-164 architecture for CIFAR-10 and CIFAR-100 datasets. Results are compared with the network slimming approach {{cite:b6508bf02d55eadf6a22a6ba572f370e198c4c2a}}, implementation details related to which can be found in Appendix REF . As constraints, we use channel budgets of 60%, 40%, 20% and 10%.
| r | 959a3d1d21dfecce2154300984f9cc33 |
Content caching is an efficient technique to handle the increase of requests for massive amounts of data and content over communication networks.
By leveraging low-cost memory components at the user sides, caching reduces
peak-time traffic by prefetching contents closer to users
during off-peak time, thereby reducing
the transmission delay or equivalently increasing the bandwidth in communication systems.
Traditional caching techniques aim at prefetching popular content by predicting the user demands, thus realizing a “local caching gain” (i.e., that scales with the amount of local memory) {{cite:851ca7759cfbd954abbb04d4cc621041ecf107dd}}. Maddah-Ali and Niesen (MAN) showed that it is possible to actually attain a “global caching gain” (i.e., that scales with the global amount of memory in the network) by using codes {{cite:5836fbde008315676a9a3368ccf29840a6ed3a67}}.
The idea is that, if a single transmission can serve a number of users simultaneously, the network load can be reduced by the same factor thus speeding-up communications significantly.
| i | 64e4148ee998c46af779e261e4238099 |
See Appendix .
The performance of a FA-based UE in large-scale multi-cell networks is mainly compromised by the existence of multi-user interference {{cite:05c2b433627d0158b56389ea6fb6e906bc72ef67}}. In the considered network deployment, the multi-user interference observed by the {{formula:465e238e-cacc-4c91-8129-bd505b11ed2e}} -th port of the typical UE's {{formula:c2435eaa-88b4-4eed-abe2-1217529280ee}} -th FA, where the serving BS is located at {{formula:50f42bb8-5599-44dd-95bb-394909309795}} , is given by (REF ). Although the performance of a communication network by considering the actual multi-user interference can be easily evaluated for the PPP case with independent fading channels, in most relevant (realistic) models, it is either impossible to analytically analyze or cumbersome to evaluate even numerically. Motivated by the aforementioned discussion, the following proposition states our assumption of approximate the multi-user interference distribution of large-scale wireless networks by using Gamma distribution, aiming to provide simple and tractable expressions for the outage performance.
| r | 02b3c212bb11ceb0c4ddbc28cb4bbc51 |
GraphSAGE {{cite:4f71d17697e4ce4e0da4dd08dccc275c5a6fd8a1}}: a general and inductive framework that efficiently generates node embeddings by sampling and aggregating features from a node's local neighbors.
| m | a691d8863354246ed66cb08d8d7c3bd7 |
3) Grow-and-prune: This method gradually grows and prunes the backbone model for each new task. We choose two representative works for comparison, DEN {{cite:bbf0fb30b8269b106d15ee4bd989d32f7826b14c}}, CPG {{cite:5df437b5cf7af34eaba3135cac7f8a97142819b4}}. In addition, we also compare APD {{cite:9afafafba3c764ac0adca934288d691782b37aab}}, which grows the parameter size by involving the task-specific parameters with L1 norm constrain.
| m | 2a429c9ad10a2d49ab0cde61bfb39370 |
In Figures REF (a and c) and REF (a,b,d and f) the attempt to reach chemical accuracy is displayed alongside with the number of CNOTs for both the UCCSD and fermionic ADAPT-VQE.
The UCCGSD (see Eq. REF ) method remains to be characterized. We do so using the BFGS optimizer in a similar VQE loop.
Table REF and Table REF summarize the results obtained from calculations with each of the methods for LiH and H{{formula:35fca03c-d2ad-4a92-860e-e7094d5e29d0}} , respectively.
We observe from Table REF that fermionic ADAPT-VQE brings the most accurate values for the calculated energy by around two order of magnitudes compared with that of UCCSD and UCCGSD. A comparable accuracy between UCCSD and ADAPT-VQE occurs when a norm threshold {{formula:b8e515c9-4b39-49d3-9daa-c81b118d683f}} is used in ADAPT-VQE (which could be also noticed in figure 2.b of {{cite:387866742cc3ef34b307032663dc4a041e89f2e5}}). This means that as the norm threshold decreases the ADAPT-VQE would bring better accuracy.
Remarkably, the number of parameters/CNOTs (30/4624) is still small compared to UCCSD and UCCGSD eventhough the threshold considered is 10{{formula:b4f36240-7c6d-4701-974c-65e926d23a61}} .
Results shown in Table REF demonstrate again that ADAPT-VQE yields the most accurate energy for the H{{formula:f1230f9e-b616-4d07-b079-04233c2963ac}} molecule, by at least two orders of magnitude as compared to UCCGSD and UCCSD. Although UCCSD requires fewer number of parameters and CNOTs than with ADAPT-VQE, the latter brings better accuracy. This is again due to the fact that we controlled the norm threshold to 10{{formula:77953cea-dcc7-4518-adfe-8df55e574783}} . A comparable accuracy between UCCSD and ADAPT-VQE in H{{formula:08f26199-2dea-4ae4-b783-676f81d98222}} occurs when a norm threshold {{formula:856d2bb9-55fa-4107-8767-ffeebc0debb7}} is used in ADAPT-VQE as noticed in Figure 2(h) of reference {{cite:387866742cc3ef34b307032663dc4a041e89f2e5}}). It shows the fact that, at this level of threshold, ADAPT-VQE decrease the counts of CNOTs and parameters.
UCCGSD energy appears in between UCCSD and ADAPT-VQE, but the number of CNOTs and parameters remain very high.
| m | ad386676727bcf605da3ef6d0033797c |
Q-learning is one of the typical RL algorithms which applies look-up tables to find the optimal strategy in each state of the system{{cite:bbc57ff93beb1a44ce4c23bb1833726f218e9a18}}
. However, since a bidding strategy in electricity markets is a continuous action, this method has a high computational time {{cite:f58630b191ceee9cc0f8b368e7457044b28ea089}}. Deep Q-learning can tackle this challenge by using neural networks as function approximators for obtaining the strategies of the units {{cite:db684e275ce2e5931a309b2c96e850751c114de0}}, {{cite:d7b46bbec1fcf63bf680ccfe404417a008e5aa3e}}. Some research studies address the bidding strategies using deep RL algorithm {{cite:ebfc035e479c205ebe0855f94245553c24033b4c}}, {{cite:2d68e9db16fa1da9097d8e379fc5326d9d1896d2}}, {{cite:53c9df75f5160866d2eadd804cc7384fde690ac8}}. However, they do not consider maintenance scheduling in addition to the bidding strategies.
| i | a52bb3968d038203990b55d51d5f2e60 |
It has been suggested that Ca2+ signaling among astrocytes constitutes an additional, complementary pathway for longer-term information processing and modulation of mental states {{cite:ab772c69a2248eac4ddeee2d6a35e02eb93cad66}}.
In theory, states of creative problem solving, idle thought, and rumination may be a few examples of posterior-sampling processes that are evoked by restricting Ca2+ and broadly reducing vesicle release.
In this mode, as we have shown, the network may conduct searches across its encoded distributions.
Stochastic search allows a network to jump out of one attractor state and explore others, much like the simulated annealing algorithm used in optimization {{cite:22bf78d8818bec733ee3061d333fc0c9c8b8d1e7}}.
By reducing probabilities below the optimal rates for sampling from observed distributions, a network can also sample from priors that extend beyond the boundaries of its encoded experiences.
This requires that such priors are true, literal priors, or preexisting synaptic connections that did not result from what we typically regard as learning.
In our results, this concept is visible in the form of samples drawn from a uniform distribution over the complete space of outputs where no input data were observed.
| d | cc35e4076f7431965a26275153c48916 |
In the special case of {{formula:a41fc26d-f859-4045-beff-160a86a9115e}} in Theorem REF , we need the least singular value {{formula:e117fa5b-0d0b-4fb0-9d16-491598c37f6c}} (this necessitates that {{formula:dcea65d9-2562-4969-a184-ad323a6ed4ab}} ). This corresponds to the full-rank setting considered in Theorem REF .
In contrast to the full-rank setting, for {{formula:64dfda78-dccf-4abf-ae45-1edebbe6f8af}} we only require that the set of vectors {{formula:2ca4e391-903d-45af-8b0d-1e2bd01c0000}} are linearly independent (in a robust sense), which one can expect for much larger values of {{formula:da7c3095-6788-482f-8447-304dbd4c4e72}} typically. The following corollary formalizes this in the smoothed analysis framework of Spielman and Teng {{cite:5a1a61723831e6e89b0a32633a9b19f1541b49a1}}, which is a popular paradigm for reasoning about non-worst-case instances {{cite:186f899c1c67d7971c19f127c0e9388e2b981e41}}. Combining the above theorem with existing results on smoothed analysis {{cite:a1b81f29f6f893f43b592df8dd88c36f8f65d935}} implies polynomial time learning guarantees for non-degenerate instances with {{formula:aa5d2dea-3ef1-4fd7-ac06-2702f51f8e4e}} for any constant {{formula:a75c073e-877d-4ee0-b0fd-c499b7843d72}} . Below, {{formula:c2b0e7e7-f327-4c84-8741-0f0c3480d3a0}} denotes the columns of {{formula:16681b41-f35c-410a-a6e0-a4ac53d6caad}} are {{formula:406fdcd7-246c-4c40-a636-1403807842d4}} -smoothed i.e., randomly perturbed with standard Gaussian of average length {{formula:9f20a87d-c907-4db4-8a10-84d418b4b690}} that is at least inverse polynomial (See Section for the formal smoothed analysis model and result).
| r | 422dbc66bcde1973fb915437e741bad6 |
The density-functional theory (DFT) calculations in this work are performed using the plane-wave basis projector augmented wave (PAW) method along with generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof(PBE){{cite:19645eb7cfb88adc6d377157f7d8adfeb8959d3a}}, {{cite:b214bfb443b5ee85a40303e8e8f190ba9a01126b}} functional as implemented in the Vienna ab-initio Simulation Package (VASP){{cite:1c9c24c7e85db3d2625713489eb0531ee03e64f1}}, {{cite:056a07ecf0a5dc54ec6ba227a5edb4b7f0898903}}. Moreover, for the band structure calculations Heyd-Scuseria-Ernzerhof (HSE06){{cite:126fad9856318e75f45cee37f7cca742268685d4}} screened-nonlocal-exchange functional of the generalized Kohn-Sham scheme is included for more accurate band gap calculations. The kinetic energy cut-off of 500 eV is set for plane-wave expansion and the energy is minimized for the structure until variation in the energy falls below 10{{formula:97421db3-8371-4825-a37c-aecee370ec70}} eV. To get optimized structures, total Hellmann-Feynman forces are reduced to 10{{formula:abe50cbe-8cf7-4e4d-a3a5-57a93a8ec37d}} eV/Å.
The k-points for sampling over the Brillouin zone (BZ) integration are generated using the Monkhorst-Pack scheme {{cite:6f116a65accbc80da613a0c3c6de1057716f03d5}} with 21{{formula:5a9ce0e3-3edf-4d2f-a70e-42c0efc5dd4a}} 21{{formula:531522f3-fab5-4244-8477-e5f1cc74b441}} 1 {{formula:5bdf1af3-0109-40a5-92b6-2f27869dc573}} centered k-point sampling. Charge transfer analysis is accomplished using the Bader technique{{cite:1cb5a1b20955bd4e276aac59190ec804babfebdc}}. The empirical dispersion method of DFT-D3 {{cite:ac62a589eb82ad8287b9aafde258ba9eabfb0080}} is employed to get insight into the van der Waals interactions. The vibrational properties are obtained from the small displacement method as implemented in the PHONOPY code {{cite:9534b4ecf963882625f3287b6c1c2dddcc3136a0}}. Simulated scanning tunneling microscopy (STM) images are obtained using the Tersoff-Hamann theory {{cite:27f15ce7b542a7a66ec32e98730497bc539248a1}} and are graphed using WSxM software {{cite:5fd30c7a5cf53a8089df8277ff248c33ea63187e}}. The training set is prepared by conducting ab-initio molecular dynamics (AIMD) simulations over {{formula:65409a95-3326-4ae4-b038-d7284d7dd324}} supercells with {{formula:bf48f032-c4b0-46f0-a9ed-9ed328f85877}} k-point grids.
| m | bd90d02c5f30f643165ccd9ac448664c |
A recent approach to the analysis of nuclear rates is based on Bayesian probability theory, which directly gives the probability density functions for the reaction rates (see {{cite:b3d56aac0c76d939334fc06fce0a925e6cfc6656}}, {{cite:591042f00afc21f298f28413b009d663021339ba}} for the reactions we are interested in). The results seem to be in fair agreement with the frequentist analyses for both the recommended values of the S-factors and the magnitude of the uncertainties.
| m | dfa7134e4bef6161f5b6968b8e688305 |
where the optimization is over the space {{formula:a2a58ac5-1655-4264-bdc8-59897fc538ca}} , i.e.,
the function space induced by the realizations of DNNs with depth {{formula:51887547-6bd5-4b65-b4e9-ed9d39f5a0f2}}
and width {{formula:8a32d5c9-1ffb-44d0-90db-7ddbf3541558}} . The fully-connected DNN architecture that we employ in
this work is schematically represented in Figure REF .
Although there exist more sophisticated NN architectures, e.g.,
residual NN {{cite:4b6a2eeb6f8a5fdce6a65d6390c507748ed08a91}}, we demonstrate in
Section that a rather simple fully-connected DNN is
capable of learning the solution with high accuracy.
| m | 55fb30f6903b86b81faede3e84331a46 |
In this study we explored how trust from users varied as a result of the anthropomorphic features of a robot in an industrial environment. Hancock et al. {{cite:eb782ad2011d2c04047360d3cbd9f7c7fc1c7346}} outlined the importance of robot-related factors for the development of trust in a human-robot interaction. In {{cite:bbe5a0ee768bd01f15c1fcd9a6f7872829673a19}}, the authors state that improving trust in a robot already starts with designing it appropriately. Instead of designing a new robot from scratch to increase the trust of users in industrial settings, we modified the design of an “Autonomous Guided Vehicle” (AGV) by adding an “Anthropomorphic Robotic Mock Driver” (ARMoD). AGVs such as the forklift in our experiment are frequently deployed in shared industrial environments alongside human co-workers. We used the popular anthropomorphic social robot “NAO” {{cite:980e9b4c35c2ce364f6a2fac1159f6db86102e44}}, {{cite:278fe210d267efa23d3b9101ff5658285c15947f}} as the ARMoD.
| d | f330b2fae2a8fa30193f2099cbef3346 |
where {{formula:90c1cb10-e4fb-4515-9fb2-e9d5d316aa28}} adjusts the weights of objectives with respect to different time steps, though we found that just setting all {{formula:fcf96096-323a-409c-8f0f-5c763c6ecb53}} equal to each other could work well. We resort to contrastive divergence methods {{cite:df47bc4072d6ce47536f209be93a5b616c252c6b}}, {{cite:5969058d9862decef4af97219ae018b72551712b}} to minimize the objective REF by descending the gradient w.r.t. {{formula:cc4f2f23-3afe-479b-984b-0382837cfbde}} according to Eq. REFhere, we take a minimization version of the Eq. REF . Thus the sign before each phase is converse. for all time steps. For a specific time step {{formula:c567dde7-e10a-442b-9163-f493773c875d}} , we have the gradient {{formula:dab00d1c-c529-4147-ac57-e06e78fbf76d}}
{{formula:a777f796-86f0-410c-8c01-77b77f422bf8}}
| m | e9f84fec44081a9a168091fbeb5ed90c |
Comparison with baselines. We compare our proposed method with the baseline models to validate the effectiveness of GST. In this experiment, the student is trained on the full human VisDial dataset with size {{formula:344fd52e-ddaf-432b-95e8-af754b880ced}} and a subset of the machine VisDial dataset (5 out of 30 data chunks) with size {{formula:4fe7784e-db97-4c98-9ed7-6734287cc566}} (see Section [sec:setup]3.1). First, we introduce two baseline models: the teacher and the teacher with continued pre-training. The teacher is the encoder-decoder model trained on the human VisDial dataset. It is built on the pre-trained model, i.e., VisDial-BERT {{cite:949bbad25141acc8fc6f42df4c934ee1ae62e01f}}, by adding the decoder {{cite:32d909147bd329783525c7f5f0d0e64d2dc43414}} for the multimodal conditional text generation. The teacher with continued pre-training (CPT) is the model that utilizes a slightly different encoder. Specifically, we continue pre-training the VisDial-BERT with image-caption pairs in the machine VisDial data. The sum of masked language modeling (MLM) loss and masked image region (MIR) loss is optimized by following the pre-training stage of VisDial-BERT. CPT is proposed to identify the effect of utilizing additional vision-and-language data (i.e., Conceptual 12M {{cite:d9eacd48b1d01e17773a719c9262c7cc52cca1d7}}) in the pre-training step. In Table [tab:t1]1, the student shows better performance than the teacher and the teacher with CPT on NDCG and MRR. It indicates that GST is a nontrivial approach to improving performance. Surprisingly, we observe that CPT results in a considerable drop in both evaluation metrics. We conjecture that the performance drop is due to low-precision image captions in the Conceptual 12M dataset, as mentioned in the paper. On the other hand, the student still shows
competitive performance even if it also utilizes the captions in the dialog history.
| r | 1480f9a063aecec8681fc4a18c73bfc4 |
With the help of the Palais-Smale condition, Ambrosetti and Rabinowitz established the following Mountain Pass theorem {{cite:70913765f0502ff75f72539159d7e30829852a39}}.
| r | b7b3f790970bf7ee230d840c69acaf7d |
We study the estimation precision improvement from subpopulation selection by contrasting the estimation results for the full target population to those for the subpopulation in {{formula:da165736-bdfd-4b56-a6f2-2c5c29e6ccb4}} , which are measured in terms of bias, root mean square error (RMSE), and the average width and coverage rate of 95% confidence interval (CI). Note that the subpopulation results are with respect to {{formula:6600f126-9b8f-4336-b9f4-f800a7af0988}} , the ATE on the selected subpopulation.
To construct the 95% CIs for each estimator, in each simulation run we estimate the standard error using the bootstrap {{cite:b12e08ca75ebc3d703d4f59d399631fd0cb66007}}, and then set the CI as the range within 1.96 standard error of the corresponding point estimate.
| r | 18cf3deeb096cbc76cda4b3aa28c419d |
2-DVPP is a generalization of BPP and a special case of 2-BCPP. It considers two attributes for each item and bin. The problem is to pack all items in the minimum number of bins, considering both attributes of the bin's capacity limits. In {{cite:40c368488e2863704969e30b4294cc6edb5f8530}} a 2–approximation algorithm for 2-DVPP was presented. {{cite:11fa7bde8538b9838ad3be7439713b036248dbe2}} presents a survey of approximation algorithms for 2-DVPP. The best algorithm yields a {{formula:249a0f75-65be-4491-9512-60f2dc1982b8}} –approximate solution, for any {{formula:14efe4ea-144d-4fbe-9c63-c82fd74bc871}} {{cite:17beb4d412e4667bed9e004383b507e25551527b}}.
| r | c4d3c028a875312b56cc2ece9ccea3ee |
Deep SE-based methods {{cite:ccb418465b93b75f4d10052f4d0535d3e47324c2}}, {{cite:e51bfc0196f0b600037c7f00ae92d1775827cc58}}, {{cite:740ffd1dd559ae71738abfbd120a17e96c7407fe}}, {{cite:c70dbcc4686d02a4c5616270b4365012d57c233e}}, {{cite:c5919d8471eddcd7698d1f8c2960ff4a4e5705c5}} aim to achieve clustering by exploiting the deep nonlinear representation ability. For example, Hinton et al. {{cite:ccb418465b93b75f4d10052f4d0535d3e47324c2}} proposed the auto-encoder (AE) method to extract a latent feature representation, in which the clustering can be achieved by imposing SSC on the latent feature representation. Ji et al. {{cite:8bbc8c620e12c649f7dfdd0cd38a2110748ee912}} designed a deep subspace clustering network framework (DSC-Net) to mimic the SE priori and developed the DSC-Net-L1 method with the sparse regularization and the DSC-Net-L2 method with the Tikhonov regularization. Zhou et al. {{cite:64f119cbf90500558fc4f9deec91056b9b219312}} proposed deep adversarial subspace clustering (DASC) to supervise the deep representation learning with adversarial learning. Lv et al. {{cite:1108ff20db1bf60b895f45b0fdc0fad8c39ce745}} used a pseudo-supervised deep subspace clustering (PSSC) approach to weigh the AE reconstruction by integrating the local structure-preserving, SE rule, and pseudo-supervision. However, these previous deep SE-based approaches only focus on the attribute information and barely the geometric structure information to conduct the SE, which inevitably depresses the discriminative ability of the learned affinity graph, as both those two kinds of information are of great importance.
| m | 89544d9a8d7dfff297cff1deabac25f9 |
For the near end single talk scenario, we can compare our AECMOS with DNSMOS model which was developed for evaluating noise suppression models {{cite:24821461a58a2b5a310d0d521d0c18960944d326}}.
AECMOS has a more difficult task than DNSMOS: evaluate both echo and other degradations and do so independently of each other. Nonetheless, we believe that AECMOS has very good potential to improve in the near end single talk category. For one, DNSMOS was trained on about {{formula:de94ffb9-eba1-4153-8e65-1bce5713a8b4}} audio clips {{cite:24821461a58a2b5a310d0d521d0c18960944d326}}, while AECMOS saw only about half that many for training and only a quarter as many, roughly {{formula:a2a1dcf6-eeb6-45c6-b90c-96d506829af1}} , were near end single talk clips. With this in mind, AECMOS performance is very promising.
{{table:e2e0a352-3d21-42ff-b41e-f1eea81b1538}} | r | 7b2f34a5a7767528e51338a1bfef26b3 |
In this paper, we develop novel efficient and effective screening rules for the Lasso problem; our screening rules are safe in the sense that no active features will be discarded. As the name indicated (DPP), the proposed approaches heavily rely on the geometric properties of the Lasso problem. Indeed, the dual problem of problem (REF ) can be formulated as a projection problem. More specifically, the dual optimal solution of the Lasso problem is the projection of the scaled response vector onto a nonempty closed and convex polytope (the feasible set of the dual problem). This nice property provides us many elegant approaches to accurately estimate the dual optimal solutions, e.g., nonexpansiveness, firmly nonexpansiveness {{cite:16465f700610e031b17974c284768edb15858654}}. In fact, the estimation of the dual optimal solution in DPP is a direct application of the nonexpansiveness of the projection operators. Moreover, by further exploiting the properties of the projection operators, we can significantly improve the estimation of the dual optimal solution. Based on this estimation, we develop the so called enhanced DPP (EDPP) rules which are able to detect far more inactive features than DPP. Therefore, the speedup gained by EDPP is much higher than the one by DPP.
| i | 8144cff6b60faa859e78021ce2cf3d5a |
Our construction can be seen as a realization of a quantum wire allowing tunable transfer of information between the input and the output qubits. The adjacency matrix {{formula:601ebd25-83f0-4321-949a-c5b721fa44b7}} is related to the graph {{formula:ce3765d1-132f-491a-bbfb-3a64fbe448c1}} , where we place {{formula:141fb9ef-8214-402b-bce1-5ffc2e9861a8}} spin-1/2 particles on each vertex, the {{formula:f984d91b-4b7a-45b0-a2f5-bb4c50167eb9}} spin has Zeeman energy {{formula:2fec92e5-fccd-43ef-9f0c-f8d397be7f50}} and an isotropic XY interaction, {{formula:a05cc463-32fe-44a8-8c36-c242dbc2129d}} , with the {{formula:ab495278-a6b5-448a-8cb2-4bb1d9a1b9a2}} spin. In the underlying Hamiltonian, {{formula:92dcbbff-fc52-43ed-b992-2d0ba97caa36}} , Z-component of the total angular momentum is conserved and all spins down is an eigenstate. Hence the dynamics of any arbitrary single excitation is confined to the first excitation subspace justifying our study of the evolution of {{formula:5470e2ff-6386-417e-bade-666f09081729}} to {{formula:2e598ddc-d3bd-4819-a2f6-f2923bd97749}} {{cite:5ba7352a61c2261d8627234b4be6ffa2b8ce6a18}}. Our construction is applicable to the perfect transfer of many-particle state in a network of indistinguishable non-interacting spinless Fermions obtained by the Jordan-Wigner transformation {{cite:12d8231153a2aa77ef66c20e3e7459878f47f153}}. However, it is not clear that the maximum fidelity of multi-particle excitation is same as {{formula:81b7fa12-84d7-415f-a769-69000202afcf}} even with the loss of centrosymmetry. Importantly unlike previous studies {{cite:5ba7352a61c2261d8627234b4be6ffa2b8ce6a18}}, {{cite:12d8231153a2aa77ef66c20e3e7459878f47f153}}, {{cite:0b73e2b9aa2079648f39fefc52efb06a20cd2cf8}}, our stochastic approach allows the construction of an infinite number of networks with identical transport properties. Our study proposes a possible mechanism to achieve a controlled transmission in quantum information processing over complex networks.
A.K.D. is supported by an INSPIRE Fellowship, DST, India.
| d | 981e8b8443922394ca9f667595066b10 |
A natural and interesting extension of our research is to consider the problem of variable selection. In the Bayesian setting, one could take into account alternative prior distributions of the multinomial logit coefficients per cluster, e.g. spike and slab priors that encourage sparsity in the model. Another direction for future research is to combine our mixture model with alternative Bayesian logistic regression models that exploit data augmentation schemes {{cite:b27d5b656e5f25e7474c7efd8caf06a0577e9ecc}}, {{cite:edd42e6e6807f8df0ad5709e36e339a13987560a}}, {{cite:605b7709dfeaa87554ebcade8225828755df50c2}}, {{cite:c9ede361c6cc4653bb76a2e5dd06993b48bf86c8}} and assess whether MCMC inference is improved.
| d | d5f936d025d7ff7cc5f46b9df5f80b5f |
We decided to follow a methodology upon the DBScan method of clustering {{cite:3e2e1e39eb8d28c30dffcadb866950fbb5a60f41}}. DBScan considers all distances between pairs of points. If they are under {{formula:b828ace7-000c-4a7b-8e6b-4af9902a682b}} then those two are linked. Once the number of connected points exceeds a minimum size threshold, they are considered a cluster and all other points are considered to be unclustered. This method is advantageous for our purposes because unlike other methods, such as K-Means, it does not require the number of clusters to be specified. To create a system that can build clusters dynamically, adding one point at a time, we set the minimum cluster size to one, meaning that every point is a member of a cluster.
| m | 4a0cecbed0753991a0dbc505a2723c8a |
For each candidate causal graph, one typically requires that a probability distribution satisfies two conditions relative to that graph: the Causal Markov Condition and a faithfulness condition.See, for example, {{cite:38561388bcbdc0ff0b861d07770b274a10db912f}}, {{cite:4e27b0c9716c075182b364af3926b396056e9960}}, or {{cite:b30f65ec7ecccf850d7ec737acf5a3297f5374dd}}, where the faithfulness condition is called “stability”. The Causal Markov Condition is a constraint on how the joint probability distribution P(V{{formula:87647a13-49a0-46de-b68f-ed05feefbe18}} , V{{formula:8b73e254-42a0-40e4-a639-ea65a21350a3}} , {{formula:04836e0b-d52e-43b1-89bd-a9ddc323e470}} , V{{formula:1d6811df-6509-4370-a115-9fe9511d8945}} ) factorizes into a product of conditional dependence relations according to a candidate causal graph. Speaking loosely, one requires that if all of the direct causes of a variable O in the causal graph are specified, then one cannot learn any additional information about the value of O from any variable that is not itself a descendent of O. Formally, one requires that any candidate causal graph satisfy:
{{formula:570c71fb-e19d-4d4f-a819-ad6e5612bf00}}
| m | ee9f76375b5ad6fca1315848bb00f4dc |
Afterwards, black holes with the presence of the Æther field have attracted more and more attention. After studying Einstein-Æther theory, Jacobson et al. turned their attentions to black hole solutions in GR coupled to the Æther field {{cite:34820fd324c98f39a408ff5b7ac6b5bf2c371d36}}. It is found that within a wide range of couplings external to the event horizon, these solutions are very close to their Schwarzschild counterparts. And inside the event horizon, there is a space-like singularity, but some differences in physical quantities exist. After a short while, in the non-reduced Einstein-Æther theory, the evolution of the gravitational perturbations of a spherically symmetric black hole, both in frequency and time domains was considered by Konoplya and Zhidenko {{cite:72cbcde4cdcfc3766da5de4ab39d74cc62573d43}}. The results show that compared with Schwarzschild black hole, the actual oscillation frequency and damping rate of Einstein-Æther black holes are larger. Besides, not far inside the metric horizon, these black hole solutions have a universal horizon that captures waves of any speed {{cite:b298fd0518a82f0daf99677818c199138fb8f26f}}. Berglund et al. pointed that the universal horizon still obeys the first law of black hole thermodynamics, and if it also obeys the second law, it will have entropy {{cite:dc53ed837ea9429682696209d9e04f5a1e65c53b}}, {{cite:e6d37f9989627f81e7b6adeb7e04b60ec60719c0}}. By coupling a scalar field with the time-like vector, they concluded that even though the scalar field equations violate the local Lorentz invariance, the universal horizon still radiates acting as a black body. In addition, two new types of exact charged black hole solutions in Einstein-Æther theory were found in Ref. {{cite:a1f3c29fb54f3563203a1a827e79286053c394bc}}. Slowly rotating black holes were also studied {{cite:8779c686d54433ca0d5e140e194d0620e52abe6d}}, and unconstrained by the naked finite area singularities, the solutions form a two-parameter family, which can be regarded as the mass and angular momentum of the black hole. There is also a lot of research on black holes in the framework of this theory {{cite:7279f8008ec15c3258b49da8824d477ce1920542}}, {{cite:92cccbb74837a562beec3838a01e6dc9bb0c3dcd}}, {{cite:d32d4520f89d1cbc7e7fd1ea3dbfdedf57165c2a}}, {{cite:1a9eafb65463f9e781ce721325d3fb1dca2d7575}}, {{cite:f0de15462404c761217349191c4dc572fdd17022}}. In Ref. {{cite:7279f8008ec15c3258b49da8824d477ce1920542}}, the black hole shadow in the traditional manner was studied. It was found that different coupling constants describing the Æther field have different effects on the size of the black hole shadow. In this paper, we will show how the Æther field contributes to the inner shadow of a static and spherically symmetric black hole when the thin disk is present.
| i | 49d804f74f53ca94c7eb68c60f1dd6d4 |
While it is assumed that these limitations can be overcome by adding
suitable inductive biases in current neural network architectures {{cite:0ea2a14211d6d895dc38ee573e89b87fa1e94fc1}}, {{cite:24a81e0e78c6054a740df6ac8d4dcc47398c325b}},
the notion of inductive biases itself is often left vague and does not always provide meaningful guidance.
Traditionally, inductive biases refer to biases in the hypothesis space, and in the case of neural networks, to
the structure of the parametric function captured by the architecture. More recently, the notion has been grounded on the invariant properties of such functions {{cite:1982e78c81a03bb006d2599a82e27ecf2dbbaeb9}},
but more often they are used to refer to
intuitions that are not spelled out in formal detail and are not explicitly evaluated.
| i | 6aa234d7f1c053f153fb053783ac5ac1 |
Gromov first raised the question which CAT(1) spaces do contain regular points {{cite:b4b3232751ad08858bdcaa5c7d69996f9ce793b3}}.
A general CAT(1) space does not have to contain any regular points.
On the other hand, locally compact and geodesically complete CAT(1) spaces always do,
as shown by Lytchak-Nagano in {{cite:f0be5a484e22a86b1f30ec4c3247626e9d51deb8}},
following ideas of Burago-Gromov-Perelman {{cite:bb7c77cd22c1e0a6913363974c30b16f1dec4543}}. However, the
Tits boundary of a locally compact CAT(0) space with a geometric group action
is typically not locally compact.
| r | 605c694b22acce9cd40629ec67132bf3 |
We will extend {{formula:279e0162-17e2-4026-9b05-8239ef34e288}} to be an endomorphism {{formula:5eb2a054-9933-42bf-a880-2de3e5dcfb89}} by defining {{formula:1dfb2ee5-c69f-4789-a22a-512a7bd8aa93}} . According to the definition of a contact metric structure in {{cite:22e50e3014452d436daa30d2517ee20caec87291}}, one only need to verify that {{formula:974e971c-c2a0-4a4e-afd9-cae09ddb4da0}} gives rise a contact metric structure.
| r | 3f1d972e0dabfb5b1966c78fc59099f4 |
Our main contributions are as follows: (1) we create a methodology based on local search to generate a stratified oriented-to-the-individual dataset, with each example composed of a set of posts of a single individual (section Dataset Generation) so that our inferences do not consider only snapshots of posts but the target student instead; (2) we induce and compare the performance of several models that learn from representation learning {{cite:c1ac83f3c52f6aac4131f3c5afc7694f169ca335}} techniques (section Deep Learning Models) and compare them with classifiers based on metadata features (section Feature Engineering Models), both from textual and visual data; (3) we propose an early fusion neural network-based architecture to handle together the textual and visual features from posts in a similar representational space (section Multimodal Classification). All code is available at our GitHub repositoryhttps://github.com/paulomann/ReadAndSee.
| i | 674f1773c62cee408da5aafaa49edcb4 |
Remark. Apparently, a construction of {{formula:52b4b65d-dfa7-4b8a-b08a-215632a5183e}} was firstly appeared in Aldous {{cite:65234f580f4694d7780d93af356e4e858b4da2b4}} (1985), 11.19,
with a reference to J. Pitman (see, also, Pitman {{cite:31b3d7f5597c171dd5ee27782d0e45fc4ee43940}}). The action of the group {{formula:bc796950-9931-4cf2-a01f-02f1a757297c}}
on {{formula:2776e952-7a89-45f3-8123-c91563203053}} appeared in Kerov, Olshanski, Vershik {{cite:8e1479e615ad574b8a5b85a425b18666d14fd921}}.
Notice that for a fixed {{formula:821fe322-28c1-47e6-9056-84fa314d4b09}} for each {{formula:514e7c0a-8cd3-4ca9-951f-c722bcb8ea14}} we have a distribution of lengths of cycles on {{formula:2bad7873-ae15-448a-844c-78aa049fd250}} , i.e., a distribution
on the set of partitions of {{formula:af320d10-3a0b-4344-901b-a5fef7834d44}} . So we have a Markov process of growth
of such partitions, this process arises to the work of Ewens {{cite:cf67523dc2371b645ffd41e9c96cde0aa4075ca1}}, 1972, on population genetics.
{{formula:a5837026-188b-4a63-b517-2dab4833e6ad}}
| i | c9abf011e2f1afb782428d54796e210f |
For objective evaluation, we use the Mel-Cepstral Distance metric {{cite:8bdca5973780b2724e55a73e0700066edfff702b}} as shown in Eq. (REF ) and the results are presented in Tab. REF . For subjective evaluation, we asked participants to listen to the songs generated by both the models and evaluate them on Audio Quality, Intelligibility and Overall Score. We compared our model to the WGANSing model, both trained on the same dataset and for the same number of epochs – 750.
{{formula:df1ac8e1-dded-4f08-804e-56752efefc4a}}
| m | dc7617443e5fd7eae950d13fa5fb5ee4 |
We develop a deep CNN network named SeizNet for end-to-end seizure detection solution. Comparing to
{{cite:8081f981cbef22afebb8a3c391c1aa2b2747613c}}, SeizNet contains additional dropout layers {{cite:8784217317ee0c7fd9f2a97b03a6c75cb664733e}} and batch normalization
{{cite:d9930243885559fbf0cbb810df75fcb5d9bd88bb}} after every convolution layer. Such layers are designed to avoid model overfitting.
Unlike the typical usage of dropout which is only after fully connected layer, we used dropout in
various parts of the model as it is indeed suggested by the inventors of dropout {{cite:8784217317ee0c7fd9f2a97b03a6c75cb664733e}}.
The number of filter at each convolution layer is multiplied by two every time like VGGNet {{cite:11a4af0aaef22b42396fa39b7e37bc6ff50742f3}}.
It enables SeizNet to have less number of filters at low levels in which filters learn basic shapes,
while having more filters at the higher levels where filters are capable of grasping sophisticated patterns.
As an activation function ReLU is used and other hyper-parameters of the model such as number of filters and filter sizes at each layer as well as number of unit in fully connected layer are cross-validated over a broad range.
Detailed architecture of SeizNet can be found in table REF . The total number of parameters
for SeizNet-2chn and SeizNet-18chn are {{formula:dde02e34-0657-4b12-832d-74bcccf009c3}} and {{formula:5c6d8e56-2f67-4e72-8300-2ffd4881d2a2}} respectively, both include 240 non-trainable parameters.
{{table:da9939d5-2caf-4015-b205-e8d105ca6af4}} | m | f7096e91be024d8816808831d35caaca |
Miscellaneous: We can extend the above sampling procedure on a product graph under the noisy sample acquisition setting by finding the optimal sampling operator. In addition, we can process multi-band signals by sampling optimally on a product graph by constructing filter banks analogously to {{cite:f0e87f14a0ad4af6a5883b73c216992bed47c2f3}}.
| d | 1ca759b1356a668272b0fb0b9b97260c |
Due to the advancements in computational power and a large amount of high-quality datasets, deep learning has become the state-of-the-art technology in computer vision, natural language processing, and others {{cite:4e87feb0218263bdd36bf275feba3505665e2a31}}. Deep learning has also made remarkable progress in all areas of medical image analysis, including segmentation, detection, and classification {{cite:4e87feb0218263bdd36bf275feba3505665e2a31}}. However, deep learning models are trained on large datasets, which may not be available in the medical domain due to privacy and ethical concerns {{cite:81ae5b808f999ff068dd8a71a8cf8789204f360b}}. Medical experts find it difficult to publicize the majority of medical images without patients' consent. In addition, the public datasets are also small and lack expert annotations, thus, hindering their use for training deep neural networks. Furthermore, most of the available datasets might contain unbalanced classes that may hinder the performance of deep learning models and may not produce critical biological insights.
| i | ed88404464e6cca8272220be86ed77ed |
It remains to discuss how to make simulations. For the first model in Section REF , the orientations are independent and each orientation follows the density {{formula:9387d8c0-4adc-4f93-8162-1aba64135978}} , cf. (REF ). We use rejection sampling when simulating from {{formula:de366213-a002-431c-8b81-68874bac6241}} and a two-step method for simulation of {{formula:45d5aec0-df76-440f-a2da-69367617485d}} : first {{formula:718ae4db-9770-45c4-9ea6-b3a0b8f6163e}} is sampled from the fitted beta distribution and then {{formula:c448a0b6-de2c-4088-8ce8-617ebbe35421}} is sampled from the conditional uniform distribution, cf. (REF ).
For the pairwise interaction models which are given by (REF ), we use a Metropolis-within-Gibbs algorithm with a cyclic updating scheme which updates the orientations from one end to the other (a so-called sweep, see {{cite:d85da200464c09b62327cf1e7faaab752eebf66b}}). Here, when updating the {{formula:2252297c-a846-434e-b54c-6faf7548c32f}} th orientation, if {{formula:b48819d3-8f26-4007-a106-9c1b41d584e4}} and {{formula:c8acba72-35f1-4de8-b704-b2b06c54cc7c}} specify the current state of orientations, we propose a new value {{formula:9faeb276-64bf-4c5c-86d5-236e5ba2a92d}} generated from {{formula:2d59e9a4-0a80-4b8c-9171-01e7d3fdad25}} and accept this with probability {{formula:282df750-7526-4395-a24a-d71744f11fa5}} (otherwise we keep {{formula:e401d7a8-e617-4a09-973f-576960300026}} ), where
{{formula:bb9cac4a-a880-474a-83da-5478f3c8bff1}}
| m | ac9bd88fe9fcdd379b90fdeda11243f4 |
Although contact binary merger events are predicted to be relatively frequent so far only a single event has been confirmed and that only in retrospect. The linking of orbital stability with the mass ratio of contact binary systems has long been recognised as potential avenue for identifying unstable systems {{cite:5a7520bbd3d22399c4409bb96be543f0cfcbbde5}}, {{cite:4aed5752acd603ba114247c3d95fcea33c4504a5}}, {{cite:5ade891e7b0e295094c73dcdadffb2f08b2a9ac0}}. The earlier work clearly showed that orbital instability is likely to occur at very low mass ratios and higher mass ratio configurations are likely to be stable. Our theoretical work {{cite:d116ccaf44191fa1673070ad086a1a3a2d9e7c69}} linking the instability mass ratio to the mass of the primary has progressed this further by demonstrating that there exists no global minimum mass ratio at which a system will become unstable rather the instability mass ratio is dependant on the mass of the primary component. In addition, we showed that systems with less massive primaries can have mass ratios higher than 0.2 and still be potentially unstable. When combined with work showing the suitability of survey photometry for light curve analysis {{cite:7a3b099850b08c1b531170a6ec9e461638a6a54b}}, {{cite:7ee69a5b26911740046467240d7da98fdc350d5c}}, {{cite:fdc00b350e4e6419132bfa976ab503667815a08e}} has greatly facilitated the potential for being able to to identify low mass ratio contact binary systems. In this study we enhance this capability by establishing simple light curve and colour parameters that can be used to exclude systems that are likely to have mass ratios above the theoretical instability value. By excluding likely stable systems we greatly increase our chance of identifying potentially unstable systems from the remaining sample. We apply the techniques on bright contact binary systems from the ASAS-SN and identify approximately 50 extreme low mass ratio system (most previously not reported) satisfying the mass ratio criteria for orbital instability.
| d | 5e3b4a40623b59ae35b52b00dcc13c3d |
The chirping gain should also depend on the choice of chirping amplitude. If the amplitude is reduced to zero, the chirping gain must tend to zero. If the amplitude is too large, the laser will sample velocity classes that have a smaller atomic population.Therefore, amplitudes on the order of or larger than the width of the Boltzmann distribution of 1 GHz will result in a reduced return flux. Thus, there must be an optimal range of amplitudes. Since our setup did not allow for simultaneous seeing measurements, it is not reliable to attribute one single measurement with an outstanding gain to the chirping parameters only, more likely the result can be attributed to temporary good seeing conditions. However, two general conclusions can be drawn from the data in Fig. REF . The chirping gains seem to be lower for amplitudes greater than 300 MHz and the highest chirping gains are achieved for amplitudes between 120-250 MHz, i.e. significantly below the mesospheric sodium linewidth (1 GHz). Thus, even at an optimal chirping rate it was not possible to efficiently snow-plough the complete atomic population and chirping is most efficient at the flat centre of the sodium line, where the atomic population is similar among velocity classes. This hints at the role and timescale of thermalizing collisions. In fact, the combination of 0.8 MHz {{formula:7b12ad8b-4f0e-4f00-9422-0cde70b19c43}} s{{formula:36e8bcbc-4bbd-446b-83c7-170ba141ac9d}} optimal rate and 120-250 MHz optimal amplitude leads to an estimated collision time of {{formula:5e79bb10-4c44-4e68-9bc4-76c792516e2b}} ms, which agrees with what generally has been assumed in the literature {{cite:79264b767a204f24ea03e708747e34c7bfae5b36}}, {{cite:a8a86c3a1ff430b9c931c1f85189291b31c13cfd}}. We note that sodium atoms collision rates change by about an order of magnitude over the vertical extent of the sodium layer .
| d | 2a7b445173b058d3bbb697d4d169becf |
In this work, we have proposed a validation workflow for driver models in interaction-aware AV controllers. We illustrated its utility through a case study of validating an inverse reinforcement learning-based driver model replicated from literature {{cite:e459cfb8d73baa14cbdacfd093a0fbd39934bc6d}} using naturalistic highway driving data extracted from the HighD dataset {{cite:7b55fb01d9b5c7525515654086604bd622b56ff9}}. Our validation workflow (Figure REF ) incorporates the automatic extraction of comparable lane change scenarios (5581) on which the IRL model was trained (step 1). The validation of the model was then performed in two related stages. First, we examined the tactical behavior of the model (step 2). Even though no collisions or off-road driving were present in the training data, the model produced such behavior in more than {{formula:4a22ba71-95e1-4b59-a941-d7d54b60f656}} of the cases (Table REF ). Second, we analyzed the operational behavior of the model in the {{formula:c9c98b69-4f61-432a-af49-2e2e334ec6cb}} remaining trajectories (step 3). This analysis revealed that even though the dynamics of the model's lane changes are similar to humans (Figure REF a,b), the model performed the lane changes with significantly smaller safety margins (Figure REF ). Furthermore, the dynamics of the model's car following behavior was largely inconsistent with human behavior (Figure REF c,d).
| d | e668d45ca19e24f1284feaee2bb71c0b |
The depth-resolved Laue patterns were obtained by solving Eq. REF for each pixel in the detector. We used a sequential approach by first recovering {{formula:9a87e52c-30c0-472f-8544-898df9658f01}} with an exhaustive search, and then recovering {{formula:bf0db976-b4e2-4d17-9dbe-c67f54c6c0bb}} with a non-negative least-squares solver {{cite:29b54b87c4c5da263ea5381643834250c46e66c9}}. We show the results of this process of recovering {{formula:612e3873-3e3e-4565-9a4d-b04be49d1260}} and {{formula:d20e170b-af02-4724-bb52-dbfcd07f917b}} in Fig. REF for three selected detector pixels at the position. We plot the measured and estimated signals based on the recovered {{formula:d3a4cae2-0ac9-4a7b-9189-e4d90e8733ff}} and {{formula:301c05b9-4a2f-4ac4-8965-b9fbcfcc9806}} from which we observe that they show a good agreement. Note that the estimated signals are obtained by convolving the footprints {{formula:e4f4bc0a-c644-4662-a14f-25fb2037d503}} with the coded-aperture, and the measurement signals are aligned to their recovered positions {{formula:45b80f72-b33b-4ac6-a8c3-037146a17db0}} on the coded-aperture. As a final step, with recovered {{formula:3b87915f-67c4-4c6c-b5fe-fba58b9d18f4}} and {{formula:2ca0bc4c-0ba0-4c60-955f-0b9d88de227e}} , we reconstruct the depth-resolved signals along the beam path using ray-tracing analysis as similar to the differential-aperture imaging method {{cite:332a39c2a7b8da802f98ee348f73e019c65e4018}}. We validate our reconstructions with the conventional differential-aperture method (a 100 platinum wire scanned with a 1 step size across the sample) for the same Ni sample location. While both the differential-aperture and the coded-aperture method could reconstruct the signals at all depths, the differential-aperture reconstructions yield noisier signals. In contrast, the coded-aperture is found to be more robust to noise induced in the depth-resolved signals during the reconstruction process. This reduction in noise is probably due to the increase in the number of edges that pass through each ray which increases the signal, and the fewer number of raw images most of which contain no signal for a particular pixel but still contribute noise.
| r | 17a7d34eac5926b4ee59939a09b686d1 |
As showcases, we herein report iOI calculations of a series of double-stranded DNA molecules of various lengths, hereafter termed as DNA{{formula:403a941f-1874-4c7a-8bd4-d4fed3f47502}} ,
where one strand is composed of {{formula:90402062-3a09-4cc4-a461-5021deb9bb57}} consecutive adenosines (A) and the other is composed of {{formula:222e4c6d-5ea0-44a7-9898-2051cd4f23fd}} thymidines (T). All calculations were performed with the BDF program package{{cite:fa3abc65ed77fcfd69c0378d8a693228ce629a14}}, {{cite:b84b7200aa9a19cc9c55adfffdce68a07d6df006}}, {{cite:af449a97cb0e1f271be7d0cb6d31cb5af5ce0406}}, {{cite:c47e804935a57435260349e47bd72facd227d81e}}, {{cite:dcc131094a6447b368e8a8cf632d6fed5dda5b91}}
on a server equipped with 16 Intel(R) Xeon(R) CPU E5-2640 v3 @ 2.60GHz cores. The B3LYP functional{{cite:a9a6dac75b86857a58987d94ae1fdd76361d8f78}}, {{cite:b491bad5ced1cd6cad44d62b1711916950b018ca}} and the def2-SV(P){{cite:f2f6aba3c225dd16cd3e357c38a180a2eb6122d5}}
basis set were used throughout. Unless otherwise noted, all SCF calculations of the global system (including the exact SCF and the last macroiteration of iOI) are converged to the following criteria:
{{formula:843ff7a8-80cc-4031-b532-c1d1ec2cb31e}} for the energy change and {{formula:b0ba0502-4667-4772-8cbb-e9d92c6fbe3b}} for the maximum change of density matrix elements.
The subsystem calculations of DNA{{formula:dcb6e70e-987b-4d79-a7d3-5eace8e5ae8b}} were embarrassingly parallelized over {{formula:946ad4ff-94a7-406e-b3d2-6b82885c4617}} processes,
each with {{formula:8f1c64dd-33dd-4d0a-a0a2-b4462c36b533}} OpenMP threads, while the global system calculations were performed using 16 OpenMP threads.
| r | c6387814938f535209b08ffceb8e3cfa |
The top part of Table REF shows the result of the gel detection classifier. We generated three different classifiers from the training data, one for each of the threshold values 0.15, 0.3 and 0.6. Lower threshold values lead to higher recall at the cost of precision, and vice versa. In the balanced case, we achieved an F-score of 75%. To get classifiers with precision or recall over 90%, F-score goes down significantly, but stays in a sensible range. These two classifiers (thresholds 0.15 and 0.6) are used in the next step. To interpret these values, one has to consider that gel segments are greatly outnumbered by non-gel segments. Concretely, only about 3% are gel segments. More sophisticated accuracy measures for classifier performance, such as the area under the ROC curve {{cite:0cd75409d0e8121286e66d17331b31446660eb07}}, take this into account. For the presented classifiers, the area under the ROC curve is 98.0% (on a scale from 50% for a trivial, worthless classifier to 100% for a perfect one).
{{table:59d7d58a-033a-4d21-b49d-5a3934f8def6}} | r | 26354e820f0db99d43692844d86e98d6 |
We applied the GBT within the first-principles calculation as implemented in the OpenMX code {{cite:d73cb5e45f9ddbd014bb3dec081b217e9abe5b97}}, a DFT package exploiting the localized basis function {{cite:4c74fa6b161a99917fc2103c8638f37b4aa49785}} and norm-conserving pseudopotentials {{cite:8a58d7b3294d182e33e0864ec66e5a154e4a807f}}, with a 150 Ryd cutoff energy and employed the generalized gradient approximation (GGA) {{cite:91acf8f3b89d9c66b8173fb4102e3189680ce8b7}} as the exchange-correlation functional for the electron-electron interaction. The implementation of GBT is to express the non-collinear wavefunction as the linear combination of pseudo-atomic orbitals (LCPAOs) by including the spiral wavevector {{formula:93c511b1-da55-49b0-af22-24cab11d1c4e}}
{{formula:983f86f7-bcf5-4855-b134-c21cd6822046}}
| m | 991e971c9bc8a6614c66e975a70bc9d9 |
Since the Eq. is independent of {{formula:288e7922-251f-4889-abd6-c841b56f186b}} ,
the system is effectively under a constant driving.
As a result, the system at long time limit, if classical, should obey the original TUR {{cite:82f63f19dac8497ef436013a15de62b0788a3a62}}, {{cite:0092372cc28c0810558f0480563e9c8841b76869}}, instead of the generalized TUR under time-symmetric periodic driving {{cite:88ac61e49d228298ce85a14f756ce94fa6144dee}}.
Thus, the loose TUR bound of our TLS model ({{formula:cbf70c29-7e19-4dc2-9557-50ab2d26f24a}} in Fig.REF ) stems from the quantum nature of the dynamics.
Our model further elaborates the contribution from the quantum nature to TUR:
The imaginary part of quantum coherence contributes to suppressing the Fano factor of net transitions and lowering the TUR bound, whereas the real part of the coherence always tightens the TUR bound.
The bound of TUR is determined by the competition between the dissipation and dispersion of the input light source.
| d | b9d746b94941418387bd2cb78c76c24d |
where {{formula:ba0e43d3-a27c-46f2-b0d2-599ec6999077}} is the subsequent state of the state-input pair ({{formula:ffdf96d3-0d93-4286-b732-5563fd4a2298}} ). Under some conditions {{cite:8d3f622beb292e25af5949273e75688e4bd120e4}}, the action-value function {{formula:1e0367f4-38f0-471e-acbe-917ebf335f2b}} in (REF ) can be replaced by an approximator {{formula:8ae6a965-0b52-48bd-b04c-d2231394e896}} without affecting the policy gradient. Such an approximation is labelled compatible and can, e.g., take the form:
{{formula:09593538-b221-436a-a4f3-1d42920a326b}}
| m | 4e1d289dd562d4cd6c5dfdd7c1b5a922 |
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