text stringlengths 54 548k | label stringclasses 4
values | id_ stringlengths 32 32 |
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m (-z) + d (z) ,
where the system's dielectric function is constructed out of two interfacing piecewise-constant (bulk) local-response functions, {{formula:942c8873-e29c-4ac4-9391-b90f2bc400aa}} and {{formula:a0a39692-16c9-4389-adb3-63cac57c9da0}} (and Eq. (REF ) is then solved by invoking the classical pillbox arguments at these interface {{cite:5c417c8a6088c697c401c7f50197605696054f7a}}). Here, {{formula:c035f1d7-2008-44f0-8368-736666e0d329}} is the Drude-like dielectric function of the free-electron gas {{cite:a3c79038b5887cc9d63677b8e383e1e1cd2af302}}, {{cite:81e2e2ceb3c41e289bf030c5f1f634b113a4265b}}
{{formula:95b22e70-837d-4ff2-97e7-9b2e3a02ecf3}}
| r | 1997848999830009be016e1abb3e42f3 |
The shortcomings of these explainers are due to their underlying assumptions which do not hold true for the majority of models, especially the assumptions of independent features and local linearity.
These assumptions are further impacted by the explainer hyperparameters, such as the kernel width for LIME or the background summarization method for SHAP. Tuning of these parameters is dependent upon the data and model. In practice, these knobs can be adjusted until the explanations “look right,” which is not realistic when the most faithful hyperparameters need to be derived from the black box itself.
This is especially troubling as studies show that data scientists overtrust interpretability techniques {{cite:f5d2ac35000d543548d065f9f696d59dd40b3f47}}. With the results of our study, even those practitioners who do not abuse these explanation tools may still be mislead.
| d | 5222e3f5c5568d3ce662f0f500f049fe |
In recent years, modern machine learning techniques using deep neural networks have had tremendous success in various areas from science and engineering: computer vision {{cite:09c021da5139b9acd026f79eb531490c9f391d53}}, natural language processes {{cite:b584b01f6141efdd7a207b815297c99095f10fcd}}, time series analysis {{cite:a6999d874ea25d95da0e3eea7fbc7ff4e01efb73}}, cognitive science {{cite:111737752403e9b630c8044817e0f95de1d9ab85}}, and so on.
The notable advance of deep learning algorithms has offered interesting possibilities for computational innovations.
In particular, based on the rich expressiveness of neural networks, it has recently begun to gain more attention to solving partial differential equations (PDEs) using a deep learning algorithm.
| i | af36787eb5ac1917ae6faf6f6d2248e3 |
The above criterion provides both a common framework and an extension of various existing results in the
literature, such as the criterion for constructing regular contact
manifolds (cf. {{cite:096c5209b09023e8e4d83e796c5c146b986d2b60}}), and the cohomological
criterion for the existence of completely integrable contact forms of
toric type (cf. {{cite:33f4fb1fe4014b07100e877ee5de53f71c5f4278}}). At the heart of the above result lies
the classical Spencer operator {{formula:7c01beb7-1952-4e51-9d7e-36d54429e4e6}} ,
which recently has been discovered to play a central role in Jacobi geometry
(cf. Observation
REF for a definition of {{formula:099f098b-030f-4ec5-a3df-9b0d0e4c7cdb}} and
{{cite:82319e3f34741757d7f74d93161fea36d04f8936}} for further results).
| i | 8d33690682e0854db227477135019d92 |
The determination of when to stop the training process is notoriously difficult for the training of GANs. To assess the quality of the generated samples, we repeatedly compute a custom version of the Fréchet Inception Distance {{cite:571ab158bb21a13051945bb7a70162eeda688ba3}} which is computed based on the features of the last convolutional layer of a ResNet-18 {{cite:34383fcb118668d26f6f58f758c567cac880200c}} pre-trained on the THA data set published in {{cite:99c10ca315887d5635624ca52c77f4bb2120bc85}}. The training process is stopped when the lowest FID is observed which is computed using the equation REF , where {{formula:464943c3-0e12-45c8-84d5-619675626494}} and {{formula:3e57758d-1407-49ad-9c98-42f43e2c9022}} is the feature-wise mean of the real and generated spectrograms, {{formula:870b417b-39c7-4198-abec-a7a3d206e55c}} and {{formula:095260be-a0df-44c8-b8d5-439cbc779b59}} are the covariance matrices.
{{formula:839e62e6-8673-49d1-bb37-8cbb4e3b753f}}
| m | 1816e7ad10c6d079bddf9a53be9fc271 |
The primary drawback of our proposed estimators is that they rely on regression models to estimate causal effects. A major disadvantage of this is that, in cases with incomplete overlap in the covariate distribution between treatment and control groups, the estimated response surfaces in many areas are based on extrapolation {{cite:8799c239277df849091f55c94ed1454d593a6f60}}. For this reason, regression models are sometimes avoided for causal inference, and other methods, particularly those based on propensity scores, are favored.
One of the primary advantages of the propensity score is that it allows the analyst to condition on the propensity score in the outcome model rather than specifying a complete covariate-outcome model. This is problematic when attempting to borrow from supplemental sources, however. Borrowing between data sources happens most naturally in a Bayesian setting, but propensity score use in the Bayesian paradigm is not straightforward.
Conditioning on a propensity score in the outcome model in a Bayesian design does not correspond to a valid use of Bayes theorem with correct posterior inference {{cite:df38dea99ed096ff0d8f48a42223910affa12956}}.
| d | ec8f8b62abf10b4367d29f450ac64655 |
From a completely different point of view, symbolic methods {{cite:317e7db26a41cc915e2b7f4d2bd1c11621dd554a}}, {{cite:14979b6ce148a8b22dc1da0947df0c6dcb9e7727}}
(e.g. Gröbner basis method, Border basis method, Wu's method, and method of sparse resultant) rely on symbolic manipulation of the polynomial system and successive elimination of variables to obtain a simpler but equivalent form.
In a sense, these methods generalize the Gaussian elimination method from linear systems into the nonlinear settings.
| m | ce0f4d86e1a715b8641280adf837e545 |
where {{formula:187bacb0-dc88-4d76-9582-bd9f2c420308}} denotes the reference path loss at the reference distance {{formula:45a82df9-e67e-4870-861e-c00fd682ae5d}} , {{formula:02bc23f3-1a06-4b23-b425-d1a86ca4bddf}} , {{formula:4cf3650f-d4db-4b80-98e3-0be12322fc6a}} denotes the distance of the {{formula:4d2fe0d9-c082-4b41-8872-b9bdc43417b3}} -th link and {{formula:2835c012-8423-4692-8f01-0af77f6e9956}} denotes the path loss exponent of the {{formula:aa4023e6-7195-482f-b6fa-a7cb2e607f96}} -th link.
We set {{formula:5c80e7a7-a119-4e2b-9b27-708bc46b2cc9}} , {{formula:b8351728-abc8-4221-bd9c-ae76af4592a3}} , {{formula:8b73a5b5-33fb-4766-b1fb-05b39df18d0e}} and {{formula:4c217ca8-2a36-4f89-9e1e-a6bccf8a2e54}} , which corresponds to a scenario where there is a LoS link between the BS and the RRS and a NLoS link between the RRS and the user. This scenario is motivated by the mobility of the user and, thus, the difficulty of establishing a LoS link {{cite:8de066057cf99a7ce30907570a8cfe468dfe28ee}}. Moreover, we also examine the setup where {{formula:360667da-fc53-4195-8361-4d0b9fb8aa20}} and {{formula:86a9e7db-2da7-4a72-94c3-879e5ad9225e}} in order to illustrate a performance lower bound which represents a scenario where the RRS is randomly deployed, since there is no LoS link. For both path loss links, we set {{formula:f37c16cb-1121-4d77-a2f9-601de6719ae6}} dB, {{formula:85f1f190-c240-4653-8f1d-ea3eafbfa174}} m, and the path loss exponent for the link between the BS and the RRS and the link between the RRS and the user is set as {{formula:5ef96363-474e-46c1-8726-e45e3284277d}} and {{formula:1f6c0450-c343-46e5-b21b-90584d876329}} , respectively {{cite:5ae2decf1e16449d7993e444e65971c0e40a2a62}}.
Furthermore, unless stated otherwise, the transmitted SNR is 110dB and it is assumed that the sum of the two distances is constant, i.e., {{formula:3600f22c-bbd3-4713-966f-99a5e30af0fe}} with {{formula:674c97aa-0bef-4325-8364-bef3709a0140}} m.
It is also assumed that as the number of elements increases, the size of the RRS also increases due to the fact that the inter-distance between them remains unchanged.
| r | 09644f90e3f84e5cc4147f60351de7ad |
Based on the solution of the multiple color light curves and the analysis of its uncertainties, we found that CSS J022914.4{{formula:6998513e-c5ee-40d1-a74d-7292ef86aa97}} 044340 is an extreme mass ratio ({{formula:0fa31f24-3cfb-4846-a73f-4c19d9954b78}} ), deep contact binary ({{formula:33afabba-66c9-4dbd-912a-425d93ba15a1}} %). The 38-minute-last flat bottom in light curve, as well as the high inclination ({{formula:5e1528ef-e35d-4cd8-9a95-54f94190979b}} ), indicates a total eclipse of this binary system (as shown in Figure REF ). The photometric solutions would be reliable if the system were totally eclipsing {{cite:fe37f6ba7abd8e86484100dffdddca99c0a5322b}}. Based on that, the physical parameters have been estimated by its photometric solutions with its distance determined by {{formula:718c4955-6228-4b7d-bb25-5f5c69af6f4a}} EDR3. To avoid the potential error brought from the temperature {{cite:98e7271ab511c9b89ab73f49066ebdced753ae9c}}, we have determined the temperature of CSS J022914.4{{formula:2899cb88-8969-46c8-a863-c211acd94102}} 044340 through the spectroscopic data obtained by the YFOSC. The determined value is {{formula:f1d0a0c7-4995-4837-bec9-6d54ee3dc4b6}} K which is consistent with the value of {{formula:b17f16d4-311e-4ef2-bd0a-8f4f6b5f436d}} K given by LAMOST DR5 {{cite:ecbe8a33f0268d2a3c11a17d6b2d88d226884952}} and of {{formula:b70f68b4-0f39-4e98-a24a-6dc2e0511b06}} K given by {{formula:2ec047f9-72ca-476c-9784-64dd79568f47}} DR2 {{cite:9e37e1537a7516cbd25826bd82d11ebf0e3f09a1}}. Our derived value of metallicity as [Fe/H] {{formula:be99011d-4f6a-4d5c-b58c-a3b2d612daee}} is also similar to the value of {{formula:c2a9b835-cb6b-43f4-a582-ef734297ff16}} given by LAMOST DR5 {{cite:ecbe8a33f0268d2a3c11a17d6b2d88d226884952}}.
| d | a8a08a1fa303861212a7345282509af1 |
When {{formula:6940f414-fd0f-425a-802a-6eebafeebb90}} is a square matrix with full rank,
the PDHG has a linear rate
{{formula:cecde622-9072-45ed-a8e9-a729cfcfded2}}
(see Appendix REF ),
similar to
its ODE analysis in {{cite:f08ccc679d128793a010bfb5b644292e6ab43446}}.
The standard proximal point method has a linear rate
{{formula:4c5aa956-0a2a-476d-847e-06b6b5477a0f}} for bilinear problems {{cite:0866a6bd6d838f4e2ebb1fc94253422e5e01bfb3}},
which is slower than
that
of the PDHG.
In {{cite:195356a1f0029b1c7feff1d3b558a931050b2622}}, the extragradient type method has a rate
similar but slower than that of the proximal point method,
implying that there is potential in further studying the PDHG type method.
| m | 768d8e023defdd5938642bed68496a11 |
Our first result is a positive answer to que:main-question in essentially full generality:
we show that concept classes that are efficiently learnable in the Statistical Query (SQ) model,
{{cite:6748d91d7b68077df83281336b09774b21fe785a}}, are also learnable from coarsely labeled examples.
Our result is similar in spirit with the result of {{cite:6748d91d7b68077df83281336b09774b21fe785a}}, where it is proved that
SQ learnability implies learnability under random classification noise.
| r | e9fc5dc39f88b49b7c7f1e964eda5cc3 |
At present, a fully quantised theory of gravity is still to be reached (for some recent developments, see e.g., {{cite:41eed0d84d4ca0e37c1bdc63a154d108b02611d3}}, {{cite:0a1802e97014532dd8cd3d8dd78cc297d0f50d0a}}, {{cite:6bda0f6259431aad5f674350b467377c5348e451}} and references therein). Nevertheless, the effective QFT for linearised general relativity is expected to yield satisfactory physical descriptions at energies sufficiently lower than the Planck scale
{{cite:35534908a28df4ea79a100b6cd27bbf0b3ee833a}}, {{cite:37ec89fa98dde0227e01b3010769f60f45850460}}, {{cite:6197e98afb5cf2179144c85a36a875e1f765a806}}.
Indeed, the spontaneous emission rate of gravitons for a nonrelativistic bound system due to the zero-point fluctuations of spacetime in linearised quantum gravity has been recently shown {{cite:cdcf28c1204954229a578f26f2088b397d106f1a}}, {{cite:54fd640dc2f6710ffbe35206dac5cd8521262606}} to agree with the quadrupole formula of gravitational wave radiation in general relativity {{cite:62e966aa3f4233dcf2aef24a903bb90adc980894}}. The preservation of the local translational symmetry of linearised gravity is crucial in the theoretical steps of establishing this agreement through the gauge invariant Dirac quantisation technique {{cite:37ec89fa98dde0227e01b3010769f60f45850460}}.
| i | 1be201d94829e0a24991016c3b2da090 |
Generalized Adjusted Count Models (GAC, GPAC). As noted before, the most simple work-around to avoid estimating {{formula:8e7034f2-aa55-44ea-b96f-a3844265ce36}} is to apply a classifier to build a system of linear questions as in Equation REF , and solve it via constrained least-squares regression {{cite:f6467291d6d238eaed50126fd6d52483fbd9954e}}.
That approach can be considered as a Generalized Adjusted Count (GAC) method, which also naturally includes the multiclass case.
In a similar fashion, one can also obtain a Generalized Probabilistic Adjusted Count (GPAC) method, by utilizing the confidence scores from probabilistic classifiers as in the PAC method.
The DyS Framework (DyS, FMM). More recently, {{cite:605af707a17c7e34f7cc898377a8bf6889037ddd}} proposed the DyS framework, in which the main idea is to utilize confidence scores resulting from the decision functions of a binary classifier.
More precisely, the confidence scores obtained on the training data are divided into bins, and then the probability that the confidence of a training sample ends up in that bin is estimated from the training set.
Thus, in our context the number of linear equations we obtain from Equation REF equals the chosen number of bins, which, next to the distance function that this set of equations is optimized on, can be seen as a parameter of this framework.
A main drawback of this framework is that it only works for the binary case, and that many of the distance functions that were proposed and evaluated for this framework are not convex, requiring methods such as ternary search to estimate the optimal solution.
Since in their evaluation, using the Topsøe distance {{cite:91db7eac671cca574434447540ae131b3229954c}} has proven to yield consistently good results, we are including this setup as DyS method in our experiments.
Furthermore, it is noteworthy that Forman's mixture model (FMM) {{cite:783c0c07db0d9b697b9782491605c6412985993f}} can also be regarded as a method of this framework which uses Manhattan distance along with a particularly large number of bins.
readme. Instead of applying a classifier, in the readme method {{cite:0669d3078711543a415ce9c57d52839460cea872}} the focus lies on modeling the distribution of the feature space, or more precisely the single features {{formula:5ba2dae1-e425-4687-9865-2da67a7e36f2}} . This method was originally developed to be used on document-term matrices in the context of text mining. Due to sparsity issues, it requires all features to be binned, and only a subset of all features is projected on to form the system as in Equation REF , which is then optimized by means of general least-squares regression. In practice, one samples an ensemble of such subsets and averages the corresponding results in the end to obtain the final prediction.
Hellinger Distance Minimization (HDx, HDy). {{cite:8db2a579910ea18391d96c223d382a985ff4d322}} have proposed two methods that are based on minimizing the Hellinger distance to match distributions in Equation REF . Similar to the readme method, in the HDx method one considers the distributions of single features {{formula:4ee88160-8523-41ae-8d73-7fbe182bcc2a}} , while in the HDy method, one applies classifiers as in the {{formula:a6b74b61-2dc8-464d-9103-a0d79d77980b}} method to form the system in Equation REF .
Friedman's Method (FM). Similar to the GPAC method, {{cite:1b4b75e3304c854e9c830207a62a9a9e1de3682f}} proposed to utilize the confidence scores from probabilistic classifiers. However, instead of averaging the class-conditional confidence scores, he proposes to utilize the fraction of class-conditional confidence scores that are above and below the observed class prevalences in the training data.
Energy Distance Minimization (ED). As the name of this method suggests, its core idea is to minimize the energy distance between the left-hand and right-hand side distribution in Equation REF . In that context, the distribution of the feature space is intrinsically modeled by the Euclidean distances between individual instances, and therefore no classifiers or additional parameters are required {{cite:510568df83c89f517791bbc6f5a46c5affd4b76f}}.
The EM Algorithm (EM). This method applies the classic EM algorithm {{cite:6d3a6dc4dc2f9f9d422e44e0d3d1549592d25f85}} on the outputs of probabilistic classifiers to adjust them for potential distribution shift between the target class distributions in training and test data. While quantification was not the main focus in the original proposal of the algorithm {{cite:93e422e3d8416ae5d045566c51251c4e3697a4ef}}, the sought-for target class prevalences are obtained as a side-product.
CDE Iteration (CDE). The CDE iterator has been proposed by {{cite:6f8dcb0e7a389b2c0e1a0e4e6ec93529f3a64bee}} and applies principles from cost-sensitive classification to account for changes in class distributions between training and target data. For that purpose, the misclassification costs are updated iteratively, and in the original proposition of the algorithm, the underlying classifier is retrained in every iteration step.
In our experiments, we use the more efficient variant proposed by {{cite:2a120e33d670322ce257eb44fe1b7d9dd60b9357}}, in which each iteration rather updates the decision threshold of an underlying probabilistic classifier. For this variant of the algorithm, Tasche has also proven that the iteration will eventually converge.
| m | 59b1f45e2d07188cadf0777e01e4d681 |
Additionally, our study revealed that the Bayesian paradigm presented in this work is robust with respect to {{formula:9a6f2301-db78-4b88-95a8-31fc8757e96f}} , so that it can be started well away from the true value of {{formula:25925350-59d7-474b-81d5-86489a940bfd}} . In the case of the three-parameter Weibull distribution, similar to the JSB distribution, we used {{formula:30681134-851a-4406-a41c-a44f7b7b4fc7}} as the initial value for {{formula:7b2e82b2-389e-4692-8f4f-b9fd1c5ce226}} . The initial values of the shape and scale parameters obtained by using the method of moments {{cite:ae337091379e9b0e52753f7d6f473cb3d9c3c939}}. We also performed a simulation study to check the robustness of the Bayesian paradigm with respect to the initial values for estimating the parameters of the JSB distribution. For this purpose, we confine ourselves to the case in which we have simulated 300 samples each of size 100 from JSB distribution with parameter vector {{formula:72afcea8-6304-4d3f-bedb-75a5b84b5982}} , i.e., {{formula:da17039e-6c60-4183-b3d4-aa3f915d4d05}} , {{formula:f7730b3c-e984-46f7-bcaa-0ad4cbcd3cfb}} , {{formula:b868bdc6-f6e9-4bde-baa8-f560f6de48cf}} , and {{formula:03691ba6-9867-4144-910b-c265a31e8105}} . The results of simulation are given in Table REF .
We note that in each of 200 runs, the initial values were not chosen by the method suggested above. Instead, the initial values were generated randomly from uniform distribution. We used this scenario in order to check the robustness of the Gibbs sampler. The initial values for {{formula:0e645fe2-dd71-411b-b77b-c4c2f489f467}} , {{formula:8624b10d-1536-4187-b275-969bb9c705f5}} , {{formula:7149d44c-4c53-4d61-a601-263f52f1440d}} ,and {{formula:6f9aad4a-992c-4aed-bb82-8fbaf3152ead}} were generated from uniform distribution (0.1,15), (-15,15), (20.1,60), and (-10,10), respectively. For example, the general motion of the Gibbs sampler has been shown in Figure REF , when the initial values were chosen as {{formula:c60da97d-3b59-4a6e-a92e-5b93bc36bb17}} , {{formula:47744cd1-8a76-4621-bc08-d911922a8f4a}} , {{formula:8d5caf4e-2406-4f50-8f88-5961e4232cdf}} , and {{formula:d642244c-c3cc-4cfe-9ec1-590eea6b6cb3}} to show the robustness of the Bayesian paradigm.
| d | e17e18e1691957b52627f7a916d071eb |
Reversal mechanism. The hysteresis loops in
Fig. REF show that skyrmionic textures in
confined thin film helimagnetic nanostructures undergo hysteretic
behaviour and that an external magnetic field can be used to change their
orientation from core pointing up to core pointing down and vice versa. In
this section, we discuss the mechanism by which the skyrmionic texture core
orientation reversal occurs. We simulate a {{formula:9dee72eb-97a4-42eb-8caf-c984f98c7d09}} diameter thin
film FeGe disk sample with {{formula:39e57d7c-cbd4-4851-a7ec-fa91ca842c70}} thickness. The maximum spacing
between two neighbouring finite element mesh nodes is reduced to {{formula:2c95872e-7f0d-48f6-a314-ef70b1997bcb}}
in order to better resolve the magnetisation field. According to
the hysteresis loop in Fig. REF (b), the switching field
{{formula:249931d3-644c-4c61-8229-f5a239697a9d}} of the isolated skyrmion state in this geometry from core
orientation down to core orientation up is {{formula:731e9555-ed5c-4cb1-a57e-30aae3c9ad95}} .
Therefore, we first relax the system at {{formula:a135d8ae-8a3f-4609-9715-325029660342}}
external magnetic field and then decrease it abruptly to {{formula:f6f46cc7-02c5-4000-b4d4-b213e2428fc1}} .
We simulate the magnetisation dynamics for {{formula:10b0e0dc-105b-4340-8a69-e43415ca5628}} , governed by a
dissipative LLG equation {{cite:c15d97f189f2624a5aaae79211e17a480925d5da}} with Gilbert damping
{{formula:be446ef2-1b7f-43e7-a207-6e94fa7fc0bc}} {{cite:ee2f828e23b22af30b7996579a033b998968f55c}}, and record it every {{formula:a14f49a3-a967-434d-ae99-f89113a62c63}} .
{{figure:6d1749af-c106-4742-ad8e-09302d2d5a32}} | r | b4689051e59c5f5df851627083784707 |
There are many occasions in real life when we have to quickly choose one
among extremely many options. In addition, we want our choice to be optimal in
a certain sense. Such combinatorial optimization problems are ubiquitous and
possibly quite hard to solve them fast. In particular, NP-hard problems cannot
be solved in polynomial time {{cite:2462ef5b2894c37acdb4d5e47e57ae2eb9e7379d}}.
| i | c4c4e637e0280d8498259847de3da7aa |
To calculate QNMs, a master equation is derived under the background (REF ) and the perturbation (REF ), where the RW gauge {{cite:28f3ca43671c0a2bba9c4306bd1628cf2a043f0e}} is what we adopt. Notice that, in {{cite:f459c48e894133bffbb05a4aff4665e4466c5f5e}} the axial (odd-parity) perturbation has been studied, and here we focus on the polar (even-parity) sector. By using the Einstein's field equations {{cite:f0ded39a990ff6b7cd26d683aa62816f2c51e642}} and following {{cite:62d121001cd0df3843e00b07d1b90efc0932ba36}}, our result of master equation for the polar sector is given by (REF ), with an effective potential given by (REF ). Since the resultant QNM frequency, viz., {{formula:be14b4f9-30f7-45e4-b063-802a8af75167}} , is directly related to the patterns of an effective potential, we want to first take a loot to that. For this purpose, {{formula:21e10304-a23c-4d1d-9b83-d9dc25d5a41b}} 's are plotted in Fig. REF for the four cases listed in Table REF (including the Schwarzschild case).
| d | 3ee10282e8a3cd0ea0c52241e2348087 |
The minimal time during which a quantum system evolves between two extinguishable states is recognized as the quantum speed limit time (QSLT). This interval determines the maximal rate of evolution that a quantum system can reach. Regarding the literature, Leonid Mandelstam and Igor Tammthe had a pioneering role in formulating the QSLT concept by means of time-energy uncertainty relation which bounded the speed of evolution reads as MT bound {{cite:70921d9060ef5ab86260f9da0e05391ad89ea501}}. Later, Norman Margolus and Lev Levitin refined this relation and derived a more rigorous relation (ML bound) according to which the speed of evolution cannot exceed the mean energy {{cite:5ee8e1f9e49f72df916a27ac3483c185773da67e}}, {{cite:e125fcc14207c02b630b933d47afdd4b12e8e949}}. The MT and ML bounds had been applicable for closed quantum systems, despite the fact that the realistic quantum systems are not isolated. It was of crucial importance to generalize the notion of QSLT to open quantum systems. Hence, Deffner and Lutz {{cite:e125fcc14207c02b630b933d47afdd4b12e8e949}} filled this gap by introducing a unified quantum speed limit time. On the other hand, since in the open quantum systems the environmental effects cannot be ignored, this question is posed that how non-Markovianity can affect the QSLT. Although the early studies suggested that non-Markovianity can speed up the quantum evolution {{cite:e125fcc14207c02b630b933d47afdd4b12e8e949}}, the recent reports indicate the existence of a direct relationship between the QSLT and memory effect is still open to debate for the most general dynamics of open quantum systems. Thus, increasing the non-Markovianity, quantified by the backflow of information {{cite:10643e100afa4003dd4184f19f3fe8d17a3d1881}}, does not necessarily lead to the speedup in the evolution {{cite:c806a1aa0dd7c92ecc73700cfe83b037f515b914}}.
This minimum bound also determines the maximum rate of quantum information {{cite:90dab89fae6142597fdce2a0c0b981ff5d21444d}}, computation {{cite:9192227403594b56ff829bd4fa34d72f6e21ce5a}}, entropy production {{cite:ef29c9bca93b71739600f6a0dfce2a5fd06927eb}}, the ultimate precision in quantum sensing {{cite:a65cdd33765f16640cc5b0aab25284ccffd61034}}, and scrambling the spectral form factor {{cite:64e8a2118ba21edf38faaf4dfd0a2895d93b69a3}}. Moreover, the QSLT serves as the inherent limitations of quantum optimal control algorithms {{cite:2bdebfdfd77eb32868e6b754aeff1ba15e0c8e97}}.
| i | cb5e00ef5139e98579ec76f679ae8b5a |
The morphoRNN was proposed by Luong et al {{cite:5193f82abf3fd91d8ee134921e8262e7a82c75de}}, which has been introduced in Section . In their work, they proposed two kinds of morphoRNNs, cimRNN which is context insensitive and csmRNN which is context sensitive. Since the context sensitive models are consistently better than the context insensitive models as expected, we only compare KNET with their context sensitive models. In their experiments, they make use of two publicly-available embeddings provided by {{cite:4c7932c422efee840b38ac04d6d8018a701958fa}} and {{cite:cc1d7f0ab1f77ab90a1fa2e8dbf64aecc300029a}} to initialize their models. Following their notation, we denote these two morphoRNN models as C&W + csmRNN and HSMN + csmRNN which are the best models in their work. The results of these two models and our KNET models are shown in Table REF .
{{table:0e865791-e7aa-4343-9f04-5967dfcb5f4c}} | m | 28befb44815d29f7914166f6e62dbd67 |
where {{formula:847a5ce0-07e6-4f93-82e6-7c8850694bac}} is the one parameter Mittag-Leffler function {{cite:1c4d179a0a85cb51ebb3a5e5cdb6f04aa1ec3010}}.
| r | 6fac1dbeb3c968fe150546e9344bce39 |
Unless stated otherwise, we set {{formula:3e9939a8-625e-4bee-a33b-f34cff8b3285}} . Four users are evenly located on a circle centered at the RIS with a radius of {{formula:adcd9008-591b-4a31-b399-b7b8a249f0db}} m as in {{cite:53751aa3bfd6c42fa6e6211b4fb9458cfa3c134d}}. RIS-BS distance is {{formula:b4a7cf7e-bc9e-4544-a57a-8d388bf7db4f}} m and the distance between user {{formula:95138042-c16e-4af7-98df-afb2383db99c}} and BS is calculated by {{formula:fb1bb393-1c12-4693-9910-0c32536e1cd5}} . All the AoA and AoD are generated randomly from {{formula:5a44c043-39ad-46e7-8818-416c9951458b}}{{cite:c39f2e3e655d922b16739d062b33999c28651b20}}, {{cite:a76cb84e16d32ebbc0e4ee35a53c1fe7f755d0b4}}. The distance-based path-loss are {{formula:215033d8-8922-491d-a754-21021764756a}} and {{formula:56a1f7a6-7e63-4fd0-bcf9-2b759487641a}} .
{{figure:d4a49564-6d15-4be0-acc7-79d6ec861766}} | r | b9169cb021f6bdca21c20b19ec29357d |
In time, the equations are advanced using an implicit-explicit order 3 additive Runge-Kutta (ARK3) scheme {{cite:d94eff31fb41d2040e9ed55fac2802a5bec234e4}} whereby the non-linear terms of the governing equations are treated explicitly and the linear terms are treated implicitly (see {{cite:101133fe8854bbf08cc9c58e2d7a258783e18cb2}}). As for the space discretization, we use
spectral elements and show results for both continuous and discontinuous approximations.
This section focuses on the space discretization alone.
| m | 400248956c0890a7b6c833c18b09654d |
In this section, simulation results are presented to numerically validate our analytical propositions and the effectiveness of the proposed I-HMA protocol in the IRS-aided UL transmission system.
As shown in Fig. REF , the BS and IRS are located at {{formula:83404ea7-ceff-4e0b-9a79-0dd932b95d17}} meter (m) and {{formula:c6ae9820-de5b-4473-9db2-f2d901b541f1}} m, respectively, and the devices are distributed along the {{formula:5824050a-15b1-4207-ba9a-a0d363a05fef}} -axis, if not specified otherwise.
For the involved channels, we adopt the path loss model in {{cite:12dee8718d57d52d2a35f69c51f3949c4163939c}}, where the path loss exponent is set to be 2.2 for {{formula:c3ae0473-69bb-46e5-8680-9193130c826b}} and {{formula:c27b8ec8-d3b1-4bba-bf2c-949a6aad7e78}} , {{formula:6a716758-0f33-4000-a88c-d1d5dd58fab0}} , whereas 3.6 for {{formula:7443337c-3ac3-4e59-b07c-b651e2fb5d00}} , {{formula:047a854a-fe3a-41b9-b83e-f1d21b995370}} . Rayleigh fading is adopted to characterize the small-scale fading for all the channels. Unless otherwise stated, other system parameters are set as follows: {{formula:78925bf5-0780-4d73-9502-02b788e8d18f}} kHz, {{formula:77889b8d-879f-442a-93e9-5ae45f5219c7}} dBm and {{formula:a77e2d5e-9096-4100-9a4b-d7840163a1ce}} .
{{figure:0c043782-8d0a-4a02-9fc4-2167a2717248}}{{figure:51d082d0-c25d-4bca-90bf-82189155e113}}{{figure:285a18b2-fb5f-4726-95f3-4899daac883c}} | r | c98aee8d37e1e71707718f47efc7965b |
During the last century, the analysis of a great number of phenomena modeled with dynamical systems, i.e., with sets of nonlinear ordinary differential equations, highlighted the existence of at least two time scales for their evolution: a slow time and a fast time. This was transcribed by the presence of at least a small multiplicative parameter {{formula:d1910016-3c4d-4712-af36-1fc4680d22cb}} in the velocity vector field of these dynamical systems. They were thus called singularly perturbed dynamical systems and it was proved that they possess slow invariant manifolds. Then, various methods were developed to compute such slow invariant manifolds or, at least an asymptotic expansion in power of {{formula:99f486aa-7650-4bac-9dcc-865e31ac5442}} . Thus, determination of the slow invariant manifold equation turned into a regular perturbation problem and the seminal works of Wasow {{cite:e6c8554fcd3dbdfc9c322fdb0eb2b5d1e253cca5}}, Cole {{cite:41393d39bbfdd41a17aded34cc113c8ad4388fc2}}, O'Malley {{cite:49ccd690b7d8742e14a9734eb064bfec5726d5ad}}, {{cite:516b3ca4b800524e67b5ceaddbee5e7b25a36dc0}} and Fenichel {{cite:ec791639e17944d9202559590f989df12d4f60fd}}, {{cite:e8aadf8eb92775b3a6accc7d565140f17bf87acf}}, {{cite:c0d5d2de960d09aa9daa0529ce5fe6465c8e37f1}}, {{cite:5ca21c6bb51813255aa7fed738cebd5b8c44d8bc}} gave rise in the 1960s-1970s to the so-called Geometric Singular Perturbation Theory. At the end of the 1980s, Rossetto {{cite:ef83ea9deb29dd4bec08d3c2f019a08c1dc1a29f}}, {{cite:21edc9e2225c1772a231198de44e46c8a22c1b7d}} developed the Successive Approximations Method to approximate the slow invariant manifold of singularly perturbed dynamical systems. In 2005, Gear et al. {{cite:7d5903a1b4744e7a13220b42dd8e8478314178c9}} and then, Zagaris et al. {{cite:bea87f888d2e82ac6d5d2bb936d09ca5b9ef6669}} used the Zero-Derivative Principle for the same purpose. We have established in this work that Geometric Singular Perturbation Theory, Successive Approximations Method and Zero-Derivative Principle are absolutely identical, i.e., provide exactly the same approximation of slow invariant manifold equation and so belong to the first category we have called: Singular Perturbation-Based Methods. However, according to O'Malley {{cite:49ccd690b7d8742e14a9734eb064bfec5726d5ad}}, Rossetto {{cite:21edc9e2225c1772a231198de44e46c8a22c1b7d}} and Benoît et al. {{cite:43e11d6da294d40b666ff1c704f9235f4272c758}}, the main drawback of these methods is that the validity of the asymptotic expansion in power of {{formula:30fd6cd7-7e19-429e-b001-4eeeb6e09d24}} , approximating the slow invariant manifold equation, is expected to breakdown near the fold or, near non-hyperbolic regions.
| d | 5b4f51b0aea0cc6ca4cdfd1a928f14b9 |
RAND: It is a weak baseline that randomly picks up explanations from the collection.
It is devised to examine whether personalization is needed for explanation ranking.
RUCF: Revised User-based Collaborative Filtering.
Because traditional CF methods {{cite:8ddec65e84182ad6a675939ac6828aab7b30f982}}, {{cite:bf90b33ab973fcad346ca3fc4c4438027d7b9798}} cannot be directly applied to the ternary data, we make some modifications to their formula, following {{cite:a3b9db5a8732142a88d05742dd5332e657a85967}}.
The similarity between two users is measured by their associated explanation sets via Jaccard Index.
When predicting the final score for the triplet {{formula:f0c35fd5-3486-43a7-b7b1-9ae7f7d38204}} , we first find users associated with both item {{formula:41b9077a-4ad9-415f-aca3-b096905f4169}} and explanation {{formula:9f2a8a23-4bf6-4e77-b95e-f4cdb6105a23}} , i.e., {{formula:e0ab5a2e-f4cd-4a48-96d3-4f8c43b7c24e}} , and then keep the ones appeared in user {{formula:8fd1aa6d-e273-46f3-8eb4-39d3f67fa823}} 's neighbor set {{formula:cb46ced5-8647-4a0e-8949-5407ad509436}} .
{{formula:7e71a723-196f-49bc-83b3-9f2f97b17782}}
RICF: Revised Item-based Collaborative Filtering.
Accordingly, this method predicts a score for a triplet from the perspective of items, whose formula is similar to Eq. (REF ).
CD: Canonical Decomposition {{cite:6cbd2c2dd9ae4d18844b818ca958261a93a99c00}} shown in Eq. (REF ).
This method only predicts one score instead of two for the triplet {{formula:9eb5daaf-0b9a-4085-8eed-20a54b5317e0}} , so its objective function shown below is slightly different from ours in Eq. (REF ).
{{formula:e31f09f0-60b0-45f5-b68c-51e0e1b74ec5}}
where {{formula:cab2cd4f-1caa-40f0-ac81-ba60c970c6c8}} is the score difference between a pair of interactions.
PITF: Pairwise Interaction Tensor Factorization {{cite:1cf766007c029225ef3ccf3ec222bf86a6cd0ed9}}.
It makes prediction for a triplet based on Eq. (REF ), and its objective function is identical to CD's in Eq. (REF ).
| m | 4fde6d0c4e5b06e09f5bfc37579719fe |
Matching-adjusted indirect comparison (MAIC). The trial assignment model in Equation REF contains main effect terms for all three effect modifiers — only covariate means are balanced. The objective function in Equation REF is minimized using BFGS {{cite:863f86e16abb6f3c4b1b3dd1c06b89d69294a7cb}}. The weights estimated by Equation REF are used to fit a weighted simple linear regression of outcome on treatment to the index trial IPD.
Two-stage matching-adjusted indirect comparison (2SMAIC). We follow the same steps as for the standard MAIC. In addition, the treatment assignment model in Equation REF is fitted to the index study IPD, including main effect terms for all three baseline covariates. Propensity score estimates are generated by Equation REF and combined with the weights generated by Equation REF as per Equation REF . The resulting weights are used to fit a weighted simple linear regression of outcome on treatment to the index trial IPD.
Truncated matching-adjusted indirect comparison (T-MAIC). This approach is identical to MAIC but the highest estimated weights (Equation REF ) are truncated using a 95th percentile cutpoint, following Susukida et al. {{cite:3fe447262760d0a0e2bc6b5f09d1a0822684d3bf}}, {{cite:a7ffd76dd6e5017f866167fdfe5272e2a93fa4cf}} and Lee et al. {{cite:bf884d213c18a0d137038b2386215da09aa5dae0}}. Specifically, all weights above the 95th percentile are replaced by the value of the 95th percentile.
Truncated two-stage matching-adjusted indirect comparison (T-2SMAIC). This approach is identical to 2SMAIC but all the estimated weights (Equation REF ) larger than the 95th percentile are set equal to the 95th percentile.
| m | 90a233e83a7dcca71ae40c7d21a10e12 |
Most recent work focuses on time series data, where observations are time-correlated and
the interaction graph is inferred from the joint time evolution of the node-states {{cite:e470e1f85fb4f2c1944b0b1b96a26f3681eb1a99}}, {{cite:6bb64f6891690a39d2548dc1a430012abb912b7b}}.
Naturally, time series data typically contains more information on the system's interaction than snapshot data.
However, in many cases, such data is not available.
For instance, in some cases, one has to destroy a system to access their components (e.g., slice a brain {{cite:3cccb3f528e305f7860bb8ad1654d258668e5537}}, observe a quantum system {{cite:1ebafcf8af146016b500f81b209261a8ac73cb42}}, or terminate a cell {{cite:415f11d36ad46136f8516c770442db40b5e89238}}).
Sometimes, the relevant time scale of the system is too small (e.g., in particle physics) or too large (e.g., in evolutionary dynamics) to be observed.
Often, there is a trade-off between spatial and temporal resolution of a measurement {{cite:be57fb2077fac20d25a06596fa775a592e201665}}.
In addition, measurements may be temporally decoupled due to large observation intervals and thus become unsuitable for methods that exploit correlations in time.
Yet, machine learning techniques for graph inference from independent data remain underexplored in the literature.
{{figure:73827c43-2b01-4087-89d5-868a1acf37f9}} | i | 010408d8244b62c7008dcc631de820b4 |
With the availability of large-scale annotated datasets like ImageNet {{cite:3ac4084bb60a350ddb0887453ccd00c5353f0825}},
convolution neural networks (CNNs) have achieved unprecedented success in computer vision {{cite:9b04988ade624ca733d726f08f0cd58c2e39b198}}.
Benefiting from CNNs, medical imaging research has made great advancements in the classification {{cite:6a756587f55ddd9622ed02eccf7076bcff0cce6b}}, segmentation {{cite:67a255b01897108d0931fe4e2f8b39bed421acf6}}, detection {{cite:98168df391986af164b4f3ffb516e448837e4108}}, and registration {{cite:8c3bbe9a666696ee7272f90e95681efde5a2033c}} of two-dimensional (2D) medical images.
However, 3D medical image research is lagging behind due to the lack of large-scale 3D medical image datasets.
As a result of the complex collection procedure, expert annotation, and privacy concerns and patient consent, it is challenging to build a large-scale, 3D medical dataset similar to ImageNet.
| i | b6b90ec9a0ecd5c814f41d77ea60256c |
To recover what EEG features are necessary to obtain an accurate facial emotion classification, we must first understand which XAI methods are reliable. With this goal, we analyze the following methods: Layer-Wise Relevance Propagation (LRP) {{cite:813ed0e1ea5db69f6d208a896a0b4a2972e2cc5c}}, {{cite:9d184507ab0258a1eeea79da27f19e7bc213fe03}}, PatternNet, Pattern-Attribution {{cite:70a4d43df92ecb53ce228c69b7ef07f9e82977f4}}, and Smooth-Grad Squared {{cite:3dc5f627b04dfcbaf1f6f53e517f871a61039b04}} using an approach called RemOve-And Retrain (ROAR) {{cite:fd26083b4604e5088b0f7a33d98e2176b7378a2f}}. ROAR works by systematically removing features, indicated to be informative according to the XAI methods, one a time from the CNN and obtaining classifier accuracies without that features. If after their feature-removal the classifier cannot obtain a high categorization accuracy, then the feature identified by XAI methods is indeed informative, reliable and necessary for decoding. This approach allows us to recover which XAI methods are definitely reliable for classifying correct facial emotion using features from neural activity.
| i | c5c6e737c118c36dd9e41230a51bc9c7 |
As a practical matter, evaluating series approximations derived from our
framework is straightforward but can become tedious when one
desires to include many terms.
In these situations, computer algebra systems or numerical software can readily
compute the required expressions. Moreover, manipulating the resulting series
can improve the accuracy for a fixed number of terms. For example, instead of
truncating the series expansion at a finite number of terms, giving a
polynomial approximation, often better numerical approximations arise from Pade
approximants, which are rational functions whose coefficients match the
truncated Taylor series {{cite:7a3db9e726b27581f295d7ed5abe6a80ecef7c49}} (cf. Fig. REF ).
| d | 4668e4cab1aa3c427853284370a7882d |
The results indicates that it is more valuable and informative to provide training data that evenly describes the latent representation space generated during self-supervised training, than it is to provide training data that evenly describes the targets that are of final interest to humans. Figure REF shows the representative images selected by (a) Balanced, (b) Random and (c) H-kmeans strategies based on their location in the GeoCLR latent representations embedded by {{formula:c5c3d915-fde6-452f-b5a1-9c4b5f136862}} -SNE{{cite:1241f4c005f7c5a57fe90c0b81efe7033e36931e}}. In this figure, {{formula:c809d0ca-922a-4bcf-9a8c-c0b8e71a0be1}} images are shown for ease of visualisation, where the background points show the image representations that are not selected. The colour of the points and selected image borders illustrate the human class annotation of each annotated image using the same colour key as Figure REF . The visualisation shows that random selection strategy fails to select images from the central region of the latent representation space that is relatively sparsely populated. On the other hand, H-kmeans selects images evenly from the different regions of the latent representation. When compared to the balanced selection strategy, it can be seen that there are several regions of the latent representation space that are not sampled. This is because they are mapped to different regions of the latent space as more densely populated regions that have the same class. These undersampled regions of the latent space can be easily confused by a classifier, where the final assigned class will depend on the distribution of nearby training samples.
{{figure:c9d4f7fc-7e99-45a4-9858-6ab65dafeebc}} | m | 2dd612ffb3e46ac1439bcaf24fc4e6ca |
Since the 3D scattering volume can be tuned via a p-wave Feshbach resonance {{cite:c2b25322f9460aba8008b16efb75c2ba6f846cd1}}, the confinement strength can tune both {{formula:6d7f59f6-9b10-480e-b2f9-f7402b8d6b8d}} and {{formula:405f7fdf-1f19-42c0-858e-51a5c5c09da0}} ; a phenomenon called the confinement induced resonance {{cite:07ef6e0039f00da81a7900be475909ef390e10a3}}, {{cite:5ab225bf662f0b3f181733ef9050c58ecf5fbfe9}}. Across the confinement induced resonance {{formula:fd184f31-cd0f-4e0c-a599-5d0629a72f3f}} can be tuned continuously from positive to negative infinity via the confinement induced resonance. The 1D effective range is more or less constant, but its value can be enhanced when {{formula:15d2b4f2-0cb3-4d68-9881-b36b1893ff55}} is larger than the 3D effective range, {{formula:ad3e820b-ccb2-4fcd-b824-e78590fda709}} . Hence the energy dependence of the 1D scattering can be enhanced by the confinement. For example the effective range for spin-polarized {{formula:6ff6d412-6b99-4233-a64f-06e9bcc1d294}} is {{cite:c2b25322f9460aba8008b16efb75c2ba6f846cd1}}: {{formula:88082759-2911-4130-8552-385c586741ee}} nm. For a radial confinement of {{formula:99769a8e-72bb-48ff-bcee-04bd1937a2c6}} kHz, or equivalently {{formula:f111edaf-aaf4-44dc-b2a3-b4cd4be335dd}} nm, the 1D effective range is {{formula:909b3d1b-9afa-4a73-80d0-d8d2db1f8eae}} nm, which is larger than the 3D effective range by almost a factor of 5. In fact this effect becomes stronger for weaker radial confinement. Although the 1D effective range is an irrelevant quantity to the energetics and dynamics in the renormalization group sense {{cite:cff2e42ac142a004fe9b5cc76d2197d512a16194}}, the effective range may be important to the dynamics due to its enhancement from the radial confinement. The importance of the effective range then depends not only on the typical energy scale in the problem, according to the effective range expansion Eq. (REF ), but also this enhancement from the radial confinement.
| d | dd7d016e848b1cea99df954c0ffec20a |
Comparing our algorithm to the QAOA is also interesting from a different perspective. In sec:ansatz we have seen that our ansatz can be regarded as a special case of a QAOA-type ansatz, where instead of encoding a problem Hamiltonian we encode a graph instance directly, and include mixing terms only for a problem-dependent subset of qubits. This lets us derive an exact formulation of the expectation values of our model at depth one from those of the QAOA given in {{cite:acdb4617a27886ccb0e864b7c79f620a66e77e64}}. For the QAOA, it is known that in the limit of infinite depth, it can find the ground state of the problem Hamiltonian and therefore the optimal solution to a given combinatorial optimization problem {{cite:19773c0c6dea86a80d6dbd8130f70e850b87bf73}}. Additionally, it has been shown that even at low depth, the probability distributions generated by QAOA-type circuits are hard to sample from classically {{cite:87420ed99bdc06c20de44a14f43d71f63d8ab1d8}}. These results give a clear motivation of why using a quantum model in these settings can provide a potential advantage. While our model is structurally almost identical to that of the QAOA, in our case the potential for advantage is less clear. We saw in eq:analexpectation that at depth one, in each step the expectation value of each edge that we consider to be selected consists of i) a term corresponding to the edge between the last added node and the candidate node, and ii) all outgoing edges from the candidate node. So our model considers the one-step neighborhood of each candidate node at depth one. In the case of the TSP it is not clear whether this can provide a quantum advantage for the learning task as specified in sec:deflearningtask. In terms of QAOA, it was shown that in order to find optimal solutions, the algorithm has to “see the whole graph" {{cite:43e2edb823f2fd4ff7841279f88d7e479492c186}}, meaning that all edges in the graph contribute to the expectation values used to minimize the energy. To alleviate this strong requirement on depth, a recursive version of the QAOA (RQAOA) was introduced in {{cite:e607a180adf851b3187d03751c02cf333a486e35}}. It works by iteratively merging edges in the problem graph based on their correlation, and thereby gradually reducing the problem to a smaller instance that can be solved efficiently by a classical algorithm, e.g. by brute-force search. The authors of {{cite:e607a180adf851b3187d03751c02cf333a486e35}} show that the depth-one RQAOA outperforms QAOA with constant depth {{formula:1872a85a-2a61-43d0-a367-e1c82d8d5101}} , and that RQAOA achieves an approximation ratio of one for a family of Ising Hamiltonians. While the RQAOA at depth one can be considered a classical algorithm due to its efficient simulability, a subsequent work compared higher depth versions of RQAOA to the best known generic classical algorithm for graph coloring and showed that these deeper versions of RQAOA outperform the classical approach {{cite:940131917c2d4f7fe88e57cae1fbbc61c7f93a76}}. This suggests that there is a potential for advantage in this setting as well. The node selection process performed by our algorithm with the EQC used as the ansatz is similar to RQAOA, where instead of merging edges, the mixer terms for nodes that have already been selected are turned off, therefore effectively turning expectation values of edges corresponding to unavailable nodes to zero. It is and interesting question whether this type of model can lead to a quantum advantage on the TSP problem that we study here, and we leave this for future work.
| d | f7a7e3da80950f2b57d18270d21bb229 |
for any vector fields {{formula:5e568f5e-4c7f-4afe-a1d6-2692123b0e50}} . Obviously, any Einstein Riemannian metric {{formula:82a1395d-fbed-496b-b99d-d32479105e70}} and more generally any Ricci-parallel metric {{formula:b984cea1-9898-474b-87d6-520f95e9f3ea}} satisfy (REF ). Thus the interesting case will be where {{formula:544dca25-01b4-4f34-b0de-072d7466c022}} satisfies (REF ) and {{formula:122ab8eb-4c35-4a02-bb56-877893220864}} . Unfortunately, such metrics are difficult to find and some examples were given in {{cite:d2e2c899bdcbeb67bcf6a9dacc54da5e7368cd10}}, {{cite:f855ee3e7aeb9e384793ea2626a9ce48848eebb8}}, {{cite:176ea19dad595ef684489748cd6202fe7ab09f10}}, {{cite:53c6e307092a8ebf5b71476b1fc347d33af9c3be}}. To our knowledge, there is no example of a non Ricci-parallel homogeneous Riemannian manifold with harmonic curvature which supports the following conjecture.
| i | a80661c3e6bcbb4c9e0b5a4555405843 |
Large pre-trained language models (LLMs) have brought significant breakthroughs in artificial intelligence (AI), with impressive results approaching human-level in various NLP tasks {{cite:3de45aa285a0431038610927b236a948cc7eefc0}}, {{cite:2a629d5d31faa6210dcf0e086e3d66a6260fca40}}, {{cite:3c6b139be9de07f48d30ec1d3fa5dd8dac834150}}. Explorations of their limitations and capabilities have also been made, for instance, by studying their ability to answer open-ended, real-world questions {{cite:fab9205f41a884c9b54ef4d581d8e08e6744c4be}}, {{cite:3806d32df7aacb52b677040fc1cb4356003896c3}}, {{cite:cbb04b6b4436b11ce7eaa9a9169d590755119f58}}, {{cite:5fe6bbeec2e563ad409726e2cbe5e4195dfa9498}}. Ethical quandary questions can be viewed as one of the most challenging forms of questions to address because they have no single definite answer. Instead, a discussion with multiple perspectives (i.e., a manner of debate) is crucial {{cite:e9af7d6917636fa4c06f35e507868a028a6a814c}}, {{cite:5fe6bbeec2e563ad409726e2cbe5e4195dfa9498}} and sophisticated logical reasoning is required to answer such questions.
In this work, we challenge the capability of LLMs to provide relevant and nuanced answers to ethical quandary questions in the style of a human ethicist — Ethical Quandary Generative Question Answering (GQA).
| i | b19623284746f58158ff903573c161f6 |
Experimental setting: Due to the lack of previous study that purely utilizes web-based image-caption data to learn to segment novel object categories, we compare our method with several popular zero-shot segmentation (ZSS) methods, which also segment new object categories but via exploiting the relationships between the word embeddings of seen base classes and unseen class. Specifically, the comparison methods include (1) SPNet {{cite:0cd3da5bb5589ccfbc67553608cb4c7af4020a21}}, a semantic projection network which maps each image pixel to a semantic word embedding space for ZSS; (2) ZS3 {{cite:189e61e3b675ffa1dd0431fac2e00dad66c514ac}}, which addresses unseen-class segmentation by combining a segmentation model with an approach to generate visual representations from semantic word embedding; (3) CaGNet {{cite:d7e4707bac3c1e96e9b96b82ebda68053de02511}}, which devises a contextual module into the segmentation network to capture more diverse contextual information from semantic word embedding; and (4) SIGN {{cite:5ab708fdeac370b18d5ad6f868dd66b4d286bb3c}}, a very latest ZSS method which incorporates spatial information into semantic features using positional encodings to improve the segmentation of unseen classes. (5)
CLIP {{cite:0fa0597286d9f21726a436d7bd2836419858b50f}} + Seg, we simply use the CLIP's image encoder(ViT-B/16) with its global attention pooling layer removed, to serve as a backbone for semantic segmentation. Classification for dense prediction can be directly obtained from the text embeddings of CLIP's text encoder.
All these methods follow the same zero-shot segmentation setting described in Sec. REF , and for a fair comparison, we compare the performance of all these methods under both scenarios of using or without using self-training as followup. For each comparison method, the results are either referenced from their official paper or the number reproduced by other previous works.
| m | cb015e966cd92b0e880ef41a78854e74 |
A neural speech-to-text model transforms a source speech input with {{formula:0d45edf0-2990-44ea-b5aa-85ea19429617}} frames {{formula:48de88a6-acbf-4122-8a3a-a6d4ab5e4a72}} into a target text sequence with {{formula:0b8dc571-c8f4-4330-a97c-e99db3c33dca}} tokens {{formula:77a7257a-156e-4878-a2a9-588501fe7737}} . The encoder transforms the speech input into higher level feature vectors {{formula:a1896a2c-cb36-4ef0-a291-43bbf6a14af7}} . The decoder jointly learns to generate the output distribution {{formula:8dc74a45-24ff-411d-b843-7abba06ac14f}} based on the previous target tokens {{formula:60f5e2b0-c1f8-4198-8a84-3def3b3bd4a1}} while looking for the relevant inputs from the input via the attention mechanism {{cite:712137acd2b1554ec9799071beedc68cd991c61d}}, {{cite:77ed174f57cc3007752a17fa4dff108735a486fe}}.
| m | 680b7aa98f8e96c8bea349949aca4388 |
A lower bound for {{formula:b96bfebe-c6be-487e-a40d-bf10fd4d92a5}} dating back to Yao's original article is the invariant {{formula:8220f329-7f73-4fd7-9498-802856a9c0b9}} which is the minimum number of tilings of any {{formula:4cbbe366-69cc-4089-a15a-50b122a4565c}} -monochromatic tiling of {{formula:f26fc2c1-c4b6-4f2e-8cbf-af9ce1c80942}} . By taking any protocol {{formula:d5d54458-f84d-4ce7-9127-83e3f85f9004}} that computes {{formula:84bc7190-4bba-45e2-b234-6de637ef1a9e}} and labeling every element {{formula:ee5f768f-eaa7-4fd1-b037-433afeaca418}} by the communication history between Alice and Bob when the protocol is run on the input {{formula:c1710e38-42d7-49f4-9440-9ff9abe8c55b}} , Yao observed that the subset of {{formula:bbc27d53-239f-473a-a122-29561a884e2f}} with a given communication history is not arbitrary, but rather is always combinatorial rectangles, thus leading to the bound {{formula:28b3b70a-e562-4d6a-b40e-829f7da616d4}} . Many other lower bound techniques in this setting follow by giving lower bounds for {{formula:db3b168c-4052-4ede-a44a-24f5ea1709ae}} (for example, the size of a fooling set for {{formula:d5be8da6-1f74-4901-a9a9-55d007569534}} , the rank of {{formula:4fcac6d6-b228-4879-b17f-d370069a2131}} , or the reciprocal of the discrepancy of {{formula:201da734-967f-4015-8654-290e63cf5f6a}} all yield lower bounds for {{formula:0214b06a-f531-404a-9200-f28a1563aab9}} by giving lower bounds for {{formula:ceb21f34-2aea-4635-9f82-849faa46f2f0}} – see {{cite:4879dbeb3838a5d7efa14dd5ad142518d9538f57}}).
| i | 53d651074c39282194fb69bbc0aabbac |
Multilingual machine translation models {{cite:f2ac4a2570daddc637d67f46197d4b62a82a1c90}}, {{cite:4815af08c6a41f416d22d3749836e1d52432b824}} translate between multiple languages. They have better parameter-efficiency than building one bilingual model per language pair, and they are able to transfer knowledge from high-resource languages to low-resource ones. They have become an attractive solution for expanding the language coverage of AR models {{cite:0d441ce7542dcb3192a435bc5a99559fcb9e4ef2}}, {{cite:00383772421d2dbdb654f9a8502c49d903f776f3}}. The capability of doing multilingual modeling is a major feature of the AR regime, and it is one that we should seek to maintain in NAR models.
| i | a97dc3740e4dd7b1811d29a9ae6dcf8f |
We compare K-Arm with the following state-of-the-art detection methods: ABS {{cite:edf18b51825b72b857758fbd3ea65006a665e522}}, NC {{cite:57e5e82526bde4340d61fe633ef136fb10ead110}}, NC+pre-selection {{cite:57e5e82526bde4340d61fe633ef136fb10ead110}} (or Pre-selection for short), ULP {{cite:81e8cb06c53b251a7c82e01b71a9beaf08345f06}}, TABOR {{cite:caf01e07be1c94066b2a90e28db9609cb25cec63}}, DLTND {{cite:9957c228ccf79511ff6d2d9d229c0c51dabf9d62}}. For the optimization based methods including ABS, NC, Pre-selection, TABOR and DLTND, we use the same batch size for fair comparison. For NC, Pre-selection and our method, we use the same early stop condition to terminate the optimization. For ABS, we select top10 neuron candidates after the stimulation analysis and perform the trigger reverse engineering. For Pre-selection, we set the number of optimization epochs as {{formula:7a24c9c5-9f32-4202-b4e8-79c8f65dd7b8}} for each label with {{formula:06a5fd8a-65b8-4433-9385-2ca254b34f6f}} the number of epochs when the first valid trigger is found. Recall Pre-selection performs a few rounds of optimizations and then selects a promising subset to finish.
We select the top 3 among the 5 labels for round 1 models and the top 20% labels/label-pairs for rounds 2-4.
For the ImageNet models, we follow {{cite:57e5e82526bde4340d61fe633ef136fb10ead110}} and select the top 100.
For ULP, we train it on 500 TrojAI round 1 models and test it on the 100 test models. We did not run it on later rounds as it cannot handle model structure variations in those rounds. For TABOR and DLTND, we use the implementation provided by the authors.
{{table:e354eb67-08b7-44e7-a7e2-9288fb4685d9}} | m | a7461ac0f3b6a7389400755390f02026 |
For character frame matching, all visual encoders outperform the random predictor and heuristics {{formula:e6ae5402-2393-40c3-bb10-b2efdcb21b9d}} and {{formula:ce37d06b-4f3f-4445-96c7-b92503653050}} , while {{formula:a1a71a97-f900-46a2-9284-5281c040471e}} outperforms CLIP and R(2+1)D. The compound scaling methodology in EN7 {{cite:afbd5de00e72e65239455203b5c5cdbbb21b16f5}} tends to produce representations that capture additional object details, which may explain why it performs best for this task (see Supplementary REF for a description of the nuanced criteria for this task).
| r | 343020ac363a3118c8ec8756cb6a70c4 |
where {{formula:eb9fe864-6b10-4511-9c48-ba256ee6b750}} is the upper critical field including only the orbital pair-breaking effect {{cite:f46632863312e786e96b98a6e5b69b04cdc8816f}}, {{cite:f92efe0865d234c35f9aa6f656b811875b0137ff}}. Considering the fact that {{formula:cad8b105-30f8-41c5-9ad9-d70a3f6eea82}} ,
a simple relation {{formula:38887bc0-c47c-4d58-bf50-b94ed4f04f88}} can be obtained {{cite:4e21f84e1164fd7e79e4b4df637022c64abb7fda}}. This relation, which is represented by the red dashed line in Fig. 6(a),
is compared with the data obtained from the fitting using the extended WHH theory (Eq. 1). The results from the
Fe-based SCs {{cite:f65fc5e8008df3f0d0472b7eea9ad3876a5158c5}}, {{cite:73425f52f68261720bf39f6c6dbea4f6026fa619}}, {{cite:c506d6dde2d07b29f287343f0c8a5c00b8652040}}, {{cite:d936d0008524adcef4e36a515a0b2259a448de9b}}, {{cite:13aae78011b94a148b7271d38408b6827d4f6ab2}}, {{cite:accaf8cb091e109c464687ce67f133a2f5c065df}}, {{cite:6359a3a478664fa1feb42256a4e50b9965bd8cc9}}, {{cite:a59b851e8cfe45abd40d1e8a9bb55ce71785d8fd}}, {{cite:f2433113fa9b0fc2fb741af285753a405c8050b0}}, {{cite:d27da99f77565156ffa5c871277607d6e5e0b167}}, {{cite:4e21f84e1164fd7e79e4b4df637022c64abb7fda}} are also shown to have a comparison.
It is clear that, similar to the behavior of Fe-based system, the data of NbN films
also roughly follows the
tendency of the Maki formula. The departure of the data from the red dashed line has been attributed to the enhancement of {{formula:4919e333-2335-4809-9181-cd2774b0547a}} due to the strong-coupling effect.
The similarity between the present NbN films and Fe-based SCs indicates that the two systems share a similar strength of SC coupling.
An important difference between the two systems is the field orientation: the Pauli paramagnetic effect and the related Maki parameter are observed in the in-plane field direction in Fe-based SCs, while this effect
emerges in the perpendicular direction in the NbN films.
| d | 0b6a5f78e95d1d3400d598fa460a7cb9 |
Inferring models to predict future behaviour based on past observations is a key task permeating quantitative science. Ideally, when two candidate models require storing the same amount of data from the past, the one that offers predictions with greater statistical fidelity is preferred.
Here we demonstrate that quantum models have a provable advantage, and present an algorithm to infer such advantaged models directly from data.
When given training data in terms of a data sequence and a memory of limited dimension, our algorithm is able to encode relevant past information into the memory and discover a quantum process that can sequentially output predictions.
The accuracy of these predictions – as measured by their statistical fidelity to the true process generating the training data – can greatly exceed that of provably optimal classical counterparts.
The accuracy advantage is realized on an IBM quantum computer, illustrating potential near-term applicability.
Our work substantially expands upon prior work in memory-enhanced quantum models, which focus on the memory advantages in the exact modelling of a given stochastic process {{cite:324f07e47e5a0d1ef87e42287c36968b495f6553}}, {{cite:cdb0bc3f9004ccd2b7a64f8b7a70d504c2e7fd88}}, {{cite:524e5f54be953fcdb726ecc9cad4534af62c2a8c}}.
The results here illustrate that when the memory dimension is fixed, quantum models can exhibit a significant accuracy advantage.
This establishes the advantage of quantum models in real-world settings, where there is a trade-off between model complexity and accuracy.
In this context, our results provide a quantum counterpart to classical tools for structural inference {{cite:972f54c145d83951b127ca14f65705303f6c29ed}}, {{cite:2d4a997b58dd350675a166036165001822828678}}, {{cite:c5378d471eba7178359c749be75cb48c62e7e846}} and dimensional reduction in stochastic modelling {{cite:a5be3512d0aa6f90e6afda9f841273147b08bbe7}}.
| d | 52359151dbbff26331fd8f919a6e978c |
From the point of view of an inertial observer, such as Pelagibacter ubique in fig. REFc, the global de Sitter vacuum appears thermal {{cite:9f858b79f9380c00e7c658b8d83715ba1b1c1cb9}}, {{cite:82eb0a5123a880084547ed6107194f8dd4d7c741}}, {{cite:0befab84c8657c6d5b490ef4ad82f35c8ec76212}}: P. ubique perceives
its universe, the southern static patch (S in fig. REFa),
{{formula:d3582247-f31d-4205-83b7-929776811944}}
| r | c3e8ad88cd6ecdc7b22ee1692a3a0213 |
Our work provides us an important guiding principle to search for new materials hosting the negative thermal expansion because there are a huge number of antiferromagnetic {{cite:828d4d3592cc6ab2940758637a2a7e63c854ea33}}, {{cite:5b9d3d74545ef16f5454e83bf58f6a30c8550e15}}, {{cite:5ab17054025f2ce24487965c4dbfbcd7f0f9cd92}}, {{cite:e9f1d101416c07372c4bb97f4bc9cc48a7afa141}}, {{cite:e5ba38433bc358d0f098e941ea46fc8d740decc5}}, {{cite:54e7fad8d282094d9b21fc70716df662e9abac81}}, {{cite:b692f8862d8a3c94f39528a56ef6a50f3735638c}}, {{cite:988eb53f5a006fba85105f7a2ff264d5b44de473}}, {{cite:74ff869af3d7840a42ba0e22f19f07e9868457c8}}, {{cite:44065eb0b2a9e26414c3251a1c21b73540d1d8ab}}, {{cite:7c1ad0ffb26dda5f98b6572deea0e33e58ddc83b}}, {{cite:3786505a8dc2cf3cbeb65ff608823b97703242ed}}, {{cite:e03d43d6f87a7bb3a6491ddc40fe7a0b208aac0c}}, {{cite:02c6d4ca8693fd906d78dfb4270e88b21c013ea1}}, {{cite:2d49cc07f78dc3f694978ee47b25d0bf867c65da}}, {{cite:40388c27c8ed2b6071db036b057ce692f548fa5b}}, {{cite:11db5f1433a86190c838806c4b0690d25e8c443d}}, {{cite:b612b0383adcd61e4a58f79519d219b326e646eb}}, {{cite:6e50de4577118860ee507e16a9f71b24b8253916}}, {{cite:4b645810c05cb13c6a461052f668a7b03d2862ca}}, {{cite:6db40d7eb6d344239eb388713360aab18048b095}}, {{cite:4ed432d7b52fbd3eb187ca6d32eeb4ec92c30250}}, {{cite:bb24d721c4c4fe44776668c353a841e9610d2921}}, {{cite:c58e76ddf69b1a319e2220a1e44536067419e42d}}, {{cite:1c6cdd7a22820a9bfa0dc796d77bb4a76fab4cec}}, {{cite:af7b4f8fdfb5c237b0bb419159280324a3abe4d2}}, {{cite:1896219c2ab95808f2f597306756a10726a64e56}}, {{cite:a7c1bada99422ca3a1afa2a211ecac5d849a4e32}}, {{cite:163a6fc2faa44f01611641c6dc4249874d337a5d}}, {{cite:d79ef697a97ee1a7a5655ff140511fc36812d009}} and ferrimagnetic {{cite:100552609c67e9081fc62bab0c98bcf64e52628d}}, {{cite:e2d507d22fdfd8fc2c4edf2b06bb8629f87cbfe0}}, {{cite:82974b85ac8bebee312c7ada50f9ff2d4e5ea1cb}}, {{cite:fd93a0924072ad300f11943a96ef51a1be6f508e}} honeycomb-lattice magnets with edge-sharing octahedra. One promising candidate is a solid solution system of the ilmenite-type manganese oxide Mg{{formula:db9ea3c8-80e7-4227-a1ff-a128e33b34d2}} Zn{{formula:6d40de21-828a-46df-a923-c0355e94e1d6}} MnO{{formula:5c073b1b-0144-4484-8725-75c253e894d8}} , in which we can change the nearest-neighbor exchange coupling from antiferromagnetic (MgMnO{{formula:90a4566b-123f-46e8-94dd-56c8399b2b79}} ) to ferromagnetic (ZnMnO{{formula:6a72f846-9d95-47d7-87f4-d4d352a84ca8}} ) by cation substitution {{cite:bb24d721c4c4fe44776668c353a841e9610d2921}}. Because the negative thermal expansion is expected to occur in the antiferromagnetic phase near the boundary to the ferromagnetic phase, the solid solution system is promising because the strength ratio {{formula:57d15688-4daf-4898-a737-e667a1a2947e}} can be tuned rather continuously by varying the Zn concentration. In addition to the honeycomb-lattice antiferromagnets, magnets having edge-sharing {{formula:4129bcd6-2688-4a25-8476-7bf9e5b232e9}} octahedra also provide candidate materials {{cite:ad24b5301966e39857a761b814c10e265229c90a}}, {{cite:7f598c570eaa30d8e12088971e0ab4b0829670aa}}, {{cite:e1798e01349205ba2ede0f4877fba16db07f67c8}}, {{cite:1e2b22945398d63ac309b49135a370e738845ab6}}, {{cite:fc9d96b6770e2c9f9a333713c2fc3359ca2bb61d}}, {{cite:bf8f82079ec862d29eb8a1ad84277fb43c4038d1}}, {{cite:3a135ffdb1f9d2ddf3d9e299c042f06deddd4629}}. We expect that the present work will contribute to diversify the family of materials hosting the magnetism-induced negative thermal expansion.
| d | eb4c054f1f4b65fe80c924ae86ea7387 |
Another limitation when using single-feature PDPs as in our examples is that hyperparameter interactions are not visible. However, two-way interactions can be visualized by plotting two-dimensional PDPs within sub-regions. Another possibility to detect interactions is to look at ICE curves within the sub-regions.
If the shape of ICE curves within a sub-region is very heterogeneous, it indicates that the hyperparameter under consideration interacts with one of the other hyperparameters.
Hence, having the additional possibility to look at ICE curves of individual observations within a sub-region is an advantage compared to other global feature effect plots such as ALE plots {{cite:d43a38abadaca03b4962d2e58cc2bd01b1d89bbd}}, as they are not defined on an observational level.
While we mainly discussed GP surrogate models on a numerical hyperparameter space in our examples, our methods are applicable to a wide variety of distributional regression models and also for mixed and hierarchical hyperparameter spaces.
We also considered in Appendix REF different impurity measures. While the one introduced in this paper performed best in our experimental settings, this impurity measure as well as other components are exchangeable within the proposed algorithm.
In the future, we will study our method on more complex, hierarchical configuration spaces for neural architecture search.
| d | 1bb1a4600f8a4f1ebc33bba249074716 |
We use these models in combination with a neural vocoder, HiFiGAN {{cite:9230aa42681a897effb30f5cc1495d008fda0189}}, to synthesize high-quality clean speech. The HiFiGAN architecture consists of transposed convolutions which progressively up-sample the input representation into a time-domain waveform and convolutions with varying receptive fields which provide the model with important context. If necessary, we up-sample representations in time using nearest neighbor interpolation to match the HiFiGAN resolution. Figure REF depicts this framework.
| m | 0cfb151b3ff6e593feff808b01c7fd40 |
Identification of TEH has been conventionally carried out by first enumerating potential effect modifiers with subject-matter experts and then estimating the average treatment effect within each subgroup.{{cite:45ef1208a530c4993854bb54b156510e17d33a28}}, {{cite:4b3aa5f6c44b175281a321de9c175a4ef80c6687}} In randomized clinical trials, this approach could also facilitate pre-specification and therefore is particularly suitable to confirmatory TEH analysis.{{cite:45ef1208a530c4993854bb54b156510e17d33a28}} In observational data with complex heterogeneity of treatment effect, such a priori specification that separates the issues of confounding and TEH is often practically infeasible, especially with a large number of pre-treatment covariates. Such complications motivate exploratory TEH analysis for generating scientifically meaningful hypotheses and treatment effect discovery, which is the focus of this current paper.{{cite:45ef1208a530c4993854bb54b156510e17d33a28}}, {{cite:67138df74d9bbf0ab2d41b9dcb47a7a7d7ee764e}}, {{cite:4b3aa5f6c44b175281a321de9c175a4ef80c6687}} Exploiting on the counterfactual framework, flexibly modeling of the outcome has been shown to be well-suited for exploratory TEH analysis. However, ongoing discussions about causal methods for estimating TEH in observation data have largely focused on non-survival data. For example, tree-based methods such as BART and random forests have recently emerged as popular approaches to causal effect estimation for continuous or binary outcomes.{{cite:256a006b2a5571699013bdc0e588558dcb6421cc}}, {{cite:9b0627d623dd39e8f6c5cec74f348f95857de5ab}} On the other hand, several modern deep learning methods (DeepSurv, DR-DL, BJ-DL) have been developed for censored survival data {{cite:87ec96873f908750b221072e1d3c4f23e160b303}}, {{cite:dc83e5defa13676bc918e00091d119d4344cc18b}}, and a TMLE based method has recently been proposed to estimate the survival heterogeneous effect. {{cite:f85b6ee44ba03a9657899b9fb5a86c0da7ba153a}}
The GAPH model is adept at
flexibly fitting complex main effects, which are often of great interest in health studies.{{cite:54f24a08b2c3e7acb3d3089acf6148136b3c37de}} We adapt these machine learning modeling tools for estimating ISTE and provide new empirical evidence using simulations representative of complex confounding and heterogeneity settings with right-censored survival data.
| d | 06fd54998b51fe7d388b949c9369d5f3 |
In this section, we experimentally evaluate the proposed method against state-of-the-art techniques to explore multiple solutions. While the proposed method is general and holds for different generative models and different inverse problems, we focus on two notable inverse problems, i.e., image super-resolution (SR) and inpainting (IP), presenting results for two different generative models, i.e. BigGAN {{cite:11db048f5f965cfba5ac87263ca9051d1eccb689}} and PGGAN {{cite:1c6a1cef6fa630512f789d03716c1088dbaa98c5}}.
For super-resolution, we downscale the {{formula:aa46729d-ca1f-4888-8146-8e44dedb91d6}} image to a {{formula:144a511c-905a-4128-9f3f-d4a959508c78}} image, while for inpainting, we delete a semantically interesting area of a face from a full image of size {{formula:7840bbc7-e4c4-41f8-b8f6-f95874c4fe0a}} .
| r | e732af4bfdf282e34bc6e11db5783505 |
According to the statistics {{cite:b574ca8ca368fba0d8a9d30ed9a8b7394ff8725f}}, the peak of the metallicity for EW-type binaries is about {{formula:cea80317-8d6a-4c7a-8296-7c307d533f34}} . CSS J022914.4{{formula:79ef4a12-09a9-4bdf-b80c-f8d9e9f46747}} 044340 is close to the critical poorer metallicity boundary. This may be caused by the luminous third body. Our solved third body contributes over 54% light in the system. Although it is very common that there is a third body in contact binaries {{cite:4c1d8f4848c1243db560ead7b599e899973cc1ca}}, {{cite:62dce12e9e5b367da851d3565684cc15789575a1}}, {{cite:20c21855f41e561ae6a80f9d21d3b570c11a4778}}, the luminous contribution of the third bodies being over 20% is few. About 23% luminosity of V345 Gem comes from the third body {{cite:d71d431e6fa269a5c9417a5ce44bd9353ea648d1}}. These fractions are 25% for MQ UMa {{cite:5d23b21e7b06a0135255c4d5f8a8dd4e1d896b87}}, 28% for II UMa {{cite:9015088ff97abf51af854c78576f938a5aa6b010}}, and 20% for TZ Boo {{cite:bc7c9a1bb1beb85066cbb6c025bd85f5f1ec6652}}. Except for II UMa, the orbital periods of these targets showed cyclic variations which would be caused by the light-travel-time effect (LTTE) {{cite:901a2697df95534ff37c8037e0a3c0a8ad2afdf1}}. According to {{cite:62dce12e9e5b367da851d3565684cc15789575a1}}, II UMa contains a 0”.87-separation third body. Lack of the LTTE may be due to the long orbital period of the third body or it is a foreground/background star. The luminosity of the third body in CSS J022914.4{{formula:b2bba3c0-3647-49d1-9eb2-611012a55dc0}} 044340 is about 54%. This fraction is very high. According to this fraction, the luminosity of this third body is estimated as {{formula:460e9d7b-8970-43be-98d3-66b0a452cebc}} , corresponding to a main-sequence star with a mass of {{formula:a26f3ee3-50ea-4e98-b154-2c563dcaa999}} or a G5 subgiant with a mass of 1.1{{formula:7227279b-266c-4760-bff5-62f854f86fdf}} {{cite:6749c95ce9673cb2cc5717a44bd7fe4f09bf8e52}}. If it were former, its temperature as well as the metallicity would be a little higher than that of the Sun so that the corresponding values of CSS J022914.4{{formula:9618972e-43da-4567-9b1b-9480c110780a}} 044340 should be lower than the derived valves mentioned above. The results would be reversed if it were later one. We also note that the mass of the primary is {{formula:f527c7ec-695e-440c-a402-63d84d723648}} , but the temperature is {{formula:259697d5-0a2b-4105-b399-aa5188e17f34}} K. The observed temperature of CSS J022914.4{{formula:76aa3d9b-9b7c-4165-b0d2-ff2166a23bcf}} 044340 may be lower because of the existence of the conjectural subgiant third body. For the same reason, the observed metallicity may be lower, too. Hence, the real metallicity of CSS J022914.4{{formula:289f9e79-1934-45a2-b061-8620666c4f76}} 044340 may be not as low as the value of [Fe/H] {{formula:7605b0e0-e499-4c3b-a81f-5455fa0ba129}} . Whether the parallax was affected by the third body is not clear.
| d | 5d008ea5eba801431f1fe8cb432a5a28 |
Other machine learning methods based on subgraphs have also been proposed. Methods like mGCMN {{cite:ff63a4d32fa282643698dd9f576657a61ec28042}}, HONE {{cite:4c8949c634d4f583ac9d16e908013f0b50fa5599}}, and MCN {{cite:bd492587b7295c3eed373f82c1aff597f6a0fb3a}} learn representations for vertices by extending classical methods over edges to a new neighborhood structure based on subgraphs; for instance, mGCMN runs a GNN on the new graph. These methods do not exploit all subgraphs of size {{formula:a2a9f80e-ff3e-4d4b-b6f7-b961048ff76c}} and will not learn subgraph representations in a manner consistent with our extrapolation framework.
{{cite:26f020c94c0bd414c4817a8cb297ed0021d7e489}} use subgraphs around vertices to predict missing facts in a knowledge base.
Further examples include the Subgraph Prediction Neural network {{cite:3deb3da4c04e299bf5b9769deed9800792ee5a75}} that predicts subgraph classes in one dynamic heterogeneous graph; counting the appearance of edges in each type of subgraph for link prediction tasks {{cite:d506f8b8632ae1a6f4664c07c98750837b41f96f}}; and SEAL {{cite:e9255b73314a992d8b2d94c1bb5e136c18d439b0}} runs a GNN over subgraphs extracted around candidate edges to predict whether an edge exists. While these methods exploit small subgraphs for their effective balance between rich graph information and computational tractability, they are along an orthogonal thread of work.
| m | 6de5162a88d7ee021915befad7ce8c47 |
where {{formula:121c5f27-bcea-4280-972f-cc58ef3a5fd0}} is the time-dependent quantity of interest defined on an open, connected and bounded region {{formula:c97a0d59-c531-45e7-8d69-638251e8d568}}
with Lipschitz boundary {{formula:46f87c2a-39cb-4696-94a8-b564b12e502a}} ,
{{formula:ec4042ab-28bb-48d7-ad80-ab43af85a1cb}} is a linear, local (classic) or nonlocal, elliptic operator, and {{formula:772b8168-b71c-40f8-bda1-e842dbe203fc}} represents a nonlinear operator.
For some specific {{formula:fa047ba3-3a9d-4d43-997a-a368124735ed}} and {{formula:71738634-30fd-464a-b3c1-97fc35385068}} ,
the solution to (REF ) under appropriate initial and boundary conditions satisfies some important properties,
such as existence of invariant sets and energy dissipation.
The existence of invariant sets also means that
the solution satisfies the maximum bound principle (MBP) {{cite:f83e69e0acebf026426dfcceba96d2eb7880af5c}} in the sense that
if the initial data and/or the boundary value are pointwisely bounded by some specific constant in absolute value,
then the absolute value of the solution is also bounded by the same constant everywhere for all time.
A well-known case is the classic Allen-Cahn equation {{cite:f97ba2f5e46bf7cf5cb65ff5fd8ce6be6a0949fa}}, {{cite:4a8526914b00ecf3d3d7b2e020909f831a13e55b}}
with {{formula:e7b390d8-702a-4319-9205-37dfe1fad261}} given by the Laplace operator and {{formula:d8f70bd7-ae15-4efc-a053-d50f4414e0ac}} in (REF ),
where the constant bounding the solution is 1.
In addition to the MBP, the Allen-Cahn equation also satisfies the energy dissipation, namely,
the solution decreases some free energy in time.
The energy dissipation is a common property shared by phase-field models,
which are typical cases of the semilinear parabolic equations (REF )
derived as the gradient flows with respect to some specific free energy functional.
When designing numerical schemes for phase-field models,
the MBP and the energy dissipation are desired to be preserved in the discrete setting
for the equations possessing these two properties.
| i | 32f5f8b73ebd479036d1978f58f4dde4 |
Word Embeddings.
We also consider models based on pre-trained word embeddings. We use the word2vec embeddings, trained on 6B tokens of Google News articles using language modeling as a training objective {{cite:972899778a530679bbbda62c18f8dc6987f2236b}}.
To obtain tweet embeddings, we consider two ways of aggregating the word embeddings. (1) We average the embeddings of the tweet's words. (2) We use self-attention: we compute an average of the word embeddings weighted by the words' attention scores, which we learn using a two-layer neural network followed by a softmax {{cite:2defdad0e020cecaf4028bc312370670118e3bef}}.
| m | b6bb21107a0245d1f517c0da6a7c2ed3 |
When {{formula:36853bf6-e1c6-4e46-897e-983e436eac86}} is algebraically closed, a classical result in differential Galois theory states that a Picard–Vessiot field exists for the system (REF ) and it is unique up to a {{formula:2ca819fd-9ced-492f-8445-4461224fe5c2}} -differential isomorphism (see, e.g., {{cite:3fd021f558c2783874ca0d0092c67a813783e411}} for the ordinary case and {{cite:62a3b331741792fbb9348f12f5fecb6fdf45ad1b}} for the partial case).
| r | e91789de98b06ca3ed89a2bfff212126 |
(3) The aspect of the quantum information. There exist a traversable wormhole between the island and the radiation region in the spirit of “ER=EPR" {{cite:f191cadedb33fc901f970c2377e79c1c19a84853}}. There is a protocol called quantum teleportation {{cite:4ae5821b46638dc084791f5a43a886bfc574a182}} to extract the information residing on the island. We can create the negative energy shock wave in the bulk and the information transfers to the bath {{cite:ecb9a2d459201c4c4ce369123fefa73e772be8a7}}. However, the large amount of shock wave with negative energy not only backreacts on the bulk geometry but also affects the
(averaged) null energy condition. Thus, this operation can not be continued.
| d | a8058e654ea27865a6d6e824e02cbeda |
The expansion of the HII regions is extreme interest to studies of star formation as their expansion may trigger new generations of star formation into being within the molecular material surrounding the bubbles (Thompson et al. {{cite:497e3c4640774dfee21d846f8e7dd1ce17521eba}}). Evidence of triggering has been reported by many authors (e.g. Deharveng et al. {{cite:89ada17a9ee7ca503fb918efed43a6ad1b1b56b5}}; Zavagno et al. {{cite:805f0d916fd525913ca9017ef2dc01b7fa3effe1}}; Kang et al. {{cite:39cdbda9e0c511a7f0482c107941c9ab35cd3a48}}). It should be noted, the majority of observational studies into triggered star formation near SNR or HII regions take a phenomenological approach, the evidence of triggered star formation is not very conclusive (Kendrew et al. {{cite:5a55ef7baa8cf1a03de471926ef08f501cce2dfa}}). The statistical approach may address the uncertainties inherent in observations of individual HII regions. One detailed statistical study of massive star formation in the environment of 322 Spitzer mid-infrared bubbles by using the Red MSX source survey for massive young stellar objects (YSOs) suggest that the fraction of massive stars in the Milky Way formed by triggering could be between 14 and 30 per cent (Thompson et al. {{cite:497e3c4640774dfee21d846f8e7dd1ce17521eba}}). Kendrew et al. ({{cite:5a55ef7baa8cf1a03de471926ef08f501cce2dfa}}) made a similar statistical study with 5106 infrared bubbles, they estimated that approximately 22 per cent of massive young stellar stars may have formed as a result of feedback from expanding HII regions.
Therefore, the infrared dust bubbles could be good sites for us to find high-mass YSOs and study the process of high-mass star formation.
| i | 5706a26680f620620366e60e9548cbac |
Since the major decay channel of the {{formula:73039c0b-22db-4dbf-ad98-88b7315bbf4d}} is the three pion state and its width is narrow, we take
{{formula:8ac2000d-604a-47df-bad9-695388fee531}} MeV and {{formula:2d572485-9d6d-43d5-84c5-902a84aa439f}} MeV from PDG
{{cite:dcad4195101bc79a21d8993e716616d08b68685e}}. The physical coupling {{formula:dd27c14d-63b9-49a0-a209-518ec2c20bec}} can be determined from the
decay width of {{formula:f9833fc6-7648-437e-823d-28d1e30aa9a3}} . Using the Lagrangian
in Eq. (REF ), one can derive the decay width
{{formula:7ef204ff-3549-4d94-a7f9-7db819987b67}}
| d | 4ca150b9fc140ec25b1e40ac2c06efca |
Overview. HICO {{cite:aa1816592127d98ee99f8992a5e34b77c0a8f4b1}} features the human-object interaction (HOI) recognition, i.e. predicting all the possible HOI categories of the input image. It contains 600 HOI categories with 117 unique actions and 80 object classes. The training set includes 38116 images and the test set includes 9658 images. For a fair comparison, we follow the standard practice and mainly focus on those previous methods that do not require extra supervision {{cite:cc41e20d0f191759c3b66600a6f3afafd2f35f34}}
or data {{cite:51f1830ce3a5c00ba82fb115e1529917d94dbcfa}}, {{cite:8870336761a68c47c22fee810d0c2ce9c80a19a8}}, {{cite:7bb3ceac95dc7f74a11e17afb3067d2492496c69}}.
By default, we choose PVTv2-b2 {{cite:e6575251c130a8b8481973affc254a3eb2f74687}} as the ViT backbone. Regarding the concept-feature dictionary, we use the “most-recent” sampling and a queue length {{formula:6b07b545-064e-4006-8650-e4a5bf8df7e2}} of 10. The trade-off weight {{formula:5e170cef-913f-4606-ba45-fc88dec860d0}} in the overall loss is fixed to 0.1. Other hyper-parameters are inherited from DINO {{cite:a5f1055ab12395f8574b8e818bc2955e4893960d}}.
| r | beb2a833bb40951ac4e65e64ff300f95 |
Following the works of {{cite:a33725aa1341cec1aa99afa021f1dfd52178657f}}, {{cite:da8d52072ce73a09fb0d87f96db1d0f3544c6470}}, we omit the use of the noise vector {{formula:75e8c37d-2cc5-43c8-a058-fbb56b639316}} as the Generator will learn to ignore it and produce deterministic outputs. Nevertheless, several recent works on conditional generative models already addressed the stochastic data generation {{cite:b54aecdfd7d15e8acce855839d7ea34ae961fbcb}}, {{cite:1c23b075d8bf33c20e8923fe9789dbc5843a5e2b}}.
We focus only on the domain translation task with an intermediary representation between image and point cloud domains.
| m | 2fec239a4c4f11f195acfe9a0a1d57fd |
The covering factor of the gas can be estimated studying the absorption properties of large samples of AGN. In Fig. REF we compare the results found by {{cite:6402aa69ed6b7cb0fd07d613ee845ab8861599e3}} using the BASS sample and those found in this study (numbers are reported in Table REF ). Using this technique, recent hard X-ray studies have shown that the fraction of CT sources below {{formula:92fe7ab4-6bc0-437f-9100-93943263e02a}} is {{formula:f89373bc-514c-4a94-9fd8-6bdd8b35bdfe}} (blue shaded area in Fig. REF ). {{cite:14261cb05ea4ccaa77f31d996475da58e675f409}} find that the fraction of CT sources decreases when using NuSTAR data thanks to a better covering and sensitivity above 10 keV which allows a better restriction in the LOS obscuration affecting the intrinsic continuum.
| d | 73c1ca96c9a2eb0e1ab75207571454ae |
As illustrated in Table REF , our method (denoted as DLB) consistently improved the performance on various backbones (baseline). To be more specific, the averaged error rate improvement achieved by DLB ranged from 0.83% to 2.50% on CIAFR-100, 0.37% to 1.01% on CIFAR-10, and 0.81% to 3.17 on TinyImageNet. It shows the effectiveness of DLB that can significantly improve the generalization ability on various classification tasks. Moreover, DLB outperformed the state-of-the-art approaches, achieving the lowest top-1 error. The best and second-best performances on each set were highlighted in red and green respectively. We can observe that DLB on CIFAR-10 succeeded the state-of-the-arts by 0.30% with WRN20-8; whilst on CIFAR-100 by 0.47%. These improvements are attributed to the self-distillation regularization from the last mini-batch. We notice that DLB significantly outperformed Tf-KD {{cite:2c8e06ea637ca303b32b9c7cefa77be4e0876955}}, and PS-KD {{cite:089202c3f9301bc1ff91d03f583417b2d9cb97ec}}. It demonstrates the performance advantage of DLB to generalize CNN. Furthermore, the identical teacher from the last mini-batch provides dynamically updated smoothed labels that fit the training process better than a pre-trained teacher or the last-epoch backup. Conclusively, DLB can efficiently serve as a universal regularization to normally train neural networks.
| r | 4923aa5ad8e9267b366efff8a9c55ce9 |
In Sec. we will see that {{formula:ae9f4031-2bae-4d6f-bcd0-a41f7413ba0b}} which is known as the Jarzynski equality {{cite:432923395f3318e18883adb5bc6eeade70188fff}}. Then,
the results in Thm. REF could be alternatively stated in terms of properties of the work distribution alone.
| r | e410cfe8ea4d46cc80fd14a461424258 |
Using the Eqn.(REF ), we calculate the {{formula:03d9bd13-94a7-4da5-a2fa-b394f4adcbc8}} contribution to {{formula:65f2008c-df23-4d2c-aed0-87672d368f93}} which has been shown in {{formula:802f6310-dadf-4490-8508-609d065dab44}} plane in Fig.REF . The gauge coupling is randomly varied in the range {{formula:97bfa2dd-4d35-4a03-ac5d-8b8f843a9077}} . It is evident from Fig.REF that the model accommodates the observed muon ({{formula:37f6ecb6-c252-420f-94fe-a618c16d6142}} ) for {{formula:43ca519b-7ffd-4f1c-b84e-c0ef67d2262b}} in the range ({{formula:e7a147cd-e151-490b-a284-3f5d8ade5989}} GeV-{{formula:56052833-4bd9-47a8-8acb-33c5bae81fb1}} GeV) and {{formula:9599593f-bc57-4510-84f1-4b7bec9e8303}} ), which is consistent with constraints coming from experiments like COHERENT{{cite:a1e60e4150e4b2cb44bd41e528522538f038bcdb}}, {{cite:6a3b9d4b213c4a0a814929537958a0696a62707d}}, BABAR{{cite:681c9f70452343c51f54f6e9bf9eafa617f44ba3}} and CCFR{{cite:c473495a78552955c81c5351fe4909f79604f2aa}}. The sensitivities of future experiments NA62{{cite:eb68099a917580659cedebc875486e605bfa71a7}} and NA64{{cite:3b6d5de9b6d491b3f2d833db036f29e02ec44295}}, {{cite:7354a076f52d848456db4a701f71507f35b33d71}} are, also, shown in Fig.REF . The upper left triangular region is excluded by the astrophysical bound from cooling of white dwarf (WD){{cite:784d314811d3c38cad9ddee992218a95a8460300}}.
| d | fb821128aa951a462dc334f79ceefaae |
We next consider an alternate method for calculating the imaginary part of the action, making use of the Hamilton-Jacobi equation {{cite:0e2060fd2b86d42b28df9e153108ffcce6e5cf07}}, {{cite:b36ab26fb55dcf128f40f08a760404ef1fa4eaf5}}, {{cite:3b362cebd15faa80efd5cdce1858587f196ef5cf}}, from which we will calculate the Hawking temperature. The analysis goes beyond the semiclassical approximation by including all possible quantum corrections. The semiclassical Hawking temperature is thereby appropriately altered. Equivalent results are obtained by using either the standard Schwarzschild like coordinates or other types, as for instance, the Painleve ones. We discuss both cases in this section.
| m | 86266de2ea7e4ee1157ef57621393af3 |
Score-based generative modeling (SGM) may be viewed as the first stage in
approximating a solution to the Schrödinger bridge problem. Through this
interpretation we have developed a novel methodology, the Diffusion Schrödinger Bridge (DSB), that extends initial SGM approaches and allows one to perform
generative modeling with fewer diffusion steps. DSB complements recent
techniques used to speed up existing SGM algorithms which rely on either
different noise schedules
{{cite:b90e1f74f4b4b06f6f5c24bbf9132088cd439500}}, {{cite:d7fc069d0362ab5b6c5052605b7e95e8b5322f84}}, {{cite:7541f43bc0e4ea3dcbe744c71224b5a1202ceed9}}, alternative
discretizations {{cite:3f0fb8615948d2c977da68b4af4c96d8c2d76ef1}} or knowledge distillation
{{cite:963380dfce89e057441aa6c060d17f82f39f3dd2}}. Additionally, as the solution of the Schrödinger problem is a diffusion, it is possible as in {{cite:2c8912567600efb88476369533da3653eb4d9f5a}}
to obtain an equivalent neural ordinary differential equation that admits the
same marginals as the diffusion but enables exact likelihood computation. From a
theoretical point of view, we have provided quantitative convergence result for
SGM methods and derived new state-of-the-art convergence bounds for IPF as well
as novel monotonicity results. We have demonstrated DSB on generative modeling
and interpolation tasks. Finally, while motivated by generative modeling, DSB is
much more widely applicable as it can be thought of as the continuous
state-space counterpart of the celebrated Sinkhorn algorithm
{{cite:9cf556ac7d7ca79bde264f2d81cdcb8ee0ccb041}}, {{cite:a995e32dd70e635b9bdbae54b5ebb60f732ccc38}}. For example, DSB could be
used to solve multi-marginal Schrödinger bridges problems
{{cite:1b12cfd3d1b8dbef2c4de717f2f9eb0ae7387ae6}}, compute Wasserstein barycenters, find the
minimizers of entropy-regularized Gromov-Wasserstein problems
{{cite:22b97119627932c41679b6c335b6a9d57d4f592e}} or perform domain adaptation in continuous
state-spaces.
| d | 7bd4daf4ac244eabe4e3fb325347a552 |
which can be solved using the steepest descent and back-propagation optimization methods {{cite:986c5bc91e1afc7e1696b846d6386b098070f7bf}}. Note that {{formula:2a09670c-ef79-460e-a4a9-54217be8daec}} in (REF ) can be regarded as the denoising of {{formula:d3145ddc-39d7-45a3-9754-3d126e111108}} , which also serves as a proximity regularization that forces {{formula:8b82e71f-9790-49ba-9c18-602c22516838}} to be close to {{formula:bcefe177-385b-4fdf-91fa-46a092c1c131}} . This second term provides additional stabilizing and robustifying effect to the back-propagation method.
| m | 38aeaf49a26e9dc1b321844997118ec5 |
In calculating the fluctuation function {{formula:2ee6c80e-c36f-4c21-a894-68cfdc8040b4}} , we take {{formula:4345c4ce-2708-4179-b609-998ff8cb0d02}} varying between -25 and 25, with a step of 0.2.
The scaling exponent {{formula:0a0bc13b-8c0f-4be0-8b95-aa2d152ac3cd}} is called the generalized Hurst exponent, and
the usual Hurst exponent is given by {{formula:e4b26da2-653f-4560-aca5-3c2d05ceec9f}} .
When {{formula:0dd6221c-766c-4612-b499-4604d8ddc795}} is constant, the time series is called "monofractal."
For example, the random Gaussian time series is monofractal{{cite:c5c1b95bef15f3e9d6bbd25fe0f594fc13798763}}.
On the other hand, when {{formula:dfb85483-dc14-4eb5-940e-8626f47fb57f}} varies depending on {{formula:69978f57-2313-4966-b029-d53419ccfa0b}} ,
the time series is called "multifractal."
| m | bfcb8c3c4cf0801e21b6bf36c3a4e11e |
In recent years the ideas of holography {{cite:60cac74ae2065c01365f570aeb7aa627a627f0ce}}, {{cite:e454fa68e28eaa292d212a1ffb629fe6f6d370ff}}, {{cite:3c9854ec47b3f9a302b6b2ea598ab0b4d9d143e9}} conquered almost all corners of theoretical physics. The idea that some (or any?) strongly coupled quantum system with many degrees of freedom should have an alternative dual description in terms of the gravity/string theory in a higher dimensional spacetime is becoming more and more popular. Despite this enormous attention the holographic principle has received in the last two decades, we are still lacking the first principle derivation of it. There are, however, numerous and extremely non-trivial tests of the duality. Due to its strong-weak character, it is very hard to produce these tests.
In some special models such as {{formula:1615c8fa-7791-4c86-b6f5-06c684eaf8d7}} SYM theory, tools such as super-symmetric localization, or integrability, provide ways to compute observables for arbitrary coupling strengths and compare with the holographic predictions.
| i | 5af1719171560ceb7561ea193cde9ab7 |
The construction of an accurate seismic image is critical for the achievement of a good velocity model. Full-waveform inversion (FWI) aims to recover the velocity model from the acquired shots, using an iterative inverse method that updates the initial guess for the velocity model subsided by the wave-propagation equation {{cite:f0da94b73983252bddecdf88b3d35b5360c3a5a1}}, {{cite:dae783ad617bcc483d30e476392d5dd6147bad59}}. In theory, FWI can recover the velocity model with high accuracy and details; however easily achieves a local minimum, leading the model solution in the wrong direction.
| i | 39eb412037716a97a0c95e1b0fe40709 |
Table REF shows the performances of the teacher, baselines, and our method on the GLUE dev and test sets. We compared CILDA to the Vanilla-KD {{cite:671e6eb0fa4805fd0ba108b80153f15a74001622}} baseline, and against 2 strong recently proposed methods We compare with these models because we have published results on GLUE leaderboard using the same teacher and student backbone models.: Annealing-KD {{cite:1e59130bcfdb0e44a2edb484f52257c48697fbcb}} and MATE-KD {{cite:9080ee2ff594bd65ef7be40b95eb864ed797ed29}}. We observe that CILDA outperforms these models on all GLUE tasks, except on QNLI dev where MATE-KD performs better and SST-2 test where CILDA is on par with MATE-KD. Overall, CILDA outperforms MATE-KD and Annealing-KD by a margin of 0.6% and 2.1% on average test set respectively.
{{figure:290f636e-bb00-4b33-80e2-7c5d9b4635cb}} | r | 3e615e9c351aa4cc427c21697d285b82 |
Fortunately, it appears that we shall not have to wait very long to see a confirmation
of the EDGES measurement. Several other similar experiments are underway, including
the Large-Aperture Experiment to Detect the Dark Ages (LEDA {{cite:9b581780be1d60539ae0d116f152c20da5d2ab95}};
the Sonda Cosmológica de las Islas para la Detección de Hidrógeno Neutro
(SCI-HI {{cite:5f9c1edbc69c68888ca98e7a4103531efae0cc99}}); and the Shaped Antenna measurement of the background Radio Spectrum 2
(SARAS2 {{cite:d80ca441d4a7910560e39cd92eb741b94b0fca96}}). Farther afield, the observation of the 21-cm line
should be significantly enhanced by the use of interferometric arrays, such as
the Hydrogen Epoch of Reionization Array (HERA {{cite:58ba60f6a55aa03442d99e0368e00c4b9dcc4877}}); and the
Square Kilometre Array (SKA; https://www.skatelescope.org), among others. When
constructed, the SKA Low-Frequency Aperture Array will detect the power spectrum
associated with the EDGES absorption profile, and should also be able to image
the 21-cm signal, providing more fertile ground for testing the scenario we have
explored in this paper, in which the physical conditions producing the 21-cm
absorption line are inextricably linked to the requirements for rethermalizing
the CMB at {{formula:66831785-17d6-4079-a5f5-dc530295141f}} , just prior to the epoch of reionization.
| d | e17255351a71cc61ef69a001cf309cb1 |
In this paper, we first empirically compare state-of-the-art FHE libraries including Microsoft SEAL {{cite:51ab0eab602f03abe7baa645f6e0c8d957a7f200}}, IBM HElib {{cite:49c9d880564455817d1b59321a43afec5b98fbce}}, CKKS {{cite:a7bb7ea06e41b5f498f332068b15f4c0131b84e4}}, FHEW {{cite:17e45b684c4856a763560da80347ac1ff2ff65f7}}, TFHE {{cite:7e1a879dcc8ad84878862a262b7081fffa717ee7}}, and Palisade {{cite:fb8ce050f9e078b7477cb2292fb696f50a00c69d}}. And then, we select competitive implementations among these libraries to characterize each FHE scheme. At last, we quantitatively compare the performance of various FHE schemes including BGV, BFV, CKKS, FHEW, and TFHE. Our study enables average users to choose the most efficient FHE scheme for their privacy-preserving applications.
| i | d0a3f7b321c2ff15870e64eca5d4208c |
Since {{formula:7855f5f5-8a14-47bd-a17f-f8e7e78ab2fa}} is a polyhedral cone, we know from Theorem 19.3 of {{cite:782ed425c4ed4bc78056ef5083d6b73a32611519}} that {{formula:b6123eb0-8cf4-4f81-baf1-a5308aedbd8b}} is still a polyhedral cone. There exists {{formula:557ab99c-568a-461c-8a60-a48eaed5f7b2}} such that
{{formula:40d028b2-34b6-4452-b9e3-63501d2b67cf}}
| r | bf3e76649046b37a7fa5bb4c769f3e81 |
which were introduced by Pardoux and Peng {{cite:e62c9028c3942421f3689f75979997660a30c17b}}, where the existence and uniqueness were obtained for the case of Lipschitz continuous coefficients.
From then on, BSDEs have received numerous developments in various fields of
partial differential equations (see Pardoux and Peng {{cite:1c3a133713b29cdef848d5f5914c8aafcff4fe05}}), mathematical finance (see El Karoui, Peng, and Quenez {{cite:ec38535ce91d344b2b49910966844e6b361d2982}}), and stochastic optimal control (see Yong and Zhou {{cite:59c4da8e193b4ac63966e3f3de87539401ccc59f}}), to mention a few.
At the same time, due to various applications as well as the open problems proposed by Peng {{cite:bfafc659d44a91372718645b88efa6ab2b5cc20f}}, many efforts have been made to relax the conditions on the generator {{formula:17239423-945b-4fa6-b9ca-b709368704ae}} of BSDE (REF ) for the existence and/or uniqueness of adapted solutions.
For instance, Lepeltier and San Martin {{cite:966a0bdee656a1cdf6d9a07232f1c27e9b651326}} obtained the existence of adapted solutions for BSDEs when the generator {{formula:c84efe78-1224-4261-a40b-93623461c953}} is continuous and of linear growth in {{formula:1130aa9c-8325-4a55-80da-11c54336ce27}} .
In 2000, Kobylanski {{cite:b7e95e51211b14bfb31376bb5e0ec18a310e3132}} proved the existence and uniqueness for one-dimensional BSDEs (REF ) when the generator {{formula:dacabf0e-fdbd-4308-8cb0-d828795e1e51}} is of quadratic growth in {{formula:5db70e52-129c-4eb4-8e9c-616f8bad10fc}} and the terminal value {{formula:cc8ad31b-5a02-415c-9d3f-d95f0b20e0e1}} is bounded.
Along this way, for the existence and uniqueness of BSDEs (REF ) with quadratic growth, the one-dimensional situation with unbounded terminal value was obtained by Briand and Hu {{cite:30cdbe9ae301bbcf1a641805dc29a7ab18be96a7}}, {{cite:b1e03c8063bf84ea9986dc185fd51072303189a8}} and Bahlali, Eddahbi, and Ouknine {{cite:a440f155826690874bf908bddde1637e73db24cd}};
the multi-dimensional situation with bounded terminal value was studied by Hu and Tang {{cite:a2a7cd5b48df9f3dafd794ef250b654d5299faf8}} and Xing and Zitkovic {{cite:c6315a3d6ea65655b19e206f04c67961edbd613d}};
and the multi-dimensional situation with unbounded terminal value was investigated by Fan, Hu and Tang {{cite:74d827897d76ca915087619f0de98564f70febae}}, under different conditions and using different methods.
Some other recent developments concerning the quadratic BSDEs can be found in
Barrieu and El Karoui {{cite:2d26dd64fabd0e5903f4c18aaab64e2682a263e7}}, Delbaen, Hu and Bao {{cite:ad81949f11435b5df7dafb2f44afaea337994beb}}, Fan, Hu and Tang {{cite:98e41eff202dd567fd312b7d07a6c704125a7958}}, Hu, Li, and Wen {{cite:8226f7df3eee6b7133d31bc45b6be762ec419dbb}}, and so on.
| i | 7979e6a0e72016f214d54315d6d30361 |
The classification stage is managed with {{formula:8daffaff-0209-46cf-9ac7-4cef2fe9aac3}} {{cite:30fbae42868f8310acddddb45f3ccd009ce5758e}}. Tests are performed using a one-versus-all (OvA) paradigm for 30 executions. A shuffling operation is applied to ensure the training and test set are always different. Images are scaled to {{formula:c6669c63-d824-4059-9bfd-6f3a4c0cb774}} pixels size, to avoid performance degradation. Table REF reports experiments performed on the ALOI dataset. Results are listed in order of average accuracy and the approach that provided the best performance is highlighted. In order to perform a correct comparison the same settings reported in {{cite:600054e17e8adc26673965346e2480a6dd51854e}} and related to table REF are adopted. The results in table REF achieved by Bag of Visual Words (BoVW) {{cite:6605a645080eac08bd42de38de0bfb824e42d98f}} and those obtained in {{cite:600054e17e8adc26673965346e2480a6dd51854e}} using some variants of linear discriminant analysis (ILDAaPCA, batchLDA, ILDAonK and ILDAonL) and in {{cite:43e27aca6ac55e96dbff01f0d8e92de6b400f405}} (ARSRG{{formula:ed509a85-19bf-4ef5-b79b-3067d4cde5f6}} ) are shown.
{{table:0bb73eb3-e23c-4173-bda8-3b650e28a755}} | d | 677be6a84ec75d839b8929804f2265ec |
Modeling reservoir pressure management is challenging considering the complex heterogeneity of the reservoirs and the uncertainties of the systems' input parameters. This complex heterogeneity typically requires high-fidelity physics-based models to make CO{{formula:e036e934-7505-4cc7-9762-f373ca0c66f2}} predictions. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both heterogeneity (which contributes to the complexity and high computational cost of the physics model) and uncertainty demands many realizations. Performing many realizations makes this a computationally-intensive problem that is challenging for current reservoir simulation workflows. For some applications, such as the oil and gas industry, tens of thousands of wells have been drilled, resulting in large amounts of data and the development and usage of data-driven machine learning models {{cite:6f26474b52c909cf1965db5f846c7f50cfe6f13b}}, {{cite:965cc54b33a0a375126d9e87d8d5c9c961f6d0d0}}, {{cite:c1929381c286d3e74c684a1bf4b205d1850dfc2c}}. However, this is not the case for applications such as GCS, where few wells are in use, data is scarce, expensive, and time-consuming to obtain {{cite:cb885c8ccb5d7a9b9df821c7cc29ca29b4f9d142}}, {{cite:9ec5205fa0ebb8c49e5a0050545f91a2ab1f52fa}}. For such data-limited applications, physics constraints are often introduced into the machine learning algorithms to regularize the neural networks training and thus augment the lack of data {{cite:ce330e0f4e71005ebfe881286e6f44b212f8a725}}, {{cite:9712e9f856024b72eeab49dae94bc60a3efd3ed2}}. This approach is called physics-informed neural networks (PINN) {{cite:30fa3d3b232af46ea21f42358b1ff325981830e4}}. A limitation of the PINN approach is that if the physics are not trustworthy – there are no guarantees that the computation will quickly (or at all) converge to the correct solution. An incorrect solution could misguide the pressure management machine learning model. A major limitation of most traditional numerical models is the calculation of parameter gradients from high-fidelity physics reservoir simulations. Most fluid and transport simulators, which can simulate subsurface fluid injection/extraction rely on finite-difference gradients to evaluate many physics-based parameters {{cite:30d3f0748e2b516526da6ad087f0b71b39a43776}}, {{cite:7ef22949bfe0dfc90d28c2b4ccebcd6901338d29}}, {{cite:176d5d16c2e5dd5b87be7471514e2e4e3be42fbb}}, {{cite:35a04846a0eb17439a494701a0dc39fa3077d8cf}}, {{cite:71fb89f61807ddbc6666d7ecf0b6888221de27b0}}. This is why such simulators are built without the use of differentiable programming (DP) and automatic differentiation (AD) techniques which are standard in machine learning approaches such as PINNs. Computing finite-difference gradients for highly-dimensionalized models (e.g., those with heterogeneous permeability fields) is computationally inefficient and often prevents the traditional physical models from being included in machine learning workflows. A solution to this problem is using DP and AD that takes advantage of the chain rule to evaluate complex derivatives more efficiently {{cite:79c9502626f2f217deb7fba1f14eb8d0bab07734}}, including for implementing trustworthy numerical models based on traditional methods such as finite difference/element/volume.
| i | 713377e21299aa6d3f09de41d4d57564 |
Static Scene Layout Estimation. To evaluate the performance in the task of static scene layout estimation, we compare HFT against Monocular semantic Occupancy (MonoOcc) {{cite:01b995dd64108ee6d7be3be3fe96d91b8ae931e0}}, Monocular 3D (Mono3D) {{cite:e0d17c6b912d6c016df389a6441563626dffbc7a}}, PYVA {{cite:806c28ec487ad0eba26eebf70e8bd73848a13035}} and PON {{cite:f7846b0a1e3ed0728be255ca39357b355c59fe9c}}. Table REF summarizes the performance of existing approaches on the KITTI Raw and KITTI Odometry benchmarks. We densify the sparse semantic labels and compare all methods under the same training protocol. As observed, HFT model ranks first among all the existing baselines by large margins on both datasets. HFT achieves the highest mIoU of 66.29% and a competitive mAP of 80.20% than concurrent models in KITTI Raw benchmark. Moreover, we observe a substantial improvement on the KITTI Odometry dataset in the mIoU and mAP when compared to both CBFT and CFFT baselines.
| r | 78663fbbfe81c970d5a5ae82e04b228b |
Literature review shows that ML methods are very convenient tools on many different applications related to earthquake engineering and seismic risk assessment as they demonstrate promising and encouraging results. The proposed ML classification models in the literature are reasonably accurate but are not transparent from the point of complete understanding by users, i.e., they are black-box models. In machine learning, a black-box model is a system that does not reveal its internal mechanisms {{cite:a2bdcbc96ff095a423f7a7307e402dfe2b950184}}. From the engineering point of view, the main concern on the black-box models is that the model might fail in unexpected cases due to some possible inconsistency between the physical model and its machine learning representation while providing very good performance {{cite:c8a546f7a46907c1fc1bb3f87882f36c0b7c544d}}. The literature of the interpretation of machine learning algorithms, also known as Explainable Artificial Intelligence (xAI) in Computer Science, is quite extensive even though this concept is more recently exploited. The interpretation is addressed with two main branches: transparent models and post-hoc explainability {{cite:a35ce96c8386e9ae826f254180864e6dd523e82e}}. The former refers to a machine learning model which is understandable for a human {{cite:39befd406f70d5e33e6b617b985024602e797208}}, and the latter includes the post-hoc type methods that are specifically designed for explaining internal structure of the black-box type learning models {{cite:d4d18492a19f2362d014443b3b26be41529617f3}}. Transparency and interpretability are two concepts that are strongly tied to each other. The examples of the transparent models are Logistic Regression, Decision Trees (DT), k-Nearest Neighbors, Rule-base Learners, General Additive Models, and Bayesian methods. Among them, the DT easily fulfil most of the constraints for the transparency in terms of providing a decomposable and algorithmic transparent model at the expense of low generalization capability . Therefore, the trade-off between the performance of a model and its transparency should be properly established by means of feature relevance techniques . Besides, it is important for engineers to understand how the model makes the decision and verify that the model is physically meaningful. The technical challenge of explaining decisions made by the models is referred to as the interpretability problem. Therefore, explanatory models, known as glass-boxes, are more useful than the black-box algorithms since they provide necessary and sufficient information to assess how the input variables of a system depend on the system output . The disadvantages of black-box models and the importance of interpretability in machine learning have been pointed out by various researchers , , , , yet, not in the field of earthquake engineering.
As summarized in the literature review, the trade-off between model complexity and model interpretability is typically disregarded in the earthquake engineering field despite the importance of the explanatory models. This study aims to fill this gap and assess the ML methods to provide an interpretable (glass-box) model for failure mode classification of conventional reinforced concrete shear walls while ensuring reliability and high accuracy. To achieve this, eight ML methods are utilized to classify three wall failure modes based on the experimental evidence such that the highest possible accuracy is achieved by ensuring physical significance along with a high interpretable model having the least number of features possible. To ensure such a model, the dimensionality of the problem is reduced with a feature selection algorithm. Features that are not physically meaningful are removed from the learning model even though they improve the classification performance. The class-wise and overall classification accuracy of the failure modes were compared for the considered ML classification methods along with the ASCE 41-17 classification criteria. Novel aspects of this study are i) investigating the state-of-the-art machine learning methods from the Explainable Artificial Intelligence (xAI) point of view, ii) establishing a convenient trade-off between interpretability and classification performance, and iii) obtaining a robust, interpretable, and physically meaningful classification model without renouncing the high accuracy accuracy for predicting failure mode for conventional reinforced concrete shear walls. The proposed classification model is aimed to provide a preliminary prediction for the shear wall to achieve better nonlinear modeling for a detailed performance assessment.
| i | 4ae351349b1980b98e45063b8b39b16e |
Regarding solid bodies and structures, not only the deformation under external loads is of interest. Different fields of science and engineering, such as geophysics or civil engineering, are also concerned with the mechanism of fracture and the study thereof.
Thus, a number of different numerical techniques for the simulation of dynamic crack propagation and other fracture related phenomena have emerged. More prominent among these are the finite element method (FEM) {{cite:451d702c4c4bcad897ff2374d0f2cd8ffdf9d10f}}, {{cite:6f4f6c19345ebf9d229aa22d15b639387d603b1d}} the boundary element method {{cite:9d50365d6881c2f3f1bbdc5e2acc60260652f47c}}, {{cite:2f6bc2d4d28b1c1a7b9ca766a805b3251a3e46f9}}, or more recently peridynamics {{cite:28a5b2d50fab66793294f9134ece3f54f9430fe1}}, {{cite:ac9b0d0d59d972791831a58dfe1e60c0d8f70fcf}} and phase field methods {{cite:5ad76147921abc66e7dbbd7e1ced323349b58ec0}}, {{cite:b4ff0fa44e90138790fe0b1d8cbe1c667d2281e7}}.
| i | 8bdd53db4946e309a324f763d1b9f6f4 |
First-principles data refinement. We re-evaluated the structural, dielectric, piezoelectric and band gap properties of
the 21 compounds listed in Table I by using stringent convergence parameters and fairly accurate DFT functionals (Methods).
Specifically, we re-optimized the relevant atomic geometries with a large energy cut-off of 800 eV and a k–point grid
of spacing {{formula:7c88cdaf-7172-4325-8e2a-946dfeeff4df}} Å{{formula:4d367e6d-4d56-4ae5-b8e9-b9b8c69e05e8}} for sampling of the first-Brillouin zone, using the PBEsol exchange-correlation
functional {{cite:f791c3ac5c9e155019d78c838c56016d8b80865b}} (this DFT functional has been consistently ranked among the best performers in terms of lattice parameters
prediction for semiconductors {{cite:d2bf4524fee266a003cda999a85ae5146ffd8f1d}}). The dielectric, piezoelectric and band gap properties of the PBEsol-relaxed structures
were subsequently estimated with the range-separated hybrid HSE06 potential {{cite:d7c6db7bd0b96312d318f761eb8184328e459124}}. By proceeding in this manner, an homogeneous
and consistently high level of numerical accuracy was guaranteed for all the investigated materials.
| r | 5977e152b97ac62480c2766cd1fd5e26 |
All of these studies, used shallow learning algorithms that require a large number of discriminative and handcraft features as input data to perform {{cite:ac8b5342bd4de5492539122747cc1339e62010db}}. Thus, those authors had to generate their own features from the limited available data, and are restricted to use these algorithms on the areas where different airborne geophysical datasets are available, such as magnetic, radiometry, and gravity {{cite:0d3b16fbc60a06d5b8e4c1c8379c52d3b7be746e}}.
| i | f5a5eb4112f50913556cd320846d64f2 |
Qubit realizations of the electronic Hamiltonian are obtained after applying
one of the fermion-qubit mappings{{cite:3c90f2f8391514dfae9a883443837d7fdd630aa8}}, {{cite:953da95f5064cc6fbc4f5095f6e428c45cdb34ca}}
{{formula:ce6e4eea-4cef-473d-af5c-378f7dffbbd4}}
| m | 9682e802d52afeae913c127d4de3e610 |
where the different spacings {{formula:d1531f76-6675-4409-82a0-b418263d2c18}} represent an ordered set of {{formula:d48c30cb-4e7e-4e68-8a52-75f8c11f0204}} for different Metropolis MC trajectories {{formula:1b9f56fc-36f3-49e1-b03f-1598023501a7}} .
From Random Matrix Theory (RMT) it is known that, in the Poisson case, the ratio follows the probability distribution {{formula:68261a18-fb43-4929-88f6-a87a797a29ed}} , while for the Wigner-Dyson distribution it is {{formula:5d161fe2-85d7-471e-bb9b-c21d04d2d13c}} with {{formula:bfeadcdd-d778-4c46-8afd-bdf7d85a6a40}} (Gaussian Unitary Ensamble - GUE) and {{formula:e4f53fad-f540-4ae7-9b42-e8904a2d6204}} .
The predictions for the averages are thus {{formula:588d8df1-0a4f-48a0-b554-1bb669047035}} and {{formula:9e41ef7b-cf56-435d-a56a-3c41a305aca2}} {{cite:da58187c53a6ecdd08ce4a190195fde95cc1a440}}.
| r | 80c9b45e5a4296fddc7f8e00c690d1e8 |
From Table REF one can see SRVT significantly boosts performance for different {{formula:b40bfe8e-cf08-45c2-be56-e4ca6e6d01e9}} s. The best result was obtained with {{formula:c52e45be-9469-4f85-88e8-d082c4faa85e}} (default setup in [28]). We also notice for MMD-GAN, higher {{formula:82de910e-b9b5-4fb3-ba5d-d657cbfb31e8}} (1024) did not improve performance {{cite:9a5750e464ba6b3e653308f4186cedc54a6905c6}}, while we have shown our framework can take advantage of higher dimension critic output features.
| r | 4138e3b600bb6e80c0dba176c89eea62 |
Non-minimal solvers can usually take an arbitrary number of measurements (as long as the problem is overdetermined) as the input to estimate the solution by using least-squares methods under the assumption of Gaussian noise. Some typical examples include: Arun's SVD method {{cite:3a95796b0fb87a98fe3a73ce6efb2b92892aebd4}} for point cloud registration, Semi-Definite relaxation methods for 3D registration {{cite:ef41b88e2f255f349228af88e50a286e9ad42469}}, category-level perception {{cite:21f3ee705141b1052baca7d53833dcdb43386d0d}} and pose graph optimization {{cite:48702928c10a873931219a156fe68fb4b9ecc49d}}, and Sum-of-Squares relaxation methods for 2D-3D shape alignment {{cite:7b81daf1db7b42d7951939dc804faeb722580eea}} and shape reconstruction {{cite:c89e9a5eb29db025fd747346b92b900b4fe6b192}}. Though non-minimal solvers can minimize the influence of noise and yield optimal results, they may suffer from relatively long runtime since the relaxation techniques on high-degree polynomial optimization usually necessitate high computational cost. So, once combined with the outlier rejection frameworks (e.g. GNC {{cite:7b81daf1db7b42d7951939dc804faeb722580eea}}, ADAPT {{cite:e48fdc37a120578e3106fd5c6df97b822d795456}}) where plenty of iterations are required, the runtime problem of non-minimal solvers would appear critical.
| m | 104d6576b9e78036106c38c58fc1b9ec |
In this section, we conducted several studies to evaluate the proposed PDBL. In the following experiments, PDBL was respectively plugged on three common classification architectures, including EfficientNet-b0 {{cite:42a3a98000840cdb27cdae75443871765cb455d1}}, ResNet50 {{cite:53cc8c1c70dc17cf2b7a4c58863837a8ad76b9eb}} and a lightweight model ShuffleNetV2 {{cite:62b925880d4f6dfc81e661f914759c582af17d08}}. In Section REF , we evaluate the effectiveness of PDBL with different proportions of training samples. In Section REF , we test the limit of the proposed PDBL by an extremely difficult task by leveraging only {{formula:4ded13f0-5634-4eae-9708-f526ba9a30e1}} training samples to inference the rest of them (99%). In Section REF , we conduct an ablation study to verify the effectiveness and the necessity of the pyramidal design. Next, we demonstrate the advantages of rapid domain adaptation on PDBL in Section REF . Finally, we also show the WSI-level semantic segmentation results by stitching the patch-level classification results.
| r | e17b2cd7ff33d8701620a6e7f9355e58 |
However, early architecture search algorithms are computationally expensive despite their promising performance. They often take many thousands GPU days to search a state-of-the-art architecture, by using reinforcement learning (RL) {{cite:abf78dca94eff70792b59ed08785fdde68ce965f}}, {{cite:90e4750d9e87fe62b25bd56bb498130df1e7fef3}}, {{cite:3aa248b00b02827650f84f7df47bdc6c506f26f3}} or evolution algorithm (EA) {{cite:866642b93bd75a5aba05068ab46cf4053bd756bb}}, {{cite:51c67ecdb8158d613031ad6bdebd11d4544b7566}}, {{cite:52d12059a89d9adba27bfcb7b2f85a3866861e9c}}, {{cite:bc47b75965231e418c885761ab40b6b378e826ef}}. Recent works attempted to speed up the searching process by using weight sharing technique {{cite:3aa248b00b02827650f84f7df47bdc6c506f26f3}}, {{cite:d67182991852fb6952a162672c05174e6f55fbf5}}, {{cite:3e9ee06fc4cbeb43a05e4c26f3f956c742ef2ab9}}, {{cite:98f7c5d4a5c52e674e9e3e7dec3d0afecee3b726}}, {{cite:d7f6d0da7137dc3e3e2ce2a1fe62fe7200f7a3bf}}, {{cite:89762e7f01408854a2ff0ae0160821273b08bf5f}}.
{{figure:0ef2a4f6-47e1-488c-8672-1cd24e890049}} | i | 3bf9b1578dbc6c301655437412496225 |
The role of the Allee effect in population dynamics has been largely addressed in both empirical and theoretical literature. Surprisingly enough, there has been almost no thorough mathematical investigation into the bifurcation structure of any predator-prey model with an Allee effect in the predator, in particular, this concerns the realistic scenario, where the Allee effect is included in the numerical response of the predator without affecting its functional response {{cite:f12ffa17eb1f7db9be99910a5a9255d044f23358}}, {{cite:8ac110b21afadd32d3c1bd02b3b8e898ed937fc8}}, {{cite:3f44a9d27d7b344a86afdc2badbfe5ef5a40ad5e}}. This is in a striking contrast to the situation with single species population models or classical predator-prey models with an Allee effect in the prey growth, which have been discussed in all detail and are now included in standard student textbooks in mathematical biology {{cite:eeceff9f5912eb0fe7a7a2e691793ebd6731a4ed}}. The current study is intended to partially bridge the existing gap. Importantly, we our results are not based on a particular mathematical formulation of the function describing the Allee effect, rather we consider various parameterisations of {{formula:79f1d755-dd6e-4c43-9c88-b2a1480e8e41}} which satisfy only few qualitative constraints (A1)-(A5). We have also addressed (for the first time) the issue regarding the sensitivity of the model with respect to parameterisation of the Allee effect (known as the structural sensitivity).
| d | 11ee51860202469f5c3fd1c18e18c070 |
Free AT {{cite:247c06a87de0ba8994b3a9e4362c6f74cc061ce9}}: Instead of using the regular PGD AT, they do the FGSM AT on the same batch for m times, while updating the gradients of the input in each iteration.
| m | 5a6ad921f5e3c41591eadab66cb13bfd |
Second-order optimization methods {{cite:9c083eb5a840b01300d94553dfebc33d0a780bd7}}, {{cite:93e74340e6e0ca90ea4ac1b1861dd1188fc13380}}, {{cite:982b9a5fbe3d75aef6013ba967370780ddd62dac}} utilize the second derivatives for weight update. Newton's method arises naturally from the second-order Taylor series approximation of the loss function, ignoring higher-order derivatives. For a locally quadratic function (with positive definite H), by rescaling the gradients with the inverse of the Hessian, Newton's method jumps directly to the minimum and thus converges in a single step. If the function is nearly quadratic, then this is a very good estimate of the minimizer of f. Since f is twice differentiable, the quadratic model of f will be very accurate when x is near the local minima. When it is not truly quadratic (there are higher-order terms) but can be locally approximated as a positive definite quadratic, this update can be iterated to reach the minima, which is much faster than gradient descent. Therefore, for the quadratic case, the order of convergence is infinity for any initial point {{formula:33e0859d-e44d-48c1-aa60-4a1c75a7985e}} .
| m | 641f4fdaf482ac1b6a28c1080a7370d1 |
The excess continuum that magnetospheric accretion adds to a CTTSs optical spectrum has been investigated since {{cite:852342f7464d5fba486973fb935d1568553cedab}} first introduced the concept of veiling. With high resolution spectroscopy, it is possible to observe the photospheric absorption lines of the star and this excess due to accretion that effectively veils the spectrum. In {{cite:8f154969db94e5f0125cd095c9d188eee91e22b2}}, a quantitative method was developed to measure the amount of veiling present in a given CTTS. By comparing the spectrum of the accreting CTTS, with a spectrum that represents only the photosphere (no accretion present), the following equation is produced:
{{formula:cfaf92c9-9f1d-4eba-ae7b-b44d43191e49}}
| m | cd42953fce56510c2f7f0b142cab7253 |
The Predictive Coding (PC) paradigm in Neuroscience is endorsed by a large body of neuroscientific experimental evidence {{cite:d490fcaa3372e7b4dd4eebf23b3e2372c757804c}}, {{cite:3afccb0bab41deb1ca77e7fe82228c2779d36d52}}, {{cite:e398d7138a107da853423a038540351485e4142f}}, {{cite:89066c207e51570d82c0d737812e19eebd8ab7a4}}. It characterizes perception as an inference process in which sensory information is combined with prior expectations to attain the final percept. Accordingly, PC postulates two fundamental terms: predictions and prediction errors (PEs). Considering the visual system as a hierarchical structure, these two signals interact between subsequent brain regions in an iterative process. Ideally, the interplay between feedback predictions and feed-forward PEs converges over iterations into a state in which predictions fully represent the sensory information and PE falls to zero. Although several models implemented and described this dynamic in different conditions {{cite:1524f0681716d71c48b5b1c5be597520333b9ace}}, {{cite:1d650815d154d175922456c57b5a05004017bd1c}}, {{cite:0291dd07652ceefc8f41b77a7c5ca0019d0e3bff}}, the functional role of these two main actors remains largely unexplored.
| i | babc21514219f7022247f0f65c65f435 |
The light curve of iPTF14hls is very unusual among SNe studied so far. In
this paper, we explore the possibility of interpreting iPTF14hls as a
multiple interaction-powered SN. We find that within reasonable parameters,
the theoretical light curve matches well with the light curve of iPTF4hls.
This makes iPTF14hls a possible candidate for PPISN. {{cite:db7f44c6610069ae06e14907a22874290b417566}}
proposed that iPTF14hls is produced by a continuous outflow like a stellar
wind rather than a mass ejection. They calculated the mass-loss rates of
iPTF14hls as high as {{formula:ee6a975c-4d9c-4581-82bc-a1cfc1c89b96}} in the bright phase. Such
an extreme mass loss rate is much higher than the results obtained from our
calculations. {{cite:b60a33388d8486b55fe9f8ae82756518d02b6457}} found magnetar-powered SN ejecta reproduces
some the observed properties of iPTF14hls, including the sustained
brightness in the {{formula:6915f397-368b-4428-af6b-ab047c240bd8}} band, the blue optical color, and the broad HI lines.
However, the magnetar model is difficult to produce fluctuating light curves
with multiple peaks, unless consider variable thermal energy injection from
magnetar spin down {{cite:ecb924d7646843814852846b4ec60fdf1e7ccb90}}. In the future, more observations and
improved theoretical modelings can improve our understanding of very massive
stars {{cite:4fceba6c3370a27bba0705505027f673fa4b0b12}}.
| d | df198c3408b9123559d593e6d51f1c89 |
In contrast with Stephan's Quintet, the M101 Group is dominated by M101, with relatively few low-mass companions, making it possibly the poorest group in the Local Volume {{cite:f9534b13c24a25832ddbe750a1b9aa136334b0d2}}. The lack of an abundance of intragroup star formation in the M101 Group might be because the M101 Group involves only weak interactions with low mass companions. Given M101's “anemic” stellar halo {{cite:6cb267990c99d8b98057d92486b42d9380437357}}, {{cite:3c2792f7d504a3b5f2880e01091545647d2da863}}, it is unlikely that M101 has gone through any major mergers, and very few, if any, minor mergers. With no comparable companions nearby, it is likely that no outlying H2 regions will form until one of the low mass companions falls into and merges with M101. Clearly, detailed computer modeling is needed to unravel all of the features of the M101 Group.
| d | 11036eae6b8a517ef8a41a52d38df1f7 |
We examined three different Ferrum chains of different lengths in our simulations.
Since we map the qubit states {{formula:20619c37-9c70-4e34-aa0b-b872f4a64a33}} and {{formula:aa374850-3e8a-4f28-9689-d72dd66c187d}} to up and down spin orientations of Ferrum atoms, respectively, n+1 qubits should be employed in the quantum circuit in order to represent the entire spin configuration space of the Ferrum chain with n+1 Ferrum atoms.
The qubits were initially put into an equi-superposed state.
Then, we applied QAOA to this system by applying a phase ten times in which the two operators are applied alternately; first one is the problem unitary operator given in Eqn. REF and the second one is a mixing unitary operator selected as {{formula:bb64dffa-52fd-4bb5-bc40-da6218e16a9e}} gate {{cite:82bb400994dfae8ffb336b42cde1937664c4f70a}} applied on each qubit on the quantum circuit.
Therefore we introduced 20 input parameters into the circuit and initial values of these parameters are randomly assigned between 0 and {{formula:3fd40806-771d-4c65-bd32-932adb249d4c}} radians.
All of the qubits in the circuit was measured at the end of the circuit execution and this measurement yielded an (n+1)-bit string which represents the spin configuration of the Ferrum chain.
The energy eigenvalue corresponding to the obtained spin configuration was used to optimize the circuit parameters via QFFNN. Adam optimizer {{cite:ef1ce5503b002ef75c457c8b7bf0505a0b6b7b12}} was used for optimization with 125 epoches.
After training of QFFNN, we sampled 50 million spin configurations and counted the number of different spin configurations occurred during the sampling.
To imitate a physically infinite chain in the calculations, we have applied the periodic boundary conditions {{cite:5d1eff09d15842b91e7b74ef10672c8561d21411}}.
In literature, {{formula:bcb02097-b0fc-4412-87a7-75b54f23edec}} is taken as {{formula:15bdb9e1-286b-4edd-9d26-7fd78dea2e21}} , or {{formula:d1aa489a-00f4-4986-ae63-40c5be0c6153}} for short, for Ferrum atoms and its value is 1.5 peV/m for a Ferrum chain {{cite:c937c6face6db9fb6c0d59e0111f7bdff45f1bb1}}.
| m | 042af957e5a68f0454e6ef415987cdc6 |
In this section, we conduct experimental evaluations of the proposed SFWFL algorithm.
Particularly, we examine the performance of the proposed algorithm for two different tasks: ({{formula:b0f6513c-57fd-4a9d-ac44-01057ebe2b0a}} ) training a multi layer perceptron (MLP) on the MNIST dataset which contains the hand-written digits {{cite:17c3bd972aba3e6fb20e0af0674b0aea0de6574b}} and ({{formula:14f7738c-565b-4937-94c2-409f5ad6ffd7}} ) learning a convolutional neural network (CNN) on the CIFAR-10 dataset {{cite:d585bf5b8bb3e8d3994250b6a7f2b1e62242d904}}.
The MLP is consisted of 2 hidden layers, each has 64 units and adopts the ReLu activations.
We extract 60,000 data points from the MNIST dataset for training, where each UE is assigned with an independent portion that contains 600 data samples.
For the non-IID setting on MNIST dataset, we use the 2-class configuration {{cite:ee0ddfe77d9c7f609c4e96990315fbba7b885a67}}, in which each UE is assigned with images from at most 2 classes.
The CIFAR-10 dataset consists of 60,000 colour images in 10 classes, with 6000 images per class. And the CNN has two convolutional layers with a combination of max pooling, followed by two fully-connected layers, then a softmax output layer.
We extract 50,000 data points from the CIFAR-10 dataset for training, where each agent is assigned with an independent portion that contains 500 data samples.
We allocate 10,000 data points for testing.
Furthermore, we adopt the Rayleigh fading to model the channel gain.
Unless otherwise stated, the following parameters will be used: Tail index {{formula:ba21226d-bc34-476f-b45c-4ebacd89d136}} , number of agents {{formula:d1f33531-5238-419f-843c-bd4e503995db}} , average channel gain {{formula:20d457cc-54b5-4f17-8d3f-90743c3849b4}} .
The experiments are implemented with Pytorch on Tesla P100 GPU and averaged over 3 trials.
| r | 74a1fd1a4c3ec72ef47c6428231a482b |
The classical double copy is an extension of ideas discovered in the study of scattering amplitudes {{cite:ca775f71dff7ed09d5d4db59e97dfc4ceed46903}}, {{cite:467c831d9729dac297b617c17f0527664f7c993d}} to classical solutions of general relativity and gauge theories. The data from the amplitudes suggest a {{formula:e7c6c96f-f45c-41bf-a290-fc471ab65625}} -type relationship where the graviton amplitudes form a double copy of the gluon amplitudes of two Yang-Mills theories that are called single copies. In general, it is possible to relate the classical solutions at a fixed order in perturbation theory {{cite:25af9567dd8e5d86bab6b76f6ebb71e759219400}}, {{cite:a4a98f6445ca875c1167a87f6137b5215fd180e7}}, {{cite:d81d73d08cee91915b4fcb87fcd663cfb397a780}}, {{cite:52c8a304863ba9a0feba8ae65fd7412cfbcf576f}}, {{cite:765bd3f9904048be18791ba3cf624d36e54acd59}}, {{cite:239e1a123e4a8c40d7321c790a9be1c34ea4fb07}}, {{cite:3fb7269711d8c356cd484ebbd9d1ad79d1054dd5}}, {{cite:afffb517e90d355527d0c1eee85e64bfa4b4bbfd}}, {{cite:98c84e8ffcdeb505ee0a6b8d8a2a32ad5b217c9e}}, {{cite:1c057a4f6b7f3dca2c2ed8af76ebabee763f5c29}}, {{cite:2af7df95fb0d0bab2ed59a61597ec592102ecd32}}, {{cite:6c1af4ecde7677aabc84ead67db8e09e1446d8b8}}, {{cite:704867c18056fbb854f6dc0b324f5c1b5eb08a95}}, {{cite:90ecd80af08c84c1b0bb119bca7513b599104c51}}, {{cite:18884ac64c254dde7bb04bb1a71b011557193845}}, {{cite:ce435053ef3bd9f140583e7f3c305fe1e7952b59}}, {{cite:53fa01a1e76cda846c9983b1766c0c7af4c0fe41}}, {{cite:5b1cd169a49ef97b759335fe5d549279b6b0095e}}, {{cite:f9a775c9ee4f05bd710f189841847841063e07bd}}, {{cite:aec594abb2105257fdf2ac17034774dd263c1177}}, {{cite:7775a53956edf3474e8e6977366ebe6894f94bd3}}, {{cite:62e5224e36019f5a489eca950440aeefcbcba722}}, {{cite:374cc980dc8eec02f0523020d9d7371e81e4d605}}, {{cite:ef0ba983dfd76bea70d22492829c9f163fba7e22}}, {{cite:c12182ef6f686696b095b22b8d9a751059b1210b}}, {{cite:5fb35e6fc7497ebc4e9d611bb81d5127a9cd77b1}}, {{cite:3015a03a2a470173e0b80dd20fc4792a354315cd}}, {{cite:46eac8a62db593aa48ae92ccbba68051dc1f6a89}}, {{cite:49d2548001c3b5cecd29ea0edd359a6f4b86653a}}, {{cite:d3e9948c47e9d41e909639cc7e5991079bad21f9}}, {{cite:78748c3ae12e5c4a538d7b39eecbc4c54c5480e4}}, {{cite:e21b392bd63d0e19890de1e64a8a6388361b7586}}, {{cite:b01d1bc589b3b2a715d136aa32c46ce78c88b678}}, {{cite:f987db2e89ef08220aca1087c037e9a6f1f5cc1e}}, {{cite:a0832b6837d35a23af51d8198846c0e20d197ed0}}, {{cite:7b04e20039ad0d480ba5cb505fc219fbd3cc86fe}}; however, for a certain class of spacetimes, a simpler form can be achieved where exact solutions of general relativity are mapped to gauge theory solutions {{cite:7a3752f9fb068a6c3487031ac3f83e5916e91569}}, {{cite:cfdfd5ad982ff0c38fc11fd0d07cb1a456edbcb3}}, {{cite:5ab81d0b077d26c7e6ab05ca8e13b92b031d95f7}}, {{cite:21edeacff241113caed8b97e0a61b8b335add983}}, {{cite:07065749c482374bc4263f223d41fe2a93010583}}, {{cite:d187bb3f7d2b3a948ae9f2b94fa02fa861424507}}, {{cite:eb187b69977df0865f9d640e78aa96d72a577e9c}}, {{cite:73842b7554539f2beeef8f16bcca328bf8fb4af0}}, {{cite:9edd5ae8927bb4ecc2f7d375d228c1e32a685675}}, {{cite:440bc9b7cf143e9f68cf03f08de542bf1cb06782}}, {{cite:6aed3d728cd69f6b1600bf7ce303c6370b57b77f}}, {{cite:a1f80fbeba4137185c9b09ad2283f48ee35f0069}}, {{cite:ea97b400603b69a2640e5dd5db08d06e8162b350}}, {{cite:903caba7b8f6d0bf96c4502580073efb15f1c98b}}, {{cite:525f2ecf24ad74997428e5c125d9f51d7183093d}}, {{cite:0c45c7e83dac3039ef26f747a0d810b4b4b86516}}, {{cite:e125f8febe72398ebf1b6c5d111702918d3e90d2}}, {{cite:2c6e6a16f641801ddf36ff7d3591cbf6b8dd5ef9}}, {{cite:517b437cbd182007fd3fb0613f5f61f5fd05df3a}}, {{cite:eb28d67a21165ae030f78159be77bc6a95f509cc}}, {{cite:4d94846f53dc7f23df63d12a878590fcccb64140}}, {{cite:f2f85b53ff4b0fb47c45a3eb87251b2d6dcb279b}}, {{cite:d3b48fa65dba75396117dd2afc39f12e5c489f45}}, {{cite:eca6bd6260eedd351bce7b2b7a9731c593121fe6}}, {{cite:95c6439ced2e2053767f1e4987321f29415a87f1}}, {{cite:580e6fe83bd269237a5d262d1df914bd2692fd3f}}, {{cite:39353601aa51fbe47c8f4331f3d09f6302aac908}}, {{cite:b237e87df6994609fc93f7b694767e2ef1b43c15}}, {{cite:49278d38e6b3cab92ee347162b6975221d986d18}}, {{cite:728493f2403a2d14ee3aaa2591f72d9655f321ec}}. Recently, a particular version, the so-called Weyl Double Copy {{cite:a1f80fbeba4137185c9b09ad2283f48ee35f0069}}, was derived through the ideas from twistor theory {{cite:bb6414578baead9f3ce8810d4ec85972f564dbb4}}, implying a much deeper and general relation than previously thought.
| i | 8db0560da7043288d2808914ae4f6f66 |
In conclusion, we have shown that the inductive bias of CNNs can be effectively used to guide the practitioner's design decisions regarding the network's superstructure.
We derive a simple but effective analysis method to guide the performance oriented refinement of CNN-superstructures.
Using this analysis method, we uncover design inefficiencies in various popular architectures,
demonstrating the utility of finding and fixing issues with underutilized layers. Perhaps surprisingly, this analysis is even effective at identifying underutilized layers across a wide variety of the highest performing modern architectures.
By applying different strategies to resolve those inefficiencies we can improve the predictive performance of all tested models on the first attempt, achieving new state-of-the-art results in the process, without increasing the number of parameters in the model.
While we universally increased the parameter-efficiency of our models, this came at increased computational cost, indicating that an inherent trade-off between parameter and computational efficiency exists specific for each model class.
This is interesting from the perspective of scaling laws {{cite:8f27ea0926d1762f7be023679fc91c5a3b4d4e77}}, since we effectively demonstrate that parameters can be substituted for additional compute and do not necessarily need to be scaled together to be effective.
| d | d51dbfe45ed0b7272b5f645fcb4a1255 |
Here we ask:
What are the essential features of quantum theory that enable this spreading of classical information in the first place?
Certainly, this is possible in Quantum Theory's rich mathematical structure of complex Hilbert spaces,
but can we identify a selective subset of more physically–motivated principles that similarly enable this Darwinistic emergence of classical reality?
To approach this, we adopt the minimal–assumptions framework of generalized probabilistic theories (GPTs) {{cite:aeb12d4680a3d593b59115bcda8bf92030f64b42}}, {{cite:4be5efd94fc0f89f00ce8baf0ff96e0711fb45d7}}.
These encompass a wide class of operational scenarios, in which a physical system is entirely characterized by its experimental statistics resulting from preparation and subsequent measurement procedures.
The GPT approach has thus far enjoyed particular success in identifying which operational features are necessary or sufficient for quantum phenomena like teleportation {{cite:d749863d4f7b458ec542e3bff2575529476489f1}}, no-cloning {{cite:267f69995ee10c19ec55690efcbaa3cf90a5d93e}}, entanglement {{cite:4be5efd94fc0f89f00ce8baf0ff96e0711fb45d7}}, phase and interference {{cite:d21e9e48be4ceefde8e0f6551b1f9b9e7833ae08}}, {{cite:e521af97efbf55bfdc29b90b1d9c24380dd94ed1}}, or decoherence {{cite:914e675affcbba00c4ac231907f777074e51d79a}}.
With this article, we aim to extend this canon to include Quantum Darwinism.
| i | 21fdbd964108bb73d3990ccd7729ce1a |
The structure of our paper is as follows. In section ,
we review ideas relating to the twistor double copy of
refs. {{cite:b28938cf8021022328ee961aa3f00a4eca7c750a}}, {{cite:9812bed62efc0ea6a02260dfd44546598c37e9d8}}. In
section , we apply the methods of
ref. {{cite:fab3f8c87036b89797a8d31b03686dca010bf0b3}} to demonstrate that scattering amplitudes
in momentum space can be used to pick out the C̆ech cohomology
representatives entering the twistor double copy. In
section , we explain why locality of the double copy
is simultaneously manifest in momentum, twistor and position space,
for type-D solutions. Finally, we discuss our results and conclude in
section .
| i | 3214c4d78dff66969a459b4e85175391 |
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