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THE ELASTIC RAY TRANSFORM

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arXiv 2025年

作者： Ilmavirta, Joonas Kykkänen, Antti Saksala, Teemu Department of Mathematics and Statistics University of Jyväskylä Jyväskylä Finland Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States Department of Mathematics NC State University RaleighNC United States

We introduce and study a new family of tensor tomography problems. At rank 2 it corresponds to linearization of travel time of elastic waves, measured for all polarizations. We provide a kernel characterization for ranks up to 2. The kernels consist of potential tensors, but in an unusual sense: the associated differential operators have degree 2 instead of the familiar 1. The proofs are based on Fourier analysis, Helmholtz decompositions, and cohomology. Copyright © 2025, The Authors. All rights reserved.

关键词： Tensors

Detection of latent brain states from spontaneous neural activity in the amygdala

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PLoS computational Biology 2025年第2期21卷 e1012247页

作者： Aucoin, Alexa Lin, Kevin K. Gothard, Katalin M. Program in Applied Mathematics University of Arizona TucsonAZ United States Department of Mathematics University of Arizona TucsonAZ United States Department of Physiology University of Arizona TucsonAZ United States

The amygdala responds to a large variety of socially and emotionally salient environmental and interoceptive stimuli. The context in which these stimuli occur determines their social and emotional significance. In canonical neurophysiological studies, the fast-paced succession of stimuli and events induce phasic changes in neural activity. During inter-trial intervals neural activity is expected to return to a stable and featureless level of spontaneous activity, often called baseline. In previous studies we found that context, such as the presence of a social partner, induces brain states that can transcend the fast-paced succession of stimuli and can be recovered from the spontaneous, inter-trial firing rate of neurons. Indeed, the spontaneous firing rates of neurons in the amygdala are different during blocks of gentle grooming touches delivered by a trusted social partner, and during blocks of non-social airflow stimuli delivered by a computer-controlled air valve. Here, we examine local field potentials (LFPs) recorded during periods of spontaneous activity to determine whether information about context can be extracted from these signals. We found that information about social vs. non-social context is present in the local field potential during periods of spontaneous activity between the application of grooming and airflow stimuli, as machine learning techniques can reliably decode context from spectrograms of spontaneous LFPs. No significant differences were detected between the nuclei of the amygdala that receive direct or indirect inputs from areas of the prefrontal cortex known to coordinate flexible, context-dependent behaviors. The lack of nuclear specificity suggests that context-related synaptic inputs arise from a shared source, possibly interoceptive inputs, that signal the physiological state of the body during social and non-social blocks of tactile stimulation. © 2025 Aucoin et al. This is an open access article distributed under the terms of the

关键词： Neurons

Tensor parametric Hamiltonian operator inference

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arXiv 2025年

作者： Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Computational Mathematics Center for Computing Research Sandia National Laboratories Scientific Machine Learning Center for Computing Research Sandia National Laboratories

This work presents a tensor-based approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints—a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave *** Codes 15A69, 35B30, 65P10 © 2025, CC BY.

关键词： Tensors

CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR QUASICONVEX AND RELAXED VARIATIONAL PROBLEMS

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arXiv 2025年

作者： Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambo Vikelis, Andreas Computer Electrical Mathematical Sciences and Engineering Division KAUST Saudi Arabia Department of Mathematics University of Sussex United Kingdom Institute of Applied & Computational Mathematics Foundation for Research & Technology-Hellas Greece Department of Mathematics and Applied Mathematics University of Crete Greece Faculty of Civil Engineering Czech Technical University of Prague Czech Republic

In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential flexibility by removing inter-element continuity while also guaranteeing convergent approximations in the quasiconvex case. Notably, quasiconvexity is the weakest form of convexity pertinent to elasticity. Furthermore, we show that in the non-convex case discrete minimisers converge to minimisers of the relaxed problem. In this case, the minimisation problem corresponds to the energy defined by the quasiconvex envelope of the original energy. Our approach covers all discontinuous Galerkin formulations known to converge for convex energies. This work addresses an open challenge in the vectorial calculus of variations: developing and rigorously justifying numerical schemes capable of reliably approximating nonlinear energy minimization problems with potentially singular solutions, which are frequently encountered in materials science. © 2025, CC BY.

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Batched Nonparametric Contextual Bandits

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IEEE Transactions on Information Theory 2025年

作者： Jiang, Rong Ma, Cong University of Chicago Committee on Computational and Applied Mathematics IL60637 United States University of Chicago Department of Statistics ChicagoIL60637 United States

We study nonparametric contextual bandits under batch constraints, where the expected reward for each action is modeled as a smooth function of covariates, and the policy updates are made at the end of each batch of observations. We establish a minimax regret lower bound for this setting and propose a novel batch learning algorithm that achieves the optimal regret (up to logarithmic factors). In essence, our procedure dynamically splits the covariate space into smaller bins, carefully aligning their widths with the batch size. Our theoretical results suggest that for nonparametric contextual bandits, a nearly constant number of policy updates can attain optimal regret in the fully online setting. © 1963-2012 IEEE.

关键词： batch learning contextual bandits dynamic binning minimax rate regret bounds

Correction: Evaluation of beta integrals of Ramanujan type and integral representations for bilateral hypergeometric series

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The Ramanujan Journal 2025年第3期67卷 1-2页

作者： Cohl, Howard S. Volkmer, Hans Applied and Computational Mathematics Division National Institute of Standards and Technology Mission Viejo USA Department of Mathematical Sciences University of Wisconsin–Milwaukee Milwaukee USA

Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds

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arXiv 2025年

作者： Guan, Yunrui Balasubramanian, Krishnakumar Ma, Shiqian Department of Computational Applied Mathematics and Operations Research Rice University United States Department of Statistics University of California Davis United States

We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy sampling guarantees for the Riemannian Proximal Sampler, showing that generating samples with Ε-accuracy requires O(log(1/Ε)) iterations in Kullback-Leibler divergence assuming access to exact oracles and O(log2(1/Ε)) iterations in the total variation metric assuming access to sufficiently accurate inexact oracles. Furthermore, we present practical implementations of these oracles by leveraging heat-kernel truncation and Varadhan’s asymptotics. In the latter case, we interpret the Riemannian Proximal Sampler as a discretization of the entropy-regularized Riemannian Proximal Point Method on the associated Wasserstein space. We provide preliminary numerical results that illustrate the effectiveness of the proposed methodology. © 2025, CC BY.

关键词： Numerical methods

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

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Physical Review B 2025年第9期111卷 094113-094113页

作者： Pinchen Xie Yixiao Chen Weinan E Roberto Car Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA AI for Science Institute Beijing China and Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

关键词： Ferroelectricity

An artificial viscosity approach to high order entropy stable discontinuous Galerkin methods

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arXiv 2025年

作者： Chan, Jesse Department of Computational Applied Mathematics and Operations Research Rice University 6100 Main St HoustonTX77005 United States

Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic flux differencing formulation which involves both summation-by-parts (SBP) discretization matrices and entropy conservative two-point finite volume fluxes. However, explicit expressions for such two-point finite volume fluxes may not be available for all systems, or may be computationally expensive to compute. This paper proposes an alternative approach to constructing entropy stable DG methods using an artificial viscosity coefficient based on the local violation of a cell entropy inequality and the local entropy dissipation. The resulting method recovers the same global semi-discrete entropy inequality that is satisfied by entropy stable flux differencing DG methods. The artificial viscosity coefficients are parameter-free and locally computable over each cell, and the resulting artificial viscosity preserves both high order accuracy and a hyperbolic maximum stable time-step size under explicit time-stepping. Copyright © 2025, The Authors. All rights reserved.

关键词： Viscosity