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THE NO-UNDERRUN SAMPLER: A LOCALLY ADAPTIVE, GRADIENT-FREE MCMC METHOD

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arXiv 2025年

作者： Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan Department of Mathematical Sciences Rutgers University United States Center for Computational Mathematics Flatiron Institute United States Institute for Applied Mathematics University of Bonn Germany

In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal’s funnel, a challenging multi-scale distribution from Bayesian hierarchical *** Codes 60J05, 65C05 Copyright © 2025, The Authors. All rights reserved.

关键词： Monte Carlo methods

GLOBAL WELL-POSEDNESS OF VLASOV-POISSON-BOLTZMANN EQUATIONS WITH NEUTRAL INITIAL DATA AND SMALL RELATIVE ENTROPY

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arXiv 2025年

作者： Jiang, Zaihong Wang, Yong Xiong, Hang Department of Mathematics Zhejiang Normal University Jinhua321004 China Institute of Applied Mathematics AMSS CAS Beijing100190 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the self-induced electric field. In this paper, we are concerned with global well-posedness of mild solutions of the equations. We establish the global existence and uniqueness of mild solutions to the two species Vlasov-Poisson-Boltzmann equations in the torus for a class of initial data with bounded time-velocity weighted L∞ norm under nearly neutral condition and some smallness condition on L1xL∞v norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Due to the nonlinear effect of electric field, we consider the problem in Wx,v1,∞ with large amplitude data, new difficulty arises when establishing globally uniform Wx,v1,∞ bound, which has been overcome based on nearly neutral condition, time-velocity weight function and a logarithmic estimate. Moreover, the large time behavior of solutions in Wx,v1,∞ norm with exponential decay rates of convergence is also obtained. Copyright © 2025, The Authors. All rights reserved.

关键词： Entropy

AN INVERSE SIGNORINI OBSTACLE PROBLEM

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arXiv 2025年

作者： de Hoop, Maarten V. Lassas, Matti Lu, Jinpeng Oksanen, Lauri Zhao, Ziyao Computational and Applied Mathematics and Earth Science Rice University HoustonTX77005 United States Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress for the Signorini problem on an open subset of the boundary up to a natural obstruction. In addition to considering the Signorini problem, we develop techniques that can be used to study inverse problems for general differential *** Codes 35R30, 74M15 Copyright © 2025, The Authors. All rights reserved.

关键词： Inverse problems

INEXACT SUBSPACE PROJECTION METHODS FOR LOW-RANK TENSOR EIGENVALUE PROBLEMS

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arXiv 2025年

作者： Dektor, Alec Delmastro, Peter Ye, Erika van Beeumen, Roel Yang, Chao Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Mathematics Virginia Tech BlacksburgVA United States

We compare two approaches for solving high-dimensional eigenvalue problems with low-rank structure: the inexact Lanczos method and inexact polynomial-filtered subspace iteration. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor format. A primary challenge in these methods is that standard operations, such as matrix-vector products and linear combinations, increase tensor rank, necessitating rank truncation and hence approximation. The Lanczos method constructs an approximate orthonormal Krylov basis, which is often difficult to represent accurately using low-rank tensor formats, even when the eigenvectors themselves exhibit low-rank structure. In contrast, the low-rank polynomial-filtered subspace iteration uses approximate eigenvectors (Ritz vectors) directly as a subspace basis, bypassing the need for an orthonormal Krylov basis. Our analysis and numerical experiments demonstrate that inexact subspace iteration is much more robust to rank-truncation errors compared to the inexact Lanczos method. We further demonstrate that rank-truncated subspace iteration can converge for problems where the density matrix renormalization group method (DMRG) *** Codes 65F15, 15A69 © 2025, CC BY.

关键词： Tensors

The Fokas method for evolution partial differential equations

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Partial Differential Equations in applied mathematics 2025年 14卷

作者： Chatziafratis, A. Fokas, A.S. Kalimeris, K. Department of Mathematics and Statistics School of Pure and Applied Sciences University of Cyprus Cyprus Institute of Applied and Computational Mathematics Foundation for Research and Technology Crete Greece Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Mathematics Research Center Academy of Athens Greece

In the late 1990s a novel methodology was introduced for solving boundary value problems for linear and integrable nonlinear PDEs. This new approach is known as the Unified Transform or the Fokas method. Here we discuss important developments regarding the implementation of this methodology to evolution PDEs. In particular, we analyse linear PDEs, including the heat equation, the Sobolev–Barenblatt pseudo-parabolic model, the Rubinshtein–Aifantis double-diffusion system, and the linearized Cahn–Hilliard model, as well as certain integrable nonlinear PDEs, like the nonlinear Schrödinger equation. Regarding the latter equation, emphasis is placed on the so-called linearizable boundary conditions, which remarkably, include the well-studied x-periodic initial value problem. © 2025 The Authors

关键词： Evolution PDEs Fokas method Integrable PDEs Unified transform

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

Comments on "relaxed Conditions for the Input-to-State Stability of Switched Nonlinear Time-Varying Systems"

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IEEE Transactions on Automatic Control 2025年第6期70卷 4233-4236页

作者： Şahan, Gökhan Trenn, Stephan Izmir Institute of Technology Department of Mathematics and Computational Science and Engineering Program Urla Izmir Turkey University of Groningen Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence Groningen9722BA Netherlands

This study addresses the deficiencies in the assumptions of the results in Chen and Yang, 2017 [1] due to the lack of uniformity. We first show the missing hypothesis by presenting a counterexample. Then we prove why they are wrong in that form and show the errors in the proof of the main result of [1]. Next, we compare the assumptions and related results of [1] with similar works in the literature. Lastly, we give suggestions to complement the shortcomings of the hypotheses and thus correct them. © 1963-2012 IEEE.

关键词： Nonlinear simulations