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Essentially Commuting with a Unitary

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arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

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Sampling Decisions

arXiv 2025年

作者： Chertkov, Michael Ahn, Sungsoo Behjoo, Hamidreza Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ United States Graduate School of AI KAIST Korea Republic of

In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous-space, continuous-time Path Integral Diffusion sampling technique of [1] to discrete time and space, while also generalizing the Generative Flow Network framework of [2]. In its most basic form – an explicit, Neural Network (NN)-free formulation – DF leverages the linear solvability of the underlying MDP [3] to adjust the transition probabilities of the prior sampler. The resulting Markov process is expressed as a convolution of the reverse-time Green’s function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN-based extensions, and outline how DF can enhance guided sampling across various applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

Radiative Vlasov-Maxwell Equations

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arXiv 2025年

作者： Constantin, Peter Grayer, Hezekiah Department of Mathematics Princeton University PrincetonNJ08544 United States Program in Applied an Computational Mathematics Princeton University PrincetonNJ08544 United States

In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-free in momentum space, which has an effect of concentration to zero momentum. We prove unconditional global regularity of solutions for a class of radiative Vlasov-Maxwell equations with large initial *** Codes 35Q70, 35Q83 © 2025, CC BY.

关键词： Maxwell equations

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

Fast alignment of heterogeneous images in sliced Wasserstein distance

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arXiv 2025年

作者： Shi, Yunpeng Singer, Amit Verbeke, Eric J. Department of Mathematics University of California at Davis DavisCA United States Department of Mathematics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two L × L images using the sliced 2-Wasserstein distance in O(L2 log L) operations. We show that our method is robust to translations, rotations and deformations in the images. Copyright © 2025, The Authors. All rights reserved.

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PHEONA: An Evaluation Framework for Large Language Model-based Approaches to Computational Phenotyping

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arXiv 2025年

作者： Pungitore, Sarah A. Yadav, Shashank Subbian, Vignesh Program in Applied Mathematics The University of Arizona TucsonAZ United States College of Engineering The University of Arizona TucsonAZ United States

Computational phenotyping is essential for biomedical research but often requires significant time and resources, especially since traditional methods typically involve extensive manual data review. While machine learning and natural language processing advancements have helped, further improvements are needed. Few studies have explored using Large Language Models (LLMs) for these tasks despite known advantages of LLMs for text-based tasks. To facilitate further research in this area, we developed an evaluation framework, Evaluation of PHEnotyping for Observational Health Data (PHEONA), that outlines context-specific considerations. We applied and demonstrated PHEONA on concept classification, a specific task within a broader phenotyping process for Acute Respiratory Failure (ARF) respiratory support therapies. From the sample concepts tested, we achieved high classification accuracy, suggesting the potential for LLM-based methods to improve computational phenotyping processes. © 2025, CC BY.

关键词： Electronic health record

The planar projectivity of PG (2, q3) of order 3 under field reduction

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arXiv 2025年

作者： Barwick, S.G. Hui, Alice M.W. Jackson, Wen-Ai School of Mathematical Sciences University of Adelaide Adelaide5005 Australia Applied Mathematics Program BNU-HKBU United International College Zhuhai China

Let be a collineation of PG (2, q3) of order 3 which fixes a plane of order q pointwise. The points of PG (2, q3) can be partitioned into three types with respect to orbits of : fixed points;points P with P, P, P2 distinct and collinear;and points P with P, P, P2 not collinear. Under field reduction, the collineation corresponds to a projectivity σ of PG(8, q) of order 3 . With respect to the field reduction and the orbits of σ, the points of PG(8, q) can be partitioned into six types. This article looks at the projectivity σ in detail, and classifies and counts the fixed points, fixed lines and fixed planes. The motivation is to give a description of the lines of the Figueroa projective plane in the PG(8, q) field reduction setting. Copyright © 2025, The Authors. All rights reserved.

关键词： Fixed point arithmetic

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

Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

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arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time