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Eight-stage pseudo-symplectic Runge–Kutta methods of order (4, 8)

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arXiv 2023年

作者： Stepanov, Misha Department of Mathematics and Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge–Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic structure up to order 8, is derived. An example of 7-stage method of order (4, 9) is *** Codes 65L05, 65L06 Copyright © 2023, The Authors. All rights reserved.

关键词： Runge Kutta methods

MOMENT-BASED METRICS FOR MOLECULES COMPUTABLE FROM CRYO-EM IMAGES

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arXiv 2024年

作者： Zhang, Andy Mickelin, Oscar Kileel, Joe Verbeke, Eric J. Marshall, Nicholas F. Gilles, Marc Aurèle Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Oden Institute University of Texas At Austin AustinTX78712 United States Department of Mathematics Oregon State University CorvallisOR97331 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Single particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution 3-D structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3-D reconstruction, known as Kam's method, relies on the moments of the 2-D images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3-D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3-D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity. Copyright © 2024, The Authors. All rights reserved.

关键词： Method of moments

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

Discrete unified gas kinetic scheme for the solution of electron Boltzmann transport equation with Callaway approximation

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Physical Review E 2024年第6期109卷 065310-065310页

作者： Meng Lian Chuang Zhang Zhaoli Guo Jing-Tao Lü Institute for Quantum Science and Engineering and Wuhan National High Magnetic Field Center School of Physics Department of Physics Institute of Interdisciplinary Research for Mathematics and Applied Science

Electrons are the carriers of heat and electricity in materials and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation (eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obtain the numerical solutions of the eBTE within one unified scheme involving ballistic, hydrodynamics, and/or diffusive regimes. In this work, a discrete unified gas kinetic scheme (DUGKS) in the finite-volume framework is developed based on the eBTE with the Callaway relaxation model for electron transport. By reconstructing the distribution function at the cell interface, the processes of electron drift and scattering are coupled together within a single time step. Numerical tests demonstrate that the DUGKS can be adaptively applied to multiscale electron transport, across different regimes.

关键词： Mesoscopics Physics of computation Transport phenomena Boltzmann theory Hydrodynamics Multiscale modeling

Differentiable Simulator For Dynamic & Stochastic Optimal Gas & Power Flows

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Differentiable Simulator For Dynamic & Stochastic Optimal Ga...

IEEE Conference on Decision and Control

作者： Criston Hyett Laurent Pagnier Jean Alisse Igal Goldshtein Lilah Saban Robert Ferrando Michael Chertkov Program in Applied Mathematics & Department of Mathematics University of Arizona Tucson AZ USA Noga The Israel Independent System Operator Haifa Israel

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

In many power systems, particularly those isolated from larger intercontinental grids, reliance on natural gas is crucial. This dependence becomes particularly critical during periods of volatility or scarcity in renewable energy sources, further complicated by unpredictable consumption trends. To ensure the uninterrupted operation of these isolated gas-grid systems, innovative and efficient management strategies are essential. This paper investigates the complexities of achieving synchronized, dynamic, and stochastic optimization for autonomous transmission-level gas-grid infrastructures. We introduce a novel methodology grounded in differentiable programming, which synergizes symbolic programming, a conservative numerical method for solving gas-flow partial differential equations, and automated sensitivity analysis powered by SciML/Julia. Our methodology refines the co-optimization landscape for gas-grid systems by grounding gas dynamics in physics-adherent simulation. We demonstrate efficiency and precision of the methodology by solving a stochastic optimal gas flow problem, phrased on an open source model of Israel’s gas grid model.

关键词： Renewable energy sources Sensitivity analysis Partial differential equations Power system dynamics Stochastic processes programming Mathematical models Synchronization Optimization Natural gas

Asymptotic Quantum State Discrimination for Mixtures of Unitarily Related States.

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arXiv 2024年

作者： Acevedo, Alberto Wehr, Janek Program in Applied Mathematics The University of Arizona Tucson85721 United States Department of Mathematics The University of Arizona Tucson85721 United States

Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements of a one-parameter unitary group, and the corresponding quantum state discrimination (QSD) problems. We will be particularly interested in QSD as time goes to infinity. We first present an approach to QSD in the case of countable mixtures and address the respective asymptotic QSD optimization problems, proving necessary and sufficient conditions for minimal error to be obtained in the asymptotic regime (we say that in such a case QSD is fully solvable). We then outline an analogous approach to uncountable mixtures, presenting some conjectures that mirror the results presented for the cases of countable mixtures. As a technical tool, we prove and use an infinite dimensional version of the well-known Barnum-Knill bound [8]. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum communication

Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence

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Physical Review Fluids 2023年第5期8卷 054602-054602页

作者： Michael Woodward Yifeng Tian Criston Hyett Chris Fryer Mikhail Stepanov Daniel Livescu Michael Chertkov Graduate Interdisciplinary Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA Department of Mathematics University of Arizona Tucson Arizona 85721 USA Computer Computational and Statistical Sciences Division LANL Los Alamos New Mexico 87544 USA

Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and it investigates the effects of enforcing physical structure through smoothed particle hydrodynamics (SPH) versus relying on neural networks (NNs) as universal function approximators. Starting from NN parametrizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational, and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using automatic differentiation and sensitivity analysis. Each model within the hierarchy is trained on two data sets associated with weakly compressible homogeneous isotropic turbulence: (1) a validation set using weakly compressible SPH; and (2) a high-fidelity set from direct numerical simulations. Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

关键词： Sensitivity analysis

Exploring Human Attribution of Emotional Intent to Motion Features in a Humanoid Robot 16th

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Exploring Human Attribution of Emotional Intent to Motion ...

16th International Conference on Social Robotics, ICSR + AI 2024

作者： Otterdijk, Marieke van Neggers, Margot Torresen, Jim Barakova, Emilia RITMO Centre for Interdisciplinary Studies in Rhythm Time and Motion and the Faculty of Mathematics and Natural Sciences Department of Informatics University of Oslo Oslo Norway Academy for AI Games & Media Breda University of Applied Sciences Breda Netherlands Department of Industrial Design University of Technology Eindhoven Eindhoven Netherlands

ISBN: (纸本)9789819635184

Nonverbal communication is essential for acceptance and seamless interaction with robots. However, which features of a social robot influence the perception of valance, arousal, and dominance? Our pilot study addresses this question by letting 30 senior adult participants observe twenty-seven short videos of a Pepper robot moving into an expressive pose, after which they filled out a questionnaire. Our results indicate that the torso influences the perceived valence, movement speed influences the perceived arousal, and the position of the arms influences the perceived dominance. These findings can aid in designing emotional intent behaviors for robots more effectively and intuitively in future studies. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Microrobots

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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