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P1–NONCONFORMING QUADRILATERAL FINITE ELEMENT SPACE WITH PERIODIC BOUNDARY CONDITIONS: PART I. FUNDAMENTAL RESULTS ON DIMENSIONS, BASES, SOLVERS, AND ERROR ANALYSIS

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arXiv 2022年

作者： Yim, Jaeryun Sheen, Dongwoo Interdisciplinary Program in Computational Science & Technology Seoul National University Seoul08826 Korea Republic of Department of Mathematics Seoul National University Seoul08826 Korea Republic of

The P1–nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We show that the situation is totally different based on the parity of the number of discretization on coordinates. Based on the analysis on the space, we propose several numerical schemes for elliptic problems with periodic boundary condition. Some of these numerical schemes are related with solving a linear equation consisting of a non-invertible matrix. By courtesy of the Drazin inverse, the existence of corresponding numerical solutions is guaranteed. The theoretical relation between the numerical solutions is derived, and it is confirmed by numerical results. Finally, the extension to the three dimensional is *** Codes 65N30 Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

CONVERGENCE SPEED AND APPROXIMATION ACCURACY OF NUMERICAL MCMC

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arXiv 2022年

作者： Cui, Tiangang Dong, Jing Jasra, Ajay Tong, Xin T. School of Mathematics Monash University Australia Graduate School of Business Columbia University United States Applied Mathematics and Computational Science Program Computer Electrical Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Saudi Arabia Department of Mathematics National University of Singapore Singapore

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects the convergence speed and Monte Carlo estimation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has similar convergence speed and high approximation accuracy as well. We discuss two different analysis frameworks: ergodicity and spectral gap, both are widely used in the literature. Our results can be easily extended to obtain non-asymptotic error bounds for MCMC estimators. We also demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis and Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally we present some simple numerical examples to verify our theoretical claims. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

Angklung Smart Band: An IoT-Based System to Support Music Activities for Elderly in Thailand

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Angklung Smart Band: An IoT-Based System to Support Music Ac...

2022 IEEE European Technology and Engineering Management Summit, E-TEMS 2022

作者： Hiranpanthaporn, Saranya Phoasavadi, Pornprapit Cooharojananone, Nagul Technopreneurship and Innovation Management Program Graduate School Chulalongkorn University Bangkok Bangkok Thailand Emili Sagol Creative Arts Research and Innovation for Well-being Center Chulalongkorn University Faculty of Fine and Applied Arts Department of Thai Music Bangkok Bangkok Thailand Chulalongkorn University Faculty of Science Department of Mathematics and Computer Science Bangkok Bangkok Thailand

ISBN: (数字)9781665411004

ISBN: (纸本)9781665411004

Organizing music activities for the elderly is another way that supports their well-being. Angklung, an Indonesian musical instrument, has been used for music activities for the elderly in Thailand with the hand signs method. Unfortunately, music activity is not widely used because the experts with the hand sign skills are few and not enough for demanding in the aging healthcare. At the same time, technologies of remote systems using the Internet of Things (IoT) have been developed to assist the elderly in supporting and improving their quality of life. This paper will introduce 'Angklung Smart Band,' an IoT-based system to support Angklung music activities for the elderly in Thailand. This work aims at setting up Angklung music activities for the elderly by using technology instead of hand signs. The system is composed of a web application, IoT devices, and Angklung musical instruments connected together via a wireless network. We did a preliminary study with the experts to improve experiences and system performance. After that, we asked the music experts to use the smart band to conduct the music activities experiment with the elderly for three days and give us feedback. The results found that the smart band could assist the Angklung music experts and help with the shortage of music expertise in aged care facilities or nursing homes. © 2022 IEEE.

关键词： Music

Not all spacetime coordinates for general-relativistic ray tracing are created equal

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Physical Review D 2023年第8期108卷 084004-084004页

作者： Gabriele Bozzola Chi-kwan Chan Vasileios Paschalidis Department of Astronomy University of Arizona Tucson Arizona USA Data Science Institute University of Arizona Tucson Arizona USA and Program in Applied Mathematics University of Arizona Tucson Arizona USA Department of Astronomy University of Arizona Tucson Arizona USA and Department of Physics University of Arizona Tucson Arizona USA

Models for the observational appearance of astrophysical black holes rely critically on accurate general-relativistic ray tracing and radiation transport to compute the intensity measured by a distant observer. In this paper, we illustrate how the choice of coordinates and initial conditions affect this process. In particular, we show that propagating rays from the camera to the source leads to different solutions if the spatial part of the momentum of the photon points towards the horizon or away from it. In doing this, we also show that coordinates that are well suited for numerical general-relativistic magnetohydrodynamic (GRMHD) simulations are typically not optimal for generic ray tracing. We discuss the implications for black hole images and show that radiation transport in optimal and nonoptimal spacetime coordinates lead to the same images up to numerical errors and algorithmic choices.

关键词： Classical black holes General relativity Accretion disk & black-hole plasma Astronomical black holes Numerical techniques Relativistic magnetohydrodynamics

Utopia point method based robust vector polynomial optimization scheme

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arXiv 2022年

作者： Han, Tianyi Jiao, Liguo Lee, Jae Hyoung Yin, Junping School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Academy for Advanced Interdisciplinary Studies Northeast Normal University Jilin Province Changchun130024 China Department of Applied Mathematics Pukyong National University Busan48513 Korea Republic of Institute of Applied Physics and Computational Mathematics Beijing100094 China Shanghai Zhangjiang Academy of Mathematics Shanghai201203 China

In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By combining/improving the utopia point method (a nonlinear scalarization) for vector optimization and "joint+marginal" relaxation method for polynomial optimization, we solve the RVPOP successfully. Both theoratical and computational aspects are considered. © 2022, CC BY-NC-ND.

关键词： Multiobjective optimization

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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arXiv 2023年

作者： Beckers, Thomas Seidman, Jacob Perdikaris, Paris Pappas, George J. Department of Electrical and Systems Engineering University of Pennsylvania PhiladelphiaPA19104 United States graduate program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems. © 2023, CC BY-NC-ND.

关键词： Hamiltonians

A Traffic Evacuation Model for Enhancing Resilience During Railway Disruption

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arXiv 2025年

作者： Ge, Hangli Yang, Xiaojie Chen, Jinyu Flammini, Francesco Koshizuka, Noboru Interfaculty Initiative in Information Studies The University of Tokyo Tokyo Japan Graduate School of Interdisciplinary Information Studies The University of Tokyo Tokyo Japan Department of Mathematics and Computer Science Ulisse Dini University of Florence Florence Italy IDSIA USI-SUPSI University of Applied Sciences and Arts of Southern Switzerland Lugano Switzerland

This paper introduces a traffic evacuation model for railway disruptions to improve resilience. The research focuses on the problem of failure of several nodes or lines on the railway network topology. We proposed a holistic approach that integrates lines of various operator companies as well as external geographical features of the railway system. The optimized evacuation model was mathematically derived based on matrix computation using nonlinear programming. The model also takes into account the capacity of the surrounding evacuation stations, as well as the travel cost. Moreover, our model can flexibly simulate disruptions at multiple stations or any number of stations and lines, enhancing its applicability. We collected the large-scale railway network of the Greater Tokyo area for experimentation and evaluation. We simulated evacuation plans for several major stations, including Tokyo, Shinjuku, and Shibuya. The results indicate that the evacuation passenger flow (EPF) and the average travel time (ATT) during emergencies were optimized, staying within both the capacity limits of the targeted neighboring stations and the disruption recovery time. © 2025, CC BY.

关键词： Nonlinear programming

Error Bounds for Native Space Embedding Observers with Operator-Valued Kernels

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Error Bounds for Native Space Embedding Observers with Opera...

American Control Conference (ACC)

作者： John A. Burns Jia Guo Andrew J. Kurdila Sai Tej Paruchuri Haoran Wang Interdisciplinary Center for Applied Mathematics (ICAM) Virginia Tech Blacksburg VA School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA Department of Mechanical Engineering Virginia Tech Blacksburg VA Department of Mechanical Engineering and Mechanics Lehigh University Bethlehem PA

This paper derives new rates of convergence for observers for a class of uncertain systems governed by non-linear ODEs. We assume that the generally nonlinear function appearing in the ODEs that represents the unknown dynamics is an element of a vector-valued reproducing kernel Hilbert space ℍ (RKHS) that is induced by an operator-valued kernel. The vector-valued RKHS embedding method described in the paper yields a nonparametric adaptive estimator that takes the form of distributed parameter system (DPS). The original ODEs in ℝ d are thus embedded in a product space ℝ d × ℍ in which state and functional uncertainty estimates evolve. We first discuss the well-posedness of the DPS formulation, and subsequently describe an approximation scheme in finitedimensional subspaces based on certain types of history dependent bases. We derive sufficient conditions that ensure the consistency of the finite-dimensional approximation scheme, and further derive rates of convergence in some particular cases when the samples that define the scattered bases are dense in some sufficiently regular and invariant subset of the observation space. A numerical example is given to illustrate the qualitative behavior of implementations of the theoretical results derived in the paper.

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Reconsider photoplethysmogram signal quality assessment in the free living environment

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Physiological Measurement 2024年第6期45卷 06NT01-06NT01页

作者： Su, Yan-Wei Hao, Chia-Cheng Liu, Gi-Ren Sheu, Yuan-Chung Wu, Hau-Tieng Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu Taiwan Data Science Degree Program National Taiwan University Academia Sinica Taipei Taiwan Department of Mathematics National Cheng-Kung University Tainan Taiwan National Center for Theoretical Sciences National Taiwan University Taipei Taiwan Courant Institute of Mathematical Sciences New York University New YorkNY10012 United States

Objective. Assessing signal quality is crucial for biomedical signal processing, yet a precise mathematical model for defining signal quality is often lacking, posing challenges for experts in labeling signal qualities. The situation is even worse in the free living environment. Approach. We propose to model a PPG signal by the adaptive non-harmonic model (ANHM) and apply a decomposition algorithm to explore its structure, based on which we advocate a reconsideration of the concept of signal quality. Main results. We demonstrate the necessity of this reconsideration and highlight the relationship between signal quality and signal decomposition with examples recorded from the free living environment. We also demonstrate that relying on mean and instantaneous heart rates derived from PPG signals labeled as high quality by experts without proper reconsideration might be problematic. Significance. A new method, distinct from visually inspecting the raw PPG signal to assess its quality, is needed. Our proposed ANHM model, combined with advanced signal processing tools, shows potential for establishing a systematic signal decomposition based signal quality assessment model. © 2024 Institute of Physics and Engineering in Medicine.

关键词： free-living environment photoplethysmogram signal quality index synchrosqueezing transform