检索结果-内蒙古大学图书馆

An accurate front capturing scheme for tumor growth models with a free boundary limit

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Liu, Jian-Guo Tang, Min Wang, Li Zhou, Zhennan Department of Mathematics Department of Physics Duke University Department of Mathematics Institute of Natural Sciences MOE LSC Shanghai Jiao Tong University Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States Department of Mathematics Duke University

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure p and density ρ is p(ρ) = mm−1 ρm−1, and when m 1, the cell density ρ may evolve its support due to a pressure-driven geometric motion with sharp interface along the boundary of its support. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations, let alone the capturing of the singular free boundary limit. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as m 1. In this paper, we develope a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as m → ∞, and with proper spacial discretization, the fully discrete scheme has improved stability, preserves positivity, and implements without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties and showcase good performance in various applications.35K55, 35B25, 76D27, 92C50 Copyright © 2017, The Authors. All rights reserved.

关键词： Tumors

Clustering in Networks Via Kernel-ARMA Modeling and the Grassmannian: The Brain-Network Case

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Ye, Cong Slavakis, Konstantinos Patil, Pratik V. Nakuci, Johan Muldoon, Sarah F. Medaglia, John NY14260 United States Neuroscience Program University at Buffalo BuffaloNY14260 United States Department of Mathematics and the Computational and Data-Enabled Science and Engineering Program University at Buffalo SUNYNY14260 United States Department of Psychology Drexel University Perelman School of Medicine University of Pennsylvania PA19104 United States

This paper introduces a clustering framework for networks with nodes are annotated with time-series data. The framework addresses all types of network-clustering problems: State clustering, node clustering within states (a.k.a. topology identification or community detection), and even subnetwork-state-sequence identification/tracking. Via a bottom-up approach, features are first extracted from the raw nodal time-series data by kernel autoregressive-moving-average modeling to reveal non-linear dependencies and low-rank representations, and then mapped onto the Grassmann manifold (Grassmannian). All clustering tasks are performed by leveraging the underlying Riemannian geometry of the Grassmannian in a novel way. To validate the proposed framework, brain-network clustering is considered, where extensive numerical tests on synthetic and real functional Magnetic Resonance Imaging (fMRI) data demonstrate that the advocated learning framework compares favorably versus several state-of-the-art clustering schemes. Copyright © 2020, The Authors. All rights reserved.

关键词： Time series

Finite-size effects on the convergence time in continuous-opinion dynamics

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Jo, Hang-Hyun Masuda, Naoki Department of Physics The Catholic University of Korea Bucheon14662 Korea Republic of Department of Mathematics State University of New York at Buffalo 14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 14260-5030 United States

We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., [0;1], and a uniformly randomly chosen individual updates its opinion by partially mimicking the opinion of a uniformly randomly chosen neighbor. We numerically find that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks. In contrast, unless the individuals perfectly copy the opinion of their neighbors in each opinion updating, the convergence time is approximately independent of the system size in the case of regular random graphs, uncorrelated scale-free networks, and complete graphs. We also provide a mean-field analysis of the model to understand the case of the complete graph. Copyright © 2021, The Authors. All rights reserved.

关键词： Graph theory

A NEW NUMERICAL APPROACH TO INVERSE TRANSPORT EQUATION WITH ERROR ANALYSIS

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Li, Qin Shu, Ruiwen Wang, Li Mathematics Department University of Wisconsin-Madison 480 Lincoln Dr. MadisonWI53705 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 244 Mathematics Building BuffaloNY14206 United States

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering coefficient of the media, through the source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

Entropy-isomap: Manifold learning for high-dimensional dynamic processes

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Schoeneman, Frank Chandola, Varun Napp, Nils Wodo, Olga Zola, Jaroslaw Computer Science & Engineering University at Buffalo BuffaloNY United States Computer Science & Engineering Computational and Data-enabled Science & Engineering University at Buffalo BuffaloNY United States Materials Design & Innovation University at Buffalo BuffaloNY United States Computer Science & Engineering Biomedical Informatics University at Buffalo BuffaloNY United States

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. In this paper, we first show that off-the-shelf non-linear spectral dimensionality reduction methods, e.g., Isomap, fail for such data, primarily due to the presence of strong temporal correlations. Then, we propose a novel method, Entropy-Isomap, to address the issue. The proposed method is successfully applied to large data describing a fabrication process of organic materials. The resulting low-dimensional representation correctly captures process control variables, allows for low-dimensional visualization of the material morphology evolution, and provides key insights to improve the process. Copyright © 2018, The Authors. All rights reserved.

关键词： Entropy

Gillespie algorithms for stochastic multiagent dynamics in populations and networks

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Masuda, Naoki Vestergaard, Christian L. Department of Mathematics State University of New York at Buffalo NY United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo NY United States Decision and Bayesian Computation Department of Neuroscience Cnrs Umr 3571 Department of Computational Biology Cnrs Usr 3756 Institut Pasteur Paris France

Many multiagent dynamics, including various collective dynamics occurring on networks, can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. In the first main part of this volume, we provide a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. We do not assume advanced knowledge of mathematics (or computer science or physics). We clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. In the remainder of this volume, we review recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. © 2021, CC BY.

关键词： Stochastic systems

The Waiting-Time Paradox

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Masuda, Naoki Porter, Mason A. Department of Mathematics State University of New York at Buffalo BuffaloNY United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY United States Department of Mathematics University of California Los Angeles Los AngelesCA United States

Suppose that you’re going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer — possibly much longer — than what the bus schedule suggests intuitively. This phenomenon, called the waiting-time paradox, has a purely mathematical origin. Different buses arrive with different intervals, leading to this paradox. In this article, we look at the waiting-time paradox, explain why it happens, and explore some of its implications (beyond the possibility of being late for school). Copyright © 2020, The Authors. All rights reserved.

关键词： Buses

Concurrency measures in the era of temporal network epidemiology: A review

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Masuda, Naoki Miller, Joel C. Holme, Petter Department of Mathematics State University of New York Buffalo United States Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States School of Engineering and Mathematical Sciences La Trobe University Australia Institute of Innovative Research Tokyo Institute of Technology Yokohama226-8503 Japan

Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency-quantifying individuals' tendency to form time-overlapping "partnerships". Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches. © 2020, CC BY.

关键词： Epidemiology

Waiting-time paradox in 1922

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Masuda, Naoki Hiraoka, Takayuki Department of Mathematics University at Buffalo State University of New York BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York BuffaloNY14260-5030 United States Department of Computer Science Aalto University Espoo00076 Finland

We present an English translation and discussion of an essay that a Japanese physicist, Torahiko Terada, wrote in 1922. In the essay, he described the waiting-time paradox, also called the bus paradox, which is a known mathematical phenomenon in queuing theory, stochastic processes, and modern temporal network analysis. He also observed and analyzed data on Tokyo City trams to verify the relevance of the waiting-time paradox to busy passengers in Tokyo at the time. This essay seems to be one of the earliest documentations of the waiting-time paradox in a sufficiently scientific manner. Copyright © 2020, The Authors. All rights reserved.

关键词： Queueing theory