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A NEW NUMERICAL APPROACH TO INVERSE TRANSPORT EQUATION WITH ERROR ANALYSIS

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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

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

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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

The Waiting-Time Paradox

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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

Nomad Platform Revisited for Reliable and Simplified Hull Construction

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SSRN

SSRN 2022年

作者： Uzunoğlu, Bahri Özçelik, Serdal Department of Engineering Sciences Department of Electrical Engineering Computational and data-enabled science and engineering in energy systems Uppsala University The Ångström Laboratory Box 534 Uppsala751 21 Sweden Department of Mathematics Florida State University The Ångström Laboratory Box 534 TallahasseeFL32310 United States Computational Renewables LLC The Ångström Laboratory Box 534 TallahasseeFL32309-3267 United States

The U.S. Navy (USN) in the late ’40s developed Navy Oceanographic Meteorological AutomaticDevice (NOMAD) platform for offshore autonomous meteorological measurements which has seen widespread usage since then because of its performance characteristics as meteorological and oceanographic data buoys, as energy system platform testing, as rocket data acquisition platform from Pacific to Atlantic. This article revisits the NOMAD hulls for engineering design to achieve simpler and less costly construction while this article focuses on hull construction and aspects and seakeeping are investigated in further work. Two hull forms namely NOMAD and HACIYATMAZ are analyzed. The HACIYATMAZ hull which is built from flat surfaces achieve similar structural performance to a streamlined NOMAD hull while simplifying the hull construction significantly with similar stability characteristics. Shell element-based finite element approach is employed for computational analysis. © 2022, The Authors. All rights reserved.

关键词： Rockets

Waiting-time paradox in 1922

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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

A Modified Clustering Using Representatives to Enhance and Optimize Tracking and Monitoring of Maritime Traffic in Real-time Using Automatic Identification System data

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A Modified Clustering Using Representatives to Enhance and O...

International Conference on computational science and computational Intelligence (CSCI)

作者： Cheronika Manyfield-Donald Tor A. Kwembe Jing-Ru C. Cheng Computational Data-Enabled Science and Engineering Jackson State University Jackson MS USA Department of Mathematics and Statistical Sciences Jackson State University Jackson MS USA Information Technology Lab. Engineer Research and Development Center U.S. Army Corps of Engineers Vicksburg MS USA

ISBN: (纸本)9781665458429

In this paper, we introduce a modification of the Clustering Using Representatives (CURE) algorithm to enhance and optimize the tracking and monitoring of maritime traffic in real-time using the Automatic Identification System (AIS) data. In doing so, we present a 2-D points data collection system for the utilization of a modified unsupervised machine learning clustering method of the CURE algorithm integrated with a data streaming algorithm to develop a more efficient method that will directly assist in adverting accidents and support in vessels avoiding dangerous environments. Results are presented that show tracking in inland as well as open sea waterways.

关键词： Machine learning algorithms Tracking Scientific computing Clustering methods Clustering algorithms Machine learning data collection

Generative models of simultaneously heavy-tailed distributions of interevent times on nodes and edges

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Physical Review E 2020年第5期102卷 052303-052303页

作者： Elohim Fonseca dos Reis Aming Li Naoki Masuda Department of Mathematics State University of New York at Buffalo Buffalo New York 14260 USA Department of Zoology University of Oxford Oxford OX1 3PS United Kingdom Department of Biochemistry University of Oxford Oxford OX1 3QU United Kingdom Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo New York 14260 USA Faculty of Science and Engineering Waseda University 169-8555 Tokyo Japan

Intervals between discrete events representing human activities, as well as other types of events, often obey heavy-tailed distributions, and their impacts on collective dynamics on networks such as contagion processes have been intensively studied. The literature supports that such heavy-tailed distributions are present for interevent times associated with both individual nodes and individual edges in networks. However, the simultaneous presence of heavy-tailed distributions of interevent times for nodes and edges is a nontrivial phenomenon, and its origin has been elusive. In the present study, we propose a generative model and its variants to explain this phenomenon. We assume that each node independently transits between a high-activity and low-activity state according to a continuous-time two-state Markov process and that, for the main model, events on an edge occur at a high rate if and only if both end nodes of the edge are in the high-activity state. In other words, two nodes interact frequently only when both nodes prefer to interact with others. The model produces distributions of interevent times for both individual nodes and edges that resemble heavy-tailed distributions across some scales. It also produces positive correlation in consecutive interevent times, which is another stylized observation for empirical data of human activity. We expect that our modeling framework provides a useful benchmark for investigating dynamics on temporal networks driven by non-Poissonian event sequences.

关键词： Network structure Social networks Stochastic networks Network Models

Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics

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arXiv 2018年

作者： Liu, Jian-Guo Tang, Min Wang, Li Zhou, Zhennan Department of Mathematics Department of Physics Duke University School of Mathematics and Institute of Natural Sciences MOE-LSC Shanghai JiaoTong University Department of Mathematics Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States Beijing International Center for Mathematical Research Peking University

In this paper, we study the tumor growth equation along with various models for the nutrient component, including the in vitro model and the in vivo model. At the cell density level, the spatial availability of the tumor density n is governed by the Darcy law via the pressure p\(n\) = nγ. For finite γ, we prove some a priori estimates of the tumor growth model, such as boundedness of the nutrient density, and non-negativity and growth estimate of the tumor density. As γ → ∞, the cell density models formally converge to Hele-Shaw flow models, which determine the free boundary dynamics of the tumor tissue in the incompressible limit. We derive several analytical solutions to the Hele-Shaw flow models, which serve as benchmark solutions to the geometric motion of tumor front propagation. Finally, we apply a conservative and positivity preserving numerical scheme to the cell density models, with numerical results verifying the link between cell density models and the free boundary dynamical *** Codes 35K55, 35B25, 76D27, 92C50 Copyright © 2018, The Authors. All rights reserved.

关键词： Tumors

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

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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