检索结果-内蒙古大学图书馆

Stability of stationary inverse transport equation in diffusion scaling

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Chen, Ke Li, Qin 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

We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a dimensionless parameter-the Knudsen number (Kn). In the diffusive scaling (Kn 1), the stationary RTE is well approximated by an elliptic equation in the forward setting. However, the inverse problem for the elliptic equation is acknowledged to be severely ill-posed as compared to the well-posedness of inverse transport equation, which raises the question of how uniqueness being lost as Kn → 0. We tackle this problem by examining the stability of inverse problem with varying Kn. We show that, the discrepancy in two measurements is amplified in the reconstructed parameters at the order of Knp (p = 1 or 2), and as a result lead to ill-posedness in the zero limit of Kn. Our results apply to both continuous and discrete settings. Some numerical tests are performed in the end to validate these theoretical findings. Copyright © 2017, The Authors. All rights reserved.

关键词： Parameter estimation

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

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

Mean-field theory for double-well systems on degree-heterogeneous networks

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Kundu, Prosenjit MacLaren, Neil G. Kori, Hiroshi Masuda, Naoki Department of Mathematics State University of New York BuffaloNY14260-2900 United States Department of Complexity Science and Engineering The University of Tokyo Chiba277-8561 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behavior of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems. © 2022, CC BY.

关键词： Mean field theory

Accuracy of a one-dimensional reduction of dynamical systems on networks

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Kundu, Prosenjit Kori, Hiroshi Masuda, Naoki Department of Mathematics State University of New York BuffaloNY14260-2900 United States Department of Complexity Science and Engineering The University of Tokyo Chiba277-8561 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature, 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on several assumption in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction. © 2021, CC BY.

关键词： Dynamical systems

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

Network Intrusion Detection System Using Principal Component Analysis Algorithm and Decision Tree Classifier

学校读者我要写书评

暂无评论

Network Intrusion Detection System Using Principal Component...

International Conference on computational Science and computational Intelligence (CSCI)

作者： Oyeyemi Osho Sungbum Hong Tor A. Kwembe Department of Computational Data-Enabled Science and Engineering(CDS&#x0026 E) Jackson State University Jackson MS USA Department of Electrical &#x0026 Computer Engineering and Computer Science Jackson State University Jackson MS USA Department of Mathematics &#x0026 Statistical Sciences Jackson State University Jackson MS USA

ISBN: (纸本)9781665458429

Network Intrusion Detection Systems (IDS) have become expedient for network security and ensures the safety of all connected devices. Network Intrusion Detection System (IDS) alludes to observing network data information swiftly, detecting any intrusion pattern and preventing any harmful effect of anomaly intrusion that will cost the network. To combat this issue, we present in this concept paper an IDS based on the Principal Component Analysis (PCA) and Decision Tree Classifier algorithm, a supervised machine learning model to detect intrusion in the Network.

关键词： Machine learning algorithms Costs Scientific computing Network intrusion detection Network security Classification algorithms Safety

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

Fast sequential clustering in riemannian manifolds for dynamic and time-series-annotated multilayer networks

学校读者我要写书评

暂无评论

TechRxiv

TechRxiv 2020年

作者： Ye, Cong Slavakis, Konstantinos Nakuci, Johan Muldoon, Sarah F. Medaglia, John NY14260 United States State University of New York at Buffalo China The Neuroscience Program UB SUNY United States The Department of Mathematics and the Computational and Data-Enabled Science and Engineering Program UB SUNY United States The Department of Psychology Drexel University PA19104 United States The Perelman School of Medicine University of Pennsylvania PA19104 United States

This work exploits Riemannian manifolds to build a sequential-clustering framework able to address a wide variety of clustering tasks in dynamic multilayer (brain) networks via the information extracted from their nodal time-series. The discussion follows a bottom-up path, starting from feature extraction from time-series and reaching up to Riemannian manifolds (feature spaces) to address clustering tasks such as state clustering, community detection (a.k.a. network-topology identification), and subnetwork-sequence tracking. Kernel autoregressive-moving-average modeling and kernel (partial) correlations serve as case studies of generating features in the Riemannian manifolds of Grassmann and positive-(semi)definite matrices, respectively. Feature point-clouds form clusters which are viewed as submanifolds according to Riemannian multi-manifold modeling. A novel sequential-clustering scheme of Riemannian features is also established: feature points are first sampled in a non-random way to reveal the underlying geometric information, and, then, a fast sequential-clustering scheme is brought forth that takes advantage of Riemannian distances and the angular information of tangent spaces. By virtue of the landmark points and the sequential processing of the Riemannian features, the computational complexity of the framework is rendered free from the length of the available time-series data. The effectiveness and computational efficiency of the proposed framework are validated by extensive numerical tests against several state-of-the-art manifold-learning and brain-network-clustering schemes on synthetic as well as real functional-magnetic-resonance-imaging (fMRI) and electroencephalogram (EEG) data. © 2020, CC BY.

关键词： Time series