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Analysis of node2vec random walks on networks

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arXiv 2020年

作者： Meng, Lingqi Masuda, Naoki 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

Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The performance of the node2vec algorithm in these applications is considered to depend on properties of random walks that the algorithm uses. In the present study, we theoretically and numerically analyze random walks used by the node2vec. Those random walks are second-order Markov chains. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyze the stationary probability, relaxation times in terms of the spectral gap of the transition probability matrix, and coalescence time. In particular, we show that node2vec random walk accelerates diffusion when walkers are designed to avoid both back-tracking and visiting a neighbor of the previously visited node but do not avoid them completely. Copyright © 2020, The Authors. All rights reserved.

关键词： Relaxation time

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

Nuclear Neural Networks: Emulating Late Burning Stages in Core Collapse Supernova Progenitors

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arXiv 2025年

作者： Grichener, Aldana Renzo, Mathieu Kerzendorf, Wolfgang E. Farmer, Rob de Mink, Selma E. Bellinger, Earl Patrick Chan, Chi-Kwan Chen, Nutan Farag, Ebraheem Justham, Stephen Steward Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 Garching85748 Germany Department of Physics Technion Haifa3200003 Israel Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Ludwig-Maximilians-Universitat Munchen Geschwister-Scholl-Platz 1 Munchen80539 Germany Department of Astronomy Yale University New HavenCT06511 United States Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Avenue TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 North Santa Rita TucsonAZ85721 United States Machine Learning Research Lab Volkswagen AG Munich38440 Germany

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of fully-coupled stiff ordinary differential equations (ODEs), making the simulations computationally intensive and prone to numerical instability. To overcome this barrier, we design a nuclear neural network (NNN) framework with multiple hidden layers to emulate nucleosynthesis calculations and conduct a proof-of-concept to evaluate its performance. The NNN takes the temperature, density and composition of a burning region as input and predicts the resulting isotopic abundances along with the energy generation and loss rates. We generate training sets for initial conditions corresponding to oxygen core depletion and beyond using large nuclear reaction networks, and compare the predictions of the NNNs to results from a commonly used small net. We find that the NNNs improve the accuracy of the electron fraction by 280 − 660 % and the nuclear energy generation by 250 − 750 %, consistently outperforming the small network across all timesteps. They also achieve significantly better predictions of neutrino losses on relatively short timescales, with improvements ranging from 100 − 106 %. While further work is needed to enhance their accuracy and applicability to different stellar conditions, integrating NNN trained models into stellar evolution codes is promising for facilitating large-scale generation of core-collapse supernova (CCSN) progenitors with higher physical fidelity. © 2025, CC BY.

关键词： Nucleosynthesis

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

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

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

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arXiv 2020年

作者： dos Reis, Elohim Fonseca Li, Aming Masuda, Naoki Department of Mathematics State University of New York at Buffalo BuffaloNY United States Department of Zoology University of Oxford Oxford United Kingdom Department of Biochemistry University ofOxford Oxford United Kingdom Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY United States

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 inter-event times associated with both individual nodes and individual edges in networks. However, the simultaneous presence of heavy-tailed distributions of inter-event times for nodes and edges is a non-trivial 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 inter-event times for both individual nodes and edges that resemble heavy-tailed distributions across some scales. It also produces positive correlation in consecutive inter-event 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. Copyright © 2020, The Authors. All rights reserved.

关键词： Continuous time systems

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

An optimal algorithm for strict circular seriation

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arXiv 2021年

作者： Armstrong, Santiago Guzmán, Cristóbal Long, Carlos A. Sing Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Santiago Chile Anid - Millennium Science Initiative Program Millennium Nucleus Center for the Discovery of Structures in Complex Data Santiago Chile Department of Applied Mathematics University of Twente Netherlands Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Santiago Chile

We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between n objects, and the goal is to find a circular order of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical linear seriation problem where the goal is to find a linear order, and for which optimal O(n2) algorithms are known. Our contributions can be summarized as follows. First, we introduce circular Robinson matrices as the natural class of dissimilarity matrices for the circular seriation problem. Second, for the case of strict circular Robinson dissimilarity matrices we provide an optimal O(n2) algorithm for the circular seriation problem. Finally, we propose a statistical model to analyze the well-posedness of the circular seriation problem for large n. In particular, we establish O(log(n)/n) rates on the distance between any circular ordering found by solving the circular seriation problem to the underlying order of the model, in the Kendall-tau *** Codes 68R01, 05C85, 05C50, 05C25, 65C20 Copyright © 2021, The Authors. All rights reserved.

关键词： Trees (mathematics)

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

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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