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Dimension reduction of dynamical systems on networks with leading and non-leading eigenvectors of adjacency matrices

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Physical Review Research 2022年第2期4卷 023257-023257页

作者： Naoki Masuda Prosenjit Kundu Department of Mathematics State University of New York at Buffalo New York 14260-2900 USA Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo New York 14260-5030 USA

Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations of the state variables at the different nodes. Recently proposed methods use the leading eigenvector of the adjacency matrix of the network as the mixture weights to obtain such observables. In the present study, we explore performances of this type of one-dimensional reductions of dynamical systems on networks when we use non-leading eigenvectors of the adjacency matrix as the mixture weights. Our theory predicts that non-leading eigenvectors can be more efficient than the leading eigenvector and enables us to select the eigenvector minimizing the error. We numerically verify that the optimal non-leading eigenvector outperforms the leading eigenvector for some dynamical systems and networks. We also argue that, despite our theory, it is practically better to use the leading eigenvector as the mixture weights to avoid misplacing the bifurcation point too distantly and to be resistant against dynamical noise.

关键词： Network resilience

Metapopulation models imply non-Poissonian statistics of interevent times

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Physical Review Research 2022年第1期4卷 013050-013050页

作者： Elohim Fonseca dos Reis Naoki Masuda Department of Mathematics State University of New York at Buffalo Buffalo 14260-2900 New York USA Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo 14260-5030 New York USA Faculty of Science and Engineering Waseda University Tokyo 169-8555 Japan

Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, which impacts contagion and other dynamical processes on networks. We theoretically show that distributions of interevent times heavier-tailed than exponential distributions are a consequence of the most basic metapopulation model used in epidemiology and ecology, in which individuals move from one patch to another according to the simple random walk. Our results hold true irrespective of the network structure and also for more realistic mobility rules such as high-order random walks and the recurrent mobility patterns used for modeling human dynamics.

关键词： Continuous-time random walk Population dynamics Networks & random structures Social networks Diffusion & random walks Markovian processes Non-Markovian processes

Early Warnings for Multistage Transitions in Dynamics on Networks

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arXiv 2022年

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

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier than others as an environment gradually changes. Here we investigate early warning signals for networked systems undergoing a multistage transition. We found that knowledge of both the ongoing multistage transition and network structure enables us to calculate effective early warning signals for multistage transitions. Furthermore, we found that small subsets of nodes could anticipate transitions as well as or even better than using all the nodes. Even if we fix the network and dynamical system, no single best subset of nodes provides good early warning signals, and a good choice of sentinel nodes depends on the tipping direction and the current stage of the dynamics within a multistage transition, which we systematically characterize. © 2022, CC BY.

关键词： Dynamics

Dimension reduction of dynamical systems on networks with leading and non-leading eigenvectors of adjacency matrices

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arXiv 2022年

作者： Masuda, Naoki Kundu, Prosenjit Department of Mathematics State University of New York BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States

关键词： Eigenvalues and eigenfunctions

Using data Analytics to Forecast Violent Crime

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Using Data Analytics to Forecast Violent Crime

International Conference on computational science and computational Intelligence (CSCI)

作者： Herious Cotton Tor A. Kwembe Computational Data Enabled Science and Engineering Jackson State University Jackson MS USA Department of Mathematics and Statistical Sciences Jackson State University Jackson MS USA

ISBN: (纸本)9781665458429

In this paper, we used data analytics to analyze criminal data. Prophet model, LSTM recurrent neural network model, a linear regression model, and traditional neural network model were used to predict homicide and rape in the Southeastern Cities of Memphis Tennessee, Jackson Mississippi, and New Orleans Louisiana. LSTM recurrent neural network model and traditional neural network model have smaller RMSE. Thus, LSTM recurrent neural network model and traditional neural network model performed better than the prophet and linear regression models. These promising outcomes will be significant to scholars, policymakers, and law enforcement officers.

关键词： Recurrent neural networks data analysis Law enforcement Scientific computing Urban areas Linear regression data visualization

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

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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

Quantifying gender imbalance in East Asian academia: Research career and citation practice

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arXiv 2023年

作者： Nakajima, Kazuki Liu, Ruodan Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Meguro-ku Tokyo152-8552 Japan Department of Mathematics State University of New York at Buffalo Buffalo14260 United States Academic Center for Computing and Media Studies Kyoto University Sakyo-ku Kyoto606-8501 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo14260 United States Center for Computational Social Science Kobe University Kobe657-8501 Japan

Gender imbalance in academia has been confirmed in terms of a variety of indicators, and its magnitude often varies from country to country. Europe and North America, which cover a large fraction of research workforce in the world, have been the main geographical regions for research on gender imbalance in academia. However, the academia in East Asia, which accounts for a substantial fraction of research, may be exposed to strong gender imbalance because Asia has been facing persistent and stronger gender imbalance in society at large than Europe and North America. Here we use publication data between 1950 and 2020 to analyze gender imbalance in academia in China, Japan, and South Korea in terms of the number of researchers, their career, and citation practice. We found that, compared to the average of the other countries, gender imbalance is larger in these three East Asian countries in terms of the number of researchers and their citation practice and additionally in Japan in terms of research career. Moreover, we found that Japan has been exposed to the larger gender imbalance than China and South Korea in terms of research career and citation practice. Copyright © 2023, The Authors. All rights reserved.

关键词： Geographical regions

Perturbation theory for evolution of cooperation on networks

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arXiv 2022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

Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio, (b/c)∗, which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that (b/c)∗ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes (b/c)∗ small to facilitate cooperation. In contrast, (b/c)∗ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes (b/c)∗ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph *** Codes 91A22, 91D30 Copyright © 2022, The Authors. All rights reserved.

关键词： Surgery

Embedding and trajectories of temporal networks

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arXiv 2022年

作者： Thongprayoon, Chanon Livi, Lorenzo Masuda, Naoki Department of Mathematics State University of New York at Buffalo BuffaloNY United States Department of Computer Science University of Manitoba WinnipegMB Canada Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY United States Faculty of Science and Engineering Waseda University Shinjuku Tokyo Japan

Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to coarse grain temporal network data into a numeric trajectory embedded in a low-dimensional space. We refer to such a procedure as temporal network embedding, which is distinct from procedures that aim at embedding individual nodes. Temporal network embedding is a challenging task because we often have access only to discrete time-stamped events between node pairs, and, in general, the events occur with irregular intervals, making the construction of the network at a given time a nontrivial question already. We propose a method to generate trajectories of temporal networks embedded in a low-dimensional space given a sequence of time-stamped events as input. We realize this goal by combining the landmark multidimensional scaling, which is an out-of-sample extension of the well-known multidimensional scaling method, and the framework of tie-decay temporal networks. This combination enables us to obtain a continuous-time trajectory describing the evolution of temporal networks. We then study mathematical properties of the proposed temporal network embedding framework. Finally, we showcase the method with empirical data of social contacts to find temporal organization of contact events and loss of them over a single day and across different days. © 2022, CC BY.

关键词： Trajectories