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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

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. © 2022, CC BY.

关键词： Eigenvalues and eigenfunctions

Fixation probability in evolutionary dynamics on switching temporal networks

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arXiv 2023年

作者： Bhaumik, Jnanajyoti 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

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks. © 2023, CC BY.

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

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Physical Review E 2021年第1期104卷 014309-014309页

作者： Hang-Hyun Jo Naoki Masuda Department of Physics The Catholic University of Korea Bucheon 14662 Republic of Korea Department of Mathematics State University of New York at Buffalo 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

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.

关键词： Complex systems Nonequilibrium statistical mechanics Social systems Homogeneous networks Scale free & inhomogeneous networks Social dynamics Master equation Monte Carlo methods Network Models

To Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-player Trust Game

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arXiv 2023年

作者： Soo Lim, Ik. Masuda, Naoki School of Computing and Mathematical Sciences University of Greenwich LondonSE10 9LS United Kingdom Department of Mathematics and Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g. to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g. not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g. to trust). A generalisation of the TG to a multiplayer (i.e. more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles;instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players. © 2023, CC BY.

关键词： Dynamics

Recurrence in the evolution of air transport networks

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arXiv 2020年

作者： Sugishita, Kashin Masuda, Naoki State University of New York at Buffalo Department of Mathematics Buffalo14260-2900 United States State University of New York at Buffalo Computational and Data-Enabled Science and Engineering Program Buffalo14260-2900 United States Waseda University Faculty of Science and Engineering Tokyo169-8555 Japan

Changes in air transport networks over time may be induced by competition among carriers, changes in regulations on airline industry, and socioeconomic events such as terrorist attacks and epidemic outbreaks. Such network changes may reflect corporate strategies of each carrier. In the present study, we propose a framework for analyzing evolution patterns in temporal networks in discrete time from the viewpoint of recurrence. Recurrence implies that the network structure returns to one relatively close to that in the past. We applied the proposed methods to four major carriers in the US from 1987 to 2019. We found that the carriers were different in terms of the autocorrelation, strength of periodicity, and changes in these quantities across decades. We also found that the network structure of the individual carriers abruptly changes from time to time. Such a network change reflects changes in their operation at their hub airports rather than famous socioeconomic events that look closely related to airline industry. The proposed methods are expected to be useful for revealing, for example, evolution of airline alliances and responses to natural disasters or infectious diseases, as well as characterizing evolution of social, biological, and other networks over time. Copyright © 2020, The Authors. All rights reserved.

关键词： Competition

Temporal Motifs for Financial Networks: A Study on Mercari, JPMC, and Venmo Platforms

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arXiv 2023年

作者： Liu, Penghang Acharyya, Rupam Tillman, Robert E. Kimura, Shunya Masuda, Naoki Sarıyüce, Ahmet Erdem Department of Computer Science and Engineering University at Buffalo United States Amazon Web Services United States Optum Labs United States Mercari Inc. Japan Department of Mathematics University at Buffalo United States Computational and Data-Enabled Science and Engineering Program University at Buffalo United States

Understanding the dynamics of financial transactions among people is critically important for various applications such as fraud detection. One important aspect of financial transaction networks is temporality. The order and repetition of transactions can offer new insights when considered within the graph structure. Temporal motifs, defined as a set of nodes that interact with each other in a short time period, are a promising tool in this context. In this work, we study three unique temporal financial networks: transactions in Mercari, an online marketplace, payments in a synthetic network generated by J.P. Morgan Chase, and payments and friendships among Venmo users. We consider the fraud detection problem on the Mercari and J.P. Morgan Chase networks, for which the ground truth is available. We show that temporal motifs offer superior performance than a previous method that considers simple graph features. For the Venmo network, we investigate the interplay between financial and social relations on three tasks: friendship prediction, vendor identification, and analysis of temporal cycles. For friendship prediction, temporal motifs yield better results than general heuristics, such as Jaccard and Adamic-Adar measures. We are also able to identify vendors with high accuracy and observe interesting patterns in rare motifs, like temporal cycles. We believe that the analysis, datasets, and lessons from this work will be beneficial for future research on financial transaction networks. Copyright © 2023, The Authors. All rights reserved.

关键词： Finance

Epidemic dynamics on metapopulation networks with node2vec mobility

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arXiv 2021年

作者： Meng, Lingqi 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 BuffaloNY14260-5030 United States Faculty of Science and Engineering Waseda University Tokyo169-8555 Japan

Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-susceptible (SIS) dynamics in a metapopulation model, in which individuals obey a parametric second-order random-walk mobility rule called the node2vec. We map the second-order mobility rule of the node2vec to a first-order random walk in a network whose each node is a directed edge connecting a pair of subpopulations and then derive the epidemic threshold. For various networks, we find that the epidemic threshold is large (therefore, epidemic spreading tends to be suppressed) when the individuals infrequently backtrack or infrequently visit the common neighbors of the currently visited and the last visited subpopulations than when the individuals obey the simple random walk. The amount of change in the epidemic threshold induced by the node2vec mobility is in general not as large as, but is sometimes comparable with, the one induced by the change in the diffusion rate for individuals. Copyright © 2021, The Authors. All rights reserved.

关键词： Random processes

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

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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

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