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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

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

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

Perturbation theory for evolution of cooperation on networks

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arXiv 2022年

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

Randomizing hypergraphs preserving degree correlation and local clustering

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arXiv 2021年

作者： Nakajima, Kazuki Shudo, Kazuyuki Masuda, Naoki Department of Mathematical and Computing Science Tokyo Institute of Technology Japan 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 Faculty of Science and Engineering Waseda University Japan

Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dk-series, by extending the so-called dk-series for dyadic networks to the case of hypergraphs. The hyper dk-series preserves up to the individual node’s degree, node’s degree correlation, node’s redundancy coefficient, and/or the hyperedge’s size depending on the parameter values. Furthermore, we numerically find that higher-order hyper dk-series more accurately preserves the shortest path length and degree distribution of the one-mode projection of the original hypergraph, which the method does not intend to preserve. We also apply the hyper dk-series to numerical simulations of epidemic spreading and evolutionary game dynamics on empirical social hypergraphs. We find that the hyperedge’s size affects these dynamics more than any of the node’s properties and that the node’s degree correlation and redundancy in the empirical hypergraphs promote cooperation. Copyright © 2021, The Authors. All rights reserved.

关键词： Redundancy

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

Brain-network clustering via kernel-ARMA modeling and the Grassmannian

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arXiv 2019年

作者： Ye, Cong Slavakis, Konstantinos Patil, Pratik V. Muldoon, Sarah F. Medaglia, John NY14260 United States Department of Mathematics Computational and Data-Enabled Science and Engineering Program University at Buffalo SUNY NY14260 United States Department of Psychology Drexel University PA19104 United States Perelman School of Medicine University of Pennsylvania PA19104 United States

Recent advances in neuroscience and in the technology of functional magnetic resonance imaging (fMRI) and electro-encephalography (EEG) have propelled a growing interest in brain-network clustering via time-series analysis. Notwithstanding, most of the brain-network clustering methods revolve around state clustering and/or node clustering (a.k.a. community detection or topology inference) within states. This work answers first the need of capturing non-linear nodal dependencies by bringing forth a novel feature-extraction mechanism via kernel autoregressive-moving-average modeling. The extracted features are mapped to the Grassmann manifold (Grassmannian), which consists of all linear subspaces of a fixed rank. By virtue of the Riemannian geometry of the Grassmannian, a unifying clustering framework is offered to tackle all possible clustering problems in a network: Cluster multiple states, detect communities within states, and even identify/track subnetwork state sequences. The effectiveness of the proposed approach is underlined by extensive numerical tests on synthetic and real fMRI/EEG data which demonstrate that the advocated learning method compares favorably versus several state-of-the-art clustering schemes. Copyright © 2019, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

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