CIF: Small: SPREADING PROCESSES OVER MULTILAYER AND INTERCONNECTED NETWORKS

该项目通过分析在多层和相互连接的网络上的传播过程，推进了网络理论的边界，这些网络在自然和人为的基础设施中比比皆是，关于这些网络，许多有趣的问题仍未得到解答。多层网络是节点间存在多种类型链路的抽象表示。互联网络是一个抽象的表示，其中两个或多个简单的网络，可能具有不同的和独立的动态，相互耦合。该项目的基本原理是，在多层和互联网络上的病毒传播动态表现出不能归因于单一网络特征的行为，并在实践中发挥高度相关的作用。项目第一部分将决定爆发条件的流行病阈值的概念扩展到互连和多层网络的阈值曲线。本研究进一步发展了互连网络中耦合强度的量化措施，并寻求它们的最佳互连设计。该项目的第二部分旨在预测多层网络上的竞争性传播和可能出现的新现象。本文分析了多层网络中多病毒竞争传播的瞬态动力学和稳态行为，并在博弈论框架下研究了竞争策略。该项目将使用严格的数学工具，包括网络科学、谱图理论、非线性动力学、随机过程、控制理论、博弈论和优化。该项目的成功完成将极大地推动网络理论的发展，在通信和信息技术方面的具体、相关应用将导致这些复杂网络系统的更高效、更稳健的设计。从更广泛的角度来看，这项研究将通过更好地理解如何预防大规模灾难，包括电网的级联故障、市场交易中的金融传染、传染病大流行和计算机恶意软件的爆发，对社会做出积极贡献。此外，研究人员将付出巨大的努力，让来自代表性不足群体的学生参与进来，并通过出版物、网络研讨会和公共网页在社会和学术界传播项目成果。

This project advances the boundaries of network theory by analyzing spreading processes over multilayer and interconnected networks, which abound in nature and man-made infrastructures, and about which many interesting questions remain unanswered. Multilayer networks are an abstract representation where multiple types of links exist among nodes. Interconnected networks are an abstract representation where two or more simple networks, possibly with different and separate dynamics, are coupled to each other. The rationale for this project is that viral-spreading dynamics over multilayer and interconnected networks exhibit behaviors that cannot be attributed to single-network characteristics and play a highly relevant role in practice. The first part of the project extends the concept of the epidemic threshold value, which determines the conditions for outbreak, to the threshold curve for interconnected and multilayer networks. This research further develops measures for quantification of coupling strength in interconnected networks and seeks optimal interconnection designs for them. The second part of the project aims at predicting competitive spreading over multilayer networks and possible emergent phenomena. This research analyzes transient dynamics and steady-state behavior of multiple-virus competitive spreading in multilayer networks, and investigates competition policy in a game-theoretic framework. This project will use rigorous mathematical tools from network science, spectral graph theory, nonlinear dynamics, stochastic processes, control theory, game theory, and optimization.Successful completion of this project will greatly advance the state of the art in network theory, with specific, relevant applications in communications and information technologies leading to more efficient and robust design of these complex networked systems. In a broader view, this research will contribute positively to society through a better understanding of how to prevent large-scale catastrophes, including cascading failures in power grids, financial contagions in market trading, infectious disease pandemics, and outbreaks of computer malware. Furthermore, the investigators will put forth significant effort to involve students from under-represented groups, and disseminate project outcomes in both general society and academia through publications, webinars, and public webpages.