Taylor Dane, Klimm Florian, Harrington Heather A, Kramár Miroslav, Mischaikow Konstantin, Porter Mason A, Mucha Peter J
Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, North Carolina 27709, USA.
Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
Nat Commun. 2015 Jul 21;6:7723. doi: 10.1038/ncomms8723.
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges-for example, due to airline transportation or communication media-allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct 'contagion maps' that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.
社会和生物传染受到网络空间嵌入性的影响。从历史上看，许多流行病如波浪般在地球表面的部分区域传播；然而，在现代传染病中，远程边缘——例如，由于航空运输或通信媒介——使得传染病集群出现在遥远的地点。在这里，我们通过一种基于拓扑数据分析和非线性降维的方法来研究传染病在网络上的传播。我们构建“传染地图”，利用网络上的多种传染病将节点映射为点云。通过分析此类点云中流形结构的拓扑、几何和维度，我们揭示有助于传播过程建模、预测和控制的见解。我们的方法还突出了传染地图作为推断网络低维结构的可行工具。
