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• W2906221684 abstract "A spreading process on a network is influenced by the network's underlying spatial structure, and it is insightful to study the extent to which a spreading process follows such structure. We consider a threshold contagion model on a network whose nodes are embedded in a manifold and which has both `geometric edges', which respect the geometry of the underlying manifold, and `nongeometric edges' that are not constrained by that geometry. Building on ideas from Taylor et al. cite{Taylor2015}, we examine when a contagion propagates as a wave along a network whose nodes are embedded in a torus and when it jumps via long nongeometric edges to remote areas of the network. We build a `contagion map' for a contagion spreading on such a `noisy geometric network' to produce a point cloud; and we study the dimensionality, geometry, and topology of this point cloud to examine qualitative properties of this spreading process. We identify a region in parameter space in which the contagion propagates predominantly via wavefront propagation. We consider different probability distributions for constructing nongeometric edges -- reflecting different decay rates with respect to the distance between nodes in the underlying manifold -- and examine the effect of such choices on the qualitative properties of the spreading dynamics. Our work generalizes the analysis in Taylor et al. and consolidates contagion maps both as a tool for investigating spreading behavior on spatial networks and as a technique for manifold learning." @default.
• W2906221684 created "2019-01-01" @default.
• W2906221684 creator A5079418634 @default.
• W2906221684 date "2018-12-24" @default.
• W2906221684 modified "2023-09-27" @default.
• W2906221684 title "Analysis of contagion maps on a class of networks that are spatially embedded in a torus" @default.
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• W2906221684 hasPublicationYear "2018" @default.
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