RT Journal Article ID 4b31ea8720555d87 A1 Rajendran, Karthikeyan A1 Tsoumanis, Andreas C. A1 Siettos, Constantinos I. A1 Laing, Carlo R. A1 Kevrekidis, Ioannis G. T1 MODELING HETEROGENEITY IN NETWORKS USING POLYNOMIAL CHAOS JF International Journal for Multiscale Computational Engineering JO JMC YR 2016 FD 2016-09-23 VO 14 IS 3 SP 291 OP 302 K1 coarse-graining K1 social networks K1 equation-free approach K1 UQ K1 polynomial chaos AB Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from uncertainty quantification, specifically, the use of polynomial chaos. The crucial assumption underlying this mathematical and computational "technology transfer" is that the evolving states of the nodes in a network quickly become correlated with the corresponding node identities: features of the nodes imparted by the network structure (e.g., the node degree, the node clustering coefficient). The node dynamics thus depend on heterogeneous (rather than uncertain) parameters, whose distribution over the network results from the network structure. Knowing these distributions allows one to obtain an efficient coarse-grained representation of the network state in terms of the expansion coefficients in suitable orthogonal polynomials. This representation is closely related to mathematical/computational tools for uncertainty quantification (the polynomial chaos approach and its associated numerical techniques). The polynomial chaos coefficients provide a set of good collective variables for the observation of dynamics on a network and, subsequently, for the implementation of reduced dynamic models of it. We demonstrate this idea by performing coarse-grained computations of the nonlinear dynamics of information propagation on our illustrative network model using the Equation-Free approach. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,35d6eeb80bd15206,4b31ea8720555d87.html