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 http://dl.begellhouse.com/journals/61fd1b191cf7e96f,35d6eeb80bd15206,4b31ea8720555d87.html