5 research outputs found
Coarse-graining the dynamics of network evolution: the rise and fall of a networked society
We explore a systematic approach to studying the dynamics of evolving
networks at a coarse-grained, system level. We emphasize the importance of
finding good observables (network properties) in terms of which coarse grained
models can be developed. We illustrate our approach through a particular social
network model: the "rise and fall" of a networked society [1]: we implement our
low-dimensional description computationally using the equation-free approach
and show how it can be used to (a) accelerate simulations and (b) extract
system-level stability/bifurcation information from the detailed dynamic model.
We discuss other system-level tasks that can be enabled through such a
computer-assisted coarse graining approach.Comment: 18 pages, 11 figure
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Modeling heterogeneity in networks using polynomial chaos
© 2016 by Begell House, Inc. 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