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25 April 2024 |
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Article overview
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Modeling Heterogeneity in Networks using Uncertainty Quantification Tools | | Karthikeyan Rajendran
; Andreas C. Tsoumanis
; Constantinos I. Siettos
; Carlo R. Laing
; Ioannis G. Kevrekidis
; | | Date: |
24 Nov 2015 | | Abstract: | 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. 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 us 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 | | Source: | arXiv, 1511.7609 | | Services: | Forum | Review | PDF | Favorites | |
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