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Equation-free analysis of a dynamically evolving multigraph

Author(s): Holiday, Alexander; Kevrekidis, Yannis G.

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Abstract: © 2016, EDP Sciences and Springer. In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling short intervals of direct dynamic network simulation with appropriately-defined lifting and restriction operators, mapping the detailed network description to suitable macroscopic (coarse-grained) variables and back. This enables the acceleration of direct simulations through Coarse Projective Integration (CPI), as well as the identification of coarse stationary states via a Newton-GMRES method. We also demonstrate the use of data-mining, both linear (principal component analysis, PCA) and nonlinear (diffusion maps, DMAPS) to determine good macroscopic variables (observables) through which one can coarse-grain the model. These results suggest methods for decreasing simulation times of dynamic real-world systems such as epidemiological network models. Additionally, the data-mining techniques could be applied to a diverse class of problems to search for a succint, low-dimensional description of the system in a small number of variables.
Publication Date: 1-Sep-2016
Citation: Holiday, A, Kevrekidis, YG. (2016). Equation-free analysis of a dynamically evolving multigraph. European Physical Journal: Special Topics, 225 (6-7), 1281 - 1292. doi:10.1140/epjst/e2016-02672-1
DOI: doi:10.1140/epjst/e2016-02672-1
ISSN: 1951-6355
EISSN: 1951-6401
Pages: 1281 - 1292
Type of Material: Journal Article
Journal/Proceeding Title: European Physical Journal: Special Topics
Version: Author's manuscript

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