Coarse-graining the Dynamics of Network Evolution: The Rise and Fall of a Networked Society

Tsoumanis, Andreas; Rajendran, Karthikeyan; Siettos, Constantinos; Kevrekidis, Ioannis G.

doi:10.1063/1.3636666

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…Over the last decade our group has proposed -and developed-the so-called Equation-Free computational framework for complex/multiscale systems modeling: given a detailed (here, individual/agent-based) simulation algorithm, this framework enables us to study coarse-grained, systems level dynamics through the design, execution and processing of the brief bursts of fine scale simulation data; Equation-Free algorithms like Coarse Projective Integration (CPI) take the form of "wrappers" around the fine scale code (say, an agent-based epidemic simulation code on an adaptive network). [8][9][10][11] Yet for this approach to be successful, one needs to a priori know what the right macroscopic statistics are (e.g., the right few leading moments of the distribution of susceptible or of infected individuals in the population) in terms of which the epidemic statistics can be informatively summarized. This paper considers the case where such informative and parsimonious system-level statistics are not a priori known.…”

Section: Introductionmentioning

confidence: 99%

Modeling epidemics on adaptively evolving networks: A data-mining perspective

et al. 2016

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The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a few "good observables") that usefully summarize the overall (macroscopic, systems-level) behavior. Obtaining reduced, small size accurate models in terms of these few statistical observables -that is, trying to coarse-grain the full network epidemic model to a small but useful macroscopic one -is even more daunting. Here we describe a databased approach to solving the first challenge: the detection of a few informative collective observables of the detailed epidemic dynamics. This is accomplished through Diffusion Maps (DMAPS), a recently developed data-mining technique. We illustrate the approach through simulations of a simple mathematical model of epidemics on a network: a model known to exhibit complex temporal dynamics. We discuss potential extensions of the approach, as well as possible shortcomings.

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Section: Introductionmentioning

confidence: 99%

Modeling epidemics on adaptively evolving networks: A data-mining perspective

et al. 2016

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“…In this approach, short bursts of simulation at the ("fine") level of nodes and edges using the detailed rules of dynamic evolution of the problem are performed in order to estimate enough information to carry out computational tasks at a more coarse-grained level. The Equation-Free approach has been, in the past, successfully implemented for a variety of specific network models [16,17,18]. The success of this approach rests heavily on (a) defining a suitable set of coarse observables in terms of which a closed, reduced description of the evolution on the network may theoretically be obtained, and (b) the ability to convert back and forth between the two levels of description of the system -the "fine" and the "coarse-grained" levels.…”

Section: Introductionmentioning

confidence: 99%

Modeling Heterogeneity in Networks Using Polynomial Chaos

Rajendran

Tsoumanis

Siettos³

et al. 2016

Int J Mult Comp Eng

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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 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.

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Coarse-graining the Dynamics of Network Evolution: The Rise and Fall of a Networked Society

Cited by 2 publications

References 28 publications

Modeling epidemics on adaptively evolving networks: A data-mining perspective

Modeling epidemics on adaptively evolving networks: A data-mining perspective

Modeling Heterogeneity in Networks Using Polynomial Chaos

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