Multiscale computations on neural networks: From the individual neuron interactions to the macroscopic-level analysis

Spiliotis, KG; Siettos, CI

dc.contributor.author	Spiliotis, KG	en
dc.contributor.author	Siettos, CI	en
dc.date.accessioned	2014-03-01T01:33:48Z
dc.date.available	2014-03-01T01:33:48Z
dc.date.issued	2010	en
dc.identifier.issn	0218-1274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20603
dc.subject	Bifurcation analysis	en
dc.subject	Equation-free approach	en
dc.subject	Multiscale computations	en
dc.subject	Neural networks	en
dc.subject	Rare-events analysis	en
dc.subject	Simulated annealing	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Multidisciplinary Sciences	en
dc.subject.other	Bifurcation analysis	en
dc.subject.other	Bifurcation diagram	en
dc.subject.other	Black boxes	en
dc.subject.other	Coarse-grained	en
dc.subject.other	Connected graph	en
dc.subject.other	Equation-Free	en
dc.subject.other	Individual-based	en
dc.subject.other	Macroscopic levels	en
dc.subject.other	Multiscale computation	en
dc.subject.other	Multiscale computations	en
dc.subject.other	Neural interactions	en
dc.subject.other	Stationary state	en
dc.subject.other	Timestepper	en
dc.subject.other	Annealing	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Computer simulation	en
dc.subject.other	Neural networks	en
dc.subject.other	Probability density function	en
dc.subject.other	Simulated annealing	en
dc.title	Multiscale computations on neural networks: From the individual neuron interactions to the macroscopic-level analysis	en
heal.type	journalArticle	en
heal.identifier.primary	10.1142/S0218127410025442	en
heal.identifier.secondary	http://dx.doi.org/10.1142/S0218127410025442	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We show how the Equation-Free approach for multiscale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states, sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective FokkerPlanck equation describing the evolving probability density function of the corresponding coarse-grained observables. © 2010 World Scientific Publishing Company.	en
heal.publisher	WORLD SCIENTIFIC PUBL CO PTE LTD	en
heal.journalName	International Journal of Bifurcation and Chaos	en
dc.identifier.doi	10.1142/S0218127410025442	en
dc.identifier.isi	ISI:000275981100008	en
dc.identifier.volume	20	en
dc.identifier.issue	1	en
dc.identifier.spage	121	en
dc.identifier.epage	134	en