論文

査読有り
2017年4月

Self-similarity and quasi-idempotence in neural networks and related dynamical systems

CHAOS
  • Ludovico Minati
  • ,
  • Julia Winkel
  • ,
  • Angelo Bifone
  • ,
  • Pawel Oswiecimka
  • ,
  • Jorge Jovicich

27
4
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1063/1.4981908
出版者・発行元
AMER INST PHYSICS

Self-similarity across length scales is pervasively observed in natural systems. Here, we investigate topological self-similarity in complex networks representing diverse forms of connectivity in the brain and some related dynamical systems, by considering the correlation between edges directly connecting any two nodes in a network and indirect connection between the same via all triangles spanning the rest of the network. We note that this aspect of self-similarity, which is distinct from hierarchically nested connectivity (coarse-grain similarity), is closely related to idempotence of the matrix representing the graph. We introduce two measures, t(1) and i(infinity), which represent the element-wise correlation coefficients between the initial matrix and the ones obtained after squaring it once or infinitely many times, and term the matrices which yield large values of these parameters "quasi-idempotent". These measures delineate qualitatively different forms of "shallow" and "deep" quasi-idempotence, which are influenced by nodal strength heterogeneity. A high degree of quasi-idempotence was observed for partially synchronized mean-field Kuramoto oscillators with noise, electronic chaotic oscillators, and cultures of dissociated neurons, wherein the expression of quasi-idempotence correlated strongly with network maturity. Quasi-idempotence was also detected for macro-scale brain networks representing axonal connectivity, synchronization of slow activity fluctuations during idleness, and co-activation across experimental tasks, and preliminary data indicated that quasi-idempotence of structural connectivity may decrease with ageing. This initial study highlights that the form of network self-similarity indexed by quasi-idempotence is detectable in diverse dynamical systems, and draws attention to it as a possible basis for measures representing network "collectivity" and pattern formation. Published by AIP Publishing.

Web of Science ® 被引用回数 : 5

リンク情報
DOI
https://doi.org/10.1063/1.4981908
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000407692500008&DestApp=WOS_CPL
URL
http://orcid.org/0000-0002-2532-1674

エクスポート
BibTeX RIS