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Hodge Decomposition of Information Flow on Small-World Networks

We investigate the influence of the small-world topology on the composition of information flow on networks. By appealing to the combinatorial Hodge theory, we decompose information flow generated by random threshold networks on the Watts-Strogatz model into three components: gradient, harmonic and...

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Autores principales: Haruna, Taichi, Fujiki, Yuuya
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5039183/
https://www.ncbi.nlm.nih.gov/pubmed/27733817
http://dx.doi.org/10.3389/fncir.2016.00077
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author Haruna, Taichi
Fujiki, Yuuya
author_facet Haruna, Taichi
Fujiki, Yuuya
author_sort Haruna, Taichi
collection PubMed
description We investigate the influence of the small-world topology on the composition of information flow on networks. By appealing to the combinatorial Hodge theory, we decompose information flow generated by random threshold networks on the Watts-Strogatz model into three components: gradient, harmonic and curl flows. The harmonic and curl flows represent globally circular and locally circular components, respectively. The Watts-Strogatz model bridges the two extreme network topologies, a lattice network and a random network, by a single parameter that is the probability of random rewiring. The small-world topology is realized within a certain range between them. By numerical simulation we found that as networks become more random the ratio of harmonic flow to the total magnitude of information flow increases whereas the ratio of curl flow decreases. Furthermore, both quantities are significantly enhanced from the level when only network structure is considered for the network close to a random network and a lattice network, respectively. Finally, the sum of these two ratios takes its maximum value within the small-world region. These findings suggest that the dynamical information counterpart of global integration and that of local segregation are the harmonic flow and the curl flow, respectively, and that a part of the small-world region is dominated by internal circulation of information flow.
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spelling pubmed-50391832016-10-12 Hodge Decomposition of Information Flow on Small-World Networks Haruna, Taichi Fujiki, Yuuya Front Neural Circuits Neuroscience We investigate the influence of the small-world topology on the composition of information flow on networks. By appealing to the combinatorial Hodge theory, we decompose information flow generated by random threshold networks on the Watts-Strogatz model into three components: gradient, harmonic and curl flows. The harmonic and curl flows represent globally circular and locally circular components, respectively. The Watts-Strogatz model bridges the two extreme network topologies, a lattice network and a random network, by a single parameter that is the probability of random rewiring. The small-world topology is realized within a certain range between them. By numerical simulation we found that as networks become more random the ratio of harmonic flow to the total magnitude of information flow increases whereas the ratio of curl flow decreases. Furthermore, both quantities are significantly enhanced from the level when only network structure is considered for the network close to a random network and a lattice network, respectively. Finally, the sum of these two ratios takes its maximum value within the small-world region. These findings suggest that the dynamical information counterpart of global integration and that of local segregation are the harmonic flow and the curl flow, respectively, and that a part of the small-world region is dominated by internal circulation of information flow. Frontiers Media S.A. 2016-09-28 /pmc/articles/PMC5039183/ /pubmed/27733817 http://dx.doi.org/10.3389/fncir.2016.00077 Text en Copyright © 2016 Haruna and Fujiki. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Neuroscience
Haruna, Taichi
Fujiki, Yuuya
Hodge Decomposition of Information Flow on Small-World Networks
title Hodge Decomposition of Information Flow on Small-World Networks
title_full Hodge Decomposition of Information Flow on Small-World Networks
title_fullStr Hodge Decomposition of Information Flow on Small-World Networks
title_full_unstemmed Hodge Decomposition of Information Flow on Small-World Networks
title_short Hodge Decomposition of Information Flow on Small-World Networks
title_sort hodge decomposition of information flow on small-world networks
topic Neuroscience
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5039183/
https://www.ncbi.nlm.nih.gov/pubmed/27733817
http://dx.doi.org/10.3389/fncir.2016.00077
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