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Hierarchical organization of multiscale communities in brain networks is non-tree structured

Hierarchical organization of multiscale communities in brain networks is non-tree structured Okamoto BMC Neuroscience 2015, 16(Suppl 1):P187 http://www.biomedcentral.com/1471-2202/16/S1/P187 POSTER PRESENTATION Open Access Hierarchical organization of multiscale communities in brain networks is non-tree structured 1,2 Hiroshi Okamoto From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 In literature of network science, a group of nodes that community (parent), thus leading to a hierarchical orga- are densely connected within the group and are less nization of multiscale communities. connected with nodes outside the group is referred to as Applying this method to the neuronal network of C. a “community” [1]. Community structure is a funda- elegans [4] and the macaque cortical network [5], we have found that hierarchical organization of multiscale mental property of a variety of social, biological and engineering networks. Specifically, communities in brain communities in these networks is non-tree structured: networks are considered to be associated with functional Some child communities have more than one parent modules of information processing in the brain [2]. To community (Figure 1). These findings suggest efficient reveal information processing architecture of the brain, architecture for integration of functional modules in therefore, it is pivotal to know individual communities brain information processing: The same functional mod- and their organization in brain networks. ules at lower levels can be shared by distinct functional Community structure in brain networks is character- modules at higher levels. ized by hierarchical organization, which reflects that functional modules at larger scales are built up from a Acknowledgements set of functional modules at smaller scales [3]. A num- This work was partly supported by JSPS KAKENHI Grant Number 23500379. ber of mathematical methods for detecting communities Authors’ details in networks have been developed so far [1], but unfortu- 1 2 RIKEN Brain Science Institute, Saitama, 351-0198, Japan. Research & nately few of them can consistently deal with hierarchi- Development Group, Fuji Xerox Co. Ltd., Kanagawa, 220-8668, Japan. cal organization of multiscale communities. Here we Published: 18 December 2015 propose a reliable method for detecting hierarchical organization of multiscale communities. Then we exam- References ine community structure of real brain networks by use 1. Newman MEJ: Communities, modules and large-scale structure in of this method. networks. Nature Phys 2012, 8:25-31. 2. Bullmore E, Sporns O: Complex brain networks: graph theoretical analysis The proposed method is based on a novel Bayesian of structural and functional systems. Nature Rev Neurosci 2009, formulation of Markov chain. The method has only one 10(3):186-198. parameter, , which comes from the precision of the 3. Meunier D, Lambiotte R, Bullmore ET : Modular and hierarchically modular organization of brain networks. Front Neurosci 2010, 4:1-11. prior distribution of a random process. The amplitude 4. Watts DJ, Strogatz SH: Collective dynamics of “small-world” networks. of controls the resolution of community detection; the Nature 1998, 393:440-442. smaller its amplitude, the finer the size of detected com- 5. CoCoMac. [http://cocomac.g-node.org/]. munities. Quasi-static increase in causes a series of dis- doi:10.1186/1471-2202-16-S1-P187 crete phase transitions; at each transition point a subset Cite this article as: Okamoto: Hierarchical organization of multiscale communities in brain networks is non-tree structured. BMC Neuroscience of smaller communities (children) agglomerate a larger 2015 16(Suppl 1):P187. Correspondence: hiroshi.okamoto@fujixerox.co.jp RIKEN Brain Science Institute, Saitama, 351-0198, Japan Full list of author information is available at the end of the article © 2015 Okamoto This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Okamoto BMC Neuroscience 2015, 16(Suppl 1):P187 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/P187 Figure 1 Hierarchical organization of communities in the neuronal network of C. elegans.Eachlayer ofthehierarchyis shownby horizontal alignment of red squares. Each square indicates a community detected at each layer. The size of each square indicates the size of the corresponding community. Note that many communities have more than one link from the upper layer, which means that these communities have more than one parent. These demonstrate non-tree structure of hierarchical organization of communities in the brain network. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BMC Neuroscience Springer Journals

Hierarchical organization of multiscale communities in brain networks is non-tree structured

BMC Neuroscience , Volume 16 (1) – Dec 18, 2015

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References (4)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Okamoto
Subject
Biomedicine; Neurosciences; Neurobiology; Animal Models
eISSN
1471-2202
DOI
10.1186/1471-2202-16-S1-P187
Publisher site
See Article on Publisher Site

Abstract

Okamoto BMC Neuroscience 2015, 16(Suppl 1):P187 http://www.biomedcentral.com/1471-2202/16/S1/P187 POSTER PRESENTATION Open Access Hierarchical organization of multiscale communities in brain networks is non-tree structured 1,2 Hiroshi Okamoto From 24th Annual Computational Neuroscience Meeting: CNS*2015 Prague, Czech Republic. 18-23 July 2015 In literature of network science, a group of nodes that community (parent), thus leading to a hierarchical orga- are densely connected within the group and are less nization of multiscale communities. connected with nodes outside the group is referred to as Applying this method to the neuronal network of C. a “community” [1]. Community structure is a funda- elegans [4] and the macaque cortical network [5], we have found that hierarchical organization of multiscale mental property of a variety of social, biological and engineering networks. Specifically, communities in brain communities in these networks is non-tree structured: networks are considered to be associated with functional Some child communities have more than one parent modules of information processing in the brain [2]. To community (Figure 1). These findings suggest efficient reveal information processing architecture of the brain, architecture for integration of functional modules in therefore, it is pivotal to know individual communities brain information processing: The same functional mod- and their organization in brain networks. ules at lower levels can be shared by distinct functional Community structure in brain networks is character- modules at higher levels. ized by hierarchical organization, which reflects that functional modules at larger scales are built up from a Acknowledgements set of functional modules at smaller scales [3]. A num- This work was partly supported by JSPS KAKENHI Grant Number 23500379. ber of mathematical methods for detecting communities Authors’ details in networks have been developed so far [1], but unfortu- 1 2 RIKEN Brain Science Institute, Saitama, 351-0198, Japan. Research & nately few of them can consistently deal with hierarchi- Development Group, Fuji Xerox Co. Ltd., Kanagawa, 220-8668, Japan. cal organization of multiscale communities. Here we Published: 18 December 2015 propose a reliable method for detecting hierarchical organization of multiscale communities. Then we exam- References ine community structure of real brain networks by use 1. Newman MEJ: Communities, modules and large-scale structure in of this method. networks. Nature Phys 2012, 8:25-31. 2. Bullmore E, Sporns O: Complex brain networks: graph theoretical analysis The proposed method is based on a novel Bayesian of structural and functional systems. Nature Rev Neurosci 2009, formulation of Markov chain. The method has only one 10(3):186-198. parameter, , which comes from the precision of the 3. Meunier D, Lambiotte R, Bullmore ET : Modular and hierarchically modular organization of brain networks. Front Neurosci 2010, 4:1-11. prior distribution of a random process. The amplitude 4. Watts DJ, Strogatz SH: Collective dynamics of “small-world” networks. of controls the resolution of community detection; the Nature 1998, 393:440-442. smaller its amplitude, the finer the size of detected com- 5. CoCoMac. [http://cocomac.g-node.org/]. munities. Quasi-static increase in causes a series of dis- doi:10.1186/1471-2202-16-S1-P187 crete phase transitions; at each transition point a subset Cite this article as: Okamoto: Hierarchical organization of multiscale communities in brain networks is non-tree structured. BMC Neuroscience of smaller communities (children) agglomerate a larger 2015 16(Suppl 1):P187. Correspondence: hiroshi.okamoto@fujixerox.co.jp RIKEN Brain Science Institute, Saitama, 351-0198, Japan Full list of author information is available at the end of the article © 2015 Okamoto This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/ zero/1.0/) applies to the data made available in this article, unless otherwise stated. Okamoto BMC Neuroscience 2015, 16(Suppl 1):P187 Page 2 of 2 http://www.biomedcentral.com/1471-2202/16/S1/P187 Figure 1 Hierarchical organization of communities in the neuronal network of C. elegans.Eachlayer ofthehierarchyis shownby horizontal alignment of red squares. Each square indicates a community detected at each layer. The size of each square indicates the size of the corresponding community. Note that many communities have more than one link from the upper layer, which means that these communities have more than one parent. These demonstrate non-tree structure of hierarchical organization of communities in the brain network.

Journal

BMC NeuroscienceSpringer Journals

Published: Dec 18, 2015

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