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Homeostatic structural plasticity increases the efficiency of small-world networks

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      Abstract

      In networks with small-world topology, which are characterized by a high clustering coefficient and a short characteristic path length, information can be transmitted efficiently and at relatively low costs. The brain is composed of small-world networks, and evolution may have optimized brain connectivity for efficient information processing. Despite many studies on the impact of topology on information processing in neuronal networks, little is known about the development of network topology and the emergence of efficient small-world networks. We investigated how a simple growth process that favors short-range connections over long-range connections in combination with a synapse formation rule that generates homeostasis in post-synaptic firing rates shapes neuronal network topology. Interestingly, we found that small-world networks benefited from homeostasis by an increase in efficiency, defined as the averaged inverse of the shortest paths through the network. Efficiency particularly increased as small-world networks approached the desired level of electrical activity. Ultimately, homeostatic small-world networks became almost as efficient as random networks. The increase in efficiency was caused by the emergent property of the homeostatic growth process that neurons started forming more long-range connections, albeit at a low rate, when their electrical activity was close to the homeostatic set-point. Although global network topology continued to change when neuronal activities were around the homeostatic equilibrium, the small-world property of the network was maintained over the entire course of development. Our results may help understand how complex systems such as the brain could set up an efficient network topology in a self-organizing manner. Insights from our work may also lead to novel techniques for constructing large-scale neuronal networks by self-organization.

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      Collective dynamics of 'small-world' networks.

      Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
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        Complex network measures of brain connectivity: uses and interpretations.

        Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis-a new multidisciplinary approach to the study of complex systems-aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets. Copyright (c) 2009 Elsevier Inc. All rights reserved.
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          Efficient Behavior of Small-World Networks

          We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative a nalysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.
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            Author and article information

            Affiliations
            1Simulation Lab Neuroscience, Bernstein Facility for Simulation and Database Technology, Institute for Advanced Simulation, Jülich Aachen Research Alliance, Forschungszentrum Jülich Jülich, Germany
            2Student of the Medical Faculty, University of Freiburg Freiburg, Germany
            3Department of Integrative Neurophysiology, VU University Amsterdam Amsterdam, Netherlands
            Author notes

            Edited by: Christian Tetzlaff, Georg-August University, Germany

            Reviewed by: Kurt Gottmann, University of Duesseldorf, Germany; Michael Fauth, Georg-August Universität Göttingen, Germany

            *Correspondence: Markus Butz, Simulation Lab Neuroscience, Bernstein Facility for Simulation and Database Technology, Institute for Advanced Simulation, Jülich Aachen Research Alliance, Forschungszentrum Jülich GmbH, JSC, 52425 Jülich, Germany e-mail: m.butz@ 123456fz-juelich.de

            This article was submitted to the journal Frontiers in Synaptic Neuroscience.

            Contributors
            Journal
            Front Synaptic Neurosci
            Front Synaptic Neurosci
            Front. Synaptic Neurosci.
            Frontiers in Synaptic Neuroscience
            Frontiers Media S.A.
            1663-3563
            01 April 2014
            2014
            : 6
            24744727
            3978244
            10.3389/fnsyn.2014.00007
            Copyright © 2014 Butz, Steenbuck and van Ooyen.

            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.

            Counts
            Figures: 11, Tables: 0, Equations: 18, References: 74, Pages: 14, Words: 11778
            Categories
            Neuroscience
            Original Research Article

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