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Self-organized criticality as a fundamental property of neural systems

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      Abstract

      The neural criticality hypothesis states that the brain may be poised in a critical state at a boundary between different types of dynamics. Theoretical and experimental studies show that critical systems often exhibit optimal computational properties, suggesting the possibility that criticality has been evolutionarily selected as a useful trait for our nervous system. Evidence for criticality has been found in cell cultures, brain slices, and anesthetized animals. Yet, inconsistent results were reported for recordings in awake animals and humans, and current results point to open questions about the exact nature and mechanism of criticality, as well as its functional role. Therefore, the criticality hypothesis has remained a controversial proposition. Here, we provide an account of the mathematical and physical foundations of criticality. In the light of this conceptual framework, we then review and discuss recent experimental studies with the aim of identifying important next steps to be taken and connections to other fields that should be explored.

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      Emergence of scaling in random networks

      Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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        Power-law distributions in empirical data

        Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.
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          Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

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            Author and article information

            Affiliations
            1Computational Neurophysiology Group, Institute for Theoretical Biology, Humboldt Universität zu Berlin Berlin, Germany
            2Bernstein Center for Computational Neuroscience Berlin Berlin, Germany
            3École Normale Supérieure Paris, France
            4Department of Engineering Mathematics, Merchant Venturers School of Engineering, University of Bristol Bristol, UK
            Author notes

            Edited by: Dietmar Plenz, National Institute of Mental Health, NIH, USA

            Reviewed by: Shan Yu, National Institute of Mental Health, USA; Woodrow Shew, University of Arkansas, USA; Hongdian Yang, Johns Hopkins University School of Medicine, USA

            *Correspondence: Janina Hesse, Computational Neurophysiology Group, Institute for Theoretical Biology, Humboldt Universität zu Berlin, Philippstr. 13, Building 4, 10115 Berlin, Germany e-mail: janina.hesse@ 123456bccn-berlin.de

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

            Contributors
            Journal
            Front Syst Neurosci
            Front Syst Neurosci
            Front. Syst. Neurosci.
            Frontiers in Systems Neuroscience
            Frontiers Media S.A.
            1662-5137
            23 September 2014
            2014
            : 8
            4171833
            10.3389/fnsys.2014.00166
            Copyright © 2014 Hesse and Gross.

            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: 4, Tables: 1, Equations: 2, References: 100, Pages: 14, Words: 13466
            Categories
            Neuroscience
            Review Article

            Neurosciences

            neural network, dynamics, phase transition, brain, self-organized criticality

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