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Spike avalanches in vivo suggest a driven, slightly subcritical brain state

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      Abstract

      In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.

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      The renormalization group: Critical phenomena and the Kondo problem

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        Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series.

        The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.
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          Crackling Noise

          Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behavior over many decades of sizes, their behavior is likely independent of microscopic and macroscopic details, and progress can be made by the use of very simple models. The fact that simple models and real systems can share the same behavior on a wide range of scales is called universality. We illustrate these ideas using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses. This field is still developing: we describe a number of continuing challenges.
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            Author and article information

            Affiliations
            1Department of Non-linear Dynamics, Max Planck Institute for Dynamics and Self-Organization Göttingen, Germany
            2Bernstein Center for Computational Neuroscience Göttingen, Germany
            3Frankfurt Institute for Advanced Studies Frankfurt, Germany
            4Department of Neurophysiology, Max Planck Institute for Brain Research Frankfurt, Germany
            5Magnetoencephalography Unit, Brain Imaging Center, Johann Wolfgang Goethe University Frankfurt, Germany
            6Ernst Strüngmann Institute for Neuroscience in Cooperation with Max Planck Society Frankfurt, Germany
            7Department of Biomedical Engineering, University of Los Andes Bogotá, Colombia
            8Neural Information Processing Group, Department of Software Engineering and Theoretical Computer Science, TU Berlin Berlin, Germany
            9Bernstein Center for Computational Neuroscience Berlin, Germany
            10Centre de Recherche de l’Institut du Cerveau et de la Moelle épinière, Hôpital de la Pitié-Salpêtrière, INSERM UMRS 975—CNRS UMR 7225-UPMC Paris, France
            11Department of Psychology, Faculty of Humanities and Social Sciences, University of Zagreb Zagreb, Croatia
            12Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics Tübingen, Germany
            Author notes

            Edited by: Valentina Pasquale, Fondazione Istituto Italiano di Tecnologia, Italy

            Reviewed by: John M. Beggs, Indiana University, USA; Mauro Copelli, Federal University of Pernambuco, Brazil; Silvia Scarpetta, University of Salerno, Italy; Miguel Angel Muñoz, Universidad de Granada, Spain

            *Correspondence: Viola Priesemann, Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany e-mail: v.priesemann@ 123456gmx.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
            24 June 2014
            2014
            : 8
            4068003
            10.3389/fnsys.2014.00108
            Copyright © 2014 Priesemann, Wibral, Valderrama, Pröpper, Le Van Quyen, Geisel, Triesch, Nikolić and Munk.

            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: 5, References: 90, Pages: 17, Words: 15282
            Categories
            Neuroscience
            Original Research Article

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