title: Avalanches in self-organized critical neural networks: a minimal model for the neural SOC universality class.
abstract: The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.
authors.affiliation: Institut für Theoretische Physik, Universität Bremen, Bremen, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Rybarsch
authors.affiliation: Institut für Theoretische Physik, Universität Bremen, Bremen, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Bornholdt
mesh_terms: D001921:Brain / Q000166:cytology / Q000502:physiology; D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology* / Q000502:physiology*; D009474:Neurons / Q000166:cytology
references.citation: Proc Natl Acad Sci U S A. 2010 Mar 2;107(9):3977-81
references.pmid: 20160107
references.citation: PLoS Comput Biol. 2013;9(3):e1002985
references.pmid: 23555220
references.citation: Phys Rev Lett. 2012 Jun 1;108(22):228703
references.pmid: 23003665
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 1):061917
references.pmid: 20365200
references.citation: J Neurosci. 2011 Jan 5;31(1):55-63
references.pmid: 21209189
references.citation: Phys Rev Lett. 2000 Jun 26;84(26 Pt 1):6114-7
references.pmid: 10991137
references.citation: J Neurosci. 2004 Jun 2;24(22):5216-29
references.pmid: 15175392
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6 Pt 2):066118
references.pmid: 16241315
references.citation: Phys Rev Lett. 2009 Jun 26;102(25):258102
references.pmid: 19659122
references.citation: Nature. 2001 Mar 8;410(6825):242-50
references.pmid: 11258379
references.citation: Phys Rev Lett. 1995 Aug 7;75(6):1222-1225
references.pmid: 10060236
references.citation: J Neurosci. 2009 Dec 9;29(49):15595-600
references.pmid: 20007483
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 2):016107
references.pmid: 17677533
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Dec;66(6 Pt 2):066137
references.pmid: 12513377
references.citation: PLoS One. 2013 Jun 20;8(6):e64162
references.pmid: 23840301
references.citation: Phys Rev A Gen Phys. 1988 Jul 1;38(1):364-374
references.pmid: 9900174
references.citation: Phys Rev Lett. 2012 May 18;108(20):208102
references.pmid: 23003192
references.citation: Proc Natl Acad Sci U S A. 2009 Sep 15;106(37):15921-6
references.pmid: 19717463
references.citation: Phys Rev Lett. 2009 Mar 20;102(11):118110
references.pmid: 19392248
references.citation: J R Soc Interface. 2013 Jan 6;10(78):20120558
references.pmid: 22977096
references.citation: Phys Rev Lett. 2006 Jan 20;96(2):028107
references.pmid: 16486652
references.citation: Neuroscience. 2008 Jun 2;153(4):1354-69
references.pmid: 18448256
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 2):026114
references.pmid: 23005832
references.citation: J Neurosci Methods. 2008 Apr 30;169(2):405-16
references.pmid: 18082894
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3 Pt 1):031912
references.pmid: 11308683
references.citation: PLoS One. 2007 May 09;2(5):e439
references.pmid: 17502919
references.citation: Proc Natl Acad Sci U S A. 2008 May 27;105(21):7576-81
references.pmid: 18499802
references.citation: J Neurosci. 2003 Dec 3;23(35):11167-77
references.pmid: 14657176
references.citation: Front Physiol. 2012 Mar 28;3:62
references.pmid: 22470347
references.citation: J Neurosci. 2012 Jan 18;32(3):1061-72
references.pmid: 22262904