×

Complexity matching in neural networks. (English) Zbl 1452.92003

Summary: In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition, but with consensus that criticality makes the brain very sensitive to external stimuli. We adopt the complexity matching principle that the maximal efficiency of communication between two complex networks is realized when both of them are at criticality. We use this principle to establish the value of the neuronal interaction strength at which criticality occurs, yielding a perfect agreement with the adoption of temporal complexity as criticality indicator. The emergence of a scale-free distribution of avalanche size is proved to occur in a supercritical regime. We use an integrate-and-fire model where the randomness of each neuron is only due to the random choice of a new initial condition after firing. The new model shares with that proposed by Izikevich the property of generating excessive periodicity, and with it the annihilation of temporal complexity at supercritical values of the interaction strength. We find that the concentration of inhibitory links can be used as a control parameter and that for a sufficiently large concentration of inhibitory links criticality is recovered again. Finally, we show that the response of a neural network at criticality to a harmonic stimulus is very weak, in accordance with the complexity matching principle.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
92C20 Neural biology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ali M M, Sellers K K and Fröhlich F 2013 Transcranial alternating current stimulation modulates large-scale cortical network activity by network resonance J. Neurosci.33 11262-75 · doi:10.1523/JNEUROSCI.5867-12.2013
[2] Allegrini P, Menicucci D, Bedini R, Fronzoni L, Gemignani A, Grigolini P, West B J and Paradisi P 2009 Spontaneous brain activity as a source of ideal 1/f noise Phys. Rev. E 80 061914 · doi:10.1103/PhysRevE.80.061914
[3] Pais-Vieira M, Lebedev M, Kunicki C, Wang J and Nicolelis M A L 2013 A brain-to-brain interface for real-time sharing of sensorimotor information Sci. Rep.3 1319 · doi:10.1038/srep01319
[4] Marmelat V and Deligniéres D 2012 Strong anticipation: complexity matching in interpersonal coordination Exp. Brain Res.222 137-48 · doi:10.1007/s00221-012-3202-9
[5] West B J and Grigolini P 2010 The living matter way to exchange information Med. Hypotheses75 475-8 · doi:10.1016/j.mehy.2010.04.028
[6] Aquino G, Bologna M, Grigolini P and West B J 2010 Beyond the death of linear response: 1/f optimal information transport Phys. Rev. Lett.105 040601 · doi:10.1103/PhysRevLett.105.040601
[7] Lukovic M and Grigolini P 2008 Power spectra for both interrupted and perennial aging processes J. Chem. Phys.129 184102 · doi:10.1063/1.3006051
[8] Bianco S, Grigolini P and Paradisi P 2005 Fluorescence intermittency in blinking quantum dots: renewal or slow modulation? J. Chem. Phys.123 174704 · doi:10.1063/1.2102903
[9] Bianco S, Geneston E, Grigolini P and Ignaccolo M 2008 Renewal aging as emerging property of phase synchronization Physica A 387 1387-92 · doi:10.1016/j.physa.2007.10.045
[10] Zare M and Grigolini P 2012 Cooperation in neural systems: bridging complexity and periodicity Phys. Rev. E 86 051918 · doi:10.1103/PhysRevE.86.051918
[11] Turalska M, Lukovic M, West B J and Grigolini P 2009 Complexity and synchronization Phys. Rev. E 80 021110 · doi:10.1103/PhysRevE.80.021110
[12] Luković M, Vanni F, Svenkeson A and Grigolini P 2014 Transmission of information at criticality Physica A 416 430-8 · doi:10.1016/j.physa.2014.08.066
[13] Haimovici A, Tagliazucchi E, Balenzuela P and Chialvo D R 2013 Brain organization into resting state networks emerges at criticality on a model of the human connectome Phys. Rev. Lett.110 178101 · doi:10.1103/PhysRevLett.110.178101
[14] Plenz D 2013 The critical brain Physics6 47 · doi:10.1103/Physics.6.47
[15] Plenz D and Niebur E 2014 Criticality in Neural Systems (New York: Wiley) · Zbl 1286.92008 · doi:10.1002/9783527651009
[16] Larremore D B, Shew W L, Ott E, Sorrentino F and Restrepo J 2014 Inhibition causes ceaseless dynamics in networks of excitable nodes Phys. Rev. Lett.112 138103 · doi:10.1103/PhysRevLett.112.138103
[17] Chialvo D 2010 Emergent complex neural dynamics Nat. Phys.6 744-50 · doi:10.1038/nphys1803
[18] Turalska M, Geneston E, West B J, Allegrini P and Grigolini P 2012 Cooperation-induced topological complexity: a promising road to fault tolerance and Hebbian learning Frontiers Physiol.3 52 · doi:10.3389/fphys.2012.00052
[19] Lovecchio E, Allegrini P, Geneston E, West B J and Grigolini P 2012 From self-organized to extended criticality Frontiers Physiol.3 1-9 · doi:10.3389/fphys.2012.00098
[20] Zare M and Grigolini P 2013 Criticality avalanches neural network Chaos Solitons Fractals55 80-94 · Zbl 1355.82036 · doi:10.1016/j.chaos.2013.05.009
[21] Politi A and Luccioli S 2010 Dynamics of networks of leaky-integrate-and-fire neurons Network Science ed E Estrada, M Fox, D J Higham and G-L Oppo (Berlin: Springer) · doi:10.1007/978-1-84996-396-1_11
[22] Jahnke S, Memmesheimer R M and Timme M 2008 Stable irregular dynamics in complex neural networks Phys. Rev. Lett.100 048102 · doi:10.1103/PhysRevLett.100.048102
[23] Zillmer R, Brunel N and Hansel D 2009 Very long transients, irregular firing, and chaotic dynamics in networks of randomly connected inhibitory integrate-and- fire neurons Phys. Rev. E 79 031909 · doi:10.1103/PhysRevE.79.031909
[24] Mirollo R E and Strogatz S H 1990 Synchronization of pulse-coupled biological oscillators SIAM J. Appl. Math.50 1645-62 · Zbl 0712.92006 · doi:10.1137/0150098
[25] Izhikevich E M 2003 Simple model of spiking neurons IEEE Trans. Neural Netw.14 1569-72 · doi:10.1109/TNN.2003.820440
[26] Eurich C W, Herrmann J M and Ernst U A 2002 Finite-size effects of avalanche dynamics Phys. Rev. E 66 1-15 · doi:10.1103/PhysRevE.66.066137
[27] Metzler R and Klafter J 2002 From stretched exponential to inverse power-law: fractional dynamics, cole – cole relaxation processes, and beyond J. Non-Cryst. Solids305 81-87 · doi:10.1016/S0022-3093(02)01124-9
[28] Pramukkul P, Svenkeson A and Grigolini P 2014 Effect of noise and detector sensitivity on a dynamical process: inverse power law and Mittag-Leffler interevent time survival probabilities Phys. Rev. E 89 022107 · doi:10.1103/PhysRevE.89.022107
[29] Podlubny I and Kacenak M 2005 Mittag-Leffler function-calculates the Mittag-Leffler function with desired accuracy, MATLAB Central File Exchange, File ID 8738, mlf.m 2005, File: http://www.mathworks.com/matlabcentral/fileexchange
[30] Fulger D, Scalas E and Germano Monte G 2008 Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation Phys. Rev. E 77 021122 · doi:10.1103/PhysRevE.77.021122
[31] Vanni F, Luković M and Grigolini P 2011 Criticality and transmission of information in a swarm of cooperative units Phys. Rev. Lett.107 078103 · doi:10.1103/PhysRevLett.107.078103
[32] Werner G 2013 Consciousness viewed in the framework of brain phase space dynamics, criticality, and the renormalization group Chaos Solitons Fractals55 3-12 · doi:10.1016/j.chaos.2012.03.014
[33] Bak P 1997 How Nature Works (Oxford: Oxford University Press)
[34] Jensen H J 1998 Self-Organized Criticality (Cambridge: Cambridge University Press) · Zbl 0945.70001 · doi:10.1017/CBO9780511622717
[35] Levina A, Herrmann J M and Geisel T 2007 Dynamical synapses causing self-organized criticality in neural networks Nat. Phys.3 857-60 · doi:10.1038/nphys758
[36] Lo C-C, Bartsch R P and Ivanov P C 2013 Asymmetry and basic pathways in sleep-stage transition Europhys. Lett.102 10008 · doi:10.1209/0295-5075/102/10008
[37] Lo C-C, Amaral L A N, Havlin S, Ivanov P Ch, Penzel T, Peter J-H and Stanley H E 2002 Dynamics of sleep – wake transitions during sleep Europhys. Lett.57 625-31 · doi:10.1209/epl/i2002-00508-7
[38] Lo C-C, Chou T, Penzel T, Scammell T E, Strecker R E, Stanley H E and Ivanov P C 2004 Common scale-invariant patterns of sleep – wake transitions across mammalian species Proc. Natl. Acad. Sci.101 17545-48 · doi:10.1073/pnas.0408242101
[39] Allegrini P, Paradisi P, Menicucci D, Laurino M, Bedini R, Piarulli A and Gemignani A 2013 Sleep unconsciousness and breakdown of serial critical intermittency: new vistas on the global workspace Chaos Solitons Fractals55 32-43 · doi:10.1016/j.chaos.2013.05.019
[40] Allegrini P, Paradisi P, Menicucci D, Laurino M, Piarulli A and Gemignani A What falling asleep tells us about brain criticality: suggestions for the physics of consciousness (unpublished work)
[41] Ivanov P Ch, Amaral L A N, Goldberger A L and Stanley H E 1998 Stochastic feedback and the regulation of biological rhythms Europhys. Lett.43 363-68 · doi:10.1209/epl/i1998-00366-3
[42] Longo G and Montévil M 2013 Extended criticality, phase spaces and enablement in biology Chaos Solitons Fractals55 64-79 · doi:10.1016/j.chaos.2013.03.008
[43] Longo G and Montévil M 2014 Perspectives on Organisms: Biological Time, Symmetries and Singularities(Lecture Notes in Morphogenesis) (Berlin: Springer) · doi:10.1007/978-3-642-35938-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.