Critical branching captures activity in living neural networks and maximizes the number of metastable States.

Recent experimental work has shown that activity in living neural networks can propagate as a critical branching process that revisits many metastable states. Neural network theory suggests that attracting states could store information, but little is known about how a branching process could form such states. Here we use a branching process to model actual data and to explore metastable states in the network. When we tune the branching parameter to the critical point, we find that metastable states are most numerous and that network dynamics are not attracting, but neutral.

[1]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[2]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[3]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[4]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[5]  B. Derrida,et al.  Evolution of overlaps between configurations in random Boolean networks , 1986 .

[6]  B. Derrida,et al.  Random networks of automata: a simple annealed approximation , 1986 .

[7]  Daniel J. Amit,et al.  Modeling brain function: the world of attractor neural networks, 1st Edition , 1989 .

[8]  Ichiro Tsuda,et al.  Dynamic link of memory--Chaotic memory map in nonequilibrium neural networks , 1992, Neural Networks.

[9]  J. Hopfield,et al.  Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements. , 1995, Physical review letters.

[10]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[11]  Paczuski,et al.  Avalanche dynamics in evolution, growth, and depinning models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  S. Martinoia,et al.  Analysis of the signals generated by networks of neurons coupled to planar arrays of microtransducers in simulated experiments. , 1998, Biosensors & bioelectronics.

[13]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[14]  B J Richmond,et al.  Stochastic nature of precisely timed spike patterns in visual system neuronal responses. , 1999, Journal of neurophysiology.

[15]  Ing Ren Tsang,et al.  Cluster size diversity, percolation, and complex systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Yasuhiko Jimbo,et al.  The dynamics of a neuronal culture of dissociated cortical neurons of neonatal rats , 2000, Biological Cybernetics.

[17]  T. Sejnowski,et al.  Origin of slow cortical oscillations in deafferented cortical slabs. , 2000, Cerebral cortex.

[18]  P. Bak,et al.  Adaptive learning by extremal dynamics and negative feedback. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  K. Abbink,et al.  24 , 1871, You Can Cross the Massacre on Foot.

[20]  J. M. Herrmann,et al.  Finite-size effects of avalanche dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[22]  S. Bornholdt,et al.  Self-organized critical neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[24]  Nils Bertschinger,et al.  Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks , 2004, Neural Computation.

[25]  Yuji Ikegaya,et al.  Synfire Chains and Cortical Songs: Temporal Modules of Cortical Activity , 2004, Science.

[26]  R. Segev,et al.  Hidden neuronal correlations in cultured networks. , 2004, Physical review letters.

[27]  John M. Beggs,et al.  Behavioral / Systems / Cognitive Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures , 2004 .

[28]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .