Stochastic synchronization in finite size spiking networks.

We study a stochastic synchronization of spiking activity in feedforward networks of integrate-and-fire model neurons. A stochastic mean field analysis shows that synchronization occurs only when the network size is sufficiently small. This gives evidence that the dynamics, and hence processing, of finite size populations can be drastically different from that observed in the infinite size limit. Our results agree with experimentally observed synchrony in cortical networks, and further strengthen the link between synchrony and propagation in cortical systems.

[1]  A. Burkitt,et al.  Shot noise in the leaky integrate-and-fire neuron. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[3]  H. Risken,et al.  The Fokker-Planck Equation: Methods of Solution and Application, 2nd ed. , 1991 .

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

[5]  Tomoki Fukai,et al.  Fokker-Planck approach to the pulse packet propagation in synfire chain , 2001, Neural Networks.

[6]  A. Reyes.  Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro , 2003, Nature Neuroscience.

[7]  Maurizio Mattia,et al.  Collective Behavior of Networks with Linear (VLSI) Integrate-and-Fire Neurons , 1999, Neural Computation.

[8]  Mark C. W. van Rossum,et al.  Fast Propagation of Firing Rates through Layered Networks of Noisy Neurons , 2002, The Journal of Neuroscience.

[9]  Lutz Schimansky-Geier,et al.  Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Idan Segev,et al.  On the Transmission of Rate Code in Long Feedforward Networks with Excitatory–Inhibitory Balance , 2003, The Journal of Neuroscience.

[11]  A. Reyes,et al.  Relation between single neuron and population spiking statistics and effects on network activity. , 2006, Physical review letters.

[12]  A. Grinvald,et al.  Linking spontaneous activity of single cortical neurons and the underlying functional architecture. , 1999, Science.

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

[14]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[15]  Feng Liu,et al.  Propagation of firing rate in a feed-forward neuronal network. , 2006, Physical review letters.

[16]  Kazuyuki Aihara,et al.  Bridging rate coding and temporal spike coding by effect of noise. , 2002, Physical review letters.

[17]  Bruce W. Knight,et al.  Dynamics of Encoding in Neuron Populations: Some General Mathematical Features , 2000, Neural Computation.

[18]  Maurizio Mattia,et al.  Finite-size dynamics of inhibitory and excitatory interacting spiking neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.

[20]  M. Draganu.  THE FOKKER-PLANCK EQUATION OF A PLASMA , 1960 .

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

[22]  M. Mattia,et al.  Population dynamics of interacting spiking neurons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  R. Segev,et al.  Long term behavior of lithographically prepared in vitro neuronal networks. , 2002, Physical review letters.

[24]  Hideo Hasegawa,et al.  Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[26]  Frances S. Chance,et al.  Effects of synaptic noise and filtering on the frequency response of spiking neurons. , 2001, Physical review letters.

[27]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[28]  N. Parga,et al.  Response of spiking neurons to correlated inputs. , 2002, Physical review letters.