Synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled Langevin model.

The synchrony and variability of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise are discussed. We have employed numerical simulations and the analytical augmented-moment method, which is the second-order moment method for local and global variables [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)]. It has been shown that the synchrony of an ensemble is increased (decreased) by a positive (negative) spatial correlation in both additive and multiplicative noise. Although the variability for local fluctuations is almost insensitive to spatial correlations, that for global fluctuations is increased (decreased) by positive (negative) correlations. When a pulse input is applied, the synchrony is increased for the correlated multiplicative noise, whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise. An application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals, which accounts for some neuronal experiments.

[1]  Hideo Hasegawa.  Generalized rate-code model for neuron ensembles with finite populations. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Jianfeng Feng,et al.  Impact of Correlated Inputs on the Output of the Integrate-and-Fire Model , 2000, Neural Computation.

[3]  Wulfram Gerstner,et al.  From spiking neurons to rate models: a cascade model as an approximation to spiking neuron models with refractoriness. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[5]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[6]  Eric Shea-Brown,et al.  Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding. , 2008, Physical review letters.

[7]  Celia Anteneodo,et al.  Multiplicative noise: A mechanism leading to nonextensive statistical mechanics , 2002 .

[8]  Stan C. A. M. Gielen,et al.  Correlation Between Uncoupled Conductance-Based Integrate-and-Fire Neurons Due to Common and Synchronous Presynaptic Firing , 2001, Neural Computation.

[9]  Si Wu,et al.  Information processing in a neuron ensemble with the multiplicative correlation structure , 2004, Neural Networks.

[10]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[11]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[12]  Jaime de la Rocha,et al.  Supplementary Information for the article ‘ Correlation between neural spike trains increases with firing rate ’ , 2007 .

[13]  Christian W. Eurich,et al.  On the functional role of noise correlations in the nervous system , 2002, Neurocomputing.

[14]  L Schimansky-Geier,et al.  Transmission of noise coded versus additive signals through a neuronal ensemble. , 2001, Physical review letters.

[15]  J García-Ojalvo,et al.  Noise-induced phase separation: mean-field results. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  H. Hasegawa.  Information Conveyed by Neuron Populations: Firing Rate, Fluctuation and Synchrony , 2008 .

[17]  Jianfeng Feng,et al.  Behavior of integrate-and-fire and Hodgkin-Huxley models with correlated inputs. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise , 2001, cond-mat/0108393.

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

[20]  F Liu,et al.  Effects of correlated and independent noise on signal processing in neuronal systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Brent Doiron,et al.  Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Stefan Rotter,et al.  Correlated input spike trains and their effects on the response of the leaky integrate-and-fire neuron , 2002, Neurocomputing.

[23]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[24]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[25]  Constantino Tsallis,et al.  What should a statistical mechanics satisfy to reflect nature , 2004, cond-mat/0403012.

[26]  Hang-Hyun Jo,et al.  Effect of spatially correlated noise on coherence resonance in a network of excitable cells. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Anthony N. Burkitt,et al.  A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input , 2006, Biological Cybernetics.

[28]  Masato Okada,et al.  Higher order effects on rate reduction for networks of hodgkin-huxley neurons , 2007 .

[29]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[30]  Anthony N. Burkitt,et al.  A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties , 2006, Biological Cybernetics.

[31]  Oren Shriki,et al.  Rate Models for Conductance-Based Cortical Neuronal Networks , 2003, Neural Computation.

[32]  Bard Ermentrout,et al.  Reduction of Conductance-Based Models with Slow Synapses to Neural Nets , 1994, Neural Computation.

[33]  H. Hasegawa.  Effects of correlated variability on information entropies in nonextensive systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Pieter R. Roelfsema,et al.  The Effects of Pair-wise and Higher-order Correlations on the Firing Rate of a Postsynaptic Neuron , 1998, Neural Computation.

[35]  Alexa Riehle,et al.  Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time , 2003, Biological Cybernetics.

[36]  Jakob Heinzle,et al.  Modulation of synchrony without changes in firing rates , 2007, Cognitive Neurodynamics.

[37]  Hideo Hasegawa,et al.  Stationary and dynamical properties of information entropies in nonextensive systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[39]  A. Pouget,et al.  Neural correlations, population coding and computation , 2006, Nature Reviews Neuroscience.

[40]  Xiao-Jing Wang,et al.  Mean-Driven and Fluctuation-Driven Persistent Activity in Recurrent Networks , 2007, Neural Computation.

[41]  Anthony N. Burkitt,et al.  Analysis of Integrate-and-Fire Neurons: Synchronization of Synaptic Input and Spike Output , 1999, Neural Computation.

[42]  W. Rüemelin.  Numerical Treatment of Stochastic Differential Equations , 1982 .

[43]  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.

[44]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[45]  Paul H. E. Tiesinga,et al.  Rapid Temporal Modulation of Synchrony by Competition in Cortical Interneuron Networks , 2004, Neural Computation.

[46]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[47]  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.

[48]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[49]  Hideo Hasegawa.  Stationary and dynamical properties of finite N-unit Langevin models subjected to multiplicative noises , 2007 .

[50]  Peter Dayan,et al.  The Effect of Correlated Variability on the Accuracy of a Population Code , 1999, Neural Computation.

[51]  Hideo Hasegawa.  N-Dependent Multiplicative-Noise Contributions in Finite N-Unit Langevin Models: Augmented Moment Approach , 2006 .

[52]  K. Hoffmann,et al.  Synchronization of Neuronal Activity during Stimulus Expectation in a Direction Discrimination Task , 1997, The Journal of Neuroscience.

[53]  Karl J. Friston,et al.  The Relationship Between Synchronization Among Neuronal Populations and Their Mean Activity Levels , 1999, Neural Computation.

[54]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[55]  Roy,et al.  Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise. , 1988, Physical review. A, General physics.

[56]  Feng Liu,et al.  Impact of spatially correlated noise on neuronal firing. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  C. Tsallis,et al.  The role of constraints within generalized nonextensive statistics , 1998 .

[58]  Brent Doiron,et al.  Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus. , 2004, Physical review letters.