The Wilson–Cowan model, 36 years later

The Wilson–Cowan model of interacting neurons (1973) is one of the most influential papers published in Biological Cybernetics (Kybernetik). This paper and a companion paper published in 1972 have been cited over 1000 times. Rather than focus on the microscopic properties of neurons, Wilson and Cowan analyzed the collective properties of large numbers of neurons using methods from statistical mechanics, based on the mean-field approach. New experimental techniques to measure neuronal activity at the level of large populations are now available to test these models, including optical recording of brain activity with intrinsic signals and voltage sensitive dyes, and new methods for analyzing EEG and MEG. These measurement techniques have revealed patterns of coherent activity that span centimetres of tissue in the cerebral cortex. Here the underlying ideas are reviewed in a historic context.

[1]  J. Leo van Hemmen,et al.  Continuum limit of discrete neuronal structures: is cortical tissue an “excitable” medium? , 2004, Biological Cybernetics.

[2]  Alexander Lerchner,et al.  Mean Field Methods for Cortical Network Dynamics , 2003, Summer School on Neural Networks.

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

[4]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[5]  Arvind Kumar,et al.  The High-Conductance State of Cortical Networks , 2008, Neural Computation.

[6]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[7]  Dima Damen,et al.  Recognizing linked events: Searching the space of feasible explanations , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[8]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[9]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[10]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[11]  Abbott,et al.  Asynchronous states in networks of pulse-coupled oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  T. Sejnowski.  On the stochastic dynamics of neuronal interaction , 1976, Biological Cybernetics.

[13]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[14]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[15]  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.

[16]  T. Sejnowski.  On global properties of neuronal interaction , 1976, Biological Cybernetics.

[17]  N. B,et al.  Firing Frequency of Leaky Integrate-and-fire Neurons with Synaptic Current Dynamics , 1998 .

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

[19]  Alain Destexhe,et al.  A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity States , 2009, Neural Computation.

[20]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[21]  Carson C. Chow,et al.  Stochastic Dynamics of a Finite-Size Spiking Neural Network , 2007, Neural Computation.

[22]  Ohira,et al.  Master-equation approach to stochastic neurodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Sompolinsky,et al.  Theory of correlations in stochastic neural networks. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Geoffrey E. Hinton,et al.  OPTIMAL PERCEPTUAL INFERENCE , 1983 .

[25]  A. Aertsen,et al.  Neuronal Integration of Synaptic Input in the Fluctuation-Driven Regime , 2004, The Journal of Neuroscience.

[26]  Néstor Parga,et al.  Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses. , 2006, Physical review letters.

[27]  B. Richmond,et al.  Intrinsic dynamics in neuronal networks. I. Theory. , 2000, Journal of neurophysiology.

[28]  Nicolas Brunel,et al.  Dynamics of the Firing Probability of Noisy Integrate-and-Fire Neurons , 2002, Neural Computation.

[29]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

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

[31]  N. Brunel,et al.  Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics. , 1998, Journal of theoretical biology.