Monthly
288 pp. per issue
6 x 9, illustrated
Founded: 1989
ISSN 0899-7667
E-ISSN 1530-888X
2010 Impact Factor: 2.290
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January 2009, Vol. 21, No. 1, Pages 46-100
Posted Online February 11, 2009.
(doi:10.1162/neco.2009.02-08-710)
© 2008 Massachusetts Institute of Technology
A Master Equation Formalism for Macroscopic Modeling of Asynchronous Irregular Activity StatesSami El BoustaniUnité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France elbousta@unic.cnrs-gif.fr Alain DestexheUnité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France destexhe@iaf.cnrs-gif.fr
Many efforts have been devoted to modeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which AI states are sustained through recurrent sparse connectivity, with or without external input. In this letter we propose a mesoscopic description of such AI states. Using master equation formalism, we derive a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks. This formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized. We compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces. Considering the randomly connected network as a unit, this approach could be used to build large-scale networks of such connected units, with an aim to model activity states constrained by macroscopic measurements, such as voltage-sensitive dye imaging. Cited byPaul C Bressloff. (2012) Spatiotemporal dynamics of continuum neural fields. Journal of Physics A: Mathematical and Theoretical 45:3, 033001 Online publication date: 27-Jan-2012. CrossRef Jonathan Touboul, Geoffroy Hermann, Olivier Faugeras. (2012) Noise-Induced Behaviors in Neural Mean Field Dynamics. SIAM Journal on Applied Dynamical Systems 11:1, 49 Online publication date: 1-Jan-2012. CrossRef John Milton, Austin Quan, Ivan Osorio. 2011. Nocturnal Frontal Lobe Epilepsy. , 501-510. CrossRef Tomer Fekete, Shimon Edelman. (2011) Towards a computational theory of experience. Consciousness and CognitionOnline publication date: 8-Mar-2011. CrossRef Jonathan D. Touboul, G. Bard Ermentrout. (2011) Finite-size and correlation-induced effects in mean-field dynamics. Journal of Computational NeuroscienceOnline publication date: 8-Mar-2011. CrossRef Pierre Yger, Sami Boustani, Alain Destexhe, Yves Frégnac. (2011) Topologically invariant macroscopic statistics in balanced networks of conductance-based integrate-and-fire neurons. Journal of Computational NeuroscienceOnline publication date: 11-Jan-2011. CrossRef Paul C Bressloff, Yi Lai. (2011) Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. The Journal of Mathematical Neuroscience 1:1, 2 Online publication date: 1-Jan-2011. CrossRef Paul Bressloff. (2010) Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics. Physical Review E 82:5, Online publication date: 1-Nov-2010. CrossRef S. Coombes. (2010) Large-scale neural dynamics: Simple and complex. NeuroImage 52:3, 731-739 Online publication date: 1-Sep-2010. CrossRef Daqing Guo, Chunguang Li. (2010) Self-Sustained Irregular Activity in 2-D Small-World Networks of Excitatory and Inhibitory Neurons. IEEE Transactions on Neural Networks 21:6, 895-905 Online publication date: 1-Jun-2010. CrossRef John G. Milton. (2010) Epilepsy as a dynamic disease: A tutorial of the past with an eye to the future. Epilepsy & Behavior 18:1-2, 33-44 Online publication date: 1-May-2010. CrossRef Michael A. Buice, Jack D. Cowan, Carson C. Chow. (2010) Systematic Fluctuation Expansion for Neural Network Activity Equations. Neural Computation 22:2, 377-426 Online publication date: 1-Feb-2010. Abstract | Full Text | PDF (3449 KB) | PDF Plus (3474 KB) Paul C. Bressloff. (2010) Stochastic Neural Field Theory and the System-Size Expansion. SIAM Journal on Applied Mathematics 70:5, 1488 Online publication date: 1-Jan-2010. CrossRef Alain Destexhe. (2009) Self-sustained asynchronous irregular states and Up–Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons. Journal of Computational Neuroscience 27:3, 493-506 Online publication date: 1-Dec-2009. CrossRef Alain Destexhe, Terrence J. Sejnowski. (2009) The Wilson–Cowan model, 36 years later. Biological Cybernetics 101:1, 1-2 Online publication date: 1-Jul-2009. CrossRef
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