Distribution of correlated spiking events in a populationbased approach for IntegrateandFire networks
 Jiwei Zhang,
 Katherine Newhall,
 Douglas Zhou,
 Aaditya Rangan
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Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous “multiple firing events” (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a firstpassage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population–based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.
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 Title
 Distribution of correlated spiking events in a populationbased approach for IntegrateandFire networks
 Journal

Journal of Computational Neuroscience
Volume 36, Issue 2 , pp 279295
 Cover Date
 20140401
 DOI
 10.1007/s1082701304726
 Print ISSN
 09295313
 Online ISSN
 15736873
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Spiking neurons
 Synchrony
 Homogeneity
 Multiple firing events
 First passage time
 Integrate and fire neuronal networks
 Industry Sectors
 Authors

 Jiwei Zhang ^{(1)}
 Katherine Newhall ^{(1)}
 Douglas Zhou ^{(2)}
 Aaditya Rangan ^{(1)}
 Author Affiliations

 1. Courant Institute of Mathematical Sciences, New York University, New York, USA
 2. Department of Mathematics, MOELSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China