Multiplicatively interacting point processes and applications to neural modeling

Autor:	Cardanobile, Stefano, Rotter, Stefan
Rok vydání:	2009
Předmět:	Mathematics - Probability Quantitative Biology - Neurons and Cognition 60K35 92B20 60G55
Druh dokumentu:	Working Paper
Popis:	We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for recurrent networks of spiking neurons with exponential transfer functions. The expected rates of all neurons in the network are approximated by a first-order differential system. We study the stability of the solutions of this equation, and use the new formalism to implement a winner-takes-all network that operates robustly for a wide range of parameters. Finally, we discuss relations with the generalised linear model that is widely used for the analysis of spike trains. Comment: 22 pages, 7 figures. Submitted to J. Comp. Neurosci. Overall changes according to suggestions of different reviewers. A conceptual error in a derivation has been corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0904.1505 Zobrazit plný text záznamu View this record from Arxiv