Multiplicatively interacting point processes and applications to neural modeling

Details Multiplicatively interacting point processes and applications to neural modeling Multiplicatively interacting point processes and applications to neural modeling

2009-04-09

arxiv.org/abs/0904.1505v3

Mathematics

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22 pages, 7 figures. Submitted to J. Comp. Neurosci. Overall changes according to suggestions of different reviewers. A concep

Scientific paper

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.

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