Multiplicatively interacting point processes and applications to neural modeling
Abstract
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.
Cite
@article{arxiv.0904.1505,
title = {Multiplicatively interacting point processes and applications to neural modeling},
author = {Stefano Cardanobile and Stefan Rotter},
journal= {arXiv preprint arXiv:0904.1505},
year = {2009}
}
Comments
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