title: Multiplicatively interacting point processes and applications to neural modeling.
abstract: We introduce a nonlinear modification of the classical Hawkes process allowing inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for recurrent networks of spiking neurons described as Wiener cascades with exponential transfer function. 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.
authors.affiliation: BCCN & Faculty of Biology, Albert-Ludwig University Freiburg, Freiburg, Germany. cardanobile@bccn.uni-freiburg.de
authors.forename: Stefano
authors.initials: S
authors.lastname: Cardanobile
authors.forename: Stefan
authors.initials: S
authors.lastname: Rotter
mesh_terms: D000200:Action Potentials / Q000502:physiology; D003198:Computer Simulation; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009433:Neural Inhibition / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics