A stochastic model and a functional central limit theorem for information processing in large systems of neurons.
The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1 < or = i < or = N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.
Höpfner
Reinhard
R
Institute of Mathematics, University of Mainz, Staudingerweg 9, 55099, Mainz, Germany. hoepfner@mathematik.uni-mainz.de
Brodda
Klaus
K
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D006801:Humans; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology; D016012:Poisson Distribution; D013269:Stochastic Processes; D009435:Synaptic Transmission / Q000502:physiology*