Preprint available

[Shin Ishii]

Dear connectionists,

We are pleased to inform you that the following preprint is now
available on our Web page:
http://www.aist-nara.ac.jp/~ishii/Papers/nc_psn.ps.gz

Comments and suggestion would be greatly appreciated.


Authors:	Ken-ichi Amemori and Shin Ishii

Title:		Gaussian process approach to spiking neurons for
		inhomogeneous Poisson inputs
		(Neural Computation, to appear)

Keywords:	spiking neuron, stochastic process,
		Markov-Gaussian process, inhomogeneous Poisson input,
		first passage time density

Abstract:
This article presents a new theoretical framework to consider the
dynamics of a stochastic spiking neuron model with general membrane
response to input spike. We assume that the input spikes
obey an inhomogeneous Poisson process. The stochastic process of the
membrane potential then becomes a Gaussian process. When a general
type of the membrane response is assumed, the stochastic process
becomes a Markov-Gaussian process. We present a calculation method for  
the membrane potential density and the firing probability density.
Our new formulation is the extension of the existing formulation
based on diffusion approximation. Although the single Markov
assumption of the diffusion approximation simplifies the stochastic
process analysis, the calculation is inaccurate when the stochastic
process involves a multiple Markov property. We find that the
variation of the shape of the membrane response, which has often been
ignored in existing stochastic process studies, significantly affects
the firing probability. Our approach can consider the reset effect,
which has been difficult to be dealt with by analysis based on the
first passage time density. 

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Shin Ishii	Nara Institute of Science and Technology
		http://www.aist-nara.ac.jp/~ishii/