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An analytic solution of the reentrant Poisson master equation and its application in the simulation of large groups of spiking neurons

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1 Author(s)
de Kamps, M. ; Tech. Univ. Munchen, Garching

Population density techniques are statistical methods to describe large populations of spiking neurons. They describe the response of such a population to a stochastic input. These techniques are sometimes defined as the interaction of neuronal dynamics and a Poisson point process. In earlier work I showed that one can transform away neuronal dynamics, which leaves only the problem of solving the master equation for the Poisson point process. Previously, I used a numerical solution for the master equation. In this work, I will present an analytic solution, which is based on a formal solution by Sirovich (2003). I will show that using this solution for solving the population density equation results in a much faster and manifestly stable algorithm.

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Neural Networks, 2006. IJCNN '06. International Joint Conference on

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