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A Markovian event-based framework for stochastic spiking neural networks

Jonathan Touboul, Olivier Faugeras
Department of Mathematical Physics, The Rockefeller University, New York, USA
arXiv:0911.3462 [stat.AP] (18 Nov 2009)

@article{touboul2009markovian,

   title={A Markovian event-based framework for stochastic spiking neural networks},

   author={Touboul, J. and Faugeras, O.},

   journal={Arxiv preprint arXiv:0911.3462},

   year={2009}

}

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In this article we introduce and study a mathematical framework for characterizing and simulating networks of noisy integrate-and-fire neurons based on the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. We apply this modeling to different linear integrate-and-fire neuron models with or without noise synaptic integration, different types of synapses, with possibly transmission delays and absolute and relative refractory period, and this way generalize results previously obtained in certain particular cases (Reutimann, Giugliano et al 2003, Turova Mommaerts et al 1994). This approach provides a powerful framework to study some properties of the network, and an extremely efficient way to simulate the dynamics of large networks. In particular, it allows a parallel implementation, that was implemented on GPU.
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