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We propose in [1] a Markov process model for spike-frequency adapting neural ensembles in the active state. Our approach synthesizes existing mean-adaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unified and tractable framework that goes beyond renewal and mean-adaptation theories by accounting for the full dynamics of the ensemble, as well as correlations between subsequent inter-spike intervals. By showing that the full five-dimensional master equation for a integrate-and-fire neuron with spike-frequency adaptation and a relative refractory mechanism driven by Poisson spike trains arriving at conductance-based synapses can be reduced to a two-dimensional generalization of the proposed Markov process by an adiabatic elimination of fast relaxing variables, the relationship between stimulus and process parameters is made explicit. Time permitting, a method for efficiently generating realizations of the proposed stimulus driven Markov process will be given, and contrasted to existing dynamic generation schemes for renewal processes. [1] E. Muller, L. Buesing, J. Schemmel, K. Meier (2007). Spike-Frequency Adapting Neural Ensembles: Beyond Mean Adaptation and Renewal Theories. Neural Computation 19:2958-3010. |
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