Abstract
This paper explores the statistics of the discharge history dependence in cat cochlear nerve. We demonstrate that self-exciting point process models which take the intensity of discharge as a stimulus related and recovery related function of the time since previous discharge adequately accounts for the non-Poisson second-order statistics of eighth nerve firing. We also examine the physical mechanisms for this kind of history dependence. The excitatory post-synaptic potential (EPSP) is modelled as a marked, filtered Poisson counting process (PCP), with the vesicle release occurring on Poisson times with intensity following the stimulus, and the single vesicle EPSP generation a random marking and filtering of the PCP due to neurotransmitter binding and post-synaptic membrane integration times. The probability of eighth nerve discharge is the probability that the EPSP process crosses threshold, with the history dependence due to the dependence of post-synaptic threshold voltage on time since previous spike.
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