Probabilistic description of neurons

In connection with model of the neuron presented by CAIANIELLO (1961), an approach to the study of a formalized linear threshold element is outlined, and the firing probability is calculated in the most general case of continuous input random variables. It is then considered the case when the number of the inputs lines becomes very large, in order to make use of asymptotic theorems. The probability for a neuron to have a given histogram of the intervals between successive spikes is then derived, making use of some results previously worked out by several authors (See FISZ, 1963 and references there cited), for the “theory of runs”. An explicit expression for this probability is presented in the case when the neuron exhibits a refractory period after each spike. Finally, a finite summation time is introduced in the model, and in a specific case the firing probability is calculated, and the behaviour of two asymptotic cases discussed.