When effects due to refractoriness (reduction of sensitivity following a nerve impulse) are taken into account, the Poisson process provides the basis for a model which accounts for all of the first-order statistical properties of the maintained discharge in-the retinal ganglion cell of the cat. The theoretical pulse-number distribution (PND) and pulse-interval distribution (PID) provide good fits to the experimental data reported by Barlow and Levick for on-center, off-center, and luminance units. The model correctly predicts changes in the shape of the empirical PND with adapting luminance and duration of the interval in which impulses are counted (counting interval). It also requires that a decrease in sensitivity to stimulation by light with increasing adapting luminance occur prior to the ganglion cell and is thus consistent with other data. Under the assumptions of the model, both on-center and off-center units appear to exhibit increasing refractoriness as the adapting luminance increases. Relationships are presented between the PND and PID for Poisson counting processes without refractoriness, with a fixed refractory period, and with a stochastically varying refractory period. It is assumed that events unable to produce impulses during the refractory period do not prolong the duration of the period (nonparalyzable counting). A short refractory period (e.g., 2% of the counting interval) drastically alters both the PND and PID, producing marked decreases in the mean and variance of the PND along with an increase in the ratio of mean to variance. In all cases of interest, a small amount of variability in refractory-period duration distinctly alters the PID from that obtainable with a fixed refractory period but has virtually no effect on the fixed-refractory period PND. Other two-parameter models that invoke scaling of a Poisson input and paralyzable counting yield predictions that do not match the data.
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