Abstract
The output of a neuron innervated by two other neurons which, in turn, are subjected to two independent Poisson showers of stimuli, is derived as a function of the frequencies of the Poisson showers under two distinct assumptions, 1) where either of the two neurons can fire the third, and 2) where the stimuli from both neurons must impinge within a certain time interval to fire the third. For very small frequencies, the output of the third neuron is very nearly the sum of the input frequencies in the first case and proportional to the product of the input frequencies in the second case. Hence the designation “addition” and “multiplication” theorems. This treatment is a generalization of a previous treatment where the Poisson shower was assumed identical for the two outer neurons.
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Literature
Rapoport, A. 1950a. “Contribution to the Probabilistic Theory of Neural Nets: I. Randomization of Refractory Periods and of Stimulus Intervals.”Bull. Math. Biophysics,12, 109–21.
— 1950b. “Contribution to the Probabilistic Theory of Neural Nets: II. Facilitation and Threshold Phenomena.” —Ibid.,,12, 187–97.
— 1950c. “Contribution to the Probabilistic Theory of Neural Nets: III. Specific Inhibition.” —Ibid.,,12, 317–25.
— 1950d. “Contribution to the Probabilistic Theory of Neural Nets: IV. Various Models for Inhibition.” —Ibid.,,12, 327–37.
Shimbel, A. 1949. “Input-Output Problems in Simple Nerve-Ganglion Systems.”Bull. Math. Biophysics,11, 165–71.
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Rapoport, A. “Addition” and “multiplication” theorems for the inputs of two neurons converging on a third. Bulletin of Mathematical Biophysics 13, 179–188 (1951). https://doi.org/10.1007/BF02478226
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DOI: https://doi.org/10.1007/BF02478226