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The bulletin of mathematical biophysics

, Volume 12, Issue 3, pp 187–197 | Cite as

Contribution to the probabilistic theory of neural nets: II. Facilitation and threshold phenomena

  • Anatol Rapoport
Article

Abstract

The output curve of a single neuron with a threshold of response with respect to the frequency of the stimuli is derived. If the stimuli are regularly spaced in time, the output curve has discontinuities. If the threshold and/or refractory period are sufficiently large, the output curve approaches the “all-or-none” curve.

In the case of completely randomized stimuli, the output curve is sigmoid. The equation of this curve is derived and some properties are studied. Threshold and “all-or-none” effects can be achieved by “pyramiding” neurons of this type to converge on neurons of higher order.

Keywords

Refractory Period Biophysics Volume Single Neuron Threshold Effect Output Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. Jost, Res. 1947. “Bemerhungen zur mathematischen theorie der zähler.”Helvetica Physica Acta,20, 173.MathSciNetGoogle Scholar
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Copyright information

© The University of Chicago Press 1950

Authors and Affiliations

  • Anatol Rapoport
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicagoUSA

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