The bulletin of mathematical biophysics

, Volume 10, Issue 3, pp 145–157 | Cite as

Cycle distributions in random nets

  • Anatol Rapoport
Article

Abstract

Characteristics of random nets are derived from assumptions concerning the distribution of connections. The single aggregate of neurons with random connections without branching and two parallel chains with normal distribution of connections are considered. The cycle saturation is derived for each type of net, that is, the fraction of neurons which are members of cycles. It is shown that in the single aggregate with random connections, the cycle saturation varies inversely as the square root of the number of neurons; in the dense two-chain net it varies inversely as the square root of the neuron density and inversely on the square root of the standard deviation of the normal distribution.

Keywords

Biophysics Volume Neuron Density Parallel Chain Iteration Formula Synaptic Delay 

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Literature

  1. Shimbel, Alfonso and Rapoport, Anatol. 1948. “A Statistical Approach to the Theory of the Central Nervous System,”Bull. Math. Biophysics,10, 41–55.MathSciNetGoogle Scholar
  2. Shimbel, Alfonso. 1948. “An Analysis of Theoretical Systems of Differentiating Nervous Tissue.”Bull. Math. Biophysics,10, 131–143.Google Scholar
  3. Uspenski, J. V. 1937.Introduction to Mathematical Probability. New York: McGraw Hill, pp. 135–136.Google Scholar

Copyright information

© The University of Chicago Press 1948

Authors and Affiliations

  • Anatol Rapoport
    • 1
  1. 1.The University of ChicagoChicagoUSA

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