Contribution to the theory of random and biased nets
 Anatol Rapoport
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The probabilistic theory of random and biased nets is further developed by the “tracing” method treated previously. A number of biases expected to be operating in nets, particularly in sociograms, is described. Distribution of closed chain lengths is derived for random nets and for nets with a simple “reflexive” bias. The “island model” bias is treated for the case of two islands and a single axon tracing, resulting in a pair of linear difference equations with two indices. The reflexive bias is extended to multipleaxon tracing by an approximate method resulting in a modification of the random net recursion formula. Results previously obtained are compared with empirical findings and attempts are made to account for observed discrepancies.
 Allanson, J. T. 1956. “Some Properties of a Randomly Connected Neural Network.”Information Theory. New York: Academic Press; London: Butterworth Scientific Publications.
 Cartwright D. and F. Harary. 1956. “Structural Balance: A Generalization of Heider’s Theory.”Psychol. Rev.,63, 277–93. CrossRef
 Foster, C. and A. Rapoport. 1957. “The Case of the Forgetful Burglar.”The Mathematical Monthly (in press).
 Harary, F. and R. Z. Norman. 1953.Graph Theory as a Mathematical Model in Social Science. Ann Arbor: Institute for Social Research.
 Katz, L. and J. H. Powell. 1954. “The Number of Locally Restricted Directed Graphs.”Proc. Amer. Math. Soc.,5, 621–26. CrossRef
 Landahl, H. D. 1947. “Outline of a Matrix Calculus for Neural Nets.”Bull. Math. Biophysics,9, 99–108. CrossRef
 — and R. Runge. 1946. “Outline of a Matrix Algebra for Neural Nets.”Ibid.,8, 75–81. CrossRef
 Landau, H. G. 1952. “On Some Problems of Random Nets.”Ibid.,14, 203–12. CrossRef
 Luce, R. D. 1950. “Connectivity and Generalized Cliques in Sociometric Group Structure.”Psychometrika,15, 169–90. CrossRef
 — and A. D. Perry. 1949. “A Method of Matrix Analysis of Group Structure.”Psychometrika,14, 95–116. CrossRef
 Polya, G. 1936. “Sur le nombre des isoméres de certains composés chimiques.”Comptes Rendus Acad. Sci. Paris,202, 1554–6.
 Rapoport, A. 1948. “Cycle Distribution in Random Nets,”Bull. Math. Biophysics,10, 145–57. CrossRef
 —. 1951a. “Nets with Distance Bias,”Ibid.,13, 85–91. CrossRef
 — 1951b. “The Probability Distribution of Distinct Hits on Closely Packed Targets,”Ibid.,13, 133–37. CrossRef
 — 1953a. “Spread of Information Through a Population with SocioStructural Bias: I. Assumption of Transitivity,”Ibid.,15, 523–33. CrossRef
 — 1953b. “Spread of Information Through a Population with Sociostructural Bias: II. Various Models with Partial Transitivity,”Ibid.,15, 535–43. CrossRef
 Rashevsky, N. 1954. “Topology and Life: In Search of General Mathematical Principles in Biology and Sociology,”Bull. Math. Biophysics,16, 317–48.
 — 1955a. “Some Theorems in Topology and a Possible Biological Application,”Ibid.,17, 111–29. CrossRef
 — 1955b. “Some Remarks on Topological Biology,”Ibid.,17, 207–18. CrossRef
 — 1956. “The Geometrization of Biology,”Ibid.,18, 31–56. CrossRef
 Shimbel, A. 1948. “An Analysis of Theoretical Systems of Differentiating Nervous Tissues,”Bull. Math. Biophysics,10, 131–43. CrossRef
 Solomonoff, R. and A. Rapoport. 1951. “Connectivity of Random Nets,”Bull. Math. Biophysics,13, 107–17. CrossRef
 Trucco, E. 1956. “On The Information Content of Graphs: Compound Symbols; Different States for Each Point,”Bull. Math. Biophysics,18, 237–53.
 Wright, S. 1932. “The Roles of Mutation, Inbreeding, Crossbreeding, and Selection in Evolution,”Proc. Sixth Int. Congress Genetics,1, 356–66.
 Title
 Contribution to the theory of random and biased nets
 Journal

The bulletin of mathematical biophysics
Volume 19, Issue 4 , pp 257277
 Cover Date
 19571201
 DOI
 10.1007/BF02478417
 Print ISSN
 00074985
 Online ISSN
 15229602
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Anatol Rapoport ^{(1)}
 Author Affiliations

 1. Mental Health Research Institute, University of Michigan, USA