Statistical Approach to the Study of Neural Networks

  • J.-Cl. Levy

Abstract

We study here a model of the function of neural networks; our aim is not to obtain a faithful reproduction of the physiological properties of living neurons by means of mathematical analysis assisted by physiological experimentation, but rather a general theoretical approach to the study of neural phenomena. We are fully aware of its shortcomings deriving from the lack of experimental testing and exhaustive evidence.

Keywords

Input Signal Dynamic Memory Synaptic Delay Spike Density Living Neuron 
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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References

  1. Brick, D. B.: Pattern recognition and self organisation using wieners canonical forms. Cybernetics of the nervous system. Elsevier publishing company 1965.Google Scholar
  2. Broadbent, D. E.: Applications of information theory and decision theory to human preception and reaction. Cybernetics of the nervous system. Elsevier publishing company 1963.Google Scholar
  3. Hebb: Organisation of behaviour, 6 eme ed. Juin 1961. London: John Wiley & Sons N.Y.; Traduit de l’anglais par M. KING sous le titre Psycho-physiologie du comportement, P.U.F. Paris 1958.Google Scholar
  4. Jenik, F.: An outline of the development of a neuron model. Cybernetics of the nervous systems. Elsevier publishing company 1965.Google Scholar
  5. Kleene: Representation of events in nerve nets and finite automata. Automata Studies. Princeton (N.Y.): University Press 1956.Google Scholar
  6. Levy, J. C.: Theorie statistique des combinaisons discernables. CR Academie des Sciences, 25 Février 1963.Google Scholar
  7. Levy, J. C.: Un modele de réseau figurant le systeme nerveux. Onde Electrique, Avril 1963.Google Scholar
  8. Levy, J. C.: Etude statistique des réseaux nerveux, circuits a majorité relative. Rapport contrat D.R.M.E. 64/34 146.Google Scholar
  9. Levy, J. C.: Systeme nerveux et reconnaissance des formes. Onde Electrique, Février 1966.Google Scholar
  10. Levy, J. C.: Complément a la théotie statistique des combinaisons discernables. CR Academie des Sciences, 2 Mai 1966.Google Scholar
  11. Levy, J. C., D. Bertaux et J. Grolleau: Structuration par apprentissage d’une mémoire a association sémantique. Symposium sur la cybernétique médicale et les intelligences artificielles. Toulouse 7.-9. Mars 1967.Google Scholar
  12. Levy, J. C., F. Liegeois, M. Ciiacron et G. Bertrand: Etude des assemblages de réseaux nerveux par le calcul electronique. Rapport du contrat D.R.M.E. 136/67.Google Scholar
  13. Liegeois, F.: Note sur la distribution des connecteurs dans les systemes composés d’un grand nombre de cellules.Google Scholar
  14. Mcculloch, W., and W. Parrs: A logical calculus of the ideas immanent in nervus activity. Bulletin of Mathématical Biophysics 1943.Google Scholar
  15. Mcculloch, W., and W. Parrs, Lerrvin, and Maturana: What the frog’s eye tells to the frog’s brain. Pire Vol. 47, 1959.Google Scholar
  16. Von Neumann, J.: Probabilistic logics. Automata studies. Princeton (N.Y.): University Press 1956.Google Scholar
  17. Rosenblatt: Principles of neuro dynamics. Spartan Books 1962.Google Scholar
  18. Simon, J. C.: Sur l’algebre des processus d’intelligence artificielle. Symposium sur la cybernetique médicale et les intelligences artificielles. Toulouse 7.-9. Mars 1967.Google Scholar
  19. Taylor, W. K.: Pattern recognition by means of automatic analogic equipment. Proceedings of the IEE vol. 106 part B, Mars 1956.Google Scholar
  20. Taylor, W. K.: A model of learning mechanism in the brain. Cybernetics of the nervous system. Elsevier publishing company 1965.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1968

Authors and Affiliations

  • J.-Cl. Levy
    • 1
  1. 1.Centre d’Etudes et de Recherches en Automation78, Velizy-VillaconblayFrance

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