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Uniform One and two Dimensional Neural Networks

  • Eric Goles
  • Servet Martínez
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 58)

Abstract

Periodical behaviour in Uniform Neural Networks has been studied since 1959 by several authors [B,FC,GT2,GT3,Kil,Ko,Shl,Sh2,Tl,T3]. The studies have been chiefly aimed at modelling sensory or cortical neural systems and diffusion processes in one or two dimensions.

Keywords

Neural Network Cellular Automaton Local Function Central Cell Local Rule 
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. [A]
    Amari, S., Homogeneous Nets of Neuron like Elements, Biol. Cybern., 17, 1975, 211–220.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [B]
    Beurle, R.L., Storage and Manipulation of Information in the Brain, J. Inst. Elec. Eng., London, 1959, 75–82.Google Scholar
  3. [FC]
    Farley, B., W.A. Clark, Activity in Neurons-Like Elements, in Proc. Fourth London Conference on Information Theory, C. Cherry ed., Butterworths, London, 1961, 242–251.Google Scholar
  4. [GT2]
    Goles, E., M. Tchuente, Erasing Multithreshold Automata, in Dynamical Systems and Cellular Automata, J. Demongeot, E. Goles, M. Tchuente eds., Academic Press, 1985, 47–56.Google Scholar
  5. [GT3]
    Goles, E., M. Tchuente, Iterative Behaviour of One-Dimensional Threshold Automata, Disc. Appl. Maths, 8, 1984, 319–322.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [Ki1]
    Kitagawa, T., Cell Space Approaches in Biomathematics, Math. Bios, 19, 1974, 27–71.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [Ko]
    Kobuchi, Y., Signal Propagation in 2-D Threshold Cellular Space, J. Math. Biol, 3, 1976, 297–312.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [Sh1]
    Shingai, R., Maximum Period of 2-Dimensional Uniform Neural Networks, Information and Control, 41, 1979, 324–341.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [Sh2]
    Shingai, R., The Maximum Period Realized in 1-D Uniform Neural Networks, Trans. IECE, Japan E61, 1978, 804–808.Google Scholar
  10. [Tl]
    Tchuente, M., Contribution a l’Etude des Méthodes de Calcul pour des Systèmes de Type Coopératif. Thesis, IMAG, Grenoble, France, 1982.Google Scholar
  11. [T3]
    Tchuente, M., Evolution de Certains Automatas Cellulaires Uniformes Binaires a Seuil, Seminaire, 265, IMAG, Grenoble, 1977.Google Scholar
  12. [W2]
    Wolfram, S., Universality and Complexity in Cellular Automata, Physica 10D, 1984, 1–35.MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Eric Goles
    • 1
  • Servet Martínez
    • 1
  1. 1.Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile

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