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Dynamical Behavior of Discrete Models of Jerne’s Network

  • G. Weisbuch
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 46)

Abstract

The arguments exchanged during this meeting give a strong evidence that the debate about the existence and biological function of the immune network proposed by N. Jerne [1] is certainly not settled. Although the existence of idiotypic interactions is well established by experimental data, part of the debate focuses on the too simplistic dynamical properties of mathematical models supposed to take into account the most important aspects of idiotypic interactions [2]. The purpose of this intervention is to remind you that our present knowledge about networks of automata enables us to present discrete mathematical models which exhibit enough dynamical complexity to overcome the apparent paradoxes presented by the opponents to the idea of a functional immune network.

Keywords

Boolean Function Cellular Automaton Immune Network Hebbian Learning Connection Structure 
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. [1]
    N. K. Jerne: Towards a netwok theory of the Immune System, Ann. Immunol. (Inst. Pasteur) 125C, 373–389, (1974).Google Scholar
  2. [2]
    Immunol. Rev. 79, Idiotypic networks, (1984).Google Scholar
  3. [3]
    A.S. Perelson: Towards a realistic model of the immune system, 377-401, in ≪Theoretical Immunology ≫ part two, ed. by A.S. Perelson, Addison Wesley (1988).Google Scholar
  4. [4]
    D.S. Holmberg, S. Forgren, F. Ivars and A. Couthinho: Reactions among IgM antibodies derived from normal neonatal mice, Eur. J. Imunol. 14, 435–441, (1984).CrossRefGoogle Scholar
  5. [5]
    R.J. De Boer: Extensive percolation in reasonable idiotypic networks, this volume (1989).Google Scholar
  6. [6]
    D. Stauffer, ≪Introduction to percolation theory≫, Taylor and Francis (1985).Google Scholar
  7. [7]
    H. Atlan, this volume (1989).Google Scholar
  8. [8]
    D. Farmer, T. Toffoli, S. Wolfram Eds: ≪Cellular Automata≫. Physica 10D, North-Holland, (1984).Google Scholar
  9. [9]
    R.B. Pandey and D. Stauffer: Immune response via interacting three dimensional network of cellular automata, Journal de Physique (1988).Google Scholar
  10. [10]
    C. Kittel and H. Kroemer, ≪Thermal Physics≫, Freeman and Co. (San Francisco 1980).Google Scholar
  11. [11]
    S. A. Kauffman, J. Theor. Biol., 22, 437–467, (1969).PubMedCrossRefGoogle Scholar
  12. [12]
    H. Atlan, F. Fogelman-Soulie, J. Salomon and G. Weisbuch: Random boolean networks, Cybernetics and Systems, 12, 103, (1981).Google Scholar
  13. [13]
    W.S Mac Culloch, W. Pitts: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophysics, 5, (1943), 115–133.CrossRefGoogle Scholar
  14. [14]
    J.J. Hopfield: Neural Networks and Physical Systems with Emergent Collective Computational Abilities, P.N.A.S. USA, 79, (1982), 2554–2558.CrossRefGoogle Scholar
  15. [15]
    E. Bienenstock, F. Fogelman Soulie, G. Weisbuch Eds: ≪Disordered Systems and Biological Organization≫, Springer Verlag, NATO ASI Series in Systems and Computer Science, no F20, (1986).Google Scholar
  16. [16]
    J. Denker Ed.: ≪Neural Networks for Computing≫. Conf. Proceedings no 151: Snowbird, Utah, 1986. American Institute of Physics (1986).Google Scholar
  17. [17]
    G. Weisbuch, ≪Dynamique des systèmes complexes, une introduction aux réseaux d’automates≫, InterEditions (Paris 1989).Google Scholar
  18. [18]
    B. Derrida and G. Weisbuch: Evolution of overlaps between configurations in random boolean networks, J. de Physique, 47, 1297, (1986).CrossRefGoogle Scholar
  19. [19]
    B. Derrida, E. Gardner and A. Zippelius: An exactly solvable asymmetric neural network model, Europhysics Let., 4, 167, (1987).CrossRefGoogle Scholar
  20. [20]
    B. Derrida: Dynamical phase transitions in non-symmetric spin glasses, J. Phys. A 20, L721–725, (1987).Google Scholar
  21. [21]
    H. Atlan, I. Cohen and G. Weisbuch, to appear (1989).Google Scholar
  22. [22]
    K. E. Kurten: Training quaskandom neural netwoks, in ≪Chaos and Complexity≫, ed. R. Livi, S. Ruffo, S. Ciliberto and M. Buiatti, World Scientific (Singapore 1988).Google Scholar
  23. [23]
    D.E. Rumelhart, J.L. Mac Clelland Eds: ≪Parallel and Distributed Processing: explorations in the Microstructure of Cognition≫. 2 vol., MIT Press, (1986).Google Scholar
  24. [24]
    M. Kaufman, this volume (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • G. Weisbuch
    • 1
  1. 1.Laboratoire de Physique Statistique de l’Ecole Normale SupérieureParis Cedex 05France

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