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.
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References
N. K. Jerne: Towards a netwok theory of the Immune System, Ann. Immunol. (Inst. Pasteur) 125C, 373–389, (1974).
Immunol. Rev. 79, Idiotypic networks, (1984).
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).
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).
R.J. De Boer: Extensive percolation in reasonable idiotypic networks, this volume (1989).
D. Stauffer, ≪Introduction to percolation theory≫, Taylor and Francis (1985).
H. Atlan, this volume (1989).
D. Farmer, T. Toffoli, S. Wolfram Eds: ≪Cellular Automata≫. Physica 10D, North-Holland, (1984).
R.B. Pandey and D. Stauffer: Immune response via interacting three dimensional network of cellular automata, Journal de Physique (1988).
C. Kittel and H. Kroemer, ≪Thermal Physics≫, Freeman and Co. (San Francisco 1980).
S. A. Kauffman, J. Theor. Biol., 22, 437–467, (1969).
H. Atlan, F. Fogelman-Soulie, J. Salomon and G. Weisbuch: Random boolean networks, Cybernetics and Systems, 12, 103, (1981).
W.S Mac Culloch, W. Pitts: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophysics, 5, (1943), 115–133.
J.J. Hopfield: Neural Networks and Physical Systems with Emergent Collective Computational Abilities, P.N.A.S. USA, 79, (1982), 2554–2558.
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).
J. Denker Ed.: ≪Neural Networks for Computing≫. Conf. Proceedings no 151: Snowbird, Utah, 1986. American Institute of Physics (1986).
G. Weisbuch, ≪Dynamique des systèmes complexes, une introduction aux réseaux d’automates≫, InterEditions (Paris 1989).
B. Derrida and G. Weisbuch: Evolution of overlaps between configurations in random boolean networks, J. de Physique, 47, 1297, (1986).
B. Derrida, E. Gardner and A. Zippelius: An exactly solvable asymmetric neural network model, Europhysics Let., 4, 167, (1987).
B. Derrida: Dynamical phase transitions in non-symmetric spin glasses, J. Phys. A 20, L721–725, (1987).
H. Atlan, I. Cohen and G. Weisbuch, to appear (1989).
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).
D.E. Rumelhart, J.L. Mac Clelland Eds: ≪Parallel and Distributed Processing: explorations in the Microstructure of Cognition≫. 2 vol., MIT Press, (1986).
M. Kaufman, this volume (1989).
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Weisbuch, G. (1989). Dynamical Behavior of Discrete Models of Jerne’s Network. In: Atlan, H., Cohen, I.R. (eds) Theories of Immune Networks. Springer Series in Synergetics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83935-1_6
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DOI: https://doi.org/10.1007/978-3-642-83935-1_6
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