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Un lien entre réseaux de neurones et systèmes de particules: Un modele de rétinotopie

  • C. Kipnis
  • E. Saada
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1626)

Résumé

Nous étudions un modèle stochastique de rétinotopie introduit par M. Cottrell et J.C. Fort. Nous faisons une nouvelle démonstration qui généralise leurs résultats sur la convergence de ce processus, grâce à des techniques de systèmes de particules. Celles-ci fournissent également une méthode de simulation de la loi limite.

Keywords

Filtration Canonique Kohonen Algorithm Nous Supposons Nous Faisons Nous Notons 
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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Références

  1. [1]
    BOUTON, C. et G. PAGES (1993). Self-organization and convergence of the one-dimensional Kohonen algorithm with non uniformly distributed stimuli. Stoch. Proc. and Appl., 47, 249–274.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    COCOZZA, C. et C. KIPNIS (1977). Existence de processus Markoviens pour des systèmes infinis de particules. Ann. Inst. Henri Poincaré, sect. B, 13, 239–257.zbMATHGoogle Scholar
  3. [3]
    COTTRELL, M. et J.C. FORT (1986). A stochastic model of retinotopy: a self-organizing process. Biol. Cybern., 53, 405–411.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    COTTRELL, M. et J.C. FORT (1987). Etude d’un processus d’auto-organisation. Ann. Inst. Henri Poincaré, sect. B, 23, 1–20.zbMATHGoogle Scholar
  5. [5]
    DUFLO, M. (1994). Algorithmes stochastiques. Poly. de DEA, univ. de Marnela-Vallée.Google Scholar
  6. [6]
    DURRETT, R. (1991). Probability: Theory and examples. Wadsworth & Brooks/Cole.Google Scholar
  7. [7]
    DURRETT, R. (1993). Ten Lectures on Particle Systems. Notes du cours d’été de Saint-Flour.Google Scholar
  8. [8]
    FELLER, W. (1968). An introduction to probability theory and its applications, vol 1, 3rd edition, Wiley, New York.zbMATHGoogle Scholar
  9. [9]
    FORT, J.C. et G. PAGES (1994). About the a.s. convergence of the Kohonen algorithm with a generalized neighbourhood function. Preprint.Google Scholar
  10. [10]
    KOHONEN, T. (1982). Self-organized formation of topogically correct feature maps. Biol. Cybern., 43, 59–69.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    KOHONEN, T. (1984). Self-organization and associative memory. Springer-Verlag, New York.zbMATHGoogle Scholar
  12. [12]
    LIGGETT, T.M. (1985). Interacting particle systems. Springer-Verlag, New-York.CrossRefzbMATHGoogle Scholar
  13. [13]
    LIGGETT, T.M. et F. SPITZER (1981). Ergodic theorems for coupled random walks and other systems with locally interacting components. Z. Warsch. Verw. Gebiete, 56, 443–448.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    SPITZER, F. (1981). Infinite systems with locally interacting components. Ann. Probab., 9, 349–364.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    YANG H. et T.S. DILLON (1992). Convergence of self-organizing neural algorithms. Neural Networks, 5, 485–493.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • C. Kipnis
  • E. Saada
    • 1
  1. 1.U.R.A. 1378, L.A.M.S. de l’Université de Rouen, U.F.R. de Sciences, mathématiquesC.N.R.S.Mont-Saint-Aignan cédex

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