Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie

Claude Kipnis; Ellen Saada

Séminaire de probabilités de Strasbourg (1996)

  • Volume: 30, page 55-67

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Kipnis, Claude, and Saada, Ellen. "Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie." Séminaire de probabilités de Strasbourg 30 (1996): 55-67. <http://eudml.org/doc/113943>.

@article{Kipnis1996,
author = {Kipnis, Claude, Saada, Ellen},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {retinotopy model; local interactions; linear system; particle systems; moments; limiting distribution},
language = {eng},
pages = {55-67},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie},
url = {http://eudml.org/doc/113943},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Kipnis, Claude
AU - Saada, Ellen
TI - Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie
JO - Séminaire de probabilités de Strasbourg
PY - 1996
PB - Springer - Lecture Notes in Mathematics
VL - 30
SP - 55
EP - 67
LA - eng
KW - retinotopy model; local interactions; linear system; particle systems; moments; limiting distribution
UR - http://eudml.org/doc/113943
ER -

References

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  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. Zbl0384.60079MR488376
  3. [3] Cottrell, M. et J.C. Fort (1986). A stochastic model of retinotopy: a self-organizing process. Biol. Cybern., 53, 405-411. Zbl0605.92001MR839498
  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. Zbl0605.92002MR877382
  5. [5] Duflo, M. (1994). Algorithmes stochastiques. Poly. de DEA, univ. de Marne-la-Vallée. 
  6. [6] Durrett, R. (1991). Probability: Theory and examples. Wadsworth & Brooks /Cole. Zbl0709.60002
  7. [7] Durrett, R. (1993). Ten Lectures on Particle Systems. Notes du cours d'été de Saint-Flour. Zbl0840.60088
  8. [8] Feller, W. (1968). An introduction to probability theory and its applications, vol 1, 3rd edition. Wiley, New York. Zbl0155.23101MR228020
  9. [9] Fort, J.C.et G. Pages (1994). About the a.s. convergence of the Kohonen algorithm with a generalized neighbourhood function. Preprint. Zbl0781.60027MR1384371
  10. [10] Kohonen, T. (1982). Self-organized formation of topogically correct feature maps. Biol. Cybern., 43, 59-69. Zbl0466.92002MR667889
  11. [11] Kohonen, T. (1984). Self-organization and associative memory. Springer-Verlag, New York. Zbl0528.68062MR728946
  12. [12] Liggett, T.M. (1985). Interacting particle systems. Springer-Verlag, New-York. Zbl0559.60078MR776231
  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. Zbl0444.60096MR621659
  14. [14] Spitzer, F. (1981). Infinite systems with locally interacting components. Ann. Probab., 9, 349-364. Zbl0462.60096MR614623
  15. [15] Yang H. et T.S. Dillon (1992). Convergence of self-organizing neural algorithms. Neural Networks, 5, 485-493. 

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