Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie
Kipnis, Claude ; Saada, Ellen
Séminaire de probabilités de Strasbourg, Tome 30 (1996), p. 55-67 / Harvested from Numdam
Publié le : 1996-01-01
@article{SPS_1996__30__55_0,
     author = {Kipnis, Claude and Saada, Ellen},
     title = {Un lien entre r\'eseaux de neurones et syst\`emes de particules : un mod\`ele de r\'etinotopie},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {30},
     year = {1996},
     pages = {55-67},
     mrnumber = {1459476},
     zbl = {0856.92001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1996__30__55_0}
}
Kipnis, Claude; Saada, Ellen. Un lien entre réseaux de neurones et systèmes de particules : un modèle de rétinotopie. Séminaire de probabilités de Strasbourg, Tome 30 (1996) pp. 55-67. http://gdmltest.u-ga.fr/item/SPS_1996__30__55_0/

[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. | MR 1239840 | Zbl 0779.60075

[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. | Numdam | MR 488376 | Zbl 0384.60079

[3] Cottrell, M. et J.C. Fort (1986). A stochastic model of retinotopy: a self-organizing process. Biol. Cybern., 53, 405-411. | MR 839498 | Zbl 0605.92001

[4] Cottrell, M. et J.C. Fort (1987). Etude d'un processus d'auto-organisation. Ann. Inst. Henri Poincaré, sect. B, 23, 1-20. | Numdam | MR 877382 | Zbl 0605.92002

[5] Duflo, M. (1994). Algorithmes stochastiques. Poly. de DEA, univ. de Marne-la-Vallée.

[6] Durrett, R. (1991). Probability: Theory and examples. Wadsworth & Brooks /Cole. | Zbl 0709.60002

[7] Durrett, R. (1993). Ten Lectures on Particle Systems. Notes du cours d'été de Saint-Flour. | Zbl 0840.60088

[8] Feller, W. (1968). An introduction to probability theory and its applications, vol 1, 3rd edition. Wiley, New York. | MR 228020 | Zbl 0155.23101

[9] Fort, J.C. et G. Pages (1994). About the a.s. convergence of the Kohonen algorithm with a generalized neighbourhood function. Preprint. | MR 1384371

[10] Kohonen, T. (1982). Self-organized formation of topogically correct feature maps. Biol. Cybern., 43, 59-69. | MR 667889 | Zbl 0466.92002

[11] Kohonen, T. (1984). Self-organization and associative memory. Springer-Verlag, New York. | MR 728946 | Zbl 0528.68062

[12] Liggett, T.M. (1985). Interacting particle systems. Springer-Verlag, New-York. | MR 776231 | Zbl 0559.60078

[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. | MR 621659 | Zbl 0444.60096

[14] Spitzer, F. (1981). Infinite systems with locally interacting components. Ann. Probab., 9, 349-364. | MR 614623 | Zbl 0462.60096

[15] Yang H. et T.S. Dillon (1992). Convergence of self-organizing neural algorithms. Neural Networks, 5, 485-493.