{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:32:46Z","timestamp":1725456766802},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540636311"},{"type":"electronic","value":"9783540696209"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/bfb0020225","type":"book-chapter","created":{"date-parts":[[2005,12,1]],"date-time":"2005-12-01T08:34:43Z","timestamp":1133426083000},"page":"631-636","source":"Crossref","is-referenced-by-count":1,"title":["Convergences of the Kohonen maps: a dynamical system approach"],"prefix":"10.1007","author":[{"given":"Jean-Claude","family":"Fort","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gilles","family":"Pag\u00e8s","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,9]]},"reference":[{"key":"101_CR1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1137\/S0363012993253534","volume":"34","author":"M. Bena\u00efm","year":"1996","unstructured":"M. Bena\u00efm, A Dynamical System Approach to Stochastic Approximations, SIAM J. Control And Optimization, 34, n\u00b0 2, 1996, pp.437\u2013472.","journal-title":"SIAM J. Control And Optimization"},{"key":"101_CR2","unstructured":"M. Bena\u00efm, J.C. Fort, G. Pag\u00e8s, Convergence of the One-dimensional Kohonen Algorithm. To appear in Adv. in Applied Proba."},{"key":"101_CR3","unstructured":"M. Benaim, J.C. Fort, G. Pag\u00e8s, Almost sure convergence of the one dimensional Kohonen Algorithm, ESANN'97 Bruges, pp.193\u2013198."},{"key":"101_CR4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0304-4149(93)90017-X","volume":"47","author":"C. Bouton","year":"1993","unstructured":"C. Bouton, G. Pag\u00e8s, Self-organization and convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli, Stoch. Proc. & Appl., 47, 1993, pp.249\u2013274.","journal-title":"Stoch. Proc. & Appl."},{"key":"101_CR5","doi-asserted-by":"crossref","unstructured":"C. Conley, Isolated invariant sets and the Morse index, Conf. Board of the Math. Science by AMS, Regional Conference Series in Mathematics, 1978.","DOI":"10.1090\/cbms\/038"},{"key":"101_CR6","first-page":"1","volume":"23","author":"M. Cottrell","year":"1987","unstructured":"M. Cottrell, J.C. Fort, \u00c9tude d'un algorithme d'auto-organisation, Ann. Inst. H. Poincar\u00e9, 23, n\u00b01, 1987, pp.1\u201320.","journal-title":"Ann. Inst. H. Poincar\u00e9"},{"key":"101_CR7","unstructured":"M. Cottrell, J.C. Fort, G. Pag\u00e8s, Theoretical aspects of the S.O.M. algorithm, WSOM'97 Helsinki, pp.246\u2013267."},{"key":"101_CR8","unstructured":"A. Flanagan, Self-organizing Neural Networks, Th\u00e8se 1306, EY.F.L., Lausanne, 1994."},{"issue":"4","key":"101_CR9","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1214\/aoap\/1177004611","volume":"5","author":"J.C. Fort","year":"1995","unstructured":"J.C. Fort, G. Pag\u00e8s, On the a.s. Convergence of the Kohonen Algorithm With a General Neighborhood Function, The Ann. of Applied Proba., 5, n\u00b0 4, 1995, pp.1177\u20131216.","journal-title":"The Ann. of Applied Proba."},{"issue":"5","key":"101_CR10","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/0893-6080(95)00089-5","volume":"9","author":"J.C. Fort","year":"1996","unstructured":"J.C. Fort, G. Pag\u00e8s, About the Kohonen algorithm: strong or weak selforganization?, Neural Networks, 9, n\u00b0 5, 1996, pp.773\u2013785.","journal-title":"Neural Networks"},{"key":"101_CR11","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.2307\/1428165","volume":"28","author":"J.C. Fort","year":"1996","unstructured":"J.C. Fort, G. Pag\u00e8s, Convergence of Stochastic Algorithms: from the Kushner & Clark Theorem to the Lyapounov Functional Method, Adv. in Applied Proba., 28,1996, pp.1072\u20131094.","journal-title":"Adv. in Applied Proba."},{"key":"101_CR12","first-page":"1","volume":"383","author":"M. Hirsch","year":"1988","unstructured":"M. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 383, 1988, pp.1\u201353.","journal-title":"J. Reine Angew. Math."},{"key":"101_CR13","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF00317973","volume":"44","author":"T. Kohonen","year":"1982","unstructured":"T. Kohonen, Ananlysis of a simple self-organizing process, Biol. Cybern., 44, 1982, p135\u2013140.","journal-title":"Biol. Cybern."},{"key":"101_CR14","doi-asserted-by":"crossref","unstructured":"T. Kohonen, Self-organization and associative memory, 3rd edition Springer, Berlin, 1989.","DOI":"10.1007\/978-3-642-88163-3"},{"key":"101_CR15","doi-asserted-by":"crossref","unstructured":"H.J. Kushner, D.S. Clark, Stochastic Approximation for Constraint and Unconstraint Systems, Appl. Math. Sci. Series, 26, Springer, 1978.","DOI":"10.1007\/978-1-4684-9352-8"},{"key":"101_CR16","unstructured":"A. Sadeghi, Asymptotic Behaviour of Self-Organizing Maps with Non-Uniform Stimuli Distribution, forthcoming in Annals of Applied Probability."}],"container-title":["Lecture Notes in Computer Science","Artificial Neural Networks \u2014 ICANN'97"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0020225","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,11]],"date-time":"2020-04-11T08:30:04Z","timestamp":1586593804000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0020225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540636311","9783540696209"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/bfb0020225","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}