Showing papers by "Gilles Pagès published in 1996"
TL;DR: In this article, a global Kushner-Clark theorem about the convergence of stochastic algorithms is proved: under some natural assumptions, one can'read' from the trajectories of its ODE whether or not an algorithm converges.
Abstract: In the first part of this paper a global Kushner-Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can 'read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.
54 citations
TL;DR: The question of self-organization for the Kohonen algorithm is investigated in this paper, where the notions of organized states, weak and strong selforganizations, are precisely defined.
38 citations
Proceedings Article•
01 Jan 1996
19 citations
TL;DR: The preliminary results suggest that NDPK Xl is able to bind to its own mRNA and stabilise it in a S 100 Xenopus oocyte extract, and there may be functional differences between the two NDPK.
1 citations