作者：Loukianova, D
摘要：This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let m denote the number of stored patterns and N that of neurons, Assuming that m/N --> alpha as N --> infinity we show that for alpha > 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as alpha --> infinity.
作者：Chen, KI; Lo, SH
作者单位：Columbia University
摘要：A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation. Fo...
作者：Arnaudon, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We prove that the derivative of a differentiable family X-t(a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bi-continuous in t and a. We consider a filtered probability space (Omega, (F-t)(0 less than or equal to t less than or equal to 1, P)) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexif...
