We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean function and indexed by positive integers reaches a high level, say b. In great generality such probability converges to zero exponentially fast in a power of b. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we deve...

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...

Local high-order autocorrelation features proposed by Otsu have been successfully applied to face recognition and many other pattern recognition problems. These features are invariant under translation, but not invariant under scale and rotation. We construct scale and rotation invariant features from the local high-order autocorrelation features. x 1 Introduction In pattern recognition problem...

It is shown that the spectrum of a one-dimensional Dirac operator with a potential q tending to infinity at infinity, and such that the positive variation of 1}q is bounded, covers the whole real line and is purely absolutely continuous. An example is given to show that in general, pure absolute continuity is lost if the condition on the positive variation is dropped. The appendix contains a di...

Abstract: We consider the question of how to de…ne sequential equilibria for multistage games with in…nite type sets and in…nite action sets. The de…nition should be a natural extension of Kreps and Wilson’s 1982 de…nition for …nite games, should yield intuitively appropriate solutions for various examples, and should exist for a broad class of economically interesting games.

Abstract: We consider how to extend Kreps and Wilson’s 1982 de…nition of sequential equilibrium to multi-stage games with in…nite sets of types and actions. A concept of open sequential equilibrium is de…ned by taking limits of strategy pro…les that can consistently satisfy approximate sequential rationality for all players at arbitrarily large …nite collections of observable open events. Exist...