A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihoo...

In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.

Data-dependent rotations have been found to be a useful component for designing block cipher including MARS and RC6, two candidates for AES. Existing analysis indicates that data-dependent rotations play an important role in thwarting di erential and linear attacks. In this paper, we study di erential properties of data-dependent rotations, and derive a complete characterization of all possible...

This paper deals with Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of di erential systems. Properties of Hermite matrix polynomials such as the three terms recurrence formula permit an e cient computation of matrix functions avoiding important computational drawbacks of other well-known methods. Results are applied to compute accurate approxi...

This paper presents a matching method which is based on invariants of the luminance function. This makes matching possible in the case of important geometric transformations between images. The method is robust to occlusion, as local properties of the image signal are used. We propose to use di erential measures invariant to rotations in a multi-scale framework. Promising results are obtained w...

The di erential equation dX dt X k X where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem Starting with the diagonal matrix whose entries are the same as the given eigenvalues the solution ow has been observed numerically to always converge a symmetric Toeplitz matrix as t This paper is an attempt to understand the dynamics involved in...

We classify all partial di¤erential equations with polynomial coe¢ cients in x and y of the form A(x)uxx + 2B(x; y)uxy + C(y)uyy +D(x)ux + E(y)uy = nu; which has weak orthogonal polynomials as solutions and show that partial derivatives of all order are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial di¤erential equations in d-variables.

Recently, the notion of data as manifolds has come into being. The subject of image manifolds has been explored but not extensively and not from the point of view of di erential geometry. It is a well known fact that image manifolds are curved. Using some basic techniques of di erential geometry this paper explores image manifold curvature and attempts get a feel for the magnitude of this curva...

In this article we consider derive a macroscopic model for root length density evolution, starting from a discrete mesh of roots, using homogenization. In the microscopic model each roots grows vertically according to an ordinary di erential equation. The roots growth rates depend on the spatial repartition of nutrient in the soil, which also evolves in time, leading to a fully coupled nonlinea...