Re nement Calculus is a formal framework for the development of provably correct software. It is also used in the development of Action Systems, which is a predicate transformer based framework for constructing distributed and reactive software systems. Recently, Action Systems were extended with a new action called the di erential action. It allows the modelling of continuous behaviour. Along ...

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...

We consider interpolation in Lie groups and homogeneous spaces. Based on points on the manifold together with tangent vectors at (some of) these points, we construct Hermite interpolation polynomials. If the points and tangent vectors are produced in the process of integrating an ordinary di erential equation on a Lie group or a homogeneous space, we use the truncated inverse of the di erential...

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

This report presents a new statistical attack on iterative block ciphers called the correlation attack which is a natural generalization of linear cryptanalysis. The attack is based on nding complex-valued functions on the input and the output of a cipher which have a high correlation. Their mutual relation is then exploited to yield information about the nal round key. Introducing the notions ...

In this thesis we study numerical methods for simulating mechanical deformations of cell membranes. Such models are given in terms of fourth order partial di erential equations. In order to enable comparisons of the models predictions to experimental results, the equations must be solved on arbitrary cell geometries. A Finite Element Method based on subdivision surfaces, which is capable of dis...

In this paper, decision{feedback di erential detection (DF{DD) ofM{ary di erential phase{shift keying (MDPSK) signals, which has been introduced previously for the additive white Gaussian noise (AWGN) channel by Leib et al. [1] and Edbauer [2], is extended to at Rayleigh fading channels. The DF{DD metric is derived from the multiple{symbol detection (MSD) metric and for error{free feedback an e...

We consider the construction of geometric integrators in the class of RKMK methods. Any di erential equation in the form of an in nitesimal generator on a homogeneous space is shown to be locally equivalent to a di erential equation on the Lie algebra corresponding to the Lie group acting on the homogenous space. This way we obtain a distinction between the coordinate-free phrasing of the di er...

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...