This review focusses on modelling of signal transduction pathways. It will introduce the general concepts of modelling and signal transduction, and then proceed with presenting the two most common approaches: Ordinary Di erential Equations (ODE) and Petri Nets (PN). Including an overview about some of the PN upgrades, such as Timed or Coloured Petri Nets, this review will show the major di eren...

We detail the implementation of basic operations on multivariate Chebyshev approximations. In most cases, they can be derived directly from well known properties of univariate Chebyshev polynomials. Besides addition, subtraction and multiplication, we discuss integration, indefinite di↵erentiation, indefinite integration and interpolation. The latter three, can be written as matrix-vector produ...

We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.

Lie Analysis of Diierential Equations (D.E.) is based on the symmetries of D.E. and their integral curves. The method looks for new variables, called canonical variables, which straighten out the group action. This article is devoted to explain what are those variables and why they simplify the D.E., trying to strike a balance between the original avor of Lie's idea and the algorithm usually pr...

This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...

During the last few years, di erent approaches for integrating ordinary di erential equations on manifolds have been published. In this work, we consider two of these approaches. We present some numerical experiments showing bene ts and some pitfalls when using the new methods. To demonstrate how they work, we compare with well known classical methods, e.g. Newmark and Runge-Kutta methods. AMS ...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...

In this paper we deene a compositional semantics for a generalized composition operator on logic programs. Static and dynamic inheritance as well as composition by union of clauses can all be obtained by specializing the general operator. The semantics is based on the notion of diierential programs, logic programs annotated with declarations that establish the programs' external interfaces.

In this paper we present an approach for the numerical solution of Delay Di erential Equations y 0 (t) = Ly (t) +My (t ) t 0 y (t) = ' (t) t 0; (1) where > 0, L;M 2 C I m m and ' 2 C ([ ; 0] ; C I m ), di erent from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it in a system of Ordinary Differential Equations. The scheme of discretizatio...

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...