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In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...
In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient ...
The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations (SODE) can be computationally very demanding, in particular for problems with a high-dimensional parameter space. In this work we c ...
Consider a diffusion field induced by a finite number of localized and instantaneous sources. In this paper, we study the problem of estimating these sources (including their intensities, spatial locations, and activation time) from the spatiotemporal samp ...
In many envisioned mobile ad hoc networks, nodes are expected to periodically beacon to advertise their presence. In this way, they can receive messages addressed to them or participate in routing operations. Yet, these beacons leak information about the n ...
Modern experimental techniques for the quantitative, time-course measurement of protein concentrations and gene activation levels enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appr ...
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the ...
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight i ...
Abstract—Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. A necessary condition for the validity of this approach is the e ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
