Volterra series for solving weakly non-linear partial differential equations: application to a dissipative Burger's equation
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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 ...
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 ...
We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerica ...
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 ...
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 existence ...
We prove the existence of quasi-stationary symmetric solutions with exactly n >= 0 zeros and uniqueness for n = 0 for the Schrodinger-Newton model in one dimension and in two dimensions along with an angular momentum m >= 0. Our result is based on an analy ...
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 ...
We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in one dimension. We prove that approximated solutions converge, in a slow time scale, to solutions of a limit problem. This limit problem evolves piecewise constan ...
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 ...
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 ...