Noise-induced desynchronization and stochastic escape from equilibrium in complex networks
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A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sig ...
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 ...
A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. I ...
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 ...
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 ...
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 ...
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 ...
We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these ...