Identification of genetic network dynamics with unate structure
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Experimental techniques in biology such as microfluidic devices and time-lapse microscopy allow tracking of the gene expression in single cells over time. So far, few attempts have been made to fully exploit these data for modeling the dynamics of biologic ...
Walking gaits of various animals have been modeled using this framework of differential equations, and more specifically, using network of coupled oscillators or CPG (Central Pattern Generators). In these models, oscillators are coupled among themselves an ...
A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by t ...
We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and every instance of ...
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 ...
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 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 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 ...
The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after success ...
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 ...