Monomial dynamical and control systems over a finite field and applications to agent-based models in immunology.

Abstract

In this dissertation we study time discrete monomial dynamical systems as well as control systems over a finite field. Furthermore, we study the performance of a recently developed “reverse engineering” method that was conceived to reconstruct a time discrete dynamical system over a finite field out of biological time series data. We establish to what extent this method can be used to approximate the stochastic agent-based model PathSim, which simulates Epstein-Barr virus infection. The main results of this work are: Theorems that forecast the long term dynamics of the systems mentioned above and their algorithmic applications. Controllability results as well as methods for the synthesis of state feedback laws. Statements about the relationship between the performance of the “reverse engineering” method and the quantity or quality of the time series data used