Small Boolean Networks

Abstract

This dissertation focuses on Boolean networks with a view to their applications in Systems Biology. We study two notions of stability, based on Hamming distance and on maintenance of a stable period length. Algorithms are given for the determination of Boolean networks from both complete and partial dynamics. The dynamics of ring networks are systematically studied. An algebraic structure is developed for derivation of adjacency matrices for the dynamics of Boolean networks from simple building blocks, both by edge-swapping and by gluing simple building blocks. Some results are implemented in Python and conclusions drawn for theta networks, a class of networks only slightly more complex than rings. A short section on applications to a known biological system closes the dissertation.