A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper

Extensive oscillatory gene expression during "C. elegans" larval development

Oscillations are common features in mathematics, physics and biology. In biology, circadian oscillations, for example, allow organisms to keep time and modify their biology and behavior accordingly. Other types of oscillating mechanisms allow for the precise timing of developmental events. We found that nearly 19% of the C. elegans transcriptome shows extensive and robust transcriptionally driven oscillations of gene expression during larval development. In the work presented in the following dissertation, we characterised this network of oscillating gene expression