A study of computational methods to analyze gene expression data

The recent advent of new technologies has led to huge amounts of genomic data. With these data come new opportunities to understand biological cellular processes underlying hidden regulation mechanisms and to identify disease related biomarkers for informative diagnostics. However, extracting biological insights from the immense amounts of genomic data is a challenging task. Therefore, effective and efficient computational techniques are needed to analyze and interpret genomic data. In this thesis, novel computational methods are proposed to address such challenges: a Bayesian mixture model, an extended Bayesian mixture model, and an Eigen-brain approach. The Bayesian mixture framework involves integration of the Bayesian network and the Gaussian mixture model. Based on the proposed framework and its conjunction with K-means clustering and principal component analysis (PCA), biological insights are derived such as context specific/dependent relationships and nested structures within microarray where biological replicates are encapsulated. The Bayesian mixture framework is then extended to explore posterior distributions of network space by incorporating a Markov chain Monte Carlo (MCMC) model. The extended Bayesian mixture model summarizes the sampled network structures by extracting biologically meaningful features. Finally, an Eigen-brain approach is proposed to analyze in situ hybridization data for the identification of the cell-type specific genes, which can be useful for informative blood diagnostics. Computational results with region-based clustering reveals the critical evidence for the consistency with brain anatomical structure.

Contributions to the theory of the A15 compounds and to the theory of the XY model

The text of this thesis provides historical introduction to the two studies Theoretical Model of Superconductivity and the Martensitic Transformation in A15 Compounds" and "A Comparison of Kadanoff-Migdal Renormalization with New Monte Carlo Results for the XY Model", contained herein as appendices.