Doctor of Philosophy / Genetics Interdepartmental Program / James C. Nelson / QTL (quantitative-trait locus) analysis aims to locate and estimate the effects of genes that are responsible for quantitative traits, by means of statistical methods that evaluate the association of genetic variation with trait (phenotypic) variation. Quantitative traits are typically controlled by multiple genes with varying degrees of influence on the phenotype. I describe a new QTL analysis method based on shrinkage and a unifying framework based on the generalized linear model for non-normal data. I develop their extensions to multiple-trait QTL analysis. Expression QTL, or eQTL, analysis is QTL analysis applied to gene expression data to reveal the eQTLs controlling transcript-abundance variation, with the goal of elucidating gene regulatory networks. For exploiting eQTL data, I develop a novel extension of the graphical Gaussian model that produces an undirected graph of a gene regulatory network. To reduce the dimensionality, the extension constructs networks one cluster at a time. However, because Fuzzy-K, the clustering method of choice, relies on subjective visual cutoffs for cluster membership, I develop a bootstrap method to overcome this disadvantage. Finally, I describe QGene, an extensible QTL- and eQTL-analysis software platform written in Java and used for implementation of all analyses.

published_or_final_version / abstract / Paediatrics and Adolescent Medicine / Master / Master of Philosophy

by Leung Hoi-Chau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Previous Works --- p.2 / Chapter 2.1. --- Facial animations and facial surgery simulations / Chapter 2.2. --- Facial Action Coding System (FACS) / Chapter 2.3. --- The Boundary Element Method (BEM) in Computer Graphics / Chapter Chapter 3. --- The Facial Expression System --- p.7 / Chapter 3.1. --- Input to the system / Chapter 3.1.1. --- Orientation requirements for the input mesh / Chapter 3.1.2. --- Topology requirements for the input mesh / Chapter 3.1.3. --- Type of the polygons of the facial mesh / Chapter 3.2. --- Facial Modeling and Feature Recognition / Chapter 3.3. --- User Control / Chapter 3.4. --- Output of the system / Chapter Chapter 4. --- Boundary Element Method (BEM) --- p.12 / Chapter 4.1. --- Numerical integration of the kernels / Chapter 4.1.1. --- P and Q are different / Chapter 4.1.2. --- P and Q are identical / Chapter 4.1.2.1. --- Evaluation of the Singular Traction Kernel / Chapter 4.1.2.2. --- Evaluation of the Singular Displacement Kernel / Chapter 4.2. --- Assemble the stiffness matrix / Chapter Chapter 5. --- Facial Modeling --- p.18 / Chapter 5.1. --- Offset of facial mesh / Chapter 5.2. --- Thickening of Face Contour / Chapter Chapter 6. --- Facial Feature Recognition --- p.22 / Chapter 6.1. --- Extract all contour edges from the facial mesh / Chapter 6.2. --- Separate different holes from the contour edges / Chapter 6.3. --- Locating the bounding boxes of different holes / Chapter 6.4. --- Determine the facial features / Chapter 6.4.1. --- Eye positions / Chapter 6.4.2. --- Mouth position and Face / Chapter 6.4.3. --- Nose position / Chapter 6.4.4. --- Skull position / Chapter Chapter 7. --- Boundary Conditions in the system --- p.28 / Chapter 7.1. --- Facial Muscles / Chapter 7.2. --- Skull Bone / Chapter 7.3. --- Facial Muscle recognition / Chapter 7.3.1. --- Locating muscle-definers / Chapter 7.3.2. --- Locating muscles / Chapter 7.4. --- Skull Bone Recognition / Chapter 7.5. --- Refine the bounding regions of the facial features / Chapter 7.6. --- Add/Remove facial muscles / Chapter Chapter 8. --- Muscles Movement --- p.40 / Chapter 8.1. --- Muscle contraction / Chapter 8.2. --- Muscle relaxation / Chapter 8.3. --- The Muscle sliders / Chapter Chapter 9. --- Pre-computation --- p.44 / Chapter 9.1. --- Changing the Boundary Values / Chapter Chapter 10 --- . Implementation --- p.46 / Chapter 10.1. --- Data Structure for the facial mesh / Chapter 10.2. --- Implementation of the BEM engine / Chapter 10.3. --- Facial modeling and the facial recognition / Chapter Chapter 11 --- . Results --- p.48 / Chapter 11.1. --- Example 1 (low polygon man face) / Chapter 11.2. --- Example 2 (girl face) / Chapter 11.3. --- Example 3 (man face) / Chapter 11.4. --- System evaluation / Chapter Chapter 12 --- . Conclusions --- p.67 / References --- p.70

The reconstruction of gene regulatory networks is one of the milestones of computational system biology. We introduce a new implementation of ARACNe (Algorithm for the Reconstruction of Accurate Cellular Networks) to reverse engineer transcriptional regulatory networks with improved mutual information estimators and significant improvement in performance. In the context of data driven network inference we identify two major confounding biases and introduce solutions to remove some of the discussed biases. First we identify prevalent spatial biases in gene expression studies derived from plate based designs. We investigate the gene expression profiles of a million samples from the LINCS dataset and find that the vast majority (96%) of the tested plates is affected by significant spatial bias. We can show that our proposed method to correct these biases results in a significant improvement of similarity between biological replicates assayed in different plates. Lastly we discuss the effect of CNV on gene expression and its confounding effect on the correlation landscape of genes in the context of cancer samples. We propose a method that removes the variance in gene expression explained by CNV and show that TF target predictions can be significantly improved.

The research reported in this thesis addresses the problem of component analysis, which aims at reducing large data to lower dimensions, to reveal the essential structure of the data. This problem is encountered in almost all areas of science - from physics and biology to finance, economics and psychometrics - where large data sets need to be analyzed. Several paradigms for component analysis are considered, e.g., principal component analysis, independent component analysis and sparse principal component analysis, which are naturally formulated as an optimization problem subject to constraints that endow the problem with a well-characterized matrix manifold structure. Component analysis is so cast in the realm of optimization on matrix manifolds. Algorithms for component analysis are subsequently derived that take advantage of the geometrical structure of the problem. When formalizing component analysis into an optimization framework, three main classes of problems are encountered, for which methods are proposed. We first consider the problem of optimizing a smooth function on the set of n-by-p real matrices with orthonormal columns. Then, a method is proposed to maximize a convex function on a compact manifold, which generalizes to this context the well-known power method that computes the dominant eigenvector of a matrix. Finally, we address the issue of solving problems defined in terms of large positive semidefinite matrices in a numerically efficient manner by using low-rank approximations of such matrices. The efficiency of the proposed algorithms for component analysis is evaluated on the analysis of gene expression data related to breast cancer, which encode the expression levels of thousands of genes gained from experiments on hundreds of cancerous cells. Such data provide a snapshot of the biological processes that occur in tumor cells and offer huge opportunities for an improved understanding of cancer. Thanks to an original framework to evaluate the biological significance of a set of components, well-known but also novel knowledge is inferred about the biological processes that underlie breast cancer. Hence, to summarize the thesis in one sentence: We adopt a geometric point of view to propose optimization algorithms performing component analysis, which, applied on large gene expression data, enable to reveal novel biological knowledge.

Microarray technology has become a dynamic tool in gene expression analysis because it allows for the simultaneous measurement of thousands of gene expressions. Uniqueness in experimental units and microarray data platforms, coupled with how gene expressions are obtained, make the field open for interesting research questions. In this dissertation, we present our investigations of two independent studies related to microarray data analysis. First, we study a recent platform in biology and bioinformatics that compares the quality of genetic information from exfoliated colonocytes in fecal matter with genetic material from mucosa cells within the colon. Using the intraclass correlation coe�cient (ICC) as a measure of reproducibility, we assess the reliability of density estimation obtained from preliminary analysis of fecal and mucosa data sets. Numerical findings clearly show that the distribution is comprised of two components. For measurements between 0 and 1, it is natural to assume that the data points are from a beta-mixture distribution. We explore whether ICC values should be modeled with a beta mixture or transformed first and fit with a normal mixture. We find that the use of mixture of normals in the inverse-probit transformed scale is less sensitive toward model mis-specification; otherwise a biased conclusion could be reached. By using the normal mixture approach to compare the ICC distributions of fecal and mucosa samples, we observe the quality of reproducible genes in fecal array data to be comparable with that in mucosa arrays. For microarray data, within-gene variance estimation is often challenging due to the high frequency of low replication studies. Several methodologies have been developed to strengthen variance terms by borrowing information across genes. However, even with such accommodations, variance may be initiated by the presence of outliers. For our second study, we propose a robust modification of optimal shrinkage variance estimation to improve outlier detection. In order to increase power, we suggest grouping standardized data so that information shared across genes is similar in distribution. Simulation studies and analysis of real colon cancer microarray data reveal that our methodology provides a technique which is insensitive to outliers, free of distributional assumptions, effective for small sample size, and data adaptive.

Microarray technology permit us to study the expression levels of thousands of genes simultaneously. The technique has a wide range of applications including identification of genes that change their expression in cells due to disease or drug stimuli. The dissertation is addressing statistical methods for the selection of differentially expressed genes in two experimental conditions. We propose two different methods for the selection of differentially expressed genes. The first method is a classical approach, where we consider a common distribution for the summary measure of equally expressed genes. To estimate this common distribution, the Johnson system of distribution is used. The advantage of using Johnson system is that, there is no need of a parametric assumption for gene expression data. In contrast to other classical methods, in the proposed method, there is a sharing of information across the genes by the assumption of a common distribution for the summary measure of equally expressed genes. The second method is the gene selection using a mixture model approach and Baye's theorem. This approach also uses the Johnson System of distribution for the estimation of distribution of summary measure. Johnson system of distribution has the flexibility of covering a wide variety of distributional shapes. This system provides a unique distribution corresponding to each pair of mathematically possible values of skewness and kurtosis. The significant flexibility of Johnson system is very useful in characterizing the complicated data set like microarray data. In this dissertation we propose a novel algorithm for the estimation of the four parameters of the Johnson system.

Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun&rsquo / s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.

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The need to analyze and closely study the gene related mechanisms motivated the research on the modeling and control of gene regulatory networks (GRN). Dierent approaches exist to model GRNs / they are mostly simulated as mathematical models that represent relationships between genes. Though it turns into a more challenging problem, we argue that partial observability would be a more natural and realistic method for handling the control of GRNs. Partial observability is a fundamental aspect of the problem / it is mostly ignored and substituted by the assumption that states of GRN are known precisely, prescribed as full observability. On the other hand, current works addressing partially observability focus on formulating algorithms for the nite horizon GRN control problem. So, in this work we explore the feasibility of realizing the problem in a partially observable setting, mainly with Partially Observable Markov Decision Processes (POMDP). We proposed a POMDP formulation for the innite horizon version of the problem. Knowing the fact that POMDP problems suer from the curse of dimensionality, we also proposed a POMDP solution method that automatically decomposes the problem by isolating dierent unrelated parts of the problem, and then solves the reduced subproblems. We also proposed a method to enrich gene expression data sets given as input to POMDP control task, because in available data sets there are thousands of genes but only tens or rarely hundreds of samples. The method is based on the idea of generating more than one model using the available data sets, and then sampling data from each of the models and nally ltering the generated samples with the help of metrics that measure compatibility, diversity and coverage of the newly generated samples.