Zhang, Wei

Microarray technology is a powerful approach for genomic research, which allows the monitoring of expressing profiles for tens of thousands genes in parallel and is already producing huge amounts of data. This thesis is motivated by a special microarray dataset for the bacteria Yersinia Pestis. It contains more than four thousands genes and each gene has different number of observations. The main purpose of this thesis is to detect essentially functional genes. Gene level adjusted multiple t‐test is proposed to handle the problem of unequal number of observations. Furthermore, a comparation study of our method with two other existing methods (Behrens‐Fisher method and Hotelling t‐square method) are presented. The comparison results show that our proposed methods is the best for identifying essential genes.

Change-point detection in hazard rate function is an important research topic in survival
analysis. In this dissertation, we firstly review existing methods for single change-point detection in
piecewise exponential hazard model. Then we consider the problem of estimating the change point in
the presence of right censoring and long-term survivors while using Kaplan-Meier estimator for the
susceptible proportion. The maximum likelihood estimators are shown to be consistent. Taking one
step further, we propose an counting process based and least squares based change-point detection
algorithm. For single change-point case, consistency results are obtained. We then consider the
detection of multiple change-points in the presence of long-term survivors via maximum likelihood
based and counting process based method. Last but not least, we use a weighted least squares based
and counting process based method for detection of multiple change-points with long-term survivors
and covariates. For multiple change-points detection, simulation studies show good performances of
our estimators under various parameters settings for both methods. All methods are applied to real
data analyses.

Thinning is a very important step in a Character Recognition System. This thesis evolves a thinning algorithm that can be hardware implemented to improve the speed of the process. The software thinning algorithm features a simple set of rules that can be applied on both hexagonal and orthogonal character images. The hardware architecture features the SIMD structure, simple processing elements and near neighbor communications. The algorithm was simulated against the U.S. Postal Service Character Database. The architecture, evolved with consideration of both the software constraints and the physical layout limitations, was simulated using VHDL hardware description language. Subsequent to VLSI design and simulations the chip was fabricated. The project provides for a feasibility study in utilizing the parallel processor architecture for the implementation of a parallel image thinning algorithm. It is hoped that such a hardware implementation will speed up the processing and lead eventually to a real time system.