Department of Mathematics and Statistics Graduate Theses
Recent Submissions

Modeling and Analysis of Dynamic Computer Experiments
Dynamic computer experiments which refer to computer experiments with time series outputs have increasingly gained popularity in both science and engineering. Analysis of dynamic computer experiments through statistical ... 
Statistical Inferences of TwoStage Phase II Cancer Clinical Trials with Two Coprimary Endpoints
In cancer research, twostage designs are usually used to assess the eﬀect of a new agent in phase II clinical trials. The optimal twostage designs with two coprimary endpoints have been proposed to assess the eﬀects ... 
Moduli spaces of vector bundles on toric surfaces
The moduli spaces parametrizing isomorphism classes of vector bundles are poorly understood. For certain choices of the first Chern class and a suitable second Chern class, we show that there exists an ample line bundle ... 
Symmetric Gaussian Rearrangement with Applications to Gaussian Noise Stability
We introduce a new symmetric Gaussian rearrangement that applies to sets and functions which are invariant with respect to a given finite subgroup of the orthogonal group. The properties of this rearrangement are developed, ... 
Reinforcement Learning for Decentralized Stochastic Control
We consider decentralized optimization of a controlled stochastic system where a finite number of decision makers seek to arrive at optimal policies using only local measurements and cost realizations. For such a context, ... 
The twovariable Artin conjecture and elliptic analogues
In 1927, Emil Artin conjectured that for any integer a other than 1 or squares, the set of primes p for which a is a primitive root modulo p has positive density in the set of all primes. This was proven subject to the ... 
Asymmetric matching allele models: imperfect matching, stability and the impact of mutation
Asymmetric matching alleles models assume that each parasite genotype specializes on a matching host genotype to a different degree. We study system behavior of a single locus diallelic asymmetric matching alleles model. ... 
Evolvability and Pleiotropic Constraint
Evolvability is a population's ability to change its underlying genetic makeup through natural selection, to evolve. Most measures of shortterm evolvability relate genetic change to the abundance and geometry of standing ... 
Modelling of Dynamic Computer Experiments with Both Qualitative and Quantitative Variables
Computer experiments are utilized as a popular tool of studying the relationship between responses and the factors that affect them. They are widely used in scientific researches and applications. Dynamic computer experiments ... 
Multitaper Methods for Cyclostationary Feature Detection in Time Series Data: Application to ACE Interplanetary Magnetic Field Data
In this thesis, a deeper understanding of the theory of cyclostationary processes is sought. Conventional spectrum estimation techniques assume that the data is a realization of a stationary process. If the data is ... 
Exploring the Evolutionary Relationship Between Virulence and Drug Resistance
One of the many possible negative outcomes of pathogen evolution is the emergence of a virulent drug resistant strain. A pathogen may exploit plasmidmediated gene transfer to gain drug resistance and virulence genes in ... 
Channel Optimized Scalar Quantization over Orthogonal Multiple Access Channels with Memory
In this thesis, the joint sourcechannel coding method, channel optimized scalar quantization, is applied to realvalued, correlated data. The data is sent over the orthogonal multiple access channel, with nonbinary noisy ... 
Pushsum Algorithm on Timevarying Random Graphs
In this thesis, we study the problem of achieving average consensus over a random timevarying sequence of directed graphs by extending the class of socalled push sum algorithms to such random scenarios. Provided that ... 
Global Fluctuations of Random Matrices and the SecondOrder Cauchy Transform
In this thesis we study the global fluctuations of random matrices (i.e., the covariance of two traces) from a secondorder free probability perspective, putting a particular emphasis on block Gaussian matrices. Our main ... 
Disease, Sex and Evolution
This thesis focuses upon some evolutionary problems related to sexual reproduction and disease. We first consider whether we should expect a fundamental difference between the outcomes of pre and postcopulatory sexual ... 
Noncommutative Independences for Pairs of Faces
In noncommutative probability theories, many different notions of independence arise in various contexts. According to the early classification work, there are only five such notions that are universal/natural in the sense ... 
Information and Estimation Theoretic Approaches to Data Privacy
Warner [145] in 1960s proposed a simple mechanism, now referred to as the randomized response model, as a remedy for what he termed “evasive answer bias” in survey sampling. The randomized response setting is as follows: ... 
Statistical Methods For Biomarker Threshold Models in Clinical Trials
In clinical trials, the main objective is to investigate the treatment effects on patients. However, many molecularly targeted drugs or treatments tend to benefit a subset of patients more, identified by a certain biomarker. ... 
An impulsive differential equation model for Marek's disease
(20160922)Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are ... 
Irreducibility of Random Hilbert Schemes
(20160913)We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the ...