Mathematics and Statistics, Department of
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Department of Mathematics and Statistics: Dr. Andrew D. Lewis
Selected preprints of Dr. Andrew D. Lewis
Recent Submissions

Sheaves of PhiPrincipal Parts
This thesis studies sheaves of phiprincipal parts, a modification of the wellknown sequence of sheaves of principal parts. In Chapter 1, we construct the sheaves of phiprincipalparts, and undertake their general study. ... 
Accelerated Convergence of SaddlePoint Dynamics
In this thesis, a secondorder continuoustime saddlepoint dynamics is introduced that mimics Nesterov's accelerated gradient flow dynamics. We study the convergence properties of this dynamics using a family of timevarying ... 
Filter Stability, Observability and Robustness for Partially Observed Stochastic Dynamical Systems
Filter stability refers to the correction of an incorrectly initialized filter for a partially observed stochastic dynamical system with increasing measurements. In this thesis, we study the filter stability problem, develop ... 
Control of nonholonomic mechanical systems using virtual surfaces
In this report we study the modelling of simple mechanical systems evolving on trivial principal bundles, specifically \emph{locomotion} systems with nonholonomic constraints. We show how we can model motion via group ... 
HighQ Spectral Peaks and Nonstationarity in the Deep Ocean Infragravity Wave Band: Tidal Harmonics and Solar Normal Modes
(Wiley, 20190220)Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389daylong deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband ... 
Nonparametric Testing Methods for TreatmentBiomarker Interaction based on Local PartialLikelihood
(Wiley, 20150617)In clinical trials, patients with different biomarker features may respond differently to the new treatments or drugs. In personalized medicine, it is important to study the interaction between treatment and biomarkers in ... 
Special values of Lseries, periodic coefficients and related themes
This thesis is centered around the theme of special values of Lfunctions and other infinite series, which are often expected to be transcendental numbers. More specifically, we focus on the following two questions in ... 
Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology
(20190312)Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host–pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly ... 
Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes
(20190320)Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form an−bn, denoted P(an−bn), by essentially proving that for integers a>b>0, P(an−bn)≥n+1 ... 
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 ...