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

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 ... 
ON STOCHASTIC TEAMS WITH COUNTABLY MANY DECISION MAKERS
(20171121)This report is concerned with the connections between team optimal and personbyperson optimal solutions for static teams with countably infinite decision makers. The average cost problem for static teams is studied and ... 
On the BorelWeil Theorem for SL_n
(2017) 
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 ... 
Evaluation and Application of a Test for TreatmentBiomarker Interaction Effects Using Probabilistic Indices
(201708)A predictive biomarker is a patient characteristic which associates with different effects of the treatment on the patient. In clinical trials, it is often of interest to assess whether the effects of the treatment differ ... 
Working with sophisticated problems in a grade 10 math classroom: The exploration of new experiences on selfefficacy
(201709)Studies show that selfefficacy is a strong indicator of student math achievement (Kitsantas et al., 2011). It has also been seen that selfefficacy changes based on the situation that one has to face (Bandura, 1997). This ... 
Experimenting with low threshold, high ceiling mathematics tasks in a Grade 10 mathematics class: a mixed method study on student engagement
(20170922)The experiment. In collaboration with the Mathematical Knowledge Network and the Fields institute, Professor Peter Taylor and his team created Math912, a new approach to curricular instruction following inquirybased ... 
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 ... 
Ensemble Controllability of Linear Control Systems
(2017)This thesis is concerned about ensemble controllability. We give an overview of the notions of ensemble controllability, in particular, $L_{2}$ensemble controllability, and uniform ensemble controllability. We review the ... 
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. ... 
Representation of numbers by quaternary quadratic forms
(20160927) 
An Rpackage for the Estimation and Testing of Multiple Covariates and Biomarker Interactions for Survival Data Based on Local Partial Likelihood
(20160927)When we study the variables that a ffect survival time, we usually estimate their eff ects by the Cox regression model. In biomedical research, e ffects of the covariates are often modi ed by a biomarker variable. This ... 
On The Dirichlet Distribution
(20160927)The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution ... 
Degeneracy of velocity constraints in rigid body systems
(20160927)The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the ...