Department of Mathematics and Statistics Graduate Projects
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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 ... 
Elliptic Functions and Elliptic Interpolation
(20160921) 
Estimation of Sample Size and Power For Quantile Regression
(20160824)Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of ... 
A Review on Repeated Games and Reputations with Incomplete Information
(20160720)In this project we review the effects of reputation within the context of game theory. This is done through a study of two key papers. First, we examine a paper from Fudenberg and Levine: Reputation and Equilibrium ... 
The Chowla Problem and its generalizations
(20150915)In this thesis, we study the vanishing of certain $L$series attached to periodic arithmetical functions. Throughout the writeup, we let $f$ be an algebraicvalued (at times even rationalvalued) arithmetical function, ... 
The Saddle Point Method and its Applications to Number Theory
(20150915)In this thesis, we study the classical procedures useful in obtaining asymptotic expansions of functions defined by integrals and their applications to number theory. The final chapter in the thesis reports on a recent ... 
Assessing the impact of exposure to bisphenol A and triclosan during early pregnancy on birth weight outcomes in Canadian studies
(20150915)It is of interest to know whether early pregnancy exposure to chemicals such as bisphenolA (BPA) and triclosan (TCS) has negative impacts on birth outcomes. These chemicals are rapidly excreted from the body and therefore ... 
Polynomial Behaviour of Kostka Numbers
(20150915) 
Prediction and Filtering of Stationary Processes: Yaglom’s Method and Minimax Filtering
(20150811)The aim of this work is to give a basic introduction to the theory of stationary stochastic processes, particularly to the somewhat specialized problem of prediction and filtering of such processes. Kolmogorov was the first ... 
Linearization and Stability of Nonholonomic Mechanical Systems
(20150623)The stability of an equilibrium point of a nonlinear system is typically analyzed in two ways: (1) stability of its linearization, and (2) Lyapunov stability. An unconstrained simple mechanical system is a type of nonlinear ... 
Examining the Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime
(20150527)This project examines the work in the article "The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime", in which authors Galbraith and McKee ask the question `What is the probability ... 
Asymptotic Liberation in Free Probability
(20150126)Recently G. Anderson and B. Farrel presented the notion of asymptotic liberation on sequences of families of random unitary matrices. They showed that asymptotically liberating sequences of families of random unitary ... 
Optimal Binary Signaling for Correlated Sources over the Orthogonal Gaussian MultipleAccess Channel
(20141203)Optimal binary communication, in the sense of minimizing symbol error rate, with nonequal probabilities has been derived in [1] under various signalling configurations for the singleuser case with a given average energy ... 
Mr.
(20141003) 
Bivariate Models for Mortality and Morbidity
(20141003)In this report, to assess the adverse effects of air pollution on health outcomes, gen eralized additive models (GAMs) were fitted to mortality and hospital admissions data for Toronto, Montreal, Ottawa and Vancouver. The ...