Mathematics (Faculty of)
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Recent Submissions

Using Infinite Server Queues Theory In Stress Testing
(University of Waterloo, 20161205)In this thesis, we propose and study a framework to model stress testing, using an infinite server queues theory, such that this framework is aligned with and integrates several existing frameworks currently used in the ... 
Balancing Fidelity and Performance in Iridal Light Transport Simulations Aimed at Interactive Applications
(University of Waterloo, 20161129)Specific light transport models based on firstprinciples approaches have been proposed for complex organic materials such as human skin and blood. The driving force behind these efforts has been the highfidelity reproduction ... 
On Asynchronous Interference Channels
(University of Waterloo, 20161115)In the first part of the thesis, a decentralized wireless network of separate transmitterreceiver pairs is studied where there is no central controller to assign the resources to the users and users do not explicitly ... 
Quantifying the Effects of Solar Panel Orientation on the Electrical Grid
(University of Waterloo, 20161108)As the prices of solar panels continue to decline, energy production from solar farms is skyrocketing, leading to a situation where, at certain times, solar farms produce more energy than can be consumed. Today, the only ... 
Creating Your Bubble: Personal Space On and Around Large Public Displays
(ACM, 201605)We describe an empirical study that explores how users establish and use personal space around large public displays (LPDs). Our study complements field studies in this space by more fully characterizing interpersonal ... 
Graph Editing to a Given Neighbourhood Degree List is FixedParameter Tractable
(University of Waterloo, 20161026)Graph editing problems have a long history and have been widely studied, with applications in biochemistry and complex network analysis. They generally ask whether an input graph can be modified by inserting and deleting ... 
The Enigma History and Mathematics
(University of Waterloo, 20161025)In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ... 
A SocioPsychological Approach to the Iterated Prisoner's Dilemma
(University of Waterloo, 20161025)Affect Control Theory (ACT), as a model of human interaction, attempts to capture a part of the human psyche that tends to go overlooked in the study of Artificial Intelligence: the role of emotion in decision making. It ... 
Iterated Function Systems with PlaceDependent Probabilities and the Inverse Problem of Measure Approximation Using Moments
(University of Waterloo, 20161025)The study of iterated function systems has close ties with the subject of fractalbased analysis. One important application is the approximation of a target object by the fixed point of a contractive iterated function ... 
Armitage Lecture 2011: The Design and Analysis of Life History Studies
(Wiley, 2013)Life history studies collect information on events and other outcomes during people’s lifetimes. For example, these may be related to childhood development, education, fertility, health, or employment. Such longitudinal ... 
Estimation of Finite Population Duration Distributions from Longitudinal Survey Panels with Intermittent Followup
(Springer, 2013)We consider survival or duration times associated with spells (sojourns in some state) or events experienced by individuals in a population over a specified time period. Duration distributions can be estimated from data ... 
Robust and Powerful Tests for Rare Variants Using Fishers Method to Combine Evidence of Association From Two or More Complementary Tests
(Wiley, 2012)Many association tests have been proposed for rare variants, but the choice of a powerful test is uncertain when there is limited information on the underlying genetic model. Proposed methods use either linear statistics, ... 
Estimation and Assessment of Markov Multistate Models with Intermittent Observations on Individuals
(Springer, 201504)Multistate models provide important methods of analysis for many life history processes, and this is an area where John Klein made numerous contributions. When individuals in a study group are observed continuously so ... 
Score Tests for Association Under Responsedependent Sampling Designs for Expensive Covariates
(Oxford Journals, 20151127)Responsedependent sampling is widely used in settings where certain variables are expensive to obtain. Estimation has been thoroughly investigated but recent applications have emphasized tests of association for expensive ... 
Case Studies of a Machine Learning Process for Improving the Accuracy of Static Analysis Tools
(University of Waterloo, 20161018)Static analysis tools analyze source code and report suspected problems as warnings to the user. The use of these tools is a key feature of most modern software development processes; however, the tools tend to generate ... 
Modeling the Effects of AUTOSAR Overhead on Automotive Application Software Timing and Schedulability
(University of Waterloo, 20161014)AUTOSAR (AUTomotive Open System ARchitecture) provides an open and standardized E/E architecture to support modularity, transferability, reusability and scalability of the various components required to implement a function ... 
Symmetries
(University of Waterloo, 20161003)Automorphisms of graphs, hypergraphs and disgraphs are investigated. The invariance of the chromatic polynomial in the rotor effect is disproved. New invariance results are obtained. It is shown that given any integer k ... 
On Polynomialtime Pathfollowing Interiorpoint Methods with Local Superlinear Convergence
(University of Waterloo, 20160930)Interiorpoint methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interiorpoint methods over other approaches are: (1) robust global convergence, and (2) the ... 
FACES OF MATCHING POLYHEDRA
(University of Waterloo, 20160930)Let G = (V, E, ~) be a finite loopless graph, let b=(bi:ieV) be a vector of positive integers. A feasible matching is a vector X = (x.: j e: E) J of nonnegative integers such that for each node i of G, the sum of ... 
COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY
(University of Waterloo, 20160929)Two extensions of a geometry are compatible with each other if they have a common extension. If the given extensions are elementary, their compatibility can be intrinsically described in terms of their corresponding linear ...