Mathematics (Faculty of)
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On The Circuit Diameters of Some Combinatorial Polytopes
(University of Waterloo, 20170920)The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P ... 
A postquantum digital signature scheme based on supersingular isogenies
(University of Waterloo, 20170920)We present the first generalpurpose digital signature scheme based on supersingular elliptic curve isogenies secure against quantum adversaries in the quantum random oracle model with small key sizes. This scheme is ... 
The Relation between Polygonal Gravity and 3D Loop Quantum Gravity
(University of Waterloo, 20170913)In this thesis, we explore the relation between ’t Hooft polygonal gravity and loop quantum gravity (LQG)  two models of discrete gravity in 2+1 dimensions. While the relation between the two theories has been studied ... 
Enabling Expressive Keyboard Interaction with Finger, Hand, and Hand Posture Identification
(University of Waterloo, 20170913)The input space of conventional physical keyboards is largely limited by the number of keys. To enable more actions than simply entering the symbol represented by a key, standard keyboards use combinations of modifier keys ... 
Statistical Learning and Stochastic Process for Robust Predictive Control of Vehicle Suspension Systems
(University of Waterloo, 20170912)Predictive controllers play an important role in today's industry because of their capability of verifying optimum control signals for nonlinear systems in a realtime fashion. Due to their mathematical properties, such ... 
Performance of the UltraWide Word Model
(University of Waterloo, 20170908)The Ultrawide word model of computation (UWRAM) is an extension of the WordRAM model which has an ALU that can operate on w^2 bits at a time, where w is the size in bits of a cell in memory. The purpose of this thesis ... 
Effective Dimensionality Control in Quantitative Finance and Insurance
(University of Waterloo, 20170906)It is wellknown that dimension reduction techniques such as the Brownian bridge, principal component analysis, linear transformation could increase the efficiency of QuasiMonte Carlo (QMC) methods. Caflisch et al. (1997), ... 
Evaluating and Characterizing the Performance of 802.11 Networks
(University of Waterloo, 20170905)The 802.11 standard has become the dominant protocol for Wireless Local Area Networks (WLANs). As an indication of its current and growing popularity, it is estimated that over 20 billion WiFi chipsets will be shipped ... 
Circle Graph Obstructions
(University of Waterloo, 20170831)In this thesis we present a selfcontained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excludedminor characterization ... 
Clustering behaviour in networks with time delayed alltoall coupling
(University of Waterloo, 20170830)Networks of coupled oscillators arise in a variety of areas. Clustering is a type of oscillatory network behavior where elements of a network segregate into groups. Elements within a group oscillate synchronously, while ... 
Restricted String Representations
(University of Waterloo, 20170829)A string representation of a graph assigns to every vertex a curve in the plane so that two curves intersect if and only if the represented vertices are adjacent. This work investigates string representations of graphs ... 
Reconfiguring Graph Colorings
(University of Waterloo, 20170829)Graph coloring has been studied for a long time and continues to receive interest within the research community \cite{kubale2004graph}. It has applications in scheduling \cite{daniel2004graph}, timetables, and compiler ... 
A quadratic programming approach to find faces in robust nonnegative matrix factorization
(University of Waterloo, 20170829)Nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique because it is easily interpretable and can discern useful features. For a given matrix M (dimension n x m) whose entries are nonnegative ... 
Stabilizing Weighted Graphs
(University of Waterloo, 20170829)An edgeweighted graph G = (V,E) is called stable if the value of a maximumweight matching equals the value of a maximumweight fractional matching. Stable graphs play an important role in some interesting game theory ... 
Some Upper and Lower Bounds regarding Query Complexity
(University of Waterloo, 20170829)Query complexity is one of the several notions of complexity de ned to measure the cost of algorithms. It plays an important role in demonstrating the quantum advantage, that quantum computing is faster than classical ... 
Technology Diffusion on Spiders
(University of Waterloo, 20170829)There has been significant research about cascade effects that occur when information is spread through a network. Most models of such cascade effects are highlylocalised, which means that they assume a node’s behaviour ... 
A Parallel Study of the Fock Space Approach to Classical and Free Brownian Motion
(University of Waterloo, 20170828)The purpose of this thesis is to elaborate the similarities between the classical and the free probability by means of developing the chaos decomposition of stochastic integrals driven by Brownian motion and its free ... 
Smith Normal Form over Local Rings and Related Problems
(University of Waterloo, 20170828)The Smith normal form is a diagonalization of matrices with many applications in diophantine analysis, graph theory, system control theory, simplicial homology, and more recently, in topological analysis of big data. ... 
Discriminators of Integer Sequences
(University of Waterloo, 20170828)The discriminator of an integer sequence \textbf{s} = $(s(n))_{n \geq 0}$, first introduced by Arnold, Benkoski and McCabe in 1985, is the function $D_s (n)$ that maps the integer $n \geq 1$ to the smallest positive integer ... 
Generating Functions for Hyperbolic Plane Tessellations
(University of Waterloo, 20170828)For a hyperbolic plane tessellation there is a generating function with respect to the distance. This generating function is the same as the growth function of a group of isometries of hyperbolic plane that acts regularly ...