Browsing Mathematics (Faculty of) by Title
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Algebraic Analysis of VertexDistinguishing EdgeColorings
(University of Waterloo, 2006)Vertexdistinguishing edgecolorings (vdec colorings) are a restriction of proper edgecolorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ... 
Algebraic and combinatorial aspects of incidence groups and linear system nonlocal games arising from graphs
(University of Waterloo, 20190606)To every linear binaryconstraint system (LinBCS) nonlocal game, there is an associated algebraic object called the solution group. Cleve, Liu, and Slofstra showed that a LinBCS game has a perfect quantum strategy if and ... 
Algebraic Approaches to State Complexity of Regular Operations
(University of Waterloo, 20191015)The state complexity of operations on regular languages is an active area of research in theoretical computer science. Through connections with algebra, particularly the theory of semigroups and monoids, many problems ... 
Algebraic Aspects of MultiParticle Quantum Walks
(University of Waterloo, 20121204)A continuous time quantum walk consists of a particle moving among the vertices of a graph G. Its movement is governed by the structure of the graph. More formally, the adjacency matrix A is the Hamiltonian that determines ... 
Algebraic characterization of multivariable dynamics
(University of Waterloo, 20090326)Let X be a locally compact Hausdorﬀ space along with n proper continuous maps σ = (σ1 , · · · , σn ). Then the pair (X, σ) is called a dynamical system. To each system one can associate a universal operator algebra called ... 
The Algebraic KirchbergPhillips Conjecture for Leavitt Path Algebras
(University of Waterloo, 20150918)This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ... 
Algebraic Methods and Monotone Hurwitz Numbers
(University of Waterloo, 20120921)We develop algebraic methods to solve joincut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ... 
Algebraic Methods for Reducibility in NowhereZero Flows
(University of Waterloo, 20070925)We study reducibility for nowherezero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counterexample to some conjecture. We derive algebraic proofs of ... 
Algebraic Multigrid for Markov Chains and Tensor Decomposition
(University of Waterloo, 20130123)The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical ... 
Algebraic Tori in Cryptography
(University of Waterloo, 2005)Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than ... 
An Algorithm for Stable Matching with Approximation up to the Integrality Gap
(University of Waterloo, 20200710)In the stable matching problem we are given a bipartite graph G = (A ∪ B, E) where A and B represent disjoint groups of agents, each of whom has ordinal preferences over the members of the opposite group. The goal is to ... 
Algorithm Substitution Attacks: Detecting ASAs Using State Reset and Making ASAs Asymmetric
(University of Waterloo, 20210827)The field of cryptography has made incredible progress in the last several decades. With the formalization of security goals and the methods of provable security, we have achieved many privacy and integrity guarantees in ... 
Algorithmic Analysis of a General Class of Discretebased Insurance Risk Models
(University of Waterloo, 20130828)The aim of this thesis is to develop algorithmic methods for computing particular performance measures of interest for a general class of discretebased insurance risk models. We build upon and generalize the insurance ... 
Algorithmic Analysis of InfiniteState Systems
(University of Waterloo, 20090210)Many important software systems, including communication protocols and concurrent and distributed algorithms generate infinite statespaces. Modelchecking which is the most prominent algorithmic technique for the verification ... 
Algorithms and Design Principles for Rural Kiosk Networks
(University of Waterloo, 20070919)The KioskNet project aims to provide extremely lowcost Internet access to rural kiosks in developing countries, where conventional access technologies, \eg\, DSL, CDMA and dialup, are currently economically infeasible. ... 
Algorithms and Models for Tensors and Networks with Applications in Data Science
(University of Waterloo, 20160119)Big data plays an increasingly central role in many areas of research including optimization and network modeling. We consider problems applicable to large datasets within these two branches of research. We begin by ... 
Algorithms for Characterizing Peptides and Glycopeptides with Mass Spectrometry
(University of Waterloo, 20130926)The emergence of tandem mass spectrometry (MS/MS) technology has significantly accelerated protein identification and quantification in proteomics. It enables highthroughput analysis of proteins and their quantities in a ... 
Algorithms for fast linear system solving and rank profile computation
(University of Waterloo, 20140716)We give randomized algorithms for linear algebra problems concerning an n*m input matrix A over a field K. We give an algorithm that simultaneously computes the row and column rank profiles of A in 2r^3 + (r^2+n+m+A)^{1+o(1)} ... 
Algorithms for Geometric Covering and Piercing Problems
(University of Waterloo, 20130110)This thesis involves the study of a range of geometric covering and piercing problems, where the unifying thread is approximation using disks. While some of the problems addressed in this work are solved exactly with ... 
Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
(University of Waterloo, 20210817)Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences ...