Browsing Mathematics (Faculty of) by Title
Now showing items 69-88 of 2992
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The Algebraic Kirchberg--Phillips Conjecture for Leavitt Path Algebras
(University of Waterloo, 2015-09-18)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, 2012-09-21)We develop algebraic methods to solve join-cut 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 Nowhere-Zero Flows
(University of Waterloo, 2007-09-25)We study reducibility for nowhere-zero flows. A reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counter-example to some conjecture. We derive algebraic proofs of ... -
Algebraic Multigrid for Markov Chains and Tensor Decomposition
(University of Waterloo, 2013-01-23)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 ... -
Algorithm Design for Ordinal Settings
(University of Waterloo, 2022-08-29)Social choice theory is concerned with aggregating the preferences of agents into a single outcome. While it is natural to assume that agents have cardinal utilities, in many contexts, we can only assume access to the ... -
An Algorithm for Stable Matching with Approximation up to the Integrality Gap
(University of Waterloo, 2020-07-10)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, 2021-08-27)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 Discrete-based Insurance Risk Models
(University of Waterloo, 2013-08-28)The aim of this thesis is to develop algorithmic methods for computing particular performance measures of interest for a general class of discrete-based insurance risk models. We build upon and generalize the insurance ... -
Algorithmic Analysis of Infinite-State Systems
(University of Waterloo, 2009-02-10)Many important software systems, including communication protocols and concurrent and distributed algorithms generate infinite state-spaces. Model-checking which is the most prominent algorithmic technique for the verification ... -
Algorithmic and Linear Programming-Based Techniques for the Maximum Utility Problem
(University of Waterloo, 2023-05-25)A common topic of study in the subfield of Operations Research known as Revenue Management is finding optimal prices for a line of products given customer preferences. While there exists a large number of ways to model ... -
Algorithmic Behaviours of Adagrad in Underdetermined Linear Regression
(University of Waterloo, 2023-08-24)With the high use of over-parameterized data in deep learning, the choice of optimizer in training plays a big role in a model’s ability to generalize well due to the existence of solution selection bias. We consider the ... -
Algorithms and Design Principles for Rural Kiosk Networks
(University of Waterloo, 2007-09-19)The KioskNet project aims to provide extremely low-cost Internet access to rural kiosks in developing countries, where conventional access technologies, \eg\, DSL, CDMA and dial-up, are currently economically infeasible. ... -
Algorithms and Models for Tensors and Networks with Applications in Data Science
(University of Waterloo, 2016-01-19)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 Analytic Combinatorics in Several Variables
(University of Waterloo, 2023-04-25)Given a multivariate rational generating function we are interested in computing asymptotic formulas for the sequences encoded by the coefficients. In this thesis we apply the theory of analytic combinatorics in several ... -
Algorithms for Characterizing Peptides and Glycopeptides with Mass Spectrometry
(University of Waterloo, 2013-09-26)The emergence of tandem mass spectrometry (MS/MS) technology has significantly accelerated protein identification and quantification in proteomics. It enables high-throughput analysis of proteins and their quantities in a ... -
Algorithms for fast linear system solving and rank profile computation
(University of Waterloo, 2014-07-16)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, 2013-01-10)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 Geometric Facility Location: Centers in a Polygon and Dispersion on a Line
(University of Waterloo, 2023-02-24)We study three geometric facility location problems in this thesis. First, we consider the dispersion problem in one dimension. We are given an ordered list of (possibly overlapping) intervals on a line. We wish to choose ... -
Algorithms for Linearly Recurrent Sequences of Truncated Polynomials
(University of Waterloo, 2021-08-17)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 ...