Browsing Mathematics (Faculty of) by Title
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Quadratic Hedging with Margin Requirements and Portfolio Constraints
(University of Waterloo, 20100428)We consider a meanvariance portfolio optimization problem, namely, a problem of minimizing the variance of the ﬁnal wealth that results from trading over a ﬁxed ﬁnite horizon in a continuoustime complete market in the ... 
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 ... 
Quadratically Dense Matroids
(University of Waterloo, 20200708)This thesis is concerned with finding the maximum density of rank$n$ matroids in a minorclosed class. The extremal function of a nonempty minorclosed class $\mathcal M$ of matroids which excludes a rank2 uniform ... 
Qualitative Properties of Hybrid Singular Systems
(University of Waterloo, 20190115)A singular system model is mathematically formulated as a set of coupled differential and algebraic equations. Singular systems, also referred to as descriptor or differential algebraic systems, have extensive applications ... 
Qualitative Properties of Stochastic Hybrid Systems and Applications
(University of Waterloo, 20110902)Hybrid systems with or without stochastic noise and with or without time delay are addressed and the qualitative properties of these systems are investigated. The main contribution of this thesis is distributed in three ... 
Qualitative Studies of Nonlinear Hybrid Systems
(University of Waterloo, 20101214)A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science ... 
Qualitative Theory of Switched Integrodifferential Equations with Applications
(University of Waterloo, 20140825)Switched systems, which are a type of hybrid system, evolve according to a mixture of continuous/discrete dynamics and experience abrupt changes based on a switching rule. Many realworld phenomena found in branches of ... 
Quantifying Location Privacy In Locationbased Services
(University of Waterloo, 20181024)Mobile devices (e.g., smart phones) are widely used in people's daily lives. When users rely on locationbased services in mobile applications, plenty of location records are exposed to the service providers. This causes ... 
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 ... 
Quantitative Analysis of Extreme Risks and Extremal Dependence in Insurance and Finance
(University of Waterloo, 20190925)In this thesis, we aim at a quantitative understanding of extreme risks and extremal depen dence in insurance and finance. We use regularly varying distribution functions in extreme value theory (EVT) to model extreme ... 
Quantitative Approaches to the Cancer Stem Cell Hypothesis
(University of Waterloo, 20150508)In this thesis, phenotype switching in cancer cell populations is modeled. We focus on the behavior of cells at the phenotypic level and present mathematical models to capture the results of available experiments. The ... 
Quantitative Testing of Probabilistic Phase Unwrapping Methods
(University of Waterloo, 2001)The reconstruction of a phase surface from the observed principal values is required for a number of applications, including synthetic aperture radar (SAR) and magnetic resonance imaging (MRI). However, the process of ... 
Quantum algorithms for searching, resampling, and hidden shift problems
(University of Waterloo, 20120921)This thesis is on quantum algorithms. It has three main themes: (1) quantum walk based search algorithms, (2) quantum rejection sampling, and (3) the Boolean function hidden shift problem. The first two parts deal with ... 
Quantum Cellular Automata: Theory and Applications
(University of Waterloo, 20070926)This thesis presents a model of Quantum Cellular Automata (QCA). The presented formalism is a natural quantization of the classical Cellular Automata (CA). It is based on a lattice of qudits, and an update rule consisting ... 
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 20201221)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ... 
Quantum Cost Models for Cryptanalysis of Isogenies
(University of Waterloo, 20190501)Isogenybased cryptography uses keys large enough to resist a farfuture attack from Tani’s algorithm, a quantum random walk on Johnson graphs. The key size is based on an analysis in the query model. Queries do not ... 
Quantum fields and machine learning
(University of Waterloo, 20200925)In this thesis, we use detector models to study various properties of quantum fields. One such property is the correlations present in fields. It is known that two uncorrelated detectors, upon coupling to a quantum field, ... 
Quantum Indefinite Spacetime: Part II
(University of Waterloo, 20180910)We adopt an operational mode of thinking to study spacetime fluctuations and their impacts on questions of quantum gravity. Particular emphasis is put on studying causal structure fluctuations. The study is guided by the ... 
Quantum independence and chromatic numbers
(University of Waterloo, 20190828)In this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the ... 
Quantum Information and Variants of Interactive Proof Systems
(University of Waterloo, 20110824)For nearly three decades, the model of interactive proof systems and its variants have been central to many important and exciting developments in computational complexity theory such as exact characterization of some well ...