Browsing Mathematics (Faculty of) by Title
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On the Excluded Minors for Dyadic Matroids
(University of Waterloo, 20190117)The study of the class of dyadic matroids, the matroids representable over both $GF(3)$ and $GF(5)$, is a natural step to finding the excluded minors for $GF(5)$representability. In this thesis we characterize the ternary ... 
On the Extrema of Functions in the Takagi Class
(University of Waterloo, 20190123)The Takagi class is a class of fractal functions on the unit interval generalizing the celebrated Takagi function. In this thesis, we study the extrema of these functions. This is a problem that goes back to J.P. Kahane ... 
On the Geometry of IFS Fractals and its Applications
(University of Waterloo, 20140123)Visually complex objects with infinitesimally fine features, naturally call for mathematical representations. The geometrical property of selfsimilarity  the whole similar to its parts  when iterated to infinity generates ... 
On the Hardness of the Quantum Separability Problem and the Global Power of Locally Invariant Unitary Operations
(University of Waterloo, 20080918)Given a bipartite density matrix ρ of a quantum state, the Quantum Separability problem (QUSEP) asks — is ρ entangled, or separable? In this thesis, we first strengthen Gurvits’ 2003 NPhardness result for QUSEP by showing ... 
On the Importance of InfrastructureAwareness in LargeScale Distributed Storage Systems
(University of Waterloo, 20210108)Big data applications put significant latency and throughput demands on distributed storage systems. Meeting these demands requires storage systems to use a significant amount of infrastructure resources, such as network ... 
On the Integrality Gap of Directed Steiner Tree Problem
(University of Waterloo, 20140527)In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V, and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an rt path for ... 
On the Integration of Unmanned Aerial Vehicles into Public Airspace
(University of Waterloo, 20200528)Unmanned Aerial Vehicles will soon be integrated in the airspace and start serving us in various capacities such as package delivery, surveillance, search and rescue missions, inspection of infrastructure, precision ... 
On the local positivity of line bundles on algebraic surfaces
(University of Waterloo, 20150109)In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface. 
On the Maintenance Costs of Formal Software Requirements Specification Written in the Software Cost Reduction and in the Realtime Unified Modeling Language Notations
(University of Waterloo, 2005)A formal specification language used during the requirements phase can reduce errors and rework, but formal specifications are regarded as expensive to maintain, discouraging their adoption. This work presents a ... 
On the Modelling of Hyperspectral Light and Skin Interactions and the Simulation of Skin Appearance Changes Due to Tanning
(University of Waterloo, 20160107)The distinctive visual attributes of human skin are largely determined by its interactions with light across different spectral domains. Accordingly, the modelling of these interactions has been the object of extensive ... 
On the Modular Theory of von Neumann Algebras
(University of Waterloo, 20100917)The purpose of this thesis is to provide an exposition of the \textit{modular theory} of von Neumann algebras. The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and ... 
On the NearOptimality of List Scheduling Heuristics for Local and Global Instruction Scheduling
(University of Waterloo, 2006)Modern architectures allow multiple instructions to be issued at once and have other complex features. To account for this, compilers perform instruction scheduling after generating the output code. The instruction ... 
On the Number of Trials Needed to Obtain k Consecutive Successes
(Elsevier, 20210430)A sequence of independent Bernoulli trials, each of which is a success with probability p, is conducted. For k ∈ Z+, let Xk be the number of trials required to obtain k consecutive successes. Using techniques from elementary ... 
On the Optical Monitoring of Anemia Severity Levels
(University of Waterloo, 20150813)Anemia is a prevalent medical condition that seriously a ects millions of people all over the world. In many regions, not only its initial detection, but also its monitoring are hindered by the limited access to laboratory ... 
On the optimal CFL number of SSP methods for hyperbolic problems
(Elsevier, 20190101)We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of linestype discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. ... 
On the orientation of hypergraphs
(University of Waterloo, 20110113)This is an expository thesis. In this thesis we study outorientations of hypergraphs, where every hyperarc has one tail vertex. We study hypergraphs that admit outorientations covering supermodulartype connectivity ... 
On the Polyhedral LiftandProject Rank Conjecture for the Fractional Stable Set Polytope
(University of Waterloo, 20080116)In this thesis, we study the behaviour of Lovasz and Schrijver's liftandproject operators N and N_0 while being applied recursively to the fractional stable set polytope of a graph. We focus on two related conjectures ... 
On the Power and Limitations of Shallow Quantum Circuits
(University of Waterloo, 20220901)Constantdepth quantum circuits, or shallow quantum circuits, have been shown to exhibit behavior that is uniquely quantum. This thesis explores the power and limitations of constantdepth quantum circuits, in particular ... 
On the power of interleaved lowdepth quantum and classical circuits
(University of Waterloo, 20220926)Lowdepth quantum circuits are a wellsuited model for nearterm quantum devices, given short coherence times and noisy gate operations, making it pivotal to examine their computational power. It was already known as early ... 
On the Properties and Structure of Bordered Words and Generalizations
(University of Waterloo, 20221012)Combinatorics on words is a field of mathematics and theoretical computer science that is concerned with sequences of symbols called words, or strings. One class of words that are ubiquitous in combinatorics on words, ...