Browsing Mathematics (Faculty of) by Title
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A Generalization to Signed Graphs of a Theorem of Sergey Norin and Robin Thomas
(University of Waterloo, 20191219)In this thesis we characterize the minimal nonplanar extensions of a signed graph. We consider the following question: Given a subdivision of a planar signed graph (G, Σ), what are the minimal structures that can be added ... 
Generalizations and Applications of the Stochastic Block Model to Basketball Games and Variable Selection Problems
(University of Waterloo, 20170124)Over the past decade, there has been an explosion of network data in a vast number of circumstances, such as the World Wide Web, social networks, gene interactions, economic networks, etc. Scientific analysis of networks ... 
Generalizations of AllorNothing Transforms and their Application in Secure Distributed Storage
(University of Waterloo, 20210126)An allornothing transform is an invertible function that maps s inputs to s outputs such that, in the calculation of the inverse, the absence of only one output makes it impossible for an adversary to obtain any information ... 
Generalizations of the Gap Principle and the ThueSiegel Principle, with Applications to Diophantine Equations
(University of Waterloo, 20190716)In this thesis we develop generalizations of two wellknown principles from the theory of Diophantine approximation, namely the gap principle and the ThueSiegel principle. Our results find their applications in the theory ... 
Generalizations to Corrections of Measurement Error Effects for Dynamic Treatment Regimes
(University of Waterloo, 20220819)Measurement error is a pervasive issue in questions of estimation and inference. Generally, any data which are measured with error will render the results of an analysis which ignores this error unreliable. This is a ... 
A Generalized Adversary Method for Quantum Query Complexity
(University of Waterloo, 20220520)Quantum query complexity measures the minimum number of queries a quantum algorithm needs to make to some input string to compute a function of that input. Query complexity models are widely used throughout quantum computing, ... 
A Generalized Blending Scheme for Arbitrary Order of Continuity
(University of Waterloo, 20230320)In this thesis, new templates and formulas of blending functions, schemes, and algorithms are derived for solving the scattered data interpolation problem. The resulting data fitting scheme interpolates the positions and ... 
Generalized Complex Structures on Kodaira Surfaces
(University of Waterloo, 20140805)In this thesis, we study generalized complex structures on Kodaira surfaces, which are nonK\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of eventype generalized ... 
Generalized GCDs as Applications of Vojta’s Conjecture
(University of Waterloo, 20230831)Starting with an analysis of the result that for any coprime integers a and b, and some ϵ > 0, we have eventually that gcd(a^n − 1,b^n − 1) < a^ϵn holds for all n, we are motivated to look for geometric reasons why this ... 
The Generalized Method of Moments for Mixture and Mixed Models
(University of Waterloo, 20150928)Mixture models can be found in a wide variety of statistical applications. However, undertaking statistical inference in mixture models, especially nonparametric mixture models, can be challenging. A general, or nonparametric, ... 
Generalized Set and Graph Packing Problems
(University of Waterloo, 20151112)Many complex systems that exist in nature and society can be expressed in terms of networks (e.g., social networks, communication networks, biological networks, Web graph, among others). Usually a node represents an ... 
Generalized Strategies for Path Integration using Neural Oscillators
(University of Waterloo, 20140820)Path integration is a process by which an animal obtains its location by integrating its velocity over time. Evidence shows that path integration may contribute to certain neural activity patterns in the entorhinal cortex ... 
Generalizing sampling theory for timevarying Nyquist rates using selfadjoint extensions of symmetric operators with deficiency indices (1,1) in Hilbert spaces
(University of Waterloo, 20110930)Sampling theory studies the equivalence between continuous and discrete representations of information. This equivalence is ubiquitously used in communication engineering and signal processing. For example, it allows ... 
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 ... 
Generating patterns on clothing for seamless design
(University of Waterloo, 20210426)Symmetric patterns are used widely in clothing manufacture. However, the discontinuity of patterns at seams can disrupt the visual appeal of clothing. While it is possible to align patterns to conceal such pattern breaks, ... 
Generating Radiosity Maps on the GPU
(University of Waterloo, 2005)Global illumination algorithms are used to render photorealistic images of 3D scenes taking into account both direct lighting from the light source and light reflected from other surfaces in the scene. Algorithms based ... 
Generation and properties of random graphs and analysis of randomized algorithms
(University of Waterloo, 20100122)We study a new method of generating random $d$regular graphs by repeatedly applying an operation called pegging. The pegging algorithm, which applies the pegging operation in each step, is a method of generating large ... 
Generative Modeling with Neural Ordinary Differential Equations
(University of Waterloo, 20191219)Neural ordinary differential equations (NODEs) (Chen et al., 2018) are ordinary differential equations (ODEs) with their dynamics modeled by neural networks. Continuous normalizing flows (CNFs) (Chen et al., 2018; Grathwohl ... 
Generic Attacks on Hash Functions
(University of Waterloo, 20100928)The subject of this thesis is a security property of hash functions, called chosentarget forcedprefix preimage (CTFP) resistance and the generic attack on this property, called the herding attack. The study of CTFP ... 
Genetic Programming for the Evolution of Functions with a Discrete Unbounded Domain
(University of Waterloo, 20130516)The idea of automatic programming using the genetic programming paradigm is a concept that has been explored in the work of Koza and several works since. Most problems attempted using genetic programming are finite in size, ...