Mathematics (Faculty of): Recent submissions
Now showing items 1-20 of 1965
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Correlation and Communication via a Quantum Field
(University of Waterloo, 2019-07-15)We study the ability of qubit detectors to i) extract correlations from, and ii) transmit quantum information through, a quantum field. We start by perturbatively studying the harvesting of correlations from thermal and ... -
Computability Theory and Some Applications
(University of Waterloo, 2019-07-15)We explore various areas of computability theory, ranging from applications in computable structure theory primarily focused on problems about computing isomorphisms, to a number of new results regarding the degree-theoretic ... -
Applications of Stochastic Gradient Descent to Nonnegative Matrix Factorization
(University of Waterloo, 2019-07-15)We consider the application of stochastic gradient descent (SGD) to the nonnegative matrix factorization (NMF) problem and the unconstrained low-rank matrix factorization problem. While the literature on the SGD algorithm ... -
Unitary Correlation Sets and their Applications
(University of Waterloo, 2019-07-04)We relate Connes' embedding problem in operator algebras to the Brown algebra Unc(n), which is defined as the universal unital C*-algebra generated by the entries of an n x n unitary matrix. In particular, we show that the ... -
A Statistical Response to Challenges in Vast Portfolio Selection
(University of Waterloo, 2019-07-04)The thesis is written in response to emerging issues brought about by an increasing number of assets allocated in a portfolio and seeks answers to puzzling empirical findings in the portfolio management area. Over the ... -
Invariant manifold theory for impulsive functional differential equations with applications
(University of Waterloo, 2019-07-03)The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous ... -
Optimization for Image Segmentation
(University of Waterloo, 2019-06-26)Image segmentation, i.e., assigning each pixel a discrete label, is an essential task in computer vision with lots of applications. Major techniques for segmentation include for example Markov Random Field (MRF), Kernel ... -
Risk Management with Non-Convex and Non-Monotone Preferences
(University of Waterloo, 2019-06-24)This thesis studies two types of problems, the theory of risk functionals and the risk sharing problem. We put a special focus on a class of non-monotone law-invariant risk functionals, called the signed Choquet integrals. The ... -
Model-Based Bayesian Sparse Sampling for Data Efficient Control
(University of Waterloo, 2019-06-24)In this work, we propose a novel Bayesian-inspired model-based policy search algorithm for data efficient control. In contrast to other model-based approaches, our algorithm makes use of approximate Gaussian processes in ... -
Mitigator: Privacy policy compliance using Intel SGX
(University of Waterloo, 2019-06-19)Privacy policies have been known to be hard to read and understand by internet users and yet users are obliged to accept these one-sided terms of usage of their data before they can effectively use websites. Although ... -
Approximation Constants for Closed Subschemes of Projective Varieties
(University of Waterloo, 2019-06-19)Diophantine approximation is a branch of number theory with a long history, going back at least to the work of Dirichlet and Liouville in the 1840s. The innocent-looking question of how well an arbitrary real algebraic ... -
Fast Multi-Level Co-Clustering
(2013)We present a new multilevel method for hierarchical co-clustering. The fast multilevel co-clustering method (FMCC) implements a bi-coarsening process on the bipartite graph induced by the feature matrix. It does so in a ... -
Degrees of Categoricity and the Isomorphism Problem
(University of Waterloo, 2019-06-12)In this thesis, we study notions of complexity related to computable structures. We first study degrees of categoricity for computable tree structures. We show that, for any computable ordinal $\alpha$, there exists a ... -
Entity Matching and Disambiguation Across Multiple Knowledge Graphs
(University of Waterloo, 2019-06-10)Knowledge graphs are considered an important representation that lie between free text on one hand and fully-structured relational data on the other. Knowledge graphs are a back-bone of many applications on the Web. With ... -
Theoretical foundations for efficient clustering
(University of Waterloo, 2019-06-07)Clustering aims to group together data instances which are similar while simultaneously separating the dissimilar instances. The task of clustering is challenging due to many factors. The most well-studied is the high ... -
Sidon and Kronecker-like sets in compact abelian groups
(University of Waterloo, 2019-06-07)Let $G$ be a compact abelian group and $\Ga$ be its discrete dual group. In this thesis we study various types of interpolation sets. A subset $E \subset \Ga$ is Sidon if every bounded function on $E$ can be interpolated ... -
Algebraic and combinatorial aspects of incidence groups and linear system non-local games arising from graphs
(University of Waterloo, 2019-06-06)To every linear binary-constraint system (LinBCS) non-local 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 ... -
Multiply Robust Empirical Likelihood Inference for Missing Data and Causal Inference Problems
(University of Waterloo, 2019-06-06)Missing data are ubiquitous in many social and medical studies. A naive complete-case (CC) analysis by simply ignoring the missing data commonly leads to invalid inferential results. This thesis aims to develop statistical ... -
Kalman Filter Based Sensor Placement For Burgers Equation
(University of Waterloo, 2019-06-03)The algorithm used for determining sensor placement in this thesis will be based on the Kalman filter. This filter is very famous and its application are numerous - some examples include aircraft navigation, finance and ... -
Numerical Simulations of Internal Solitary and Solitary-Like Waves: Wave Interactions and Instabilities
(University of Waterloo, 2019-05-31)Internal solitary and solitary-like waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a ...