Browsing Mathematics (Faculty of) by Title
Now showing items 158-177 of 3020
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Applications of Description Logic and Causality in Model Checking
(University of Waterloo, 2009-06-19)Model checking is an automated technique for the verification of finite-state systems that is widely used in practice. In model checking, a model M is verified against a specification $\varphi$, exhaustively checking ... -
Applications of Geometry in Optimization and Statistical Estimation
(University of Waterloo, 2016-01-25)Geometric properties of statistical models and their influence on statistical inference and asymptotic theory reveal the profound relationship between geometry and statistics. This thesis studies applications of convex ... -
Applications of Operator Systems in Dynamics, Correlation Sets, and Quantum Graphs
(University of Waterloo, 2020-07-24)The recent works of Kalantar-Kennedy, Katsoulis-Ramsey, Ozawa, and Dykema-Paulsen have demonstrated that many problems in the theory of operator algebras and quantum information can be approached by looking at various ... -
Applications of Projection Pursuit in Functional Data Analysis: Goodness-of- fit, Forecasting, and Change-point Detection
(University of Waterloo, 2021-01-20)Dimension reduction methods for functional data have been avidly studied in recent years. However, existing methods are primarily based on summarizing the data by their projections into principal component subspaces, namely ... -
Applications of Semidefinite Programming in Quantum Cryptography
(University of Waterloo, 2007-05-18)Coin-flipping is the cryptographic task of generating a random coin-flip between two mistrustful parties. Kitaev discovered that the security of quantum coin-flipping protocols can be analyzed using semidefinite programming. ... -
Applications of Stochastic Control to Portfolio Selection Problems
(University of Waterloo, 2018-10-16)Portfolio selection is an important problem both in academia and in practice. Due to its significance, it has received great attention and facilitated a large amount of research. This thesis is devoted to structuring optimal ... -
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 ... -
Applications of the minimal modelprogram in arithmetic dynamics
(University of Waterloo, 2021-09-07)Let F be a surjective endomorphism of a normal projective variety X defined over a number field. The dynamics of F may be studied through the dynamics of the linear action of an associated linear pull-back action on divisors. ... -
Applied Hilbert's Nullstellensatz for Combinatorial Problems
(University of Waterloo, 2016-09-23)Various feasibility problems in Combinatorial Optimization can be stated using systems of polynomial equations. Determining the existence of a \textit{stable set} of a given size, finding the \textit{chromatic number} of ... -
Applying Fair Reward Divisions to Collaborative Work
(University of Waterloo, 2019-07-18)Collaborative crowdsourcing tasks allow workers to solve more difficult problems than they could alone, but motivating workers in these tasks is complex. In this thesis, we study how to use payments to motivate groups of ... -
Approach to Evaluating Clustering Using Classification Labelled Data
(University of Waterloo, 2011-01-17)Cluster analysis has been identified as a core task in data mining for which many different algorithms have been proposed. The diversity, on one hand, provides us a wide collection of tools. On the other hand, the profusion ... -
Approaches and Techniques to Enhance Efficiency and Performance of Non-Contrastive Self-Supervised Learning Methods
(University of Waterloo, 2023-03-31)Self-supervised learning (SSL) methods have gained considerable attention in recent years due to their ability to learn useful representations of data without relying on labels during training. These methods have ... -
Approximate Private Quantum Channels
(University of Waterloo, 2006)This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps, <em>n</em> + 2log(1/ε) + <em>c</em> ... -
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2019)It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable ... -
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2017)It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable ... -
Approximately Optimum Search Trees in External Memory Models
(University of Waterloo, 2016-05-16)We examine optimal and near optimal solutions to the classic binary search tree problem of Knuth. We are given a set of n keys (originally known as words), B_1, B_2, ..., B_n and 2n+1 frequencies. {p_1, p_2, ..., p_n} ... -
Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs
(University of Waterloo, 2017-04-27)We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ... -
Approximating stable densities with Padé approximants and asymptotic series
(University of Waterloo, 2011-04-29)In this thesis, we are interested in using the Padé approximants and asymptotic series to approximate the density functions of the stable distributions. The paper specifically discusses the selection of the optimal degree ... -
An Approximation Algorithm for Character Compatibility and Fast Quartet-based Phylogenetic Tree Comparison
(University of Waterloo, 2000)Phylogenetic analysis, or the inference of evolutionary history is done routinely by biologists and is one of the most important problems in systematic biology. In this thesis, we study two computational problems in ... -
Approximation Algorithms for (S,T)-Connectivity Problems
(University of Waterloo, 2010-08-03)We study a directed network design problem called the $k$-$(S,T)$-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer $k$, the minimum cost $k$-vertex ...