Browsing Mathematics (Faculty of) by Title
Now showing items 1856-1875 of 2994
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On coloring digraphs with forbidden induced subgraphs
(University of Waterloo, 2023-04-25)This thesis mainly focuses on the structural properties of digraphs with high dichromatic number. The dichromatic number of a digraph $D$, denoted by $\dichi(D)$, is designed to be the directed analog of the chromatic ... -
On Combinatorics, Integrability and Puzzles
(University of Waterloo, 2020-10-23)In the last decade, many old and new results in combinatorics have been shown using the theory of quantum integrable systems from particle physics. The key to solving such problems is the derivation of an underlying ... -
On Computable Online Learning
(University of Waterloo, 2023-04-27)We initiate a study of computable online (c-online) learning, which we analyze under varying requirements for "optimality" in terms of the mistake bound. Our main contribution is to give a necessary and sufficient condition ... -
On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures
(University of Waterloo, 2014-09-11)Many standard problems in computational geometry have been solved asymptotically optimally as far as comparison-based algorithms are concerned, but there has been little work focusing on improving the constant factors ... -
On Convolution Squares of Singular Measures
(University of Waterloo, 2010-08-25)We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$. -
On Decoupling Concurrency Control from Recovery in Database Repositories
(University of Waterloo, 2005)We report on initial research on the concurrency control issue of compiled database applications. Such applications have a repository style of architecture in which a collection of software modules operate on a common ... -
On Design and Evaluation of High-Recall Retrieval Systems for Electronic Discovery
(University of Waterloo, 2017-03-08)High-recall retrieval is an information retrieval task model where the goal is to identify, for human consumption, all, or as many as practicable, documents relevant to a particular information need. This thesis ... -
On Diagonal Acts of Monoids
(University of Waterloo, 2007-08-30)In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely ... -
On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming
(University of Waterloo, 2007-05-18)Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound ... -
On Enumerative Structures in Quantum Field Theory
(University of Waterloo, 2020-07-13)This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further ... -
On estimands arising from misspecified semiparametric rate-based analysis of recurrent episodic conditions
(Wiley, 2019-11-10)Marginal rate-based analyses are widely used for the analysis of recurrent events in clinical trials. In many areas of application, the events are not instantaneous but rather signal the onset of a symptomatic episode ... -
On Eulerian orientations of even-degree hypercubes
(Elsevier, 2018-09-01)It is well known that every Eulerian orientation of an Eulerian 2k-edge connected (undirected) graph is strongly k-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, ... -
On Excluded Minors for Even Cut Matroids
(University of Waterloo, 2007-01-22)In this thesis we will present two main theorems that can be used to study minor minimal non even cut matroids. Given any signed graph we can associate an even cut matroid. However, given an even cut matroid, there are ... -
On Finding Large Cliques when the Chromatic Number is close to the Maximum Degree
(University of Waterloo, 2021-12-23)We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of size ∆(G) − 17. Our proof closely parallels a proof from Cranston and Rabern, who showed that graphs with χ = ∆ and ∆ ≥ ... -
On Fine-Grained Access Control for XML
(University of Waterloo, 2003)Fine-grained access control for XML is about controlling access to XML documents at the granularity of individual elements or attributes. This thesis addresses two problems related to XML access controls. The first is ... -
On First Passage Time Related Problems for Some Insurance Risk Processes
(University of Waterloo, 2022-05-13)For many decades, the study of ruin theory has long been one of the central topics of interest in insurance risk management. Research in this area has largely focused on analyzing the insurer’s solvency risk, which is ... -
On fixed points of self maps of the free ball
(Elsevier, 2018-07-01)In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ... -
On Geometric Drawings of Graphs
(University of Waterloo, 2018-04-18)This thesis is about geometric drawings of graphs and their topological generalizations. First, we study pseudolinear drawings of graphs in the plane. A pseudolinear drawing is one in which every edge can be extended ... -
On Geometric Range Searching, Approximate Counting and Depth Problems
(University of Waterloo, 2008-09-24)In this thesis we deal with problems connected to range searching, which is one of the central areas of computational geometry. The dominant problems in this area are halfspace range searching, simplex range searching ... -
On Hopf Ore Extensions and Zariski Cancellation Problems
(University of Waterloo, 2020-04-29)In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ...