Browsing Mathematics (Faculty of) by Title
Now showing items 1880-1899 of 3004
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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 ... -
On imprecision in statistical theory
(University of Waterloo, 2022-01-06)This thesis provides an exploration of the interplay between imprecise probability and statistics. Mathematically, one may summarise this relationship as how (Bayesian) sensitivity analysis involving a set of (prior) models ... -
On Improving Distributed Pregel-like Graph Processing Systems
(University of Waterloo, 2015-07-24)The considerable interest in distributed systems that can execute algorithms to process large graphs has led to the creation of many graph processing systems. However, existing systems suffer from two major issues: (1) ... -
On Infinitesimal Inverse Spectral Geometry
(University of Waterloo, 2011-09-27)Spectral geometry is the field of mathematics which concerns relationships between geometric structures of manifolds and the spectra of canonical differential operators. Inverse Spectral Geometry in particular concerns ... -
On Integrating Failure Localization with Survivable Design
(University of Waterloo, 2013-05-22)In this thesis, I proposed a novel framework of all-optical failure restoration which jointly determines network monitoring plane and spare capacity allocation in the presence of either static or dynamic traffic. The ... -
On moments and related quantities in insurance surplus analysis
(University of Waterloo, 2014-08-15)In risk theory, the time to ruin is one of the central quantities. The Laplace transform, density and moments of the time to ruin have been studied by many authors under different risk model assumptions. The Gerber-Shiu ... -
On multiple random locations of stationary processes
(University of Waterloo, 2019-01-18)We generalize the concept of intrinsic location functionals to accommodate n=2 random locations, which we combine together in either sets or vectors. For the set-valued case of "intrinsic multiple-location functionals" we ... -
On Optimizing Traffic Distribution for Clusters of Network Intrusion Detection and Prevention Systems
(University of Waterloo, 2008-09-02)To address the overload conditions caused by the increasing network traffic volume, recent literature in the network intrusion detection and prevention field has proposed the use of clusters of network intrusion detection ... -
On Pairing-Based Signature and Aggregate Signature Schemes
(University of Waterloo, 2009-01-21)In 2001, Boneh, Lynn, and Shacham presented a pairing-based signature scheme known as the BLS signature scheme. In 2003, Boneh, Gentry, Lynn, and Shacham presented the first aggregate signature scheme called the BGLS ... -
On Perturbative Methods in Spectral Geometry
(University of Waterloo, 2017-08-28)The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially Laplacians, defined on them. ... -
On Polynomial-time Path-following Interior-point Methods with Local Superlinear Convergence
(University of Waterloo, 2016-09-30)Interior-point methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interior-point methods over other approaches are: (1) robust global convergence, and (2) the ... -
On primal-dual interior-point algorithms for convex optimisation
(2015-09-29)This thesis studies the theory and implementation of interior-point methods for convex optimisation. A number of important problems from mathematics and engineering can be cast naturally as convex optimisation ... -
On primal-dual interior-point algorithms for convex optimisation
(2015-09-25)This thesis studies the theory and implementation of interior-point methods for convex optimisation. A number of important problems from mathematics and engineering can be cast naturally as convex optimisation ... -
On Prime-Order Elliptic Curves with Embedding Degrees 3, 4 and 6
(University of Waterloo, 2007-01-22)Bilinear pairings on elliptic curves have many cryptographic applications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes. The elliptic curves which are ... -
On Realistic Errors in Quantum Computers
(University of Waterloo, 2021-05-27)In this thesis, we are concerned with the problem of characterizing noise associated with implementations of quantum circuits. We first explore the notion of error rates of quantum circuits and argue that the semantic ... -
On Reconfiguration Problems: Structure and Tractability
(University of Waterloo, 2015-02-18)Given an n-vertex graph G and two vertices s and t in G, determining whether there exists a path and computing the length of the shortest path between s and t are two of the most fundamental graph problems. In the classical ... -
On Schnyder's Theorm
(University of Waterloo, 2010-08-20)The central topic of this thesis is Schnyder's Theorem. Schnyder's Theorem provides a characterization of planar graphs in terms of their poset dimension, as follows: a graph G is planar if and only if the dimension of ...