Browsing Mathematics (Faculty of) by Title
Now showing items 512-531 of 2994
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Contributions to the study of general relativistic shear-free perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computation
(University of Waterloo, 1993)It has been conjectured that general relativistic shear-free perfect fluids with a barotropic equation of state, and such that the energy density, µ, and the pressure, p, satisfy µ + p ̸= 0, cannot simultaneously be rotating ... -
Contributions to the Study of the Validity of Huygens' Principle for the Non-self-adjoint Scalar Wave Equation on Petrov Type D Spacetimes
(University of Waterloo, 2000)This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime. ... -
Contributions to the Theory of Radicals for Noncommutative Rings
(University of Waterloo, 2017-06-20)We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroup-graded rings, monomial algebras, and Ore extensions of derivation type. In ... -
Contributions to Unsupervised and Semi-Supervised Learning
(University of Waterloo, 2009-05-22)This thesis studies two problems in theoretical machine learning. The first part of the thesis investigates the statistical stability of clustering algorithms. In the second part, we study the relative advantage of ... -
Control of Hysteresis in the Landau-Lifshitz Equation
(University of Waterloo, 2013-11-15)There are two main tools for determining the stability of nonlinear partial differential equations (PDEs): Lyapunov Theory and linearization. The former has the advantage of providing stability results for nonlinear ... -
Control of Non-deterministic Transition Systems for Linear Temporal Logic Specifications
(University of Waterloo, 2021-02-01)Consider the formal synthesis problem in the continuous dynamical systems. A systematic approach is the abstraction-based method: constructing an abstraction of the original continuous system in the discrete space, and ... -
Control of the Landau–Lifshitz equation
(Elsevier, 2016-05)The Landau–Lifshitz equation describes the dynamics of magnetization inside a ferromagnet. This equation is nonlinear and has an infinite number of stable equilibria. It is desirable to control the system from one equilibrium ... -
Controlled Generation of Stylized Text Using Semantic and Phonetic Representations
(University of Waterloo, 2022-01-21)Neural networks are a popular choice of models for the purpose of text generation. Variational autoencoders have been shown to be good at reconstructing text and generating novel text. However, controlling certain aspects ... -
Controller Gain Optimization for Position Control of an SMA Wire
(University of Waterloo, 2007-05-17)There has been an increasing interest in the field of `smart structures' and `smart materials'. In constructing smart structures, a class of materials called smart materials are often used as sensors and actuators. An ... -
Controlling the false discovery rate with dynamic adaptive procedures and of grouped hypotheses
(University of Waterloo, 2018-08-08)In the multiple testing problem with independent tests, the classical Benjamini-Hochberg (BH) procedure controls the false discovery rate (FDR) below the target FDR level. Adaptive procedures can improve power by ... -
Controlling the workload of M/G/1 queues via the q-policy
(Elsevier, 2015-06-01)We consider a single-server queueing system with Poisson arrivals and generally distributed service times. To systematically control the workload of the queue, we define for each busy period an associated timer process, ... -
Convective flow reversal in self-powered enzyme micropumps
(Proceedings of the National Academy of Sciences, 2016-02-22)Surface-bound enzymes can act as pumps that drive large-scale fluid flows in the presence of their substrates or promoters. Thus, enzymatic catalysis can be harnessed for "on demand" pumping in nano-and microfluidic devices ... -
Convergence Analysis of Generalized Primal-Dual Interior-Point Algorithms for Linear Optimization
(University of Waterloo, 2002)We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the ... -
Convergence of socio-ecological dynamics in disparate ecological systems under strong coupling to human social systems
(2018-04-06)It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics ... -
A Convergent Hierarchy of Certificates for Constrained Signomial Positivity
(University of Waterloo, 2020-09-24)Optimization is at the heart of many engineering problems. Many optimization problems, however, are computationally intractable. One approach to tackle such intractability is to find a tractable problem whose solution, ... -
Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems
(University of Waterloo, 2021-08-23)The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ... -
Convex duality in constrained mean-variance portfolio optimization under a regime-switching model
(University of Waterloo, 2008-09-23)In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal ... -
Convex Large Margin Training - Unsupervised, Semi-supervised, and Robust Support Vector Machines
(University of Waterloo, 2007-05-22)Support vector machines (SVMs) have been a dominant machine learning technique for more than a decade. The intuitive principle behind SVM training is to find the maximum margin separating hyperplane for a given set of ... -
Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods
(University of Waterloo, 2017-08-24)This thesis studies the theory and implementation of infeasible-start primal-dual interior-point methods for convex optimization problems. Convex optimization has applications in many fields of engineering and science such ... -
Convex relaxation for the planted clique, biclique, and clustering problems
(University of Waterloo, 2011-08-24)A clique of a graph G is a set of pairwise adjacent nodes of G. Similarly, a biclique (U, V ) of a bipartite graph G is a pair of disjoint, independent vertex sets such that each node in U is adjacent to every node in V ...