Browsing Applied Mathematics by Type "Doctoral Thesis"
Now showing items 120 of 152

Algebraic Multigrid for Markov Chains and Tensor Decomposition
(University of Waterloo, 20130123)The majority of this thesis is concerned with the development of efficient and robust numerical methods based on adaptive algebraic multigrid to compute the stationary distribution of Markov chains. It is shown that classical ... 
Algorithms and Models for Tensors and Networks with Applications in Data Science
(University of Waterloo, 20160119)Big data plays an increasingly central role in many areas of research including optimization and network modeling. We consider problems applicable to large datasets within these two branches of research. We begin by ... 
Angles, Majorization, Wielandt Inequality and Applications
(University of Waterloo, 20130529)In this thesis we revisit two classical definitions of angle in an inner product space: realpart angle and Hermitian angle. Special attention is paid to Krein’s inequality and its analogue. Some applications are given, ... 
Application of Mixture Theory to solid tumors and normal pressure hydrocephalus
(University of Waterloo, 20140115)In this thesis, the theory of poroelasticity, namely the Mixture Theory version  a homogenized, macroscopic scale approach used to describe fluid flow through a porous medium  is employed in three separate cases ... 
Applications of Deep Learning to Differential Equation Models in Oncology
(University of Waterloo, 20230725)The integration of quantitative tools in biology and medicine has led to many groundbreaking advances in recent history, with many more promising discoveries on the horizon. Conventional mathematical models, particularly ... 
Bandlimited functions, curved manifolds, and selfadjoint extensions of symmetric operators
(University of Waterloo, 20080520)Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete ... 
Bayesian Inference Methods Applied to Cancer Research
(University of Waterloo, 20091211)The purpose of this Thesis is to present a Bayesian analysis of oncological data sets with particular focus on cervical carcinomas and ovarian cancers. Bayesian methods of data analysis have a very long history, and ... 
Bifurcation Analysis of Large Networks of Neurons
(University of Waterloo, 20151223)The human brain contains on the order of a hundred billion neurons, each with several thousand synaptic connections. Computational neuroscience has successfully modeled both the individual neurons as various types of ... 
Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties
(University of Waterloo, 20221006)In realworld applications, nominal mathematical models that are used to describe the state behaviors of dynamical systems are usually less robust to deal with environmental disruptions. Uncertainties, such as imprecision ... 
Bounded Control of the KuramotoSivashinsky equation
(University of Waterloo, 20131025)Feedback control is used in almost every aspect of modern life and is essential in almost all engineering systems. Since no mathematical model is perfect and disturbances occur frequently, feedback is required. The design ... 
Cerebrospinal Fluid Pulsations and Aging Effects in Mathematical Models of Hydrocephalus
(University of Waterloo, 20100820)In this Thesis we develop mathematical models to analyze two proposed causative mechanisms for the ventricular expansion observed in hydrocephalus: cerebrospinal fluid pulsations and small transmantle pressure gradients. To ... 
Challenges in epidemiological modelling: from sociovirulence dynamics to HIV interventions in MSM populations.
(University of Waterloo, 20200928)The spread of infectious diseases is one of the biggest challenges that public health faces nowadays. Their control is often not an easy task. Social behaviour plays an important role in disease prevention. However, the ... 
Characterizing Noise in Quantum Systems
(University of Waterloo, 20120726)In practice, quantum systems are not completely isolated from their environment and the resulting systemenvironment interaction can lead to information leakage from the system. As a result, if a quantum system is to be ... 
Clustering behaviour in networks with time delayed alltoall coupling
(University of Waterloo, 20170830)Networks of coupled oscillators arise in a variety of areas. Clustering is a type of oscillatory network behavior where elements of a network segregate into groups. Elements within a group oscillate synchronously, while ... 
Coherent delocalization in the lightmatter interaction
(University of Waterloo, 20201008)In this thesis, we study coherent delocalization in the lightmatter interaction: we investigate how the coherent center of mass delocalization of a first quantized system affects its interaction with a second quantized ... 
Complex Bases, Number Systems and Their Application to FractalWavelet Image Coding
(University of Waterloo, 2002)This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The ... 
Consensus Problems in Hybrid MultiAgent Systems
(University of Waterloo, 20220928)A multiagent system (MAS) is a dynamic system that consists of a group of interacting agents distributed over a network. In the past decades, the study of distributed coordination of multiagent systems has been widely ... 
Contributions to the study of general relativistic shearfree 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 shearfree 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 ... 
Control of Hysteresis in the LandauLifshitz Equation
(University of Waterloo, 20131115)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 ... 
Coupled models of structured contagion processes in humanenvironment systems
(University of Waterloo, 20210915)Models of infectious processes are a common feature in the landscape of applied mathematics. It is rare that these processes are isolated from other significant dynamics in nature, and therefore we can incorporate some of ...