Browsing Applied Mathematics by Title
Now showing items 298-317 of 489
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Negative Quasi-Probability in the Context of Quantum Computation
(University of Waterloo, 2013-08-09)This thesis deals with the question of what resources are necessary and sufficient for quantum computational speedup. In particular, we study what resources are required to promote fault tolerant stabilizer computation to ... -
Network centrality analysis of eye-gaze data in autism spectrum disorder
(Elsevier, 2019-08)Individuals suffering from autism spectrum disorder (ASD) exhibit impaired social communication, the manifestations of which include abnormal eye contact and gaze. In this study, we first seek to characterize the spatial ... -
Nine Challenges In Incorporating The Dynamics Of Behaviour In Infectious Diseases Models
(Elsevier, 2015-03-01)Traditionally, the spread of infectious diseases in human populations has been modelled with static parameters. These parameters, however, can change when individuals change their behaviour. If these changes are themselves ... -
Non-compact groups, tensor operators and applications to quantum gravity
(University of Waterloo, 2016-09-23)This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. Non-compact groups appear naturally if the space-time is of Lorentzian signature, but can also ... -
Non-linear Effects on Stopping of Fast Moving Molecular Ions Through Solids
(University of Waterloo, 2007-06-27)This thesis studies the non-linear (Barkas) effects on stopping of fast moving molecular ions through solids. We model the solid target by a rigid lattice of positive ion cores surrounded by a gas of electrons. To model ... -
Non-linear Interactions between Internal Wave Beams: Beyond the Traditional Approximation.
(University of Waterloo, 2017-09-22)The problem of nonlinear interactions of internal waves is solved using small-amplitude expansions beyond the traditional approximation; that is the horizontal component of the Earth’s rotation vector is included in our ... -
Nonlinear Preconditioning Methods for Optimization and Parallel-In-Time Methods for 1D Scalar Hyperbolic Partial Differential Equations
(University of Waterloo, 2017-10-18)This thesis consists of two main parts, part one addressing problems from nonlinear optimization and part two based on solving systems of time dependent differential equations, with both parts describing strategies for ... -
Nonlinear screening of external charge by doped graphene
(University of Waterloo, 2010-04-28)In the rst part of this thesis we discuss some details of properties of graphene and we explain the tight-binding approach to nd the energy spectrum in graphene. In the second part of the thesis, we solve a nonlinear ... -
Nonlinear Wave Propagation in Brass Instruments
(University of Waterloo, 2013-01-25)The study of wave production and propagation is a common phenomenon seen within a variety of math and physics problems. This thesis in particular will investigate the production and propagation of sound waves through musical ... -
Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
(Society for Industrial and Applied Mathematics, 2016)Mean field systems have recently been derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [W. Nicola and S.A. Campbell, J. Comput. Neurosci., 35 (2013), pp. 87-108]. The ... -
Normal Mode Spectra of Idealized Baroclinic Waves
(AMS, 2020-02-01)Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal spectra ... -
Normal Mode Wave-Vortex Decompositions of Mesoscale Simulations
(University of Waterloo, 2017-08-18)The kinetic energy spectrum of the atmosphere has been well observed to exhibit a k^(-3) power law at synoptic scales with a transition to a shallower k^(-5/3) power law at the mesoscale. To better understand the mesoscale ... -
Normalized Connectomes Show Increased Synchronizability with Age through Their Second Largest Eigenvalue
(Society for Industrial and Applied Mathematics, 2021-01)The synchronization of different brain regions is widely observed under both normal and pathological conditions, such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity ... -
A Novel Class of Intensity-based Metrics for Image Functions which Accommodate a Generalized Weber's Model of Perception
(University of Waterloo, 2020-04-29)Even though the usual L2 image fidelity measurements, such as MSE and PSNR, characterize the mean error for each pixel of the images, these traditional measurements are not designed to predict human visual perception of ... -
A Novel Diffusion-based Empirical Mode Decomposition Algorithm for Signal and Image Analysis
(University of Waterloo, 2018-08-09)In the area of signal analysis and processing, the Fourier transform and wavelet transform are widely applied. Empirical Mode Decomposition(EMD) was proposed as an alternative frequency analysis tool. Although shown to ... -
A Novel Mathematical Framework for the Analysis of Neural Networks
(University of Waterloo, 2017-08-22)Over the past decade, Deep Neural Networks (DNNs) have become very popular models for processing large amounts of data because of their successful application in a wide variety of fields. These models are layered, often ... -
An Npz Model With State-Dependent Delay Due To Size-Structure In Juvenile Zooplankton
(Society for Industrial and Applied Mathematics, 2016)The study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs. We study a closed nutrient-phytoplankton-zooplankton (NPZ) model that includes size structure in the juvenile ... -
Numerical analysis of divergence-free discontinuous Galerkin methods for incompressible flow problems
(University of Waterloo, 2022-04-29)In the first major contribution of this thesis, we present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact ... -
Numerical analysis of space-time hybridized discontinuous Galerkin methods for incompressible flows
(University of Waterloo, 2022-08-09)Many industrial problems require the solution of the incompressible Navier-Stokes equations on moving and deforming domains. Notable examples include the simulation of rotating wind turbines in strong air flow, wave impact ... -
Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications
(University of Waterloo, 2019-08-26)Hamilton-Jacobi-Bellman (HJB) equations are nonlinear controlled partial differential equations (PDEs). In this thesis, we propose various numerical methods for HJB equations arising from three specific applications. First, ...