Browsing Applied Mathematics by Title
Now showing items 456-475 of 499
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Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations
(University of Waterloo, 2017-01-17)In many practical large scale computational problems, the calculation of partial derivatives of the object function f with respect to input parameters are entailed and the dimension of inputs n is much larger the one of ... -
Studies of tumor heterogeneity, tumor microenvironment, and radiotherapy: A mathematical and computational approach
(University of Waterloo, 2019-01-04)Radiotherapy uses high doses of energy to eradicate cancer cells and thus destroy the bulk of tumors. Radiobiologists try to precisely deliver radiation to a targeted area in order to maximize the cancer cell kill rate ... -
A Study of Infectious Disease Models with Switching
(University of Waterloo, 2009-05-20)Infectious disease models with switching are constructed and investigated in detail. Modelling infectious diseases as switched systems, which are systems that combine continuous dynamics with discrete logic, allows for the ... -
Study of Singular Capillary Surfaces and Development of the Cluster Newton Method
(University of Waterloo, 2012-08-29)In this thesis, we explore two important aspects of study of differential equations: analytical and computational aspects. We first consider a partial differential equation model for a static liquid surface (capillary ... -
A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing
(University of Waterloo, 2012-09-07)Since its introduction in 2004, the Structural Similarity (SSIM) index has gained widespread popularity as an image quality assessment measure. SSIM is currently recognized to be one of the most powerful methods of assessing ... -
Superconvergence, Superaccuracy, and Stability of the Discontinuous Galerkin Finite Element Method
(University of Waterloo, 2015-09-08)This thesis is concerned with the investigation of the superconvergence, superaccuracy, and stability properties of the discontinuous Galerkin (DG) finite element method in one and two dimensions. We propose a novel method ... -
Synchronization in Heterogeneous Networks of Hippocampal Interneurons
(University of Waterloo, 2005)The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm ... -
Synchronization of Complex-Valued Dynamical Networks
(University of Waterloo, 2021-09-27)Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, ... -
Synchronization of coupled reaction-diffusion neural networks: Delay-dependent pinning impulsive control
(Elsevier, 2019-12)This paper studies the synchronization problem of coupled reaction-diffusion neural networks with time-varying delays. A novel pinning impulsive controller is proposed, where distributed delays and discrete delays are taken ... -
Synthetic quorum sensing in model microcapsule colonies
(Proceedings of the National Academy of Sciences, 2017-07-24)Biological quorum sensing refers to the ability of cells to gauge their population density and collectively initiate a new behavior once a critical density is reached. Designing synthetic materials systems that exhibit ... -
A Taylor polynomial expansion line search for large-scale optimization
(University of Waterloo, 2016-08-29)In trying to cope with the Big Data deluge, the landscape of distributed computing has changed. Large commodity hardware clusters, typically operating in some form of MapReduce framework, are becoming prevalent for ... -
Tensors: Entanglement, Geometry, and Combinatorics
(University of Waterloo, 2022-04-26)In this thesis, we use algebraic-geometric and combinatorial techniques to study tensor decompositions, with applications in quantum information theory, algebraic complexity theory, and algebraic statistics. A tensor is a ... -
Theoretical Description of the Forces on a Point Charge Moving Parallel to a Supported Two-dimensional Material
(University of Waterloo, 2022-09-22)A charged particle, moving at a certain distance and parallel to a target, experiences a stopping force that slows it down and an image force that deflects it towards the target's surface. In this work, we aimed to describe ... -
Theory and Mitigation of Crosstalk on Quantum Information Processors
(University of Waterloo, 2023-09-08)Successfully implementing large-scale quantum computation has proven to be an exceptionally arduous task. Decoherence and imperfect control limit the coherent manipulation of large ensembles of particles. While quantum ... -
Three Dimensional Hydrodynamic Modelling of Lake Erie: Kelvin Wave Propagation and Potential Effects of Climate Change on Thermal Structure and Dissolved Oxygen
(University of Waterloo, 2013-07-25)This thesis investigates physical processes in Lake Erie, a large, shallow mid-latitude lake, from two perspectives: climate change impacts on the thermal structure and dissolved oxygen concentration and small-scale eddy ... -
Three Results in Quantum Physics
(University of Waterloo, 2019-05-09)This thesis is split into three disjoint sections. The first deals with two practical issues regarding the use of unitary 2-designs. A simplified description of how to generate elements of the smallest known unitary 2-design ... -
Three-dimensional Simulations of an Internal Solitary Wave Shoaling Over a Shallow Slope
(University of Waterloo, 2022-05-03)The transport of sediment is vital for ecological and climatological processes. Sediment can either move up the shelf, or mix into the upper water column as nepheloid layers. Internal solitary waves (ISWs) shoaling along ... -
Three-dimensional simulations of sound propagation in a trumpet with accurate mouthpiece shank geometry
(arXiv, 2016-11-01)The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finite-amplitude wave propagation can lead to wave distortion ... -
Time-Optimal Control of Closed Quantum Systems
(University of Waterloo, 2009-08-20)Recently there has been a lot of interest in the potential applications of performing computations on systems whose governing physical laws are quantum, rather than classical in nature. These quantum computers would have ... -
Time-Optimal Control of Quantum Systems: Numerical Techniques and Singular Trajectories
(University of Waterloo, 2011-06-21)As technological advances allow us to peer into and beyond microscopic phenomena, new theoretical developments are necessary to facilitate this exploration. In particular, the potential afforded by utilizing quantum resources ...