Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits
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Formation Control of Multi-agent Systems via Impulsive Strategy
(University of Waterloo, 2023-09-08)Multi-agent systems (MASs) involving cooperative control problems such as consensus tracking of distributed networks, flocking control with obstacle avoidance, and attitude alignment have received a considerable amount of ... -
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 ... -
A comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems
(University of Waterloo, 2023-08-30)The study of dynamical systems is of great interest in many fields, with a wide range of applications. In some cases, these dynamical systems may be affected by noise and the availability of measurements may be limited. ... -
Mathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
(University of Waterloo, 2023-08-29)Ultrasound imaging is the use of sound waves beyond the human frequency range to construct images of human tissue. This is carried out through the measurement of reflected and scattered waves from the interfaces between ... -
Integrating Experimental and Computational Approaches to Optimize 3D Bioprinting of Cancer Cells
(University of Waterloo, 2023-08-21)A key feature distinguishing 3D bioprinting from other 3D cell culture techniques is its precise control over created structures. This property allows for the high-resolution fabrication of biomimetic structures with ... -
An investigation of the use of gradients in imaging, including best approximation and the Structural Similarity image quality measure
(University of Waterloo, 2023-08-18)The L^2-based mean squared error (MSE) and its variations continue to be the most widely employed metrics in image processing. This is most probably due to the fact that (1) the MSE is simple to compute and (2) it possesses ... -
Improved Diagnostics & Performance for Quantum Error Correction
(University of Waterloo, 2023-08-04)Building large scale quantum computers is one of the most exciting ventures being pursued by researchers in the 21st century. However, the presence of noise in quantum systems poses a major hindrance towards this ambitious ... -
Applications of Deep Learning to Differential Equation Models in Oncology
(University of Waterloo, 2023-07-25)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 ... -
Higher Gauge Theory and Discrete Geometry
(University of Waterloo, 2023-06-05)In four dimensions, gravity can be seen as a constrained topological model. This provides a natural way to construct quantum gravity models, since topological models are relatively straightforward to quantize. Difficulty ... -
Predictability of Stratified Turbulence
(University of Waterloo, 2023-05-19)In the study of geophysical fluid dynamics, predictability of dynamics at different scales still stands in the foreground of interest as one of the primary challenges. Following Lorenz's pioneering framework, several results ... -
Calcium Transport and Regulation in Male and Female Rat Kidney
(University of Waterloo, 2023-05-16)Calcium is an essential mineral that plays a critical role in many biological processes, such as muscle contraction, nerve function, and bone health. However, maintaining the right balance of calcium in the body is crucial ... -
Turnpike Property for Generalized Linear-Quadratic Optimal Control Problem
(University of Waterloo, 2023-04-28)The turnpike phenomenon describes the long time behavior of optimally controlled systems whose optimal trajectories over a sufficiently large time horizon stay for most of the time close to a prescribed trajectory of the ... -
Microcolony Dynamics: Motion from Growth, Order, and Incompressibility
(University of Waterloo, 2023-04-27)Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until ... -
Mathematical Modelling of the Intrarenal Renin Angiotensin System in Hypertension
(University of Waterloo, 2023-04-24)Hypertension is the leading cause of cardiovascular disease and premature death world-wide. It is a highly multi-factorial disease associated with multiple risk factors and patho-physiological changes, including impaired ... -
Data-Driven Methods for System Identification and Lyapunov Stability
(University of Waterloo, 2023-01-27)This thesis focuses on data-driven methods applied to system identification and stability analysis of dynamical systems. In the first major contribution of the theorem we propose a learning framework to simultaneously ... -
Road Surface Estimation Using Machine Learning
(University of Waterloo, 2023-01-19)Vehicle motion control systems are present on commercial vehicles to improve safety and driving comfort. Many of these control systems could be further improved given accurate online information about the road condition ... -
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid
(University of Waterloo, 2023-01-16)Flagellated bacteria categorized as microorganisms, play vital roles in human life such that their beneficial and detrimental effects on different aspects of the ecosystem are indisputable. Flagellated bacteria propel ... -
From Astrophysics of Galaxies to Binary Black Hole Mergers: Theoretical Modelling of the Gravitational-Wave Bias Parameter
(University of Waterloo, 2023-01-04)In the past few decades, the field of cosmology has become a fascinating field of study in physics. The computational advances and precision observational measurements such as Cosmic Microwave Background (CMB) measurements ... -
Decentralized contact tracing protocols and a risk analysis approach to pandemic control
(University of Waterloo, 2022-12-23)Non-pharmaceutical interventions (NPIs) can protect against pandemic pathogens, but they depend on behaviour change, and so can impose costs on quality of life and civil liberties. With careful system design and risk ... -
Sensitivity of the Thermal Structure and Circulation Patterns of a Simple Idealized Lake and Lake Erie to External Driving Forces
(University of Waterloo, 2022-12-22)Lake Erie has been a great source of economic growth and drinking water for both Canada and the United States. All lakes in temperate regions that stratify during summer are prone to hypoxia as they will experience some ...
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