Applied Mathematics: Recent submissions
Now showing items 1-20 of 491
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Discrete total variation in multiple spatial dimensions and its applications
(University of Waterloo, 2024-05-13)Total variation plays an important role in the analysis of stability and convergence of numerical solutions for one-dimensional scalar conservation laws. However, extending this approach to two or more spatial dimensions ... -
On Convergence Analysis of Stochastic and Distributed Gradient-Based Algorithms
(University of Waterloo, 2024-05-08)Optimization is a fundamental mathematical discipline focused on finding the best solution from a set of feasible choices. It is vital in various applications, including engineering, economics, data science, and beyond. ... -
Safety-Critical Control for Dynamical Systems under Uncertainties
(University of Waterloo, 2024-02-15)Control barrier functions (CBFs) and higher-order control barrier functions (HOCBFs) have shown great success in addressing control problems with safety guarantees. These methods usually find the next safe control input ... -
Spatial and Temporal Discounting in a Social-Climate Model
(University of Waterloo, 2024-01-25)This thesis analyzes how individuals' devaluation of distant impacts of climate change affects mitigation behaviours and projected climate conditions. To approach this question, spatial and temporal discounting is applied ... -
Entropy-Stable Positivity-Preserving Schemes for Multiphase Flows
(University of Waterloo, 2024-01-22)High-intensity focused ultrasound is a promising non-invasive medical technology that has been successfully used to ablate tumors, as well as in the treatment of other conditions. Researchers believe high-intensity focused ... -
Optimal trajectory calculation using neural networks
(University of Waterloo, 2024-01-08)Optimal control methods for linear systems have reached a substantial level of maturity, both in terms of conceptual understanding and scalable computational implementation. For non-linear systems, an open-loop feedback ... -
Simulations of Radiatively Driven Convection and Spatially Heterogeneous Solar Radiation Intensity in Ice-Covered Lakes
(University of Waterloo, 2023-12-22)At the end of winter as sunlight and increasing air temperatures melt the snow layer above the ice, allowing significant radiation from the sun to enter the water column. In the cold water regime (T < 4 °C, where 4 °C is ... -
Properties of difference inclusions with computable reachable set
(University of Waterloo, 2023-12-13)Dynamical systems have important applications in science and engineering. For example, if a dynamical system describes the motion of a drone, it is important to know if the drone can reach a desired location; the dual ... -
Local measurements in Relativistic Quantum Information: localization and signaling
(University of Waterloo, 2023-12-12)In this thesis, we study some foundational aspects of detector models in quantum field theory (QFT) related to signaling and localization, and we analyze certain frictions with relativistic causality. We characterize the ... -
Expanding the Scope of Random Feature Models: Theory and Applications
(University of Waterloo, 2023-12-07)Data, defined as facts and statistics collected together for analysis is at the core of every inference or decision made by any living organism. Right from the time we are born, our brain collects data from everything that ... -
Modelling the Subglacial Hydrology of Trinity-Wykeham Glaciers of the Northern Canadian Arctic
(University of Waterloo, 2023-11-09)In Canada’s High Arctic region, the melting of glacial ice contributes substantially to the world’s increasing sea levels (Harig and Simons, 2016). Of the icebergs in the region, approximately 62% are discharged by ... -
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 ...