Mathematics (Faculty of): Recent submissions
Now showing items 1-20 of 3035
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Hopf 2-Algebras: Homotopy Higher Symmetries in Physics
(University of Waterloo, 2024-06-26)The theory of Hopf algebras and quantum groups have led to very rich and interesting developments in both mathematics and physics. In particular, they are known to play crucial roles in the interplay between 3d topological ... -
Measures for risk, dependence and diversification
(University of Waterloo, 2024-06-20)Two primary tasks in quantitative risk management are measuring risk and managing risk. Risk measures and dependence modeling are important tools for assessing portfolio risk, which have gained much interest in the literature ... -
On Enabling Layer-Parallelism for Graph Neural Networks using IMEX Integration
(University of Waterloo, 2024-06-20)Graph Neural Networks (GNNs) are a type of neural networks designed to perform machine learning tasks with graph data. Recently, there have been several works to train differential equation-inspired GNN architectures, ... -
Memolet: Reifying the Reuse of User-AI Conversational Memories
(University of Waterloo, 2024-06-19)As users engage more frequently with AI conversational agents, conversations may exceed their "memory" capacity, leading to failures in correctly leveraging certain memories for better responses. Therefore, users have to ... -
Stability Analysis and Formally Guaranteed Tracking Control of Quadrotors
(University of Waterloo, 2024-06-19)Reach-avoid tasks are among the most common challenges in autonomous aerial vehicle (UAV) applications. Despite the significant progress made in the research of aerial vehicle control during recent decades, the task of ... -
Controller and Observer Designs for Partial Differential-Algebraic Equations
(University of Waterloo, 2024-06-19)Partial differential-algebraic equations (PDAEs) arise in numerous situations, including the coupling between differential-algebraic equations (DAEs) and partial differential equations (PDEs). They also emerge from the ... -
Ice/hydrology feedback in the Siple Coast, Antarctica, from two-way coupled modeling
(University of Waterloo, 2024-06-18)Subglacial hydrological processes have long been understood to play a critical role in ice dynamics (Budd et al., 1979). Consequently, the recent emergence of complex two-dimensional subglacial hydrology models with both ... -
Multiscale Modelling of Biological Rhythms and Systems
(University of Waterloo, 2024-06-17)Living organisms possess the remarkable ability to both respond to rhythms and generate them. In some instances, unintended rhythms arise, leading to undesirable or even hazardous consequences, such as synchronized neuronal ... -
Improving the Precision of Analyses Queries in Factbase Models of Software Systems
(University of Waterloo, 2024-05-31)Large software systems are developed by multiple teams of software engineers, each working on different components that are supposed to work together. Each component is responsible for a subset of system functionality and ... -
Reliable WiFi Backscatter Communication in WiTAG
(University of Waterloo, 2024-05-31)WiFi backscatter systems offer the potential to provide low-powered WiFi-compatible communication. This technology is especially promising when coupled with low-power sensors to periodically communicate readings from IoT ... -
Collective Dynamics of Large-Scale Spiking Neural Networks by Mean-Field Theory
(University of Waterloo, 2024-05-31)The brain contains a large number of neurons, each of which typically has thousands of synaptic connections. Its functionality, whether function or dysfunction, depends on the emergent collective dynamics arising from the ... -
Meta-Solving via Machine Learning for Automated Reasoning
(University of Waterloo, 2024-05-30)Automated reasoning (AR) and machine learning (ML) are two of the foundational pillars of artificial intelligence (AI) and yet have developed largely independently. The integration of these two sub-fields holds the tremendous ... -
Symbolic Regression and Sequence Modelling with Conditional and Dynamic Language Models
(University of Waterloo, 2024-05-30)In an era where the boundaries of machine learning are continuously being pushed, this thesis presents two more advancements in the field of deep learning and artificial intelligence, with a focus on symbolic regression ... -
A Differentiable Particle Filter for Jump-Diffusion Stochastic Volatility Models
(University of Waterloo, 2024-05-28)Stochastic volatility with jumps has emerged as a crucial tool for understanding and modelling the stochastic and intermittently discontinuous nature of many processes in finance. Due to the highly nonlinear structure of ... -
Parallel Transaction Execution in Public Blockchain Systems
(University of Waterloo, 2024-05-27)Public blockchain systems like Ethereum and Bitcoin suffer from poor transaction throughput, leading to delayed transaction execution and high transaction fees. They execute transactions one by one, failing to extract ... -
Writing My Own Line Drawing Software as an Artist
(University of Waterloo, 2024-05-24)I describe trying to improve my own art—line art, specifically—by developing computer science-based tools. The results of this experience are three technical contributions targeted at an NPR (Non-Photorealistic Rendering) ... -
Optimization of Policy Evaluation and Policy Improvement Methods in Portfolio Optimization using Quasi-Monte Carlo Methods
(University of Waterloo, 2024-05-24)Machine learning involves many challenging integrals that can be estimated using numerical methods. One application of these methods which has been explored in recent work is the estimation of policy gradients for ... -
A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & its connection to symmetry operators
(University of Waterloo, 2024-05-23)The theory of non-regular separation is examined in its geometric form and applied to the bi-Helmholtz equation in the flat coordinate systems in 2-dimensions. It is shown that the bi-Helmholtz equation does not admit ... -
Space-time Hybridizable Discontinuous Galerkin Method for the Advection-Diffusion Problem
(University of Waterloo, 2024-05-22)In this thesis, we analyze a space-time hybridizable discontinuous Galerkin (HDG) method for the time-dependent advection-dominated advection-diffusion problem. It is well-known that solutions to these problems may admit ... -
Deep Unsupervised Learning for Biodiversity Analyses: Representation learning and clustering of bacterial, mitochondrial, and barcode DNA sequences
(University of Waterloo, 2024-05-22)Amid the recent surge in next-generation sequencing technologies, alignment-free algorithms stand out as a promising alternative to traditional alignment-based methods in phylogenetic analyses. Specifically, the use of ...