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Fall 2024

Ding, Lei

This thesis presents a comprehensive exploration of social biases embedded within texts and Natural Language Processing (NLP) models. It develops innovative algorithms to evaluate and mitigate these biases, thereby enhancing the fairness and effectiveness of NLP applications. The initial phase of...

Fall 2024

Milanes Perez, Daniel Enrique

We consider the problem of a firm that wants to maximize its earnings. Production generates pollution as a by-product and has a negative impact on the environment. This negative impact causes disutility. The firm determines the optimal production rate and chooses between two types of technologies...

Fall 2024

Baabdulla, Arwa Abdulla

In this thesis, we explore the spatial dynamics of viral infection within tissue through mathematical modelling, aiming to understand the impact of virus spread on both cancerous and healthy tissue. Specifically, we investigate how spatial patterning and heterogeneity influence viral infection...

Spring 2024

Pineau, Mark

We consider the Cauchy problem to the Magneto-Hydrodynamics Equations (MHD) in R^3, and present specific criteria for which its corresponding energy equality holds. Specifically, we show that very weak solutions to the MHD equations (in the distributional sense) satisfy the energy equality,...

Spring 2024

Murasko, Noel

Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with zeros) and implicit dealiasing (mathematically accounting...

Fall 2024

Wu, Christopher

Selection markets describe markets in which people strategically ``select'' into certain options based on knowledge only they possess, and in doing so may communicate some of that knowledge. Examples include sick people buying more comprehensive health insurance contracts, talented students...

Spring 2024

Xie, Xiaoqi

The mountain pine beetle (Dendroctonus ponderosae, Hopkins 1902), an invasive bark beetle native to North America, has expanded its habitat from central British Columbia to Northern Alberta. This expansion poses an immediate threat to jack pine forests, which extend from Alberta to Nova Scotia....

Fall 2024

Sun, Ke

This thesis comprehensively investigates Distributional Reinforcement Learning~(RL), a vibrant research field that interplays between statistics and RL. As an extension of classical RL, distributional RL, on the one hand, embraces plenty of statistical ideas by incorporating distributional...

Fall 2024

Goldthorpe, Zachariah PL

Let Cat(oo,oo) denote the (oo,1)-category of (oo,oo)-categories with weakly inductive equivalences. The main objective of this thesis is to demonstrate that Cat(oo,oo) satisfies universal properties with respect to homotopy-coherent internalisation and enrichment. To achieve these universal...

Fall 2024

Liu, Meichen

Functional regression is a cornerstone for understanding complex relationships where predictors or responses (or both) are functions. A particularly powerful framework within this domain is the Reproducing Kernel Hilbert Space (RKHS), which facilitates the handling of infinite-dimensional data...