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Fall 2013

Helmsauer, Kathrin

We determine the decomposition of the Chow motive of a Del Pezzo surface S of degree 5 or 6 with a K-rational point pt : K → S into a direct sum of Chow motives. In each case, we give a Gal (K = K)-permutation resolution of the Picard group Pic (K x KS) and deduce that there is some étale algebra...

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...

Spring 2024

Zeng, Zhaowei

Versal torsors arise as an important tool in algebraic groups and algebraic geometry for the universal perspective they provide on the behaviour and properties of other torsors under the same group. Two classic examples of versal torsors are con- structed from general linear groups and affine...

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

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

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...

Fall 2024

Polavarapu, Achintya Raya

The interplay between order structure and probability theory has long been studied. In recent years this has led a generalization of many of the concepts from probability theory to arbitrary vector lattices. In this thesis, we study the generalization of discrete stopping times in vector...

Fall 2024

Venegas Garcia, Pablo

Increased anthropogenic greenhouse gas emissions have gained attention from researchers and world leaders due to the potential for global warming. Part of the primary greenhouse gas emitters come from the agriculture and oil and gas industrial sectors. The sources of two prioritized greenhouse...

Fall 2024

Fan, Xinyi

In the field of sleep research, the quantitative analysis of electroencephalography (EEG) data acquired during sleep offers invaluable insights. However, the presence of artifacts in such data can severely distort analytical outcomes. Therefore, this study aims to develop an innovative artifact...

Fall 2024

Wagner, Connor J

We begin with a survey of mathematical epidemic modelling from its inception to present day. We present up-to-date research on the field of variable susceptibility SIR (Susceptible-Infected-Removed system of differential equations model), which takes the classic SIR model and adds another...