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Fall 2022

Hall, Meghan

From the mechanical processes that produce the convolutions in the human brain needed for complex thought, to the precise and controlled movements derived by intuitive calculations of body position in figure skating, mechanics plays a role in everything we do. In this thesis, we apply and examine...

Fall 2022

Campbell, Connor

The objective of this thesis is to show how advanced methods based on mixture models can be used to predict the productivity of hockey players, measured by the rate at which they produce goals and assists. The performance of the methods is evaluated on existing data from one full National Hockey...

Fall 2022

Sun, Wen R

Let n ≥ 3 and B ⊂ ℝⁿ. The Illumination Conjecture states that the minimal number I(B) of directions/‘light sources’ that illuminate the boundary of a convex body B, which is not the affine image of a cube, is strictly less than 2ⁿ. The conjecture in most cases is widely open, and it has only been...

Fall 2022

Solomon, Liane

Salmonella are pathogenic bacteria that infect many species including humans. This pathogen thrives in the gastrointestinal track of their hosts and propel themselves in mucus with motion structures called flagella. Each cell has multiple flagella that can rotate either synchronously, resulting...

Fall 2022

Richard, Daniel

Universal approximation refers to the property of a collection of functions to approximate continuous functions. Past literature has demonstrated that neural networks are dense in continuous functions on compact subsets of finite-dimensional spaces, and this document extends those findings to...

Fall 2022

Joshi, Aniket

In this thesis we study some aspects of `Airy structures' first proposed in \cite{ks}, as an algebraic reformulation of the Chekhov-Eynard-Orantin (CEO) topological recursion initiated in \cite{eo} and \cite{eo1} in order to study the large $N$ expansion of matrix models. Our primary goal is to...

Spring 2022

Alsheyab, Safa' Mahmoud

The core innovation of this thesis lies in studying reflected backward stochastic differential equations (RBSDE hereafter) for informational systems. An informational system is a system where there is discrepancy in the information received by agents over time. In this thesis, we restrict to the...

Fall 2022

Zoto, Thoma

Numerical methods are one of the most important aspects in the computer modelling of physical phenomena governed by differential equations. In order to study these phenomena precisely and in a timely manner, we need to use robust and efficient numerical methods for solving the underlying...

Fall 2022

Garces Gomez, German A.

We consider the category of modules over certain subalgebras of the unrolled restricted quantum group associated to any reductive Lie algebra and show some progress towards the proof of an equivalence of categories of this with the category of local representations of a simple current extension.

Fall 2022

Pirlot, Cassidy

Convolution Neural Networks (CNNs) have rapidly evolved since their neuroscience beginnings. These models efficiently and accurately classify images by optimizing the model’s hidden representations to these images through training. These representa- tions have been shown to resemble neural data...