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Fall 2023

Shi, Haiyi

Determinantal point processes (DPPs) arise as important tools in various aspects of mathematics, such as stochastic processes, random matrices, and combinatorics. Over the last decade, DPPs have also been widely used in ma- chine learning community; they are especially popular in subset selection...

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...

Spring 2022

Harrington, Peter D

Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. Open-net salmon farms act as reservoirs for sea lice in near coastal areas, which can lead to elevated sea louse levels on wild salmon. With a free living larval stage, sea lice can...

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

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

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...

Spring 2022

Usubov, Rahim

This work develops numerical methods (finite difference methods) for equations of fluid dynamics and equations of elasticity reformulated in the stress variables (as opposed to natural variables) and applies them to the Fluid-Structure Interac- tion (FSI) problem using a new model based on the...

Fall 2022

Liu, Shuo

This thesis concerns dynamical systems subject to small noise perturbations. Our purpose is to obtain a deep understanding of how small noise perturbations influence the original unperturbed dynamical system, especially over long but finite time intervals. We consider two special systems, the...

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

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...