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Fall 2023

Gervais, Alain D

A series of three studies investigates theoretically and numerically the evolution, stability, and pseudomomentum transport of fully localized three-dimensional internal gravity wave packets, as they self-interact nonlinearly with their induced mean flow. The first study considers a rotating,...

Fall 2023

Zhang, Junxi

Bayesian nonparametric models have gained increasing attention due to their flexibility in modelling natural and social phenomena and have been widely applied in machine learning, biology, social science and so on. Unlike traditional Bayesian parametric models, Bayesian nonparametric models place...

Fall 2023

Riesen, Andrew

$G$-structures on fusion categories have been shown to be an important tool to understand orbifolds of vertex operator algebras \cite{Kirillov}\cite{Gcrossedmuger}\cite{Orbifold_Paper}. We continue to develop this idea by generalizing Eilenberg-Maclane's notion of an Abelian $3$-cocycle to...

Fall 2023

Liu, Wenyue

As one type of principal-agent problem, the insurance contract models are closely related to the extent of information disclosure. We construct two new insurance contract models with full information and adverse selection respectively. The full information model is a continuous-time model in...

Fall 2023

Shyntar, Alexandra

In this thesis, we perform a systematic study of the Allee effect in cancer stem cell (CSC) models with an application to non-small cell lung cancer (NSCLC). Previously, it was shown that an Allee effect exists in mathematical tumor growth models incorporating cancer stem cell (CSC) dynamics....

Fall 2023

Liu, Yi

This thesis presents a comprehensive study of Gaussian Differential Privacy (GDP) and Local Differential Privacy (LDP), exploring their properties, relationships, and applications in developing novel algorithms and optimization methods for efficient and accurate privacy-preserving data analysis....

Spring 2023

Han, Donglin

Since the COVID-19 outbreak in Wuhan City in December 2019, numerous model predictions on the COVID-19 epidemics in Wuhan have been reported. These model predictions have shown a wide range of variations. In our first study, we demonstrate that nonidentifiability in model calibrations using the...

Fall 2023

Jankovic, Peggy M.

This thesis establishes new Schur-Weyl functors involving the super Yangian, its deformed double current algebra, the affine super Yangian, and their respective Cherednik algebras.

Spring 2023

Pan, Bo

We consider stochastic optimization in settings where the distribution of unknown parameters is observable only through finitely dependent training samples. Using the Sample Averaging Approximation ({SAA}), we specifically study the data-driven procedure in which, instead of receiving samples...

Spring 2023

Wang, Siting

Generative Adversarial Networks (GAN) are a field of popular generating models, and there are many variants these years. Lim and Ye 2017 proposed the Geometric GAN to connect the network with the geometric interpretation. They update the discriminator based on the algorithm of Support Vector...