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Fall 2023

Rahmatidehkordi, Ardalan

Distributions of sequences modulo one (mod 1) have been studied over the past century with applications in algebra, number theory, statistics, and computer science. For a given sequence, the weak convergence of the associated empirical distributions has been the usual approach to these studies....

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...

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

Stockall, Devon

The affine vertex superalgebra A=L^1(D(2,1;-v/w)) plays a key role as the geometric Langlands kernel VOA for SVOAs associated to so(3), osp(1|2) and other rank one Lie superalgbras. Since D(2,1;a) is an extension of the direct sum of 3 copies of sl(2), A can be naturally realized as an...

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

Ge, Qi

The aim of this thesis is to provide an exposition to Mochizuki and Hoshi's approach to birational anabelian geometry of mixed characteristic local fields. In the introductory chapter, we begin by recalling the relevant backgrounds on the Grothendieck conjectures on the étale fundamental groups...

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 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....

Spring 2024

Sharma, Neha

This dissertation is concerned with the parameter estimation problem for Ornstein-Uhlenbeck processes and Vasicek models and the product formula for multiple Itˆo integrals of L´evy processes. In the first part of the thesis, we study the parameter estimation for Ornstein- Uhlenbeck processes...

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,...