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Skip to Search Results 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Hillen, Thomas (Mathematical and Statistical Sciences)
 6Mizera, Ivan (Mathematical and Statistical Sciences)

Fall 2023
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
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
Since the COVID19 outbreak in Wuhan City in December 2019, numerous model predictions on the COVID19 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
In this thesis, we perform a systematic study of the Allee effect in cancer stem cell (CSC) models with an application to nonsmall 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
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
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...

Fall 2022
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
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...

Monge solutions and uniqueness in multimarginal optimal transport: costs associated to graphs and a general condition
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This thesis is devoted to the proof of several results on the existence and uniqueness of Monge solutions to the multimarginal optimal transportation problem. These results are found in Chapters \ref{Chapter3}, \ref{Chapter4} and \ref{Chapter5}, and represent joint work with Brendan Pass. The...