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Fall 2021

Farkhutdinov, Tagir

In this thesis, I developed the ideas of applying the variational method in geometric mechanics to the porous media described as solid elastic materials with embedded ideal (incompressible) fluid, also known as Eulerian fluid. The work includes four chapters and a conclusion. In the Introduction,...

Spring 2021

Wang, Yue

In this thesis, with the purpose of correcting for potential measurement errors in repeatedly-observed matrix-valued surrogates, and examining the underlying association between latent matrix covariates and a binary response, we propose a Bayesian joint model framework. This joint model method...

Fall 2021

McLaughlin, Paul

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for asymmetric clusters in the presence of outliers and noise (referred to as bad points herein). A series of constraints are applied to a modified factor analyzer structure of the scale matrix parameters,...

Spring 2021

Ghadiri Motlagh, Mahdi

Despite the ubiquity of physical systems evolving on time-dependent spatial domains ranging from crystal growth, formation of patterns and shapes in biology and living organisms – animals skin patterns, tentacle patterns on Hydra, whorled leaves, teeth primordia in the alligator – to...

Fall 2021

Niu, Yeli

This thesis includes 2 parts. Part 1 is: Discretization on High Dimensional Compact Domains. Part 2 is: Polynomial Approximation on High Dimensional Spheres. A special example for part 1 is the result on the unit sphere of high-dimensional Euclidean spaces. In chapter 2, we obtained general...

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...