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Fall 2023

Kettle, Bryan W

This dissertation establishes various structural and representation theoretic results in super Yangian theory. In its first part, this dissertation details the algebraic structure and representation theory for the Yangians of orthosymplectic Lie superalgebras. Addressing these Yangians via the...

Spring 2023

Vasilev, Ilia

In present thesis I focus on development of method of market completions and its applications to various problems in pricing and hedging of contingent claims. Since theory of mathematical finance is well developed on complete markets, and corresponding solutions are well understood, method of...

Spring 2023

Hua, Xiaotian

Coral reefs are essential to the marine ecosystem, and provide some of the most diverse habitats in the world. Coral reef fisheries contribute 6.8 billion to the economy a year globally. However, coral reefs are under significant threat because of human activities such as overfishing, ocean...

Spring 2023

Bazrafkan, Mehrnoosh

Introduction Frailty is a syndrome that is often associated with aging. It can be identified through specific frailty scales or a comprehensive assessment by a healthcare provider. In Alberta, it appears that there are no specific billing or diagnostic codes for frailty. So, healthcare providers...

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

Salmaniw, Yurij

Habitat loss is a significant problem and the leading cause of species extinctions and decreases in biodiversity worldwide. This issue is primarily driven by human activities, making it crucial to understand the consequences of our actions as a global community. The empirical study of habitat...

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

Roda, Weston

This thesis is based on four main studies. The first two studies present a detailed methodology for completing dynamical system parameter estimation using Bayesian inference. The next two studies are about using this methodology to investigate critical human immunodeficiency virus-1 therapeutic...

Spring 2024

Zeng, Zhaowei

Versal torsors arise as an important tool in algebraic groups and algebraic geometry for the universal perspective they provide on the behaviour and properties of other torsors under the same group. Two classic examples of versal torsors are con- structed from general linear groups and affine...

Fall 2024

Yu, Peng

The evolution of data acquisition technologies and the exponential growth in computing capabilities have inaugurated an epoch wherein researchers are empowered to procure data of unprecedented dimensionality and complexity. Simultaneously, Bayesian hierarchical models distinguish themselves as...