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• ### Numerical simulation of Ricci flow on a class of manifolds with non-essential minimal surfaces

Fall 2011

In the last three decades, the Ricci flow has proved to be an extremely useful tool in mathematics and physics. We explore numerically the long time existence of the Ricci-DeTurck flow and the List flow for a one-parameter family of Riemannian manifolds with non-essential minimal surfaces. This...

• ### The Impact of Climate on the Population of Indiana Bat (Myotis Sodalis)

Fall 2010

The Indiana Bat (Myotis sodalis) population had decreased by 56% between 1967 and 2006. In summer 2006, a mysterious disease called “White Nose Syndrome” was first identified. Since then, the disease killed almost one million bats in North America. Many Biologists believe that both the...

• ### Optimal Regulation of Systemic Risk by Tax

Fall 2014

Financial systemic crisis could be broadly understood as the deterioration of the banking sector which results in damage to the real economy. From elementary accounting, a firm's financial position can be characterized by the value of its asset holdings versus the amount it borrow from others. If...

• ### A novel numerical approach to Fluid-Structure interaction problem

Spring 2022

This work develops numerical methods (finite difference methods) for equations of fluid dynamics and equations of elasticity reformulated in the stress variables (as opposed to natural variables) and applies them to the Fluid-Structure Interac- tion (FSI) problem using a new model based on the...

• ### Diagonalizable subalgebras of the first Weyl algebra

Fall 2009

Let \$A1\$ denote the first Weyl algebra over a field \$K\$ of characteristic 0; that is, \$A1\$ is generated over \$K\$ by elements \$p\$, \$q\$ that satisfy the relation \$pq-qp=1\$. One can view \$A1\$ as an algebra of differential operators by setting \$q=X\$, \$p=d/dX\$. The basic questions which are addressed...

• ### Determinantal point processes and their parameter estimations

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...

• ### Modelling Mountain Pine Beetle Abundance and Distribution in Novel Hosts and Changing Climate

Spring 2024

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....

• ### Modelling and Estimation of L´evy driven Ornstein Uhlenbeck processes

Spring 2024

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...

• ### Regularity Criteria for the Energy Equality to the 3D Magneto-Hydrodynamics Equations

Spring 2024

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,...

• ### Mathematical modeling of HIV-1 therapeutic initiatives: shock and kill strategy in the brain and the natural control of the virus in the plasma

Spring 2024

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...

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