Physical Sciences and Mathematics Commons^™

Computation Of Real Radical Ideals By Semidefinite Programming And Iterative Methods, Fei Wang

Electronic Thesis and Dissertation Repository

Systems of polynomial equations with approximate real coefficients arise frequently as models in applications in science and engineering. In the case of a system with finitely many real solutions (the $0$ dimensional case), an equivalent system generates the so-called real radical ideal of the system. In this case the equivalent real radical system has only real (i.e., no non-real) roots and no multiple roots. Such systems have obvious advantages in applications, including not having to deal with a potentially large number of non-physical complex roots, or with the ill-conditioning associated with roots with multiplicity. There is a corresponding, but more …

Essays In Market Structure And Liquidity, Adrian J. Walton

Electronic Thesis and Dissertation Repository

Market structure concerns the mechanisms for negotiating trades and the composition of trading participants, and can affect liquidity and price efficiency. More gains from trade can be realized from an asset that is more liquid, and a better allocation of risk and capital can be achieved when an asset’s price is more efficient so it is important to understand market structure. This thesis uses theory and empirical methods to examine the effects of a few specific aspects of market structure.

In Chapter 1, we study a novel market structure on the New York Stock Exchange (NYSE), the Retail Liqudity Program …

Studying Both Direct And Indirect Effects In Predator-Prey Interaction, Xiaoying Wang

Electronic Thesis and Dissertation Repository

Studying and modelling the interaction between predators and prey have been one of the central topics in ecology and evolutionary biology. In this thesis, we study two different aspects of predator-prey interaction: direct effect and indirect effect.

Firstly, we study the direct predation between predators and prey in a patchy landscape.

Secondly, we study indirect effects between predators and prey.

Thirdly, we extend our previous model by incorporating a stage-structure into prey.

Finally, we further extend our previous model by incorporating spatial structures into modelling.

A Comparison Of Solution Methods For Mandelbrot-Like Polynomials, Eunice Y. S. Chan

Electronic Thesis and Dissertation Repository

We compare two different root-finding methods, eigenvalue methods and homotopy methods, using three test problems: Mandelbrot polynomials, Fibonacci-Mandelbrot polynomials, and Narayana-Mandelbrot polynomials. For the eigenvalue methods, using both MATLAB and Maple, we computed the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix, inspired by Piers Lawrence's original construction for the Mandelbrot polynomials, for all three families of polynomials. This led us to prove that this construction works in general. Therefore, this construction is genuinely a new kind of companion matrix. For the homotopy methods, we used a special-purpose homotopy, in which we used an equivalent differential equation to solve …

Bacteria-Phage Models With A Focus On Prophage As A Genetic Reservoir, Alina Nadeem

Electronic Thesis and Dissertation Repository

Temperate bacteriophages have the ability to incorporate their genetic material in the host's DNA, which may be utilized by later generations of phage to overcome the host's receptor-based defences. This effect of temperance can have major implications for the long-term survival of the phages as well as on bacteria-phage community evolution. To study the impact of prophage on microbial communities we have developed models simulating lytic and lysogenic infection and host and phage coevolution with a focus on prophage-phage recombination. Our results show that recombination can be crucial for the phage to survive host diversification, and a higher incidence of …

Modeling The Mass Function Of Stellar Clusters Using The Modified Lognormal Power-Law Probability Distribution Function, Deepakshi Madaan

Electronic Thesis and Dissertation Repository

We use the Modified Lognormal Power-law (MLP) probability distribution function to model the behaviour of the mass function (MF) of young and populous stellar populations in different environments. We begin by modeling the MF of NGC1711, a simple stellar population (SSP) in the Large Magellanic Cloud as a pilot case. We then use model selection criterion to differentiate between candidate models. Using the MLP we find that the stellar catalogue of NGC1711 follows a pure power-law behaviour below the completeness limit with the slope α = 2.75 for dN/dlnm ∝ m^(−α+1) in the mass range 0.89 M⊙ to 7.75 M⊙. …

The Survival Probability Of Beneficial De Novo Mutations In Budding Viruses, With An Emphasis On Influenza A Viral Dynamics, Jennifer Ns Reid

Electronic Thesis and Dissertation Repository

A deterministic model is developed of the within-host dynamics of a budding virus, and coupled with a detailed life-history model using a branching process approach to follow the fate of de novo beneficial mutations affecting five life-history traits: clearance, attachment, eclipse, budding, and cell death. Although the model can be generalized for any given budding virus, our work was done with a major emphasis on the early stages of infection with influenza A virus in human populations. The branching process was then interleaved with a stochastic process describing the disease transmission of this virus. These techniques allowed us to predict …

Dynamics Of Discs In A Nematic Liquid Crystal, Alena Antipova

Electronic Thesis and Dissertation Repository

In this thesis, a new way of simulating a two-way coupling between a liquid crystal and an immersed object is proposed. It can be used for objects of various geometries and can be expanded to be used for an object of any geometry. Additionally, a simple yet effective model was suggested for calculations of transmitted light through a nematic liquid crystal sample. This model allowed us to clarify the behavior of a ferromagnetic disc in a nematic liquid crystal observed in experiments and incorrectly interpreted at that time.

Our simulations have demonstrated the following: in the absence of external forces …

Modelling The Impact Of Climate Change On The Polar Bear Population In Western Hudson Bay, Nicole Bastow

Electronic Thesis and Dissertation Repository

The aim of this thesis is to model the impact of climate change on polar bear populations. The first model is a discrete matrix model with time-dependent parameters, which are influenced by temperature increases. Sensitivity analysis is done on the model. Numerical simulations predict there exist several scenarios that result in polar bear extinction. When the impact of climate warming is low the population is predicted to die out in 300 years and for higher levels of impact the population can be extinct within 6. The second model is a system of continuous delay differential equations with time-dependent parameters, also …

Study Of Infectious Diseases By Mathematical Models: Predictions And Controls, Sm Ashrafur Rahman

Electronic Thesis and Dissertation Repository

The aim of this thesis is to understand the spread, persistence and prevention mechanisms of infectious diseases by mathematical models. Microorganisms that rapidly evolve pose a constant threat to public health. Proper understanding of the transmission machinery of these existing and new pathogens may facilitate devising prevention tools. Prevention tools against transmissions, including vaccines and drugs, are evolving at a similar pace. Efficient implementation of these new tools is a fundamental issue of public health. We primarily focus on this issue and explore some theoretical frameworks.

Pre-exposure prophylaxis (PrEP) is considered one of the promising interventions against HIV infection as …