Physical Sciences and Mathematics Commons^™

Applications Of Stochastic Control In Energy Real Options And Market Illiquidity, Christian Maxwell

Electronic Thesis and Dissertation Repository

We present three interesting applications of stochastic control in finance. The first is a real option model that considers the optimal entry into and subsequent operation of a biofuel production facility. We derive the associated Hamilton Jacobi Bellman (HJB) equation for the entry and operating decisions along with the econometric analysis of the stochastic price inputs. We follow with a Monte Carlo analysis of the risk profile for the facility. The second application expands on the analysis of the biofuel facility to account for the associated regulatory and taxation uncertainty experienced by players in the renewables and energy industries. A …

A Periodic Matrix Population Model For Monarch Butterflies, Emily Hunt

Senior Honors Projects, 2010-2019

The migration pattern of the monarch butterfly (Danaus plexippus) consists of a sequence of generations of butterflies that originate in Michoacan, Mexico each spring, travel as far north as Southern Canada, and ultimately return to the original location in Mexico the following fall. We use periodic population matrices to model the life cycle of the eastern monarch butterfly and find that, under this model, this migration is not currently at risk. We extend the model to address the three primary obstacles for the long-term survival of this migratory pattern: deforestation in Mexico, increased extreme weather patterns, and milkweed degradation.

An Optimization Method For Estimating Joint Parameters Of The Hip And Knee, Ben Tesch

Theses and Dissertations

Biomechanics, generally speaking, concerns the application of engineeringprinciples to the study of living things. This work is concerned withhuman movement analysis, a subfield of biomechanics, where the methodsof classical mechanics are applied to human movement. This field hascontributed to the general understanding of human movement, and itstechniques are used in the diagnosis and treatment of disease. Centralto the field is the process of measuring human movement. Since classicalmechanics deals with the motion of rigid bodies, and ideal measurementsystem would be able to accurately record the exact pose --- combinedposition and orientation --- of the bones. The techniques that reachthis ideal …

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

Empirical Studies On Interest Rate Derivatives, Xudong Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Interest rate models are the building blocks of financial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman filter, and studying various models empirically. We shall propose a front-fixing finite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common finite element method. Numerical test results show the superiority of our front-fixing finite element method in the aspects of computing the option …

Numerical Decoding, Johnson-Lindenstrauss Transforms, And Linear Codes, Yue Mao

All Dissertations

Many computational problems are related to the model y = Ax + e, including compressive sensing, coding theory, dimensionality reduction, etc. The related algorithms are extremely useful in practical applications for high performance computing, for example, digital communications, biological imaging and data streaming, etc. This thesis studies two important problems. One problem is related to efficient decoding for Reed-Solomon codes over complex numbers. In this case, A and y are given, and the goal is to find an efficient stable algorithm to compute x. This is related to magnetic resonance imaging (MRI). The other problem is related to fast algorithms …

Modular Monochromatic Colorings, Spectra And Frames In Graphs, Chira Lumduanhom

Dissertations

Abstract attached as separate document.

Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, Amber Sumner Robertson

Master's Theses

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (A^T y = g) systems of linear equations to approximate the scattering amplitude defined by g^Tx =y^Tb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude …

Computational Exploration Of Chaotic Dynamics With An Associated Biological System, Akshay Galande

All Theses

Study of microbial populations has always been topic of interest for researchers. This is because microorganisms have been of instrumental use in the various studies related to population dynamics, artificial bio-fuels etc. Comparatively short lifespan and availability are two big advantages they have which make them suitable for aforementioned studies. Their population dynamic helps us understand evolution. A lot can be revealed about resource consumption of a system by comparing it to the similar system where bacteria play the role of different factors in the system. Also, study of population dynamics of bacteria can reveal necessary initial conditions for the …

Diffusion And Adsorption Coefficients Of Aromatic Hydrocarbons In Gas Chromatography Capillary Columns, Gabriela Navarro Tovar

Electronic Thesis and Dissertation Repository

This study focuses on a mathematical description of aromatic species elution peaks from a gas chromatographic BPX5 capillary column. Using the chromatographic peaks, statistical moments are calculated for toluene, naphthalene, phenol and 2-naphthol. This thesis reports two modelling approaches involving laminar gas flow, distribution coefficients (K_s) and diffusion coefficients in the stationary phase (D_s).

Firstly, a model with equilibrium adsorption is considered to describe symmetric peaks for toluene and naphthalene. Moreover, a model with non-equilibrium adsorption is proposed to describe asymmetric peaks of phenol and 2-napthol. In addition to the K_s and D …

Centered-Difference Applications For Schrödinger's Equation, Matthew Thomas Murachver

Physics

This project enumerates methods utilizing discretized centered-difference approximations on the second order differential equation for quantum particles known as Schrodinger’s Equation. An eigenvalue-eigenfunction scheme is developed to sieve for valid solutions to The Time Independent Schrodinger Equation. Additionally the Crank-Nicolson method is applied to the Time Dependent Schrodinger Equation to describe wavefunction (eigenfunction) time evolution. The validity of these methods is discussed with applications to several fundamental pedagogical introductory quantum mechanic systems.

Epistemic Uncertainty Quantification In Scientific Models, Xiaoxiao Chen

Open Access Dissertations

In the field of uncertainty quantification (UQ), epistemic uncertainty often refers to the kind of uncertainty whose complete probabilistic description is not available, largely due to our lack of knowledge about the uncertainty. Quantification of the impacts of epistemic uncertainty is naturally difficult, because most of the existing stochastic tools rely on the specification of the probability distributions and thus do not readily apply to epistemic uncertainty. And there have been few studies and methods to deal with epistemic uncertainty. A recent work can be found in [J. Jakeman, M. Eldred, D. Xiu, Numerical approach for quantification of epistemic uncertainty, …

Quantitative Modeling Of Spatiotemporal Systems: Simulation Of Biological Systems And Analysis Of Error Metric Effects On Model Fitting, James Hengenius

Open Access Dissertations

Understanding the biophysical processes underlying biological and biotechnological processes is a prerequisite for therapeutic treatments and technological innovation. With the exponential growth of computational processing speed, experimental findings in these fields have been complemented by dynamic simulations of developmental signaling and genetic interactions. Models provide means to evaluate "emergent" properties of systems sometimes inaccessible by reductionist approaches, making them test beds for biological inference and technological refinement.^ The complexity and interconnectedness of biological processes pose special challenges to modelers; biological models typically possess a large number of unknown parameters relative to their counterparts in other physical sciences. Estimating these parameter …

Structured Deterministic Models Applied To Malaria And Other Endemic Diseases, Katia Patricia Vogt Geisse

Open Access Dissertations

This thesis includes modeling studies on three structured deterministic models. These models are used to study the disease dynamics of malaria or the joint disease dynamics of HIV and HSV-2. Each of the models includes multiple components containing individuals in various epidemiological classes for the purpose of addressing questions that are of interests to biologists and epidemiologists. Some of the compartments have a continuous age-structure, which is necessary for studying the specific biological questions under investigation.^ In Chapter 2 a chronological-age structured deterministic model for malaria is presented. The model includes the human and mosquito populations with the human population …

Component Trees For The Exploration Of Macromolecular Structures In Biology, Lucas Oliveira

Dissertations, Theses, and Capstone Projects

Understanding the three-dimensional structure of a macromolecular complex is essential for understanding its function. A component tree is a topological and geometric image descriptor that captures information regarding the structure of an image based on the connected components determined by different grayness thresholds. This dissertation presents a novel interactive framework for visual exploration of component trees of the density maps of macromolecular complexes, with the purpose of improved understanding of their structure. The interactive exploration of component trees together with a robust simplification methodology provide new insights in the study of macromolecular structures. An underlying mathematical theory is introduced and …

Optimal Contract Design For Co-Development Of Companion Diagnostics, Rodney T. Tembo

Electronic Thesis and Dissertation Repository

As the number of new drugs requiring companion diagnostics rises, more and more partnerships are formed between drug and diagnostics manufacturers to develop the necessary companion diagnostic. An increasingly significant issue is that of the optimal revenue/profit sharing or compensation schemes for such partnerships. We investigate the structure of an optimal compensation scheme under a scenario where a large pharmaceutical firm that is developing a drug intends to partner with a smaller diagnostics firm to develop a companion diagnostic test for the drug. We describe an optimal contract as one that maximizes the pharmaceutical firm's expected profits while offering enough …

Dark-Bright Solitons And Vortices In Bose-Einstein Condensates, Dong Yan

Doctoral Dissertations

This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the …

Bifurcation Of Limit Cycles In Smooth And Non-Smooth Dynamical Systems With Normal Form Computation, Yun Tian

Electronic Thesis and Dissertation Repository

This thesis contains two parts. In the first part, we investigate bifurcation of limit cycles around a singular point in planar cubic systems and quadratic switching systems. For planar cubic systems, we study cubic perturbations of a quadratic Hamiltonian system and obtain 10 small-amplitude limit cycles bifurcating from an elementary center, for which up to 5th-order Melnikov functions are used. Moreover, we prove the existence of 12 small-amplitude limit cycles around a singular point in a cubic system by computing focus values. For quadratic switching system, we develop a recursive algorithm for computing Lyapunov constants. With this efficient algorithm, we …

Observational Signatures From Self-Gravitating Protostellar Disks, Alexander L. Desouza

Electronic Thesis and Dissertation Repository

Protostellar disks are the ubiquitous corollary outcome of the angular momentum conserving, gravitational collapse of molecular cloud cores into stars. Disks are an essential component of the star formation process, mediating the accretion of material onto the protostar, and for redistributing excess angular momentum during the collapse. We present a model to explain the observed correlation between mass accretion rates and stellar mass that has been inferred from observations of intermediate to upper mass T Tauri stars. We explain this correlation within the framework of gravitationally driven torques parameterized in terms of Toomre’s Q criterion. Our models reproduce both the …

Understanding Recurrent Disease: A Dynamical Systems Approach, Wenjing Zhang

Electronic Thesis and Dissertation Repository

Recurrent disease, characterized by repeated alternations between acute relapse and long re- mission, can be a feature of both common diseases, like ear infections, and serious chronic diseases, such as HIV infection or multiple sclerosis. Due to their poorly understood etiology and the resultant challenge for medical treatment and patient management, recurrent diseases attract much attention in clinical research and biomathematics. Previous studies of recurrence by biomathematicians mainly focus on in-host models and generate recurrent patterns by in- corporating forcing functions or stochastic elements. In this study, we investigate deterministic in-host models through the qualitative analysis of dynamical systems, to …

Estimation Of Hidden Markov Models And Their Applications In Finance, Anton Tenyakov

Electronic Thesis and Dissertation Repository

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts …

Impacts Of Climate Change On The Evolution Of The Electrical Grid, Melissa Ree Allen

Doctoral Dissertations

Maintaining interdependent infrastructures exposed to a changing climate requires understanding 1) the local impact on power assets; 2) how the infrastructure will evolve as the demand for infrastructure changes location and volume and; 3) what vulnerabilities are introduced by these changing infrastructure topologies. This dissertation attempts to develop a methodology that will a) downscale the climate direct effect on the infrastructure; b) allow population to redistribute in response to increasing extreme events that will increase under climate impacts; and c) project new distributions of electricity demand in the mid-21^st century.

The research was structured in three parts. The first …

Newton's Method Backpropagation For Complex-Valued Holomorphic Neural Networks: Algebraic And Analytic Properties, Diana Thomson La Corte

Theses and Dissertations

The study of Newton's method in complex-valued neural networks (CVNNs) faces many difficulties. In this dissertation, we derive Newton's method backpropagation algorithms for complex-valued holomorphic multilayer perceptrons (MLPs), and we investigate the convergence of the one-step Newton steplength algorithm for the minimization of real-valued complex functions via Newton's method. The problem of singular Hessian matrices provides an obstacle to the use of Newton's method backpropagation to train CVNNs. We approach this problem by developing an adaptive underrelaxation factor algorithm that avoids singularity of the Hessian matrices for the minimization of real-valued complex polynomial functions.

To provide experimental support for the …

Homomorphic Encryption And The Approximate Gcd Problem, Nathanael Black

All Dissertations

With the advent of cloud computing, everyone from Fortune 500 businesses to personal consumers to the US government is storing massive amounts of sensitive data in service centers that may not be trustworthy. It is of vital importance to leverage the benefits of storing data in the cloud while simultaneously ensuring the privacy of the data. Homomorphic encryption allows one to securely delegate the processing of private data. As such, it has managed to hit the sweet spot of academic interest and industry demand. Though the concept was proposed in the 1970s, no cryptosystem realizing this goal existed until Craig …

Several Functional Equations Defined On Groups Arising From Stochastic Distance Measures., Heather B. Hunt

Electronic Theses and Dissertations

Several functional equations related to stochastic distance measures have been widely studied when defined on the real line. This dissertation generalizes several of those results to functions defined on groups and fields. Specifically, we consider when the domain is an arbitrary group, G, and the range is the field of complex numbers, C. We begin by looking at the linear functional equation f(pr, qs)+f(ps, qr) = 2f(p, q)+2f(r, s) for all p, q, r, s, € G. The general solution f : G x G → C is given along with a few specific examples. Several generalizations of this equation …

Magnetoviscous Effects Of Magnetized Particle Threads In Magnetized Ferrofluid, Alexander Francis Cali

Theses, Dissertations and Culminating Projects

The magnetoviscous effect of applied fields on ferrofluids has been utilized in many applications in which the ferrofluid must remain in a fixed position while this effect on ferrofluids in motion has yet to be rigorously explored. In light of potential biomedical applications such as drug targeting, experiments were conducted to probe the rheology of ferrofluids on the micrometer scale. A non-conducting glass sphere of diameter 550 μm is dropped into a cylindrical container of magnetized ferrofluid of inner diameter 5.2 mm. This was repeated for two applied field strengths (980 gauss and 480 gauss) and over multiple angles with …

Applied Statistics In Environmental Monitoring: Case Studies And Analysis For The Michigan Bald Eagle Biosentinel Program, Katherine Leith

All Dissertations

The bald eagle (Haliaeetus leucocephalus) is an extensively researched tertiary predator. Its life history and the impact of various stressors on its reproductive outcomes have been documented in many studies, and over many years. Furthermore, the bald eagle population recovery in Michigan has been closely monitored since the 1960s, as it has continued to recover from a contaminant-induced bottleneck. Because of its position at the top of the aquatic food web and the large body of ethological knowledge, the bald eagle has become a sentinel species for the Michigan aquatic ecosystem. In April 1999, the Michigan Department of Environmental Qualtity, …

Level Stripping Of Genus 2 Siegel Modular Forms, Rodney Keaton

All Dissertations

In this Dissertation we consider stripping primes from the level of genus 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level Nlr which satisfies certain mild conditions, where l is a prime not dividing N, we construct an eigenform of level N which is congruent to our original form. To obtain our results, we use explicit constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms. Furthermore, we give applications of this result to Galois representations and provide evidence for an analog of Serre's conjecture in the genus 2 case.

Numerical Simulations Of Traffic Flow Models, Puneet Lakhanpal

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traffic flow has been considered to be a continuum flow of a compressible liquid having a certain density profile and an associated velocity, depending upon density, position and time. Several one-equation and two-equation macroscopic continuum flow models have been developed which utilize the fluid dynamics continuity equation and help us find analytical solutions with simplified initial and boundary conditions. In this thesis, the one-equation Lighthill Witham and Richards (LWR) model combined with the Greenshield's model, is used for finding analytical and numerical solutions for four problems: Linear Advection, Red Traffic Light turning into Green, Stationary Shock and Shock Moving towards …

Mathematical Equations And System Identification Models For A Portable Pneumatic Bladder System Designed To Reduce Human Exposure To Whole Body Shock And Vibration, Ezzat Aziz Ayyad

UNLV Theses, Dissertations, Professional Papers, and Capstones

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose …