Applied Mathematics Commons^™

On The 3-Dimensional Fluid-Structure Interaction Of Flexible Fibers In A Flow, Ryan Howard Allaire

Theses, Dissertations and Culminating Projects

We discuss the equilibrium configurations of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s. Experimental results are presented with both two-dimensional and three-dimensional numerical simulations used to model this problem. We present the effects of flow speed and initial configuration angle between the fiber and the direction of the flow. Investigations reveal that both the orientation of the fiber and the fiber length have a significant impact on the deformation of the fiber as well as on the forces it experiences. Specifically, we …

Improved Self-Consistency For Sced-Lcao., Lyle C. Smith

Electronic Theses and Dissertations

In this document I describe a novel implementation of the generalized bisection method for finding roots of highly non-linear functions of several variables. Several techniques were optimized to reduce computation time. The implementation of the bisection method allows for the calculation of heterogeneous systems with SCED-LCAO, since derivative-based methods often fail for these systems. Systems composed of Gallium and Nitrogen are currently receiving much interest due to their behavior as semi-conductors and their ability to form nano-wires. The methods developed here were employed to create a set of SCED-LCAO parameters for homogeneous Gallium and heterogeneous Gallium Nitride systems. These parameters …

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

Department of Mathematics: Dissertations, Theses, and Student Research

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to …

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Situational Assessment Using Graph Comparison, Pavan Kumar Pallapunidi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In strategic operations, the assessment of any given situation is very important and may trigger the development of a mission plan. The mission plan consists of various actions that should be executed in order to successfully mitigate the situation. For a new mission plan to be designed or implemented, the effect of the previous mission plan should be accessed. These mission plans use various sensors to collect the data which can be very large and aggregate them to obtain detailed information of the situation. In order to implement an effective mission plan the current situation has to be assessed effectively. …

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

Random Walks On Random Lattices And Their Applications, Ryan Tyler White

Theses and Dissertations

This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

An Experimental Analysis Of Adaptive Learning In A Multi-Subject Economy, David Martin

Business and Economics Honors Papers

The rational expectations hypothesis (REH) has long served as a foundation in macroeconomic laws of motion. However, the assumptions of REH are likely too powerful to be representative of economic actors. This research evaluates adaptive learning, a developing alternative to rational expectations, using a multi-agent macroeconomic prediction “game.” Data was gathered from a group of students, each predicting the outcome of a single economy over time. Each agent was asked to forecast output (GDP) and inflation in each period based on historic levels of output, inflation, and interest rates. These data were then analyzed under various theoretical models of adaptive …

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

A Seasonal Analysis Of Extreme Precipitation Trends In The Contiguous United States, Rachael Balstad, Jaechoul Lee

College of Arts and Sciences Presentations

The purpose of this paper is to examine extreme precipitation trends in the United States. The National Climate Assessment estimated that average precipitation in the United States has increased in the last 100 years, with variation occurring regionally. Some regions have experienced larger increases in average precipitation, while others have experienced decreases. However, this aggregate increase in average precipitation does not necessarily indicate an analogous trend in extreme precipitation. Statistically, average and extreme values are nearly independent. In this paper, a changepoint technique and extreme value statistical models will be used for estimation of trend and its uncertainty. A changepoint …

Helping A Microfinance Institution Select Its Clients: A Risk Analysis Using Social Networks, Sayantan Mitra, Varunavi Newar

Black & Gold

This paper formulates an objective mathematical model for a Microfinance Institution (MFI) to measure the credit worthiness associated with a potential client. We use concepts from network theory to determine the credit worthiness of an individual in relation to other households in the community. We use the concept of eigenvector centrality to evaluate the relative credit worthiness in the network. The latter part of the model focuses on the absolute measures of credit worthiness such as income, ownership of assets and risk of the proposed investment. This model would help MFIs reduce the risk of borrowing by ensuring that there …

Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate

Senior Honors Theses

Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …

Primes And Zeros: A Million Dollar Mystery, Brian Conrey

Dalrymple Lecture Series

A prime number is an integer greater than one whose only positive divisors are 1 and itself. In 1859 G. F. B. Riemann proposed a way to understand how the prime numbers are distributed among the natural numbers. More than 150 years later mathematicians still have not proven Riemann's Hypothesis. The stature of this problem has continued to rise so that today it is widely regarded as the most important unsolved problem in all of mathematics. In this talk I will describe some of the colorful history that surrounds this question.

The Kerzman–Stein Operator For Piecewise Continuously Differentiable Regions, Michael Bolt, Andrew Raich

University Faculty Publications and Creative Works

The Kerzman–Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on a rectifiable curve. If the curve is continuously differentiable, the Kerzman–Stein operator is compact on the Hilbert space of square integrable functions; when there is a corner, the operator is noncompact. Here, we give a complete description of the spectrum for a finite symmetric wedge and we show how this reveals the essential spectrum for curves that are piecewise continuously differentiable. We also give an explicit construction for a smooth curve whose Kerzman–Stein operator has large norm.

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Standardized Testing: What Is It Good For? A Case Study In Connecticut, Megan Mapp

Honors Projects in Mathematics

The case study was developed in an attempt to shed more light on the debate of standardized testing. The goal of the study was to find evidence to support whether or not standardized testing is worth doing in public secondary schools. To investigate this question, the state standardized math test scores of three Connecticut public high schools were analyzed. The average math scores over thirteen years were observed and statistical analysis was performed to see if any significant differences existed between the three schools. Tests were performed before and after the change in standardized test. The graduation rates of the …

Mathematical Approaches To Food Nutrient Content Estimation With A Focus On Phenylalanine, Jieun Kim

Open Access Dissertations

Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of …

Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine

Doctoral Dissertations

Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.

In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …

Computational Approaches For Monitoring Of Health Parameters And Their Evaluation For Application In Clinical Setting., Mohammad Adibuzzaman

Dissertations (1934 -)

The algorithms and mathematical methods developed in this work focus on using computational approaches for low cost solution of health care problems for better patient outcome. Furthermore, evaluation of those approaches for clinical application considering the risk and benefit in a clinical setting is studied. Those risks and benefits are discussed in terms of sensitivity, specificity and area under the receiver operating characteristics curve. With a rising cost of health care and increasing number of aging population, there is a need for innovative and low cost solutions for health care problems. In this work, algorithms, mathematical techniques for the solutions …

Efficient Thermal Image Segmentation Through Integration Of Nonlinear Enhancement With Unsupervised Active Contour Model, Fatema Albalooshi, Evan Krieger, Paheding Sidike, Vijayan K. Asari

Electrical and Computer Engineering Faculty Publications

Thermal images are exploited in many areas of pattern recognition applications. Infrared thermal image segmentation can be used for object detection by extracting regions of abnormal temperatures. However, the lack of texture and color information, low signal-to-noise ratio, and blurring effect of thermal images make segmenting infrared heat patterns a challenging task. Furthermore, many segmentation methods that are used in visible imagery may not be suitable for segmenting thermal imagery mainly due to their dissimilar intensity distributions.

Thus, a new method is proposed to improve the performance of image segmentation in thermal imagery. The proposed scheme efficiently utilizes nonlinear intensity …

Discrete Epidemic Models With Arbitrarily Distributed Disease Stages, Nancy Hernandez Ceron

Open Access Dissertations

The use of discrete-time models (or discrete models) in the field of mathematical epidemiology has been limited while continuous-time models (or continuous models) are often times preferred, particularly because disease dynamics do occur continuously in time and more mathematical tools are available for model analysis. How- ever, discrete models are not only more tractable and easier to understand, but also more directly related to data, particularly when the disease stage distributions are arbitrarily distributed (e.g., when the data cannot be fitted by distributions from a parametric family). Under these circumstances continuous models usually lead to complex system of integral equations. …

Active Tile Self-Assembly And Simulations Of Computational Systems, Daria Karpenko

USF Tampa Graduate Theses and Dissertations

Algorithmic self-assembly has been an active area of research at the intersection of computer science, chemistry, and mathematics for almost two decades now, motivated by the natural self-assembly mechanism found in DNA and driven by the desire for precise control of nanoscale material manufacture and for the development of nanocomputing and nanorobotics. At the theoretical core of this research is the Abstract Tile Assembly Model (aTAM), the original abstract model of DNA tile self-assembly. Recent advancements in DNA nanotechnology have been made in developing strand displacement mechanisms that could allow DNA tiles to modify themselves during the assembly process by …

Quantitative Urbanism: A Look At Illinois Cities Using Modeling, Heather Conte

All Student Theses and Dissertations

Quantitative urbanism is described as the field of study that explores the social, economic, and physical principles that cities are a product of. This new field of mathematics is quickly growing as various disciplines are attempting to better understand urban growth. This paper will explore the latest discoveries in the relationships that exist between cities and their size. Many aspects of cities, such as crime rates, energy usage, and wealth, have been shown to change exponentially in relation to city size. This paper explores multiple urban indicators vs. population size for cities in Illinois and discusses the results compared to …

Relationship Between High School Math Course Selection And Retention Rates At Otterbein University, Lauren A. Fisher

Undergraduate Honors Thesis Projects

Binary logistic regression was used to study the relationship between high school math course selection and retention rates at Otterbein University. Graduation rates from postsecondary institutions are low in the United States and, more specifically, at Otterbein. This study is important in helping to determine what can raise retention rates, and ultimately, graduation rates. It directs focus toward high school math course selection and what should be changed before entering a post-secondary institution. Otterbein will have a better idea of what type of students to recruit and which students may be good candidates with some extra help. Recruiting is expensive, …

Accuracy Of Time Phasing Aircraft Development Using The Continuous Distribution Function, Gregory E. Brown

Theses and Dissertations

Early research on time phasing primarily focuses on the theoretical foundation for applying the continuous distribution function, or S-curve, to model the distribution of development expenditures. Minimal methodology is provided for estimating the S-curve's parameter values. Brown, White, and Gallagher (2002) resolve this shortcoming through regression analysis, but their methodology has not been widely adopted by aircraft cost analysts, as it is judged as overly broad and not specific to aircraft. Instead, analysts commonly apply the 60/40 rule of thumb to aircraft development, assuming 60 percent expenditures at 50 percent schedule. It is currently unknown if the 60/40 heuristic accurately …

Examining The Return On Investment Of Test And Evaluation, Nathan C. Smith

Theses and Dissertations

This research examined the return on investment of Department of Defense test and evaluation. The thesis analyzed the return on investment of the cost avoidance achieved if an issue discovered late in the program had been discovered and corrected during developmental test and evaluation. The methodology utilized two case study examples from the Joint Primary Training Aircraft System to calculate the potential cost avoidance and the potential return on investment if the program had discovered and corrected the issues during developmental test and evaluation. The result of one case was a 9,260% return on investment. The other case results ranged …

Symmetry Groups For Linear Programming Relaxations Of Orthogonal Array Problems, David M. Arquette

Theses and Dissertations

Integer linear programs arise in many situations, and solving such problems can be computationally demanding. One way to solve them more efficiently is by exploiting the symmetry within their formulation. This paper proves that the symmetry group for the linear programming relaxation of 2-level orthogonal array problems of strength 2 is a particular semidirect product.

An Individual-Based Model Of Chaparral Vegetation Response To Frequent Wildfire, Timothy Lucas, Dayna Mann, Reanna Dona

Seaver College Research And Scholarly Achievement Symposium

In recent years, the Santa Monica Mountains (SMM) have been plagued by frequent wildfires which threaten the native chaparral species. Nonsprouting chaparral species are completely killed by a fire, but their seeds germinate in response to fire cues. Facultative sprouters both resprout after a wildfire and release seeds that germinate post-fire. This project is based on data collected since 1986 at a biological preserve adjacent to the Malibu campus of Pepperdine University with an average fire return interval of 7.5 years. We present a spatial model that simulates the growth, seed dispersal and resprouting behavior of individual shrubs that compete …

The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks

Presentations and Publications

The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.