Applied Mathematics Commons^™

Computational Analysis Of The Sir Mathematical Model For The Dengue Fever, Joseph Phillip Diaz

Theses and Dissertations

Dengue fever is a disease affecting people in more than 100 countries. Here we consider a host and vector model for the transmission of dengue fever. This SIR model consists of three compartments of susceptible, infective and removed for host (human) and two compartments of susceptible and infective for vector (dengue mosquitos). These five compartments yield five coupled nonlinear ordinary differential equations (ODEs). After non-dimensionalization, we have a system of three nonlinear ODEs. Reproductive number and two equilibrium points are calculated for various cases. Simulation is carried out for susceptible, infective and removed and the results are presented in graphical …

Using An Agent-Based Model To Study The Effect Of Reproductive Skew On Mongoose Populations, Stacy Lee Mowry

Theses and Dissertations

Reproductive skew is the name given to the unequal partitioning of breeding

within social groups. Within these groups a mating hierarchy emerges wherein one dominant mating pair holds an unproportional majority of the group's reproductive benefit, while other members mate infrequently, yet allocate energy and resources toward the offspring of the dominant group members. In this paper, we use an agent-based model, which mimics dwarf and banded mongoose populations, to investigate how reproductive skew aftects the speed natural selection, and thus how reproductive skew affects fitness. The results of the model show that due to the geometric structure of skewed …

Testing The Adequacy Of A Semi-Markov Process, Richard S. Seymour

Theses and Dissertations

Due to the versatility of its structure, the semi-Markov process is a powerful modeling tool used to describe complex systems. Though similar in structure to continuous time Markov chains, semi-Markov processes allow for any transition time distribution which enables these processes to t a wider range of problems than the continuous time Markov chain. While semi-Markov processes have been applied in fields as varied as biostatistics and finance, there does not exist a theoretically-based, systematic method to determine if a semi-Markov process accurately fits the underlying data used to create the model. In fields such as regression and analysis of …

Modeling Radiation Effectiveness For Inactivation Of Bacillus Spores, Emily A. Knight

Theses and Dissertations

This research models and analyzes the inactivation of Bacillus spores following a radiation exposure and the process enacted by the Bacillus spore to repair the resulting damage. Irradiation of a spore and the medium surrounding the spore induces chemical reactions that produce reactive oxygen species (ROS). This research will consider the reaction- diffusion of these ROS throughout the spore. These ROS can react with the spore's DNA and enzymes to degrade them to such an extent that the DNA cannot be repaired or replicated, thus causing spore death. In order to survive a dose of radiation, a spore must repair …

On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos

Theses and Dissertations

We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the L₂-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is …

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 …

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 Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

Theses and Dissertations

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a …

Domination Numbers Of Semi-Strong Products Of Graphs, Stephen R. Cheney

Theses and Dissertations

This thesis examines the domination number of the semi-strong product of two graphs G and H where both G and H are simple and connected graphs. The product has an edge set that is the union of the edge set of the direct product of G and H together with the cardinality of V(H), copies of G. Unlike the other more common products (Cartesian, direct and strong), the semi-strong product is neither commutative nor associative.

The semi-strong product is not supermultiplicative, so it does not satisfy a Vizing like conjecture. It is also not submultiplicative so it shares these two …

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

Theses and Dissertations

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …

Applications Of Stability Analysis To Nonlinear Discrete Dynamical Systems Modeling Interactions, Jonathan L. Hughes

Theses and Dissertations

Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model …

A Comparison Of Obesity Interventions Using Energy Balance Models, Marcella Torres

Theses and Dissertations

An energy balance model of human metabolism developed by Hall et al. is extended to compare body composition outcomes among standard and proposed obesity interventions. Standard interventions include a drastic diet or a drastic diet with endurance training. Outcomes for these interventions are typically poor in clinical studies. Proposed interventions include a gradual diet and the addition of resistance training to preserve lean mass and metabolic rate. We see that resistance training, regardless of dietary strategy, achieves these goals. Finally, we observe that the optimal obesity intervention for continued maintenance of a healthy body composition following a diet includes a …

Different Formulations Of The Orthogonal Array Problem And Their Symmetries, Andrew J. Geyer

Theses and Dissertations

Modern statistical experiments routinely feature a large number of input variables that can each be set to a variety of different levels. In these experiments, output response changes as a result of changes in the individual factor level settings. Often, an individual experimental run can be costly in time, money or both. Therefore, experimenters generally want to gain the desired information on factor effects from the smallest possible number of experimental runs. Orthogonal arrays provide the most desirable designs. However, finding orthogonal arrays is a very challenging problem. There are numerous integer linear programming formulations (ILP) in the literature whose …

An Analysis Of The Impact Of Variation In Mean Time Between Demand On Air Force Fleet Level Aircraft Parts Inventories, Andrew J. Berger, Caleb S. Murphy

Theses and Dissertations

This thesis researched the accuracy of demand forecasting and impact of demand variation on requirements definition for Air Force aircraft secondary items. Specifically, this thesis sought to answer three questions: How does the Air Force calculate item requirements? , How accurate is the current system at predicting future item requirements? , and How do variations in predicted demand change item requirements? The literature review described the Air Force supply system for aircraft secondary items. Analysis into current demand forecast accuracy found that the level of error between actual and predicted historic demand was as high as 92% for the items …

Morphological Active Contours For Texture And Multiphase Segmentation, Victoria Lynn Fox

Theses and Dissertations

Natural images, in the context of this work, are images that contain complicated, local covariance structures in their statistical analysis. Owing to compound textural features, intensity inhomogeneity, image layers and variations of statistics inherent in such images, segmenting complicated images into areas of similarity is a challenging task. In this work, a morphological active contour is developed to increase efficiency of current active contour schemes and a fuzzy clustering energy is incorporated into the active contour algorithm to increase accuracy and flexibility. The savings in computational efficiency garnered from using a morphological curve evolution rather than a partial differential equation …

Spatial Scheduling Algorithms For Production Planning Problems, Sudharshana Srinivasan

Theses and Dissertations

Spatial resource allocation is an important consideration in shipbuilding and large-scale manufacturing industries. Spatial scheduling problems (SSP) involve the non-overlapping arrangement of jobs within a limited physical workspace such that some scheduling objective is optimized. Since jobs are heavy and occupy large areas, they cannot be moved once set up, requiring that the same contiguous units of space be assigned throughout the duration of their processing time. This adds an additional level of complexity to the general scheduling problem, due to which solving large instances of the problem becomes computationally intractable. The aim of this study is to gain a …

Model Uncertainty And Test Of A Segmented Mirror Telescope, Luke C. Dras

Theses and Dissertations

The future of large aperture telescopes relies heavily on the development of segmented array designs. Today's monolithic mirror technology has reached a barrier, particularly for space-based telescopes. These large diameter, dense mirrors allow stable high-resolution imaging but are incompatible with optimized space launch. Segmented mirror telescopes are designed to balance lightweight with compact stowage. The structure necessary to support the flexible mirror array often combines isogrid geometry and complex actuation hardware. High-fidelity finite element models are commonly used to economically predict how the optics will perform under different environmental conditions. The research detailed herein integrates superelement partitioning and complexity simplifying …

Airborne Wireless Communication Modeling And Analysis With Matlab, Matthew J. Vincie

Theses and Dissertations

Over the past decade, there has been a dramatic increase in the use of unmanned aerial vehicles (UAV) for military, commercial, and private applications. Critical to maintaining control and a use for these systems is the development of wireless networking systems [1]. Computer simulation has increasingly become a key player in airborne networking developments though the accuracy and credibility of network simulations has become a topic of increasing scrutiny [2-5]. Much of the inaccuracies seen in simulation are due to inaccurate modeling of the physical layer of the communication system. This research develops a physical layer model that combines antenna …

A Pollination Network Of Cornus Florida, James H. Lee

Theses and Dissertations

From the agent-based, correlated random walk model presented, we observe the effects of varying the parameter values of maximum insect turning area, ��_max, density of trees, ω, maximum pollen carryover, ��_max, and probability of fertilization, P_��, on the distribution of pollen within a population of Cornus florida (flowering dogwood). We see that varying ��_max and ��_max changes the dispersal distance of pollen, which greatly affects many measures of connectivity. The clustering coefficient of fathers is maximized when ��_max is between 60° and 90°. Varying ω does not have a major …

Superconvergence Of Finite Element Approximations For Partial Differential Equations, Rabeea Hadi Jari

Theses and Dissertations

The finite element methods (FEMs) are popular numerical methods for solving partial differential equations. They are widely used by mathematicians, scientists and engineers to solve real world problems. The superconvergence in the finite element method (FEM) is a phenomenon where the order of convergence of the numerical solution is higher than the order of convergence of the maximum of the finite element error. Improving the convergence rate by applying certain post-processing techniques to the standard finite element solutions is one of the most important and useful areas of superconvergence. Two model problems will be considered in this dissertation. They are …

Distributional Monte Carlo Methods For The Boltzmann Equation, Christopher R. Schrock

Theses and Dissertations

Stochastic particle methods (SPMs) for the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) technique, have gained popularity for the prediction of flows in which the assumptions behind the continuum equations of fluid mechanics break down; however, there are still a number of issues that make SPMs computationally challenging for practical use. In traditional SPMs, simulated particles may possess only a single velocity vector, even though they may represent an extremely large collection of actual particles. This limits the method to converge only in law to the Boltzmann solution. This document details the development of new SPMs that …

Quantifying Performance Bias In Label Fusion, Alexander M. Venzin

Theses and Dissertations

Classification systems are employed to remotely assess whether an element of interest falls into a target class or non-target class. These systems have uses in fields as far ranging as biostatistics to search engine keyword analysis. The performance of the system is often summarized as a trade-off between the proportions of elements correctly labeled as target plotted against the number of elements incorrectly labeled as target. These are empirical estimates of the true positive and false positive rates. These rates are often plotted to create a receiver operating characteristic (ROC) curve that acts as a visual tool to assess classification …

Numerical Analysis For Interface Problems, Lin Mu

Theses and Dissertations

A large number of partial differential equations in geoscience and engineering can be described as interface problems. Three interface models will be considered in this dissertation. They are elliptic interface problems, Stokes interface problems, and Brinkman problems. The purpose of the dissertation is to develop and analyze robust finite element methods and finite volume methods for solving these problems. Firstly, we report the a posteriori error estimate for interface problems by conforming finite volume methods, nonconforming finite volume methods, and discontinuous finite volume methods. Recovery-based and residual-based a posteriori error estimators are constructed by using computable quantities. Secondly, we develop …

Determining Angular Frequency From A Video With A Generalized Fast Fourier Transform, Lindsay N. Smith

Theses and Dissertations

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. …

Local Histograms For Per-Pixel Classification, Melody L. Massar

Theses and Dissertations

We introduce a rigorous mathematical theory for the analysis of local histograms, and study how they interact with textures that can be modeled as occlusions of simpler components. We first show how local histograms can be computed as a system of convolutions and discuss some basic local histogram properties. We then introduce a probabilistic, occlusion-based model for textures and formally demonstrate that local histogram transforms are natural tools for analyzing the textures produced by our model. Next, we characterize all nonlinear transforms which satisfy the three key properties of local histograms and consider the appropriateness of local histogram features in …

Analysis Of Transient Electromagnetic Scattering From An Overfilled Cavity Embedded In An Impedance Ground Plane, Robert S. Callihan

Theses and Dissertations

We consider the transient, or time-domain, scattering problem of a two-dimensional overfilled cavity embedded in an impedance ground plane. This problem is a significant advancement from previous work where more simplified boundary conditions were used, which can limit the number of applications. This research supports a wide range of military applications such as the study of cavity-like structures on aircraft and vehicles. More importantly, this research helps detect the biggest threat on today's battlefield: improvised explosive devices. An important step in solving the problem is introducing an artificial boundary condition on a semicircle enclosing the cavity; this couples the fields …

Modeling Of Bacillus Spores: Inactivation And Outgrowth, Alexis X. Hurst

Theses and Dissertations

This research models and analyzes the thermochemical damage produced in Bacillus spores by short, high-temperature exposures as well the repair process within damaged Bacillus spores. Thermochemical damage in spores is significantly due to reaction with water, hydrolysis reactions. Applying heat to the spore causes absorbed and chemically bound water molecules become mobile within the spore. These mobile water molecules react by hydrolysis reactions to degrade DNA and enzyme molecules in the spore. In order to survive the thermal inactivation, the spore must repair the damaged DNA during spore germination. The DNA repair process, as well as other germination functions, is …

Neural Extensions To Robust Parameter Design, Bernard Jacob Loeffelholz

Theses and Dissertations

Robust parameter design (RPD) is implemented in systems in which a user wants to minimize the variance of a system response caused by uncontrollable factors while obtaining a consistent and reliable system response over time. We propose the use of artificial neural networks to compensate for highly non-linear problems that quadratic regression fails to accurately model. RPD is conducted under the assumption that the relationship between system response and controllable and uncontrollable variables does not change over time. We propose a methodology to find a new set of settings that will be robust to moderate system degradation while remaining robust …