Digital Commons Network^™

Bias-Corrected Maximum Likelihood Estimation Of The Parameters Of The Weighted Lindley Distribution, Wentao Wang

Dissertations, Master's Theses and Master's Reports - Open

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data …

Finite Volume Methods For Linear Partial Differential Equations With Delta-Singularities, Nattaporn Chuenjarern

Dissertations, Master's Theses and Master's Reports - Open

In this work, we study hyperbolic conservation law in one space dimension with δ-singularities as the initial data. We use finite volume methods to find the sizes of pollution region. Firstly, we study finite volume method (FVM) with linear weights and weighted essentially non-oscillatory (WENO) scheme and apply both methods to linear partial differential equations without singularities to check the accuracy. Then we use both methods to find the numerical solutions and compute errors of linear equations with δ-singularities. Lastly, we use such results to find the size of pollution region of each method. These results show that …

Weak Isometries Of Hamming Spaces, Ryan Walter Bruner

Dissertations, Master's Theses and Master's Reports - Open

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rⁿ. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean …

Variations Of The Feast Eigenvalue Algorithm, Stephanie Kajpust

Dissertations, Master's Theses and Master's Reports - Open

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is …

Study Of A Direct Sampling Method For The Inverse Medium Scattering Problem, Natasha Weerasinghe

Dissertations, Master's Theses and Master's Reports - Open

Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.

Maximal Arcs, Above And Beyond, Diego Domenzain-Gonzale

Dissertations, Master's Theses and Master's Reports - Open

This report explores combinatorial structures in Finite Geometries by giving known constructions of maximal arcs; using maximal arcs to construct two-weight codes, partial geometries, strongly regular graphs and LDPC codes; a review on how to generalize maximal arcs to higher dimensions through Perp-Systems; and an effort in finding constructions of new Perp-Systems.

Partitioning The Blocks Of A Steiner Triple System Into Partial Parallel Classes, Jezerca Hodaj

Dissertations, Master's Theses and Master's Reports - Open

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [^v⁄₃], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks …

High Performance, Low Cost Subspace Decomposition And Polynomial Rooting For Real Time Direction Of Arrival Estimation: Analysis And Implementation, Mrudula V. Athi

Dissertations, Master's Theses and Master's Reports - Open

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna …

A Survey Of Distance Magic Graphs, Rachel Rupnow

Dissertations, Master's Theses and Master's Reports - Open

In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . . , n}, such that for every vertex x

Σ ^{l(y) = k,}
_y∈NG(x)

where N_G(x) is the set of vertices of G adjacent to x. If the graph G has a distance magic labeling we say that G is a distance magic graph.

In Chapter 1, we explore the background of …

Maximum Principle Preserving High Order Schemes For Convection-Dominated Diffusion Equations, Yi Jiang

Dissertations, Master's Theses and Master's Reports - Open

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains …

Benson's Theorem For Partial Geometries, Ellen J. Kamischke

Dissertations, Master's Theses and Master's Reports - Open

In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values …

Dimension Reduction For Power System Modeling Using Pca Methods Considering Incomplete Data Readings, Ting Zhao

Dissertations, Master's Theses and Master's Reports - Open

Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental …

Three Hundred Years Of The St. Petersburg Paradox, Keguo Huang

Dissertations, Master's Theses and Master's Reports - Open

The St. Petersburg Paradox was first presented by Nicholas Bernoulli in 1713. It is related to a gambling game whose mathematical expected payoff is infinite, but no reasonable person would pay more than $25 to play it. In the history, a number of ideas in different areas have been developed to solve this paradox, and this report will mainly focus on mathematical perspective of this paradox. Different ideas and papers will be reviewed, including both classical ones of 18th and 19th century and some latest developments. Each model will be evaluated by simulation using Mathematica.

Numerical Solutions Of Elliptic Inverse Problems Via The Equation Error Method, Mohammad F. Al-Jamal

Dissertations, Master's Theses and Master's Reports - Open

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be …

Modeling Spontaneous Three-Dimensional Polymerization, Zhitong Zhao

Dissertations, Master's Theses and Master's Reports - Open

For human beings, the origin of life has always been an interesting and mysterious matter, particularly how life arose from inorganic matter through natural processes. Polymerization is always involved in such processes. In this paper we built what we refer to as ideal and physical models to simulate spontaneous polymerization based on certain physical principles. As the modeling confirms, without taking external energy, small and simple inorganic molecules formed bigger and more complicated molecules, which are necessary ingredients of all living organisms. In our simulations, we utilized actual ranges of parameters according to their experimentally observed values. The results from …

Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics, Raymond E. Molzon

Dissertations, Master's Theses and Master's Reports - Open

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall …

Simulation Study On Using Moment Functions For Sufficient Dimension Reduction , Lipu Tian

Dissertations, Master's Theses and Master's Reports - Open

No abstract provided.

Hamilton-Waterloo Problem With Triangle And C9 Factors, David C. Kamin

Dissertations, Master's Theses and Master's Reports - Open

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Applications Of Finite Geometries To Designs And Codes, David C. Clark

Dissertations, Master's Theses and Master's Reports - Open

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures.

A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will …

Fixed Block Configuration Gdds With Block Size 6 And (3, R)-Regular Graphs , Melanie R. Laffin

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis.

In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ₁; λ₂). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s …

Enumeration Of Inequivalent Cycle Decompositions, William J. Laffin

Dissertations, Master's Theses and Master's Reports - Open

A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n.

Cyclic Automorphic Graph Decompositions , Michael Li Misson

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 introduces the tools and mechanics necessary for this report. Basic definitions and topics of graph theory which pertain to the report and discussion of automorphic decompositions will be covered in brief detail. An automorphic decomposition D of a graph H by a graph G is a G-decomposition of H such that the intersection of graph (D) @H. H is called the automorhpic host, and G is the automorphic divisor. We seek to find classes of graphs that are automorphic divisors, specifically ones generated cyclically.

Chapter 2 discusses the previous work done mainly by Beeler. …

Parallel Algorithm For Solving Integer Linear Programs, David O. Torrey Jr.

Dissertations, Master's Theses and Master's Reports - Open

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for …

Hamilton Decompositions Of 6-Regular Abelian Cayley Graphs, Erik E. Westlund

Dissertations, Master's Theses and Master's Reports - Open

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made:

Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian.

The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture:

Alspach Conjecture: Every 2k-regular, connected Cayley graph on a …

Edge Coloring Bibds And Constructing Moelrs , John S. Asplund

Dissertations, Master's Theses and Master's Reports - Open

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well.

In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic K_v into copies of K_k such that each copy of the K_k contains at most one edge from each K_v. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of …

Game-Theoretic View On Intermediated Exchange, Thomas Grassl

Dissertations, Master's Theses and Master's Reports - Open

Intermediaries permeate modern economic exchange. Most classical models on intermediated exchange are driven by information asymmetry and inventory management. These two factors are of reduced significance in modern economies. This makes it necessary to develop models that correspond more closely to modern financial marketplaces. The goal of this dissertation is to propose and examine such models in a game theoretical context.

The proposed models are driven by asymmetries in the goals of different market participants. Hedging pressure as one of the most critical aspects in the behavior of commercial entities plays a crucial role.

The first market model shows that …