Digital Commons Network^™

Analyzing The Effects Of Adolescent Risky Behaviors On Suicidal Ideation, Marchelle Elizabeth Sanchez

Mathematics Theses

This study is an analysis of adolescent risk behaviors contributing to an increased rate of suicidal ideation for 12 to 18 year olds. The Youth Risk Behavior Surveillance System Survey (YRBSS) is an epidemiologic survey designed to monitor the prevalence of risky behaviors of adolescents in middle and high school1. The YRBSS is a complex sample survey with a three-stage cluster design. Multiple logistic regression is used to analyze the data, including methods of analysis to address issues in complex survey design. Results of this study indicate several different risk factors that influence the rate of suicidal ideation among adolescents, …

Estimate The True Pass Probability For Near-Real-Time Monitor Challenge Data Using Bayesian Analysis, Yuqing Xiao

Mathematics Theses

The U.S. Army¡¯s Chemical Demilitarization are designed to store, treat and destroy the nation¡¯s aging chemical weapons. It operates Near-Real-Time Monitors and Deport Area Monitoring Systems to detect chemical agent at concentrations before they become dangerous to workers, public health and the environment. CDC recommends that the sampling and analytical methods measure within 25% of the true concentration 95% of the time, and if this criterion is not met the alarm set point or reportable level should be adjusted. Two methods were provided by Army¡¯s Programmatic Laboratory and Monitoring Quality Assurance Plan to evaluate the monitoring systems based on CDC …

Spectrally Arbitrary Tree Sign Pattern Matrices, Krishna Kaphle

Mathematics Theses

A sign pattern (matrix) is a matrix whose entries are from the set {+,–, 0}. A sign pattern matrix A is a spectrally arbitrary pattern if for every monic real polynomial p(x) of degree n there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). All 3 × 3 SAP's, as well as tree sign patterns with star graphs that are SAP's, have already been characterized. We investigate tridiagonal sign patterns of order 4. All irreducible tridiagonal SAP's are identified. Necessary and sufficient conditions for an irreducible tridiagonal …

The Association Of Hypertension Diagnosis With Smoking Cessation: Application Of Multiple Logistic Regression Using Biostatistical And Epidemiological Methods, Latonia Clay

Mathematics Theses

The Association of Hypertension Diagnosis with Smoking Cessation: Application of Multiple Logistic Regression Using Biostatistical and Epidemiological Methods by LaTonia A. Clay Under the Direction of Yu-Sheng Hsu, PhD. ABSTRACT Hypertension and smoking are two major issues threatening the nation’s health. Previous studies examining their relationship have resulted in conflicting reports. The aim of this study is to determine if a relationship exists between smoking cessation and hypertension diagnosis. Data from the Third National Health and Nutrition Examination Survey (NHANES III) were used in this investigation. Physical examination measurements of blood pressure and self-reported diagnosis and smoking behavior were used …

Characterizations In Domination Theory, Andrew Robert Plummer

Mathematics Theses

Let G = (V,E) be a graph. A set R is a restrained dominating set (total restrained dominating set, resp.) if every vertex in V − R (V) is adjacent to a vertex in R and (every vertex in V −R) to a vertex in V −R. The restrained domination number of G (total restrained domination number of G), denoted by gamma_r(G) (gamma_tr(G)), is the smallest cardinality of a restrained dominating set (total restrained dominating set) of G. If T is a tree of order n, then gamma_r(T) is greater than or equal to (n+2)/3. We show that gamma_tr(T) is …

The Relationship Between The Minimal Rank Of A Tree And The Rank-Spreads Of The Vertices And Edges, John Henry Sinkovic

Theses and Dissertations

Let F be a field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G)be the minimum rank over all matrices in S(F,G). We give a field independent proof of a well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G is the difference between the …

Variational And Partial Differential Equation Models For Color Image Denoising And Their Numerical Approximations Using Finite Element Methods, Miun Yoon

Masters Theses

Image processing has been a traditional engineering field, which has a broad range of applications in science, engineering and industry. Not long ago, statistical and ad hoc methods had been main tools for studying and analyzing image processing problems. In the past decade, a new approach based on variational and partial differential equation (PDE) methods has emerged as a more powerful approach. Compared with old approaches, variational and PDE methods have remarkable advantages in both theory and computation. It allows to directly handle and process visually important geometric features such as gradients, tangents and curvatures, and to model visually meaningful …

Properties Of Some Matrix Classes In Linear Complementarity Theory., Arup Kumar Das Dr.

Doctoral Theses

The linear complementarity problem is a fundamental problem that arises in optimization, game theory, economics, and engineering. It can be stated as follows:Given a square matrix A of order n with real entries and an n dimensional vector q, find n dimensional vectors w and z satisfying w − Az = q, w ≥ 0, z ≥ 0 (1.1.1) w t z = 0. (1.1.2)This problem is denoted as LCP(q, A). The name comes from the condition (1.1.2), the complementarity condition which requires that at least one variable in the pair (wj , zj ) should be equal to 0 …

Changepoint Analysis Of Hiv Marker Responses, Joy Michelle Rogers

Mathematics Theses

We will propose a random changepoint model for the analysis of longitudinal CD4 and CD8 T-cell counts, as well as viral RNA loads, for HIV infected subjects following highly active antiretroviral treatment. The data was taken from two studies, one of the Aids Clinical Group Trial 398 and one performed by the Terry Beirn Community Programs for Clinical Research on AIDS. Models were created with the changepoint following both exponential and truncated normal distributions. The estimation of the changepoints was performed in a Bayesian analysis, with implementation in the WinBUGS software using Markov Chain Monte Carlo methods. For model selection, …

Some Problems In Additive Number Theory., Gyan Prakash Dr.

Doctoral Theses

No abstract provided.

Multiattribute Acceptance Sampling Plans., Anup Majumdar Dr.

Doctoral Theses

Irrespective of the type of product, evaluation of conformity to specified requirements of its quality characteristics is an integral part of quality assurance. Although they form a set of necessary verification activities almost at all stages of production, these activities, known as inspection do not add value to the product on their own and are to be kept at their minimum. The sampling inspection where a portion of a collection of product units is inspected on a set of characteristics with a view to making decision about acceptance or otherwise becomes relevant in this context.The number of elements of the …

Selected Problems Of Inference On Branching Processes And Poisson Shock Model, Satrajit Roychoudhury

Dissertations

This dissertation explores the development of statistical methodology for some problems of branching processes and poisson shock model.

Branching process methods have become extremely popular in recent days. This dissertation mainly explores two fundamental inference problems of Galton-Watson processes. The first problem is concerned with statistical inference regarding the nature of the process. Two methodologies have been developed to develop a statistical test for the null hypothesis that the process is supercritical versus an alternative hypothesis that the process is non-supercritical. Another problem we investigate involves the estimation of the 'age' of a Galton-Watson Process. Three different methods are discussed …

Essays On Individual And Collective Powers In A Voting Body., Sonali Roy Dr.

Doctoral Theses

MotivationThe issue of measurement of voting power is a very important topic of discussion in social science these days. The concept of voting power concerns any collective decision making body (or, equivalently, a collectivity) which makes ‘yes’ or ‘no’ decisions on any issue, by the process of voting. Examples of such bodies abound in today’s world. The United Nations Security Council, The Council of Ministers in the European Union, the Parliament of the republic of India, the board room of any corporate house etc., are all examples of such decision making bodies.The voting process of each of these bodies is …

A Complete Characterization Of Maximal Symmetric Difference-Free Families On {1,…N}., Travis Gerarde Buck

Electronic Theses and Dissertations

Prior work in the field of set theory has looked at the properties of union-free families. This thesis investigates families based on a different set operation, the symmetricc difference. It provides a complete characterization of maximal symmetric differencefree families of subsets of {1, . . . n}

Assessing The Effect Of Prior Distribution Assumption On The Variance Parameters In Evaluating Bioequivalence Trials, Dawud A. Ujamaa

Mathematics Theses

Bioequivalence determines if two drugs are alike. The three kinds of bioequivalence are Average, Population, and Individual Bioequivalence. These Bioequivalence criteria can be evaluated using aggregate and disaggregate methods. Considerable work assessing bioequivalence in a frequentist method exists, but the advantages of Bayesian methods for Bioequivalence have been recently explored. Variance parameters are essential to any of theses existing Bayesian Bioequivalence metrics. Usually, the prior distributions for model parameters use either informative priors or vague priors. The Bioequivalence inference may be sensitive to the prior distribution on the variances. Recently, there have been questions about the routine use of inverse …

Two Biological Applications Of Optimal Control To Hybrid Differential Equations And Elliptic Partial Differential Equations, Wandi Ding

Doctoral Dissertations

In this dissertation, we investigate optimal control of hybrid differential equations and elliptic partial differential equations with two biological applications. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the opti- mality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to studying two prob- lems: one is a type of hybrid system involving ordinary differential …

Nikolski's Approach To The Theorems Of Beurling And Nyman Regarding Zeros Of The Riemann Ζ-Function, Jared R. Bunn

Masters Theses

In this thesis we present the proof of a theorem by Nikolai Nikolski. This theorem leads to a more general theorem by Nikolski regarding zero free regions of the Riemann ζ-function. This theorem is an improvement on the theorems that Nyman and Beurling proved in the nineteen fifties. Nikolski’s approach uses, in addition to step function approximations introduced by Nyman, distance functions to give more flexibility, including possible numerical experiments. The introduction discusses the Riemann Hypothesis, which always surrounds any study of the Riemann ζ-function.

The background material discussed in this thesis gives all the necessary prerequi- sites …

Adaptive Discontinuous Galerkin Finite Element Methods For Second And Fourth Order Elliptic Partial Differential Equations, Michael A. Saum

Doctoral Dissertations

A unified mathematical and computational framework for implementation of an adaptive discontinuous Galerkin (DG) finite element method (FEM) is developed using the symmetric interior penalty formulation to obtain numerical approximations to solutions of second and fourth order elliptic partial differential equations. The DG-FEM formulation implemented allows for h-adaptivity and has the capability to work with linear, quadratic, cubic, and quartic polynomials on triangular elements in two dimensions. Two different formulations of DG are implemented based on how fluxes are represented on interior edges and comparisons are made. Explicit representations of two a posteriori error estimators, a residual based type and …

Coarse Structures And Higson Compactification, Christian Stuart Hoffland

Masters Theses

FOLLOWING John Roe in his Lectures on Coarse Geometry, we begin by describing the large-scale structure of metric spaces by means of coarse maps between them, those being maps which preserve distances at large scales. Using these techniques, we demonstrate that the real numbers and the integers have the same large scale structure--or are coarsely equivalent--but that the real line is coarsely equivalent to neither the Euclidean plane nor the set of positive real numbers. Following a generalization of these concepts for general topological spaces with the introduction of an abstract coarse structure on the space, we show, among …

The Effect Of Using A Video-Case Curriculum To Promote Preservice Teachers’ Development Of A Reflective Stance Towards Mathematics Teaching, Shari L. Stockero

Dissertations

This study investigates the effects of using a coherent video-case curriculum in a university methods course. In particular, three issues are addressed: (1) howthe use of a video-case curriculum affects the reflective stance of preservice teachers; (2) the extent to which a reflective stance developed while reflecting on other teachers' practice transfers to reflecting on one's own practice; and (3) how preservice teachers' reflective stance that is developed via sustained and focused reflection using a video-case curriculum compares to the reflective stance of peers who engaged in less sustained and focused reflection. Althoughvideo cases are increasingly being used in teacher …

Three Population Models Applied To Competition, Disease And Invasion, Erika Asano

Doctoral Dissertations

In this work, we present three diffrent types of population models. The first two models are examined in the context of optimal control problems. The third involves the construction of an invasion model using a significant amount of data.

The first model describes the interaction of three populations, motivated by a combat scenario. One of the three populations can switch the mode of alliance with the other two populations between cooperation and competition. The other two populations always compete with each other. In this system of parabolic partial differential equations, the control is the function which measures the strength of …

Cohomological Dimension With Respect To Nonabelian Groups, Atish Jyoti Mitra

Doctoral Dissertations

This dissertation addresses three aspects of cohomological dimension of metric spaces with respect to nonabelian groups.

In the first part we examine when the Eilenberg-Maclane space (n = 1) of the abelianization of a solvable group being an absolute extensor of a metric space implies the Eilenberg-Maclane space of the group itself is an absolute extensor. We also give an elementary approach to this problem in the case of nilpotent groups and 2-dimensional metric spaces.

The next part of the dissertation is devoted to generalizations of the Cencelj- Dranishnikov theorems relating extension properties of nilpotent CW complexes to its homology …

On Some Aspects Of The Differential Operator, Panakkal Jesu Mathew

Mathematics Theses

The Differential Operator D is a linear operator from C1[0,1] onto C[0,1]. Its domain C1[0,1] is thoroughly studied as a meager subspace of C[0,1]. This is analogous to the status of the set of all rational numbers Q in the set of the real numbers R. On the polynomial vector space Pn the Differential Operator D is a nilpotent operator. Using the invariant subspace and reducing subspace technique an appropriate basis for the underlying vector space can be found so that the nilpotent operator admits its Jordan Canonical form. The study of D on Pn is completely carried out. Finally, …

Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr.

Doctoral Theses

No abstract provided.

Markov Chain Monte Carlo Methods For Regression Splines With A Penalized Acceptance Ratio, David Keith Stamps

Dissertations

An increasingly popular method for fitting complex models, particularly with a hierchical structure involvese the use of Markov Chain Monte Carlo simulation. Within a Bayesian framework, two major strategies are Gibbs sampling and Metropolis-Hastings methods. Recent research in the area of MCMC methods has witnessed the emergence of modeling efforts which permit the movement of the chain across models of varying dimensions. When properly constructed, such Markov chains converge to the joint posterior distribution of the parameters to be estimated, making Bayesian averaging an attractive option after convergence has occurred. With this transdimensional methodology, the Bayesian averaging process takes place …

Image Segmentation By Energy And Related Functional Minimization Methods, Eric Hudson Mason

Dissertations

Effective and efficient methods for partitioning a digital image into image segments, called ¿image segmentation,¿ have a wide range of applications that include pattern recognition, classification, editing, rendering, and compressed data for image search. In general, image segments are described by their geometry and similarity measures that identify them. For example, the well-known optimization model proposed and studied in depth by David Mumford and Jayant Shah is based on an L₂ total energy functional that consists of three terms that govern the geometry of the image segments, the image fidelity (or closeness to the observed image), and the prior …

On The N-Body Problem, Zhifu Xie

Theses and Dissertations

In this thesis, central configurations, regularization of Simultaneous binary collision, linear stability of Kepler orbits, and index theory for symplectic path are studied. The history of their study is summarized in section 1. Section 2 deals with the following problem: given a collinear configuration of 4 bodies, under what conditions is it possible to choose positive masses which make it central. It is always possible to choose three positive masses such that the given three positions with the masses form a central configuration. However, for an arbitrary configuration of 4 bodies, it is not always possible to find positive masses …

Knots Not For Naught, Sharleen Adrienne Roberts

Theses and Dissertations

The goal of this paper is to find the Homfly polynomial for each knot in a specific family of knots. This family of knots is generated from placing the Whitehead link into a solid torus, slicing the torus at a spot where the Whitehead has no crossings and then twisting the torus 360 degrees in either direction an integral number of times. Let L(n) denote the knot obtained by twisting the torus 360 degrees, n times. Note that n is an integer. Let the twists be towards the center of the torus for positive n and away from the center …

Conjugacy Classes Of The Piecewise Linear Group, Matthew L. Housley

Theses and Dissertations

The piecewise linear group is the set of all piecewise linear orientation preserving homeomorphisms from the interval to itself under the operation of composition. We present here a complete set of invariants to classify the conjugacy classes of this group. Our approach to this problem relies on the factorization of elements into elements having only a single breakpoint.

Topics On The Spectral Theory Of Automorphic Forms, Dustin David Belt

Theses and Dissertations

We study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's Eigenvalue Conjecture to the study of the nonvanishing of the Eisenstein Series $E(z,s)$ for Hecke congruence subgroups $Gamma_0(N)$ at $s=frac {1+i}{2}$.