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Analyzing The Effects Of Adolescent Risky Behaviors On Suicidal Ideation, Marchelle Elizabeth Sanchez Dec 2006

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 Dec 2006

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 Dec 2006

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 Dec 2006

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 Dec 2006

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 …


Changepoint Analysis Of Hiv Marker Responses, Joy Michelle Rogers Nov 2006

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, …


Assessing The Effect Of Prior Distribution Assumption On The Variance Parameters In Evaluating Bioequivalence Trials, Dawud A. Ujamaa Aug 2006

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 …


On Some Aspects Of The Differential Operator, Panakkal Jesu Mathew Jul 2006

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, …


Some Significant Results In The Classification Analysis Of The Spectroscopic Evaluation Of Cervical Cancer, C Shen Jun 2006

Some Significant Results In The Classification Analysis Of The Spectroscopic Evaluation Of Cervical Cancer, C Shen

Mathematics Theses

Cervical Cancer is the second most common type of cancer in women worldwide (500,000 cases/year) and one of the leading causes of cancer-related mortality in women in developing countries (230,000 cases/year). The Spectrx LightTouch™ device uses light to detect chemical and structural changes in cervical tissue. Light responds differently when exposed to normal cells and cancerous cells. The purpose of this research is to find the best model that can be used to diagnose the early cervical cancerous conditions. To achieve this goal, we first tried to reduce the number of variables. We use statistical and non-statistical methods to search …


Algebraic Concepts In The Study Of Graphs And Simplicial Complexes, Christopher Michael Zagrodny Jun 2006

Algebraic Concepts In The Study Of Graphs And Simplicial Complexes, Christopher Michael Zagrodny

Mathematics Theses

This paper presents a survey of concepts in commutative algebra that have applications to topology and graph theory. The primary algebraic focus will be on Stanley-Reisner rings, classes of polynomial rings that can describe simplicial complexes. Stanley-Reisner rings are defined via square-free monomial ideals. The paper will present many aspects of the theory of these ideals and discuss how they relate to important constructions in commutative algebra, such as finite generation of ideals, graded rings and modules, localization and associated primes, primary decomposition of ideals and Hilbert series. In particular, the primary decomposition and Hilbert series for certain types of …


Rational Realizations Of The Minimum Rank Of A Sign Pattern Matrix, Selcuk Koyuncu Feb 2006

Rational Realizations Of The Minimum Rank Of A Sign Pattern Matrix, Selcuk Koyuncu

Mathematics Theses

A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The minimum rank of a sign pattern matrix A is the minimum of the rank of the real matrices whose entries have signs equal to the corresponding entries of A. It is conjectured that the minimum rank of every sign pattern matrix can be realized by a rational matrix. The equivalence of this conjecture to several seemingly unrelated statements are established. For some special cases, such as when A is entrywise nonzero, or the minimum rank of A is at most 2, or the minimum rank …


Semidefinite Programming And Stability Of Dynamical System, Kazumi Niki Stovall Jan 2006

Semidefinite Programming And Stability Of Dynamical System, Kazumi Niki Stovall

Mathematics Theses

In the first part of the thesis we present several interior point algorithms for solving certain positive definite programming problems. One of the algorithms is adapted for finding out whether there exists or not a positive definite matrix which is a real linear combination of some given symmetric matrices A1,A2, . . . ,Am. In the second part of the thesis we discuss stability of nonlinear dynamical systems. We search using algorithms described in the first part, for Lyapunov functions of a few forms. A suitable Lyapunov function implies the existence of a hyperellipsoidal attraction region for the dynamical system, …