Physical Sciences and Mathematics Commons^™

Some Contributions In Statistical Discrimination Of Different Pathogens Using Observations Through Ftir, Dongmei Wang

Mathematics Theses

Fourier Transform Infrared (FTIR) has been use to discriminate different pathogens by signals from cells infected with these versus normal cells as references. To do the statistical analysis, Partial Least Square Regression (PLSR) was utilized to distinguish any two kinds of virus‐infected cells and normal cells. Validation using Bootstrap method and Cross‐validations were employed to calculate the shrinkages of Area Under the ROC Curve (AUC) and specificities corresponding to 80%, 90%, and 95% sensitivities. The result shows that our procedure can significantly discriminate these pathogens when we compare infected cells with the normal cells. On the height of this success, …

Theoretical And Numerical Study Of Tikhonov's Regularization And Morozov's Discrepancy Principle, Marygeorge L. Whitney

Mathematics Theses

A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori information (normally available), in order to solve …

Analyzing Gene Expression Data In Terms Of Gene Sets: Gene Set Enrichment Analysis, Wei Li

Mathematics Theses

The DNA microarray biotechnology simultaneously monitors the expression of thousands of genes and aims to identify genes that are differently expressed under different conditions. From the statistical point of view, it can be restated as identify genes strongly associated with the response or covariant of interest. The Gene Set Enrichment Analysis (GSEA) method is one method which focuses the analysis at the functional related gene sets level instead of single genes. It helps biologists to interpret the DNA microarray data by their previous biological knowledge of the genes in a gene set. GSEA has been shown to efficiently identify gene …

Analysis Of The Total Food Folate Intake Data From The National Health And Nutrition Exa-Amination Survey (Nhanes) Using Generalized Linear Model, Kyung Ah Lee

Mathematics Theses

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

Comparative Studies Between Robotic Laparoscopic Myomectomy And Abdominal Myomectomy With Factors Affecting Short-Term Surgical Outcomes, Amy N. Fomo

Mathematics Theses

The purpose of this study is to compare short-term surgical outcomes of robotic and abdominal myomectomy and to analyze the factors affecting the total operative time, estimated blood loss and length of hospital stay from a retrospective study of a consecutive case series of 122 pa-tients with symptomatic leiomyomata. Wilcoxon, t tests, multiple linear and logistic regressions analyses were performed. Patients in abdominal group had larger number of leiomyomata, larger tumor size and BMI. The operative time was longer in robotic group and was affected by the size and number of tumors, parity and interaction between parity and BMI. Estimated …

Comparing Cognitive Decision Models Of Iowa Gambling Task In Indivituals Following Temporal Lobectomy, Jenny Vennukkah Jeyarajah

Mathematics Theses

This study examined the theoretical basis for decision making behavior of patients with right or left temporal lobectomy and a control group when they participated in the Iowa Gambling Task. Two cognitive decision models, Expectancy Valence Model and Strategy Switching Heuristic Choice Model, were compared for best fit. The best fitting model was then chosen to provide the basis for parameter estimation (sources of decision making, i.e. cognitive, motivational, and response processes) and interpretation. Both models outperformed the baseline model. However comparison of G2 means between the two cognitive decision models showed the expectancy valence model having a higher mean …

An Application Of Armitage Trend Test To Genome-Wide Association Studies, Nigel A. Scott

Mathematics Theses

Genome-wide Association (GWA) studies have become a widely used method for analyzing genetic data. It is useful in detecting associations that may exist between particular alleles and diseases of interest. This thesis investigates the dataset provided from problem 1 of the Genetic Analysis Workshop 16 (GAW 16). The dataset consists of GWA data from the North American Rheumatoid Arthritis Consortium (NARAC). The thesis attempts to determine a set of single nucleotide polymorphisms (SNP) that are associated significantly with rheumatoid arthritis. Moreover, this thesis also attempts to address the question of whether the one-sided alternative hypothesis that the minor allele is …

Multistability In Bursting Patterns In A Model Of A Multifunctional Central Pattern Generator., Matthew Bryan Brooks

Mathematics Theses

A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along …

Two Problems On Bipartite Graphs, Albert Bush

Mathematics Theses

Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3.

The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that …

Advanced Statistical Methodologies In Determining The Observation Time To Discriminate Viruses Using Ftir, Shan Luo

Mathematics Theses

Fourier transform infrared (FTIR) spectroscopy, one method of electromagnetic radiation for detecting specific cellular molecular structure, can be used to discriminate different types of cells. The objective is to find the minimum time (choice among 2 hour, 4 hour and 6 hour) to record FTIR readings such that different viruses can be discriminated. A new method is adopted for the datasets. Briefly, inner differences are created as the control group, and Wilcoxon Signed Rank Test is used as the first selecting variable procedure in order to prepare the next stage of discrimination. In the second stage we propose either partial …

Applications Of Linear Algebra To Information Retrieval, Jhansi Lakshmi Vasireddy

Mathematics Theses

Some of the theory of nonnegative matrices is first presented. The Perron-Frobenius theorem is highlighted. Some of the important linear algebraic methods of information retrieval are surveyed. Latent Semantic Indexing (LSI), which uses the singular value de-composition is discussed. The Hyper-Text Induced Topic Search (HITS) algorithm is next considered; here the power method for finding dominant eigenvectors is employed. Through the use of a theorem by Sinkohrn and Knopp, a modified HITS method is developed. Lastly, the PageRank algorithm is discussed. Numerical examples and MATLAB programs are also provided.

Primary Decomposition And Secondary Representation Of Modules Over A Commutative Ring, Muslim Baig

Mathematics Theses

This paper presents the theory of Secondary Representation of modules over a commutative ring and their Attached Primes; introduced in 1973 by I. MacDonald as a dual to the important theory of associated primes and primary decomposition in commutative algebra. The paper explores many of the basic aspects of the theory of primary decomposition and associated primes of modules in the hopes to delineate and motivate the construction of a secondary representation, when possible. The thesis discusses the results of the uniqueness of representable modules and their attached primes, and, in particular, the existence of a secondary representation for Artinian …

Primary Decomposition In Non Finitely Generated Modules, Somaya Muiny

Mathematics Theses

In this paper, we study primary decomposition of any proper submodule N of a module M over a noetherian ring R. We start by briefly discussing basic facts about the very well known case where M is a finitely generated module over a Noetherian ring R, then we proceed to discuss the general case where M is any module over a Noetherian ring R. We put a lot of focus on the associated primes that occur with the primary decomposition, essentially studying their uniqueness and their relation to the associated primes of M/N.

The Impact Of Midbrain Cauterize Size On Auditory And Visual Responses' Distribution, Yan Zhang

Mathematics Theses

This thesis presents several statistical analysis on a cooperative project with Dr. Pallas and Yuting Mao from Biology Department of Georgia State University. This research concludes the impact of cauterize size of animals’ midbrain on auditory and visual response in brains. Besides some already commonly used statistical analysis method, such as MANOVA and Frequency Test, a unique combination of Permutation Test, Kolmogorov-Smirnov Test and Wilcoxon Rank Sum Test is applied to our non-parametric data. Some simulation results show the Permutation Test we used has very good powers, and fits the need for this study. The result confirms part of the …