Physical Sciences and Mathematics Commons^™

Statistical Partition Problem For Exponential Populations And Statistical Surveillance Of Cancers In Louisiana, Jin Gu

University of New Orleans Theses and Dissertations

In this dissertation, we consider the problem of partitioning a set of

k population with respect

to a control population. For this problem some multistage methodologies are proposed and their

properties are derived. Using the Monte Carlo simulation techniques, the small and moderate

sample size performance of the proposed procedure are studied.

We have also considered at statistical surveillance of various cancers in Louisiana.

Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik

Electronic Thesis and Dissertation Repository

Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.

Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.

Applications Of Nonlinear Optimization, Yao Xie

Arts & Sciences Electronic Theses and Dissertations

We apply an interior point algorithm to two nonlinear optimization problems and achieve improved results. We also devise an approximate convex functional alternative for use in one of the problems and estimate its accuracy.

The first problem is maximum variance unfolding in machine learning. The traditional method to solve this problem is to convert it to a semi-definite optimization problem by defining a kernel matrix. We obtain better unfolding and higher speeds with the interior point algorithm on the original non-convex problem for data with less than 10,000 points.

The second problem is a multi-objective dose optimization for intensity modulated …

Cohomology Of Absolute Galois Groups, Claudio Quadrelli

Electronic Thesis and Dissertation Repository

The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group.

We define a new class of pro-p groups, called Bloch-Kato …

K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.

Doctoral Theses

This thesis discusses the K-theory of quadratic modules by studying Roys elementary orthogonal group of the quadratic space Q1H(P) over a commutative ring A. We estab- lish a set of commutator relations among the elementary generators of Roys elementary orthogonal group and use this to prove Quillens local-global principle for this elementary group. We also obtain a result on extendability of quadratic modules. We establish nor- mality of the elementary orthogonal group under certain conditions and prove stability results for the Ki group of this orthogonal group. We also prove that Roys elementary orthogonal group and Petrovs odd hyperbolic unitary …

A Price-Volume Model For A Single-Period Stock Market, Yun Chen-Shue

HIM 1990-2015

The intention of this thesis is to provide a primitive mathematical model for a financial market in which tradings affect the asset prices. Currently, the idea of a price-volume relationship is typically used in the form of empirical models for specific cases. Among the theoretical models that have been used in stock markets, few included the volume parameter. The thesis provides a general theoretical model with the volume parameter for the intention of a broader use. The core of the model is the correlation between trading volume and stock price, indicating that volume should be a function of the stock …

Scattering Amplitudes In Flat Space And Anti-De Sitter Space, Savan Kharel

Doctoral Dissertations

We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto- Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on-shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied …

A Markov Model For Baseball With Applications, Daniel Joseph Ursin

Theses and Dissertations

In this work we confirm a Markov chain model of baseball for 2013 Major League Baseball batting data. We describe the transition matrices for individual player data and their use in generating single and nine-inning run distributions for a given lineup. The run distribution is used to calculate the expected number of runs produced by a lineup over nine innings. We discuss batting order optimization heuristics to avoid computation of distributions for the 9! = 362, 880 distinct lineups for 9 players. Finally, we describe an implementation of the algorithms and review their performance against actual game data.

Truckload Shipment Planning And Procurement, Neo Nguyen

Graduate Theses and Dissertations

This dissertation presents three issues encountered by a shipper in the context of truckload transportation. In all of the studies, we utilize optimization techniques to model and solve the problems. Each study is inspired from the real world and much of the data used in the experiments is real data or representative of real data.

The first topic is about the freight consolidation in truckload transportation. We integrate it with a purchase incentive program to increase truckload utilization and maximize profit. The second topic is about supporting decision making collaboration among departments of a manufacturer. It is a bi-objective optimization …

The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen

Theses and Dissertations

Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We …

Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor

Theses and Dissertations

Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …

A Covering System With Minimum Modulus 42, Tyler Owens

Theses and Dissertations

We construct a covering system whose minimum modulus is 42. This improves the previous record of 40 by P. Nielsen.

Analyzing State Attempts At Implementing The Common Core State Standards For High School Geometry: Case Studies Of Utah And New York, Edward Steltenpohl

Theses and Dissertations

This study analyzes two state attempts at aligning curricula to the Common Core State Standards (CCSS) in secondary school geometry. The education departments of Utah and New York have approved curricula aimed at aligning to the Common Core State Standards: the Mathematics Vision Project (MVP) and EngageNY (ENY) respectively. This study measures the extent to which those curricula align with the content demands of the relevant Common Core Standards. The results indicate that, while the two curricula vary in structure and assumptions about learners, each one aligns well with the Common Core State Standards in secondary school geometry. We conclude …

Contractible N-Manifolds And The Double N-Space Property, Pete Sparks

Theses and Dissertations

We are interested in contractible n-manifolds M which decompose or split as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space or A,B, and A intersect B are all homeomorphic to the n-dimensional unit ball. We introduce a 4-manifold M containing a spine which splits as A union B with A,B, and A intersect B all collapsible which in turn implies M splits as the union of two 4-balls whose intersection is also a 4-ball. From M we obtain a countably infinite collection of distinct 4-manifolds all of which split this way. …

A Survey Of Ekeland's Variational Principle And Related Theorems And Applications, Jessica Robinson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Ekeland's Variational Principle has been a key result used in various areas of analysis such as fixed point analysis, optimization, and optimal control theory. In this paper, the application of Ekeland's Variational Principle to Caristi's Fixed Point Theorem, Clarke's Fixed Point Theorem, and Takahashi's Minimization theorem is the focus. In addition, Ekeland produced a version of the classical Pontryagin Mini- mum Principle where his variational principle can be applied. A further look at this proof and discussion of his approach will be contrasted with the classical method of Pontryagin. With an understanding of how Ekeland's Variational Princple is used in …

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

Radio Number For Fourth Power Paths, Linda V. Alegria

Electronic Theses, Projects, and Dissertations

A path on n vertices, denoted by Pn, is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the order. A fourth power path, Pn4, is obtained from Pn by adding edges between any two vertices, u and v, whose distance in Pn, denoted by dPn(u,v), is less than or equal to four. The diameter of a graph G, denoted diam(G) is the greatest distance between any two distinct vertices of G. A radio labeling of a graph G is a function f that assigns to each …

The Structure And Properties Of Clique Graphs Of Regular Graphs, Jan Burmeister

Master's Theses

In the following thesis, the structure and properties of G and its clique graph cl_t (G) are analyzed for graphs G that are non-complete, regular with degree δ , and where every edge of G is contained in a t -clique. In a clique graph cl_t (G), all cliques of order t of the original graph G become the clique graph’s vertices, and the vertices of the clique graph are adjacent if and only if the corresponding cliques in the original graph have at least 1 vertex in common. This thesis mainly investigates if …

Two Dimensional Mathematical Model Of Fluid Flow In A Growing Solid Tumor, Adriana Gracia

Theses and Dissertations - UTB/UTPA

We investigate the problem of steady and unsteady fluid flow in a growing solid tumor. We develop a mathematical model for the two dimensional fluid flow in a spherical tumor where the spatial variations of the interstitial velocity, interstitial pressure and the drug concentration within the tumor are, in general, with respect to the radial distance and the latitudinal angle in the spherical coordinates. The expressions for radial and latitudinal variations of the interstitial velocity, interstitial pressure, and the two investigated drug concentrations were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal …

Hybrid Meshless Method For Numerical Solution Of Partial Differential Equations, Jeanette Marie Monroe

Dissertations

A meshless method for solving partial differential equations (PDEs) which combines the method of fundamental solutions (MFS) and the method of particular solutions (MPS) is formulated and tested. The hybrid method finds a numerical approximation by solving only one system of equations as opposed to the two-stage method of fundamental solutions and method of particular solutions. This new approach, denoted MFS-MPS, one-stage MFS-MPS, or hybrid method, can be applied to a wide variety of PDEs including PDEs with variable coefficients. The MFS-MPS can simplify Helmholtz-type differential operators to Laplacian-type differential operators providing flexibility and simplification to calculating particular solutions and …

A Study Of Graphical Permutations, Jessica Thune

UNLV Theses, Dissertations, Professional Papers, and Capstones

A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1

Exact Controllability Of The Lazer-Mckenna Suspension Bridge Equation, Lanxuan Yu

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is well known that suspension bridges may display certain oscillations under external aerodynamic forces. Since the collapse of the Tacoma Narrows suspension bridge in 1940, suspension bridge models have been studied by many researchers. Based upon the fundamental nonlinearity in suspension bridges that the stays connecting the supporting cables and the roadbed resist expansion, but do not resist compression, new models describing oscillations in suspension bridges have been developed by Lazer and McKenna [Lazer and McKenna (1990)]. Except for a paper by Leiva [Leiva (2005)], there have been very few work on controls of the Lazer-McKenna suspension bridge models …

Lnference On Differences In K Means For Data With Excess Zeros And Detection Limits, Haolai Jiang

Dissertations

Many data have excess zeros or unobservable values falling below detection limit. For example, data on hospitalization costs incurred by members of a health insurance plan will have zeros for the percentage who did not get sick. Benzene exposure measurements on petroleum re nery workers have some exposures fall below the limit of detection. Traditional methods of inference like one-way ANOVA are not appropriate to analyze such data since the point mass at zero violates typical distribution assumptions.

For testing for equality of means of k distributions, we will propose a likelihood ratio test that accounts for excess zeros or …

The Use Of Variable-Bagging And The Cross-Validation Selector In The Prediction Of Alzheimer’S Using The Adni Database., Michael Wayne Godbey

Electronic Theses and Dissertations

Dimensionality plays a huge part in the modeling process. If there are more elements in a data set than variables in each element then there are very few restrictions in selection of an algorithm. Bagging, bootstrap aggregating (Breiman, 1994), may also be used to improve a model’s prediction capability. On the other hand, if there more variables in each observation than the number of observations in the dataset, the number of usable algorithms is greatly reduced. The recently developed algorithm, support vector machines, was designed for such situations, in comparison to algorithms such as logistic regression which have instability issues …

Modular Monochromatic Colorings, Spectra And Frames In Graphs, Chira Lumduanhom

Dissertations

Abstract attached as separate document.

Empirical Studies On Interest Rate Derivatives, Xudong Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Interest rate models are the building blocks of financial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman filter, and studying various models empirically. We shall propose a front-fixing finite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common finite element method. Numerical test results show the superiority of our front-fixing finite element method in the aspects of computing the option …

Modeling And Analysis Of Pedestrian Flows, Romesh Khaddar

UNLV Theses, Dissertations, Professional Papers, and Capstones

According to the Traveler Opinion and Perception Survey of 2005, about 107.4 million Americans regularly use walking as a mode of transport during their commute, which amounts for 51% of the total American population. In 2009, 4092 pedestrian fatalities were reported nationwide, out of 59,000 pedestrian crashes. This amounts for 12% of the fatalities in the total traffic accidents recorded, and shows an over-representation of pedestrians incidents. Thus, it is imperative to understand the causes behind such statistics, and conduct a comprehensive research on pedestrian walking behavior and their interaction with surroundings.

A lot of researches on pedestrian flows have …

Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.

Doctoral Theses

Completely positive (CP-) maps are special kinds of positivity preserving maps on C ∗ -algebras. W.F. Stinespring [Sti55] obtained a structure theorem for CP-maps showing that they are closely connected with ∗-homomorphisms. W. Arveson and other operator algebraists quickly realized the importance of these maps. Presently the role of the theory of CP-maps in our understanding of C ∗ -algebras and von Neumann algebras is well recognised. It has been argued by physicists that CPmaps are physically more meaningful than just positive maps due to their stability under ampliations. From quantum probabilistic point of view CP-maps are quantum analogues of …

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu

Open Access Dissertations

Nowadays it is common to collect large volumes of data in many fields with an extensive amount of variables, but often a small or moderate number of samples. For example, in the analysis of genomic data, the number of genes can be very large, varying from tens of thousands to several millions, whereas the number of samples is several hundreds to thousands. Pharmacogenomics is an example of genomics data analysis that we are considering here. Pharmacogenomics research uses whole-genome genetic information to predict individuals' drug response. Because whole-genome data are high dimensional and their relationships to drug response are complicated, …