Mathematics Commons^™

A Discrete Nonlinear Model Of Resonant Scattering, Katherine Hollister Smith

Honors Capstones

No abstract provided.

Representing Propositional Logic Connectives With Modular Polynomials, Shawn Davis

McNair Scholars Research Journal

This paper explores the relationship between n-valued propositional logic connectives and modular polynomials. Namely the representing of logic connectives using modular polynomials. The case for n = 2 is explored and a method is developed for finding the coefficients of the unique polynomial that represents any given binary logic connective. Examples are then given for using the modular polynomial representations of connectives to determine the validity of propositional arguments. A similar procedure is shown for when n = 3 and an evaluation of the axioms of Łukasiewicz’s 3-valued logic is given using modular polynomials. The general case is explored to …

Applying Metric Regularity To Compute Condition Measure Of Smoothing Algorithm For Matrix Games, Boris S. Mordukhovich, Javier Peña, Vera Roshchina

Mathematics Research Reports

Abstract. We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in (4] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

Detection Of Outliers In Time Series Data, Samson Sifael Kiware

Master's Theses (2009 -)

This thesis presents the detection of time series outliers. The data set used in this work is provided by the GasDay Project at Marquette University, which produces mathematical models to predict the consumption of natural gas for Local Distribution Companies (LDCs). Flow with no outliers is required to develop and train accurate models. GasDay is using statistical approaches motivated by normally distributed samples such as the 3 -sigma rule and the 5 -sigma rule to aid the experts in detecting outliers in residuals from the models. However, the Jarque-Bera statistical test shows that the residuals from the GasDay models are …

Maximal Class Numbers Of Cm Number Fields, Ryan C. Daileda, Raju Krishnamoorthy, Anton Malyshev

Mathematics Faculty Research

Fix a totally real number field F of degree at least 2. Under the assumptions of the generalized Riemann hypothesis and Artin's conjecture on the entirety of Artin L-functions, we derive an upper bound (in terms of the discriminant) on the class number of any CM number field with maximal real subfield F. This bound is a refinement of a bound established by Duke in 2001. Under the same hypotheses, we go on to prove that there exist infinitely many CM-extensions of F whose class numbers essentially meet this improved bound and whose Galois groups are as large …

2010 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2010 Spring Colloquium.

Analysis Of Boolean Functions With High Second Order Nonlinearity, Corneliu A. Bodea

Honors Theses

Highly nonlinear Boolean functions play a central role in the design and security analysis of high speed stream cyphers and block cyphers. We focus on analyzing the structure of Boolean functions that exhibit high second order nonlinearity. We commence with a theoretical overview of Boolean functions and Reed- Muller codes. We then introduce a new equivalence relation, 2-equivalence, for which we prove a number of important properties. Finally, we analyze the second order nonlinearity of concatenations of two Boolean functions.

On The Non-Existence Of A Projective (75, 4,12, 5) Set In Pg(3, 7), Aaron C.S. Chan, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.

Non Bayesian Conditioning And Deconditioning, Jean Dezert, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn’t satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination developed in DSmT (Dezert-Smarandache Theory) which abandons Bayes’ conditioning principle. Such Non-Bayesian conditioning allows to take into account judiciously the level of conflict between the prior belief available and the conditional evidence. We also introduce the deconditioning problem …

Importance Sampling For Dispersion-Managed Solitons, Elaine T. Spiller, Gino Biondini

Mathematics, Statistics and Computer Science Faculty Research and Publications

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that …

Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.

Volume 03, Cheryl Peck, Charles Hoever, Longwood Theater Department, Brittany Anderson, J. Ervin Sheldon, Richard Hayden, Yuri Calustro, Candice Fleming, Rebecca Franklin, Ashley Yocum, Danielle M. Jagoda, Cristina M. Valdivieso, Jameka Jones, Amy Ellis, Ashley Maser, Erikk Shupp, Jamie Yurasits, Joshua Davis, Alexander Leonhart, Kenny Wolfe, Sally Meadows, J. Haley, Amy Jackson, Morgan Howard, Adrienne Heinbaugh, Melissa Dorton, Ciarra Stalker

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Little Shop of Horrors by Longwood Theater Department

Who Has the Hottest Hotsauce in Farmville: A Quantitative Comparison of Sauces from Local Restaurants by Cheryl Peck and Charles Hoever

Precipitation Effects on the Growth of White Oaks and Virginia Pines on the Mt. Vernon Plantation by Brittany Anderson

Design and Synthesis of Novel Ion Binding Molecules for Self-Assembly and Sensing Applications by J. Ervin Sheldon

A Statistical Analysis of Algorithms for Playing SameGame by Richard Hayden

Intersecting Cylinders at Arbitrary Angles by Yuri Calustro

Putting a Foot in the Revolving Door: Strategies for Reducing …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Towards A Formal Theory Of Interoperability, Saikou Y. Diallo

Computational Modeling & Simulation Engineering Theses & Dissertations

This dissertation proposes a formal theory of interoperability that explains 1) what interoperability is as opposed to how it works, 2) how to tell whether two or more systems can interoperate and 3) how to identify whether systems are interoperating or merely exchanging bits and bytes. The research provides a formal model of data in M&S that captures all possible representations of a real or imagined thing and distinguishes between existential dependencies and transformational dependencies. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally …

Statistical Learning And Behrens-Fisher Distribution Methods For Heteroscedastic Data In Microarray Analysis, Nabin K. Manandhr-Shrestha

USF Tampa Graduate Theses and Dissertations

The aim of the present study is to identify the di®erentially expressed genes be- tween two di®erent conditions and apply it in predicting the class of new samples using the microarray data. Microarray data analysis poses many challenges to the statis- ticians because of its high dimensionality and small sample size, dubbed as "small n large p problem". Microarray data has been extensively studied by many statisticians and geneticists. Generally, it is said to follow a normal distribution with equal vari- ances in two conditions, but it is not true in general. Since the number of replications is very small, …

Randomized Kaczmarz Solver For Noisy Linear Systems, Deanna Needell

CMC Faculty Publications and Research

The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b. Theoretical convergence rates for this algorithm were largely unknown until recently when work was done on a randomized version of the algorithm. It was proved that for overdetermined systems, the randomized Kaczmarz method converges with expected exponential rate, independent of the number of equations in the system. Here we analyze the case where the system Ax=b is corrupted by noise, so we consider the system where Ax is approximately b + r where r is an arbitrary error vector. We prove that in this noisy version, …

Applications Of Descriptive Set Theory In Homotopy Theory, Samuel M. Corson

Theses and Dissertations

This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.

Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi

Systems Science Friday Noon Seminar Series

Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.

Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker …

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …

Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher

Theses and Dissertations

This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …