Mathematics Commons^™

Multicollinearity In Regression Analyses Conducted In Epidemiologic Studies, Kristina Vatcheva, Minjae Lee, Joseph B. Mccormick, Mohammad H. Rahbar

School of Mathematical & Statistical Sciences Faculty Publications

The adverse impact of ignoring multicollinearity on findings and data interpretation in regression analysis is very well documented in the statistical literature. The failure to identify and report multicollinearity could result in misleading interpretations of the results. A review of epidemiological literature in PubMed from January 2004 to December 2013, illustrated the need for a greater attention to identifying and minimizing the effect of multicollinearity in analysis of data from epidemiologic studies. We used simulated datasets and real life data from the Cameron County Hispanic Cohort to demonstrate the adverse effects of multicollinearity in the regression analysis and encourage researchers …

Generalized Splines On Arbitrary Graphs, Simcha Gilbert, Julianna Tymoczko, Shira Viel

Mathematics Sciences: Faculty Publications

Let G be a graph whose edges are labeled by ideals of a commutative ring. We introduce a generalized spline, which is a vertex labeling of G by elements of the ring so that the difference between the labels of any two adjacent vertices lies in the corresponding edge ideal. Generalized splines arise naturally in combinatorics (algebraic splines of Billera and others) and in algebraic topology (certain equivariant cohomology rings, described by Goresky, Kottwitz, and MacPherson, among others). The central question of this paper asks when an arbitrary edge-labeled graph has nontrivial generalized splines. The answer is “always”, and we …

What Moser Could Have Asked: Counting Hamilton Cycles In Tournaments, Neil J. Calkin, Beth Novick, Hayato Ushijima-Mwesigwa

Publications

Moser asked for a construction of explicit tournaments on n vertices having at least Hamilton cycles. We show that he could have asked rather more.

Nested Monte Carlo Tree Search As Applied To Samurai Sudoku, Laura Finley

All Student Theses and Dissertations

As Sudoku has come into prominence as a favorite logic puzzle, mathematicians and computer scientists alike have analyzed the game for interesting properties. The large search space presents a challenge for both generating and solving Sudoku puzzles without relying on techniques that simply permute a valid puzzle. These permutations result in puzzles that are essentially the same since they follow the same solution path. Many Sudoku generating or solving programs rely on brute-force methods to avoid this pitfall, but this is inefficient since there is no heuristic to navigate the huge search space. A nested Monte Carlo tree search has …

On Emmy Noether And Her Algebraic Works, Deborah Radford

All Student Theses and Dissertations

In the early 1900s a rising star in the mathematics world was emerging. I will discuss her life as a female mathematician and the struggles she faced being a rebel in her time. I will also take an in depth look at some of her contributions to the mathematics and science community . Her work in algebra and more specifically, ring theory, are said to be foundations for much of the work done since then. Her developments in abstract algebra helped to unify topology, geometry, logic and linear algebra. Also, Noether's theorem is a widely used theorem in physics along …

The Impact Of Students’ Attitudes After Implementing A Leadership Collaborative Grouping Method In A Collegiate Technical Mathematics Class, Robert J. Belin

All Student Theses and Dissertations

This research paper explored students’ attitudes towards mathematics before and after the implementation of an experimental instructional method. The measurement tool that was used is the Mathematics Attitude Inventory for Students (ATMI). The experimental methodology implemented in the collegiate class is a leadership based cooperative learning model. Students were surveyed twice. The first installment of the ATMI was conducted prior to a mathematics unit that spanned three classes. The second installment of the ATMI survey was conducted after the unit was completed. Student surveys were assessed and determined if the experimental model had any impact of students’ attitudes towards mathematics. …

History Of Mathematics From The Islamic World, Asamah Abdallah

All Student Theses and Dissertations

Learning the history of mathematics is crucial to fully understanding the world of mathematics today. This paper will explore the history of mathematics from the Islamic world. It will focus on the contributions of well-recognized mathematicians including, Al-Khwarizmi, Al-Khayyam, Uqlidisi, Kushyar ibn Labban, and Abu Kamil. It will also concentrate on the contributions that the Islamic world had on algebra, beginning with Al-Khwarizmi and his contribution to the developmental of algebraic equations, and Khayyam and his contribution to the geometrization of algebra. This paper will also discuss the ways in which the Muslims applied the mathematics they learned into their …

Beta Linear Failure Rate Geometric Distribution With Applications, Broderick O. Oluyede, Ibrahim Elbatal, Shujiao Huang

Mathematical Sciences: Faculty Publications

This paper introduces the beta linear failure rate geometric (BLFRG) distribution, which contains a number of distributions including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh and exponential distributions as special cases. The model further generalizes the linear failure rate distribution. A comprehensive investigation of the model properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are presented. Estimates of model parameters are given. Real data examples are presented to illustrate the usefulness and applicability of the distribution.

Finite Semifields And Their Applications, Shamsa Ali Rashed Al Saedi

Theses

This thesis is concerned with finite semi fields. The objective of this thesis is to give a full description of Knuth orbits of known commutative semi fields. We also describe planar functions corresponding to commutative semi fields. Results are presented by tables. Nuclei of semi fields are studied. Finally we consider applications of semi fields, planar functions and spreads to construction of mutually unbiased bases.

Some Algebraic Aspect And Applications Of A Family Of Functions Over Finite Fields, Shaima Ahmed Thabet

Theses

We study two families of functions over finite fields; the Multivalued Threshold

Functions and the Multivariate Polynomials. Recent advances made in our Conception and our understanding of Boolean Threshold Functions and Multivariate Threshold Functions have considerably increased the importance of the role that they Play in our days in areas like cryptography, circuit complexity, learning theory, social choice, quantum complexity, and in many other areas. Theoretical aspects of Bovid and Gauche who gave an algebraic first studied threshold functions Approach of Boolean Threshold Functions using group ring theory. We will present some algebraic properties of Boolean threshold functions. For the …

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Mustafa Ozen

Mathematical Sciences: Faculty Publications

We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP) which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size …

Research And Evaluation Of The Effectiveness Of E-Learning In The Case Of Linear Programming, Ljiljana Miletić, Goran Lesaja

Mathematical Sciences: Faculty Publications

The paper evaluates the effectiveness of the e-learning approach to linearprogramming. The goal was to investigate how proper use of information andcommunication technologies (ICT) and interactive learning helps to improve high schoolstudents’ understanding, learning and retention of advanced non-curriculum material.The hypothesis was that ICT and e-learning is helpful in teaching linear programmingmethods. In the first phase of the research, a module of lessons for linear programming(LP) was created using the software package Loomen Moodle and other interactivesoftware packages such as Geogebra. In the second phase, the LP module was taught asa short course to two groups of high school students. …

Conjugacy Geodesics In Coxeter Groups, Aaron Calderon

UCARE: Research Products

Take a square and flip it over the vertical axis, rotate it 90 degrees counterclockwise and then flip it again over the vertical axis. This sequence is the same as a 90 degree clockwise rotation but takes more steps to demonstrate the same symmetry. In general, the question of when a sequence of symmetries has minimal length is hard to answer and is dependent on the chosen generating set (in our toy example, rotation by 90 degrees and reflection). By realizing sequences of symmetries as paths in a group's Cayley graph, the problem becomes one about the set of shortest …

The History And Applications Of Fibonacci Numbers, Cashous W. Bortner, Allan C. Peterson

UCARE: Research Products

The Fibonacci sequence is arguably the most observed sequence not only in mathematics, but also in nature. As we begin to learn more and more about the Fibonacci sequence and the numbers that make the sequence, many new and interesting applications of the have risen from different areas of algebra to market trading strategies. This poster analyzes not only the history of Leonardo Bonacci, but also the elegant sequence that is now his namesake and its appearance in nature as well as some of its current mathematical and non-mathematical applications.

Trigonometry: An Overview Of Important Topics, Lauren Johnson

All Capstone Projects

The purpose of this project was to help students achieve a better understanding of Trigonometry, in order to better prepare them for future Calculus courses. The project is a tutorial that walks the student through important Trigonometry topics. The topics range from, but are not limited to, finding the measure of an angle to analyzing the graphs of Trigonometric Functions. Each topic allows an opportunity for the student to assess their understanding by working through practice problems and checking their solutions.

At any university, incoming students will have a wide variety of mathematical backgrounds. These students differ in age, in …

Integrable Abel Equations And Vein's Abel Equation, S.C. Mancas, Haret C. Rosu

Publications

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.

The Foundations Of Mathematics History, Concepts, And Applications In Higher Level Mathematics, Clifton Henry

Undergraduate Research Conference

When people hear the word mathematics, some think numbers and others think solving for x and y. In all truth, the field of mathematics is more than numbers and equations. Mathematics was founded based off the principle of counting in 50,000 B.C.E. Mathematical contributions and ideas increased from the Babylonian Empire in 2000 BC to the 18th century, where mathematicians and philosophers developed ideas in algebra, geometry and calculus.

Asymptotic Stability Of Non-Unique Solutions Of Initial Value Problems, Muhammad Islam

Mathematics Colloquium Series

We consider an initial value problem (I. V. P.) of a first order nonlinear ordinary differential equations. We assume that the I. V. P. can have more than one solution. We study a new type of stability property of these solutions. This stability is not the standard Liapunov stability, commonly studied in the field of differential equations.

Combinatorial Descriptions Of The Crystal Structure On Certain Pbw Bases (Extended Abstract), Ben Salisbury, Adam Schultze, Peter Tingley

Mathematics and Statistics: Faculty Publications and Other Works

Lusztig's theory of PBW bases gives a way to realize the infinity crystal for any simple complex Lie algebra where the underlying set consists of Kostant partitions. In fact, there are many different such realizations, one for each reduced expression for the longest element of the Weyl group. There is an algorithm to calculate the actions of the crystal operators, but it can be quite complicated. For ADE types, we give conditions on the reduced expression which ensure that the corresponding crystal operators are given by simple combinatorial bracketing rules. We then give at least one reduced expression satisfying our …

The Geometry Of Spacetime And Its Singular Nature, Filip Dul

Honors Scholar Theses

One hundred years ago, Albert Einstein revolutionized our understanding of gravity, and thus the large-scale structure of spacetime, by implementing differential geometry as the pri- mary medium of its description, thereby condensing the relationship between mass, energy and curvature of spacetime manifolds with the Einstein field equations (EFE), the primary compo- nent of his theory of General Relativity. In this paper, we use the language of Semi-Riemannian Geometry to examine the Schwarzschild and the Friedmann-Lemaˆıtre-Robertson-Walker met- rics, which represent some of the most well-known solutions to the EFE. Our investigation of these metrics will lead us to the problem of …

The Power Of Two: Two Tips For Mathematicians, Gizem Karaali

Pomona Faculty Publications and Research

This post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.

Cognitive And Behavioral Deficits Arising From Neurodegeneration And Traumatic Brain Injury: A Model For The Underlying Role Of Focal Axonal Swellings In Neuronal Networks With Plasticity, Samuel Rudy, Pedro D. Maia, J. Nathan Kutz

Mathematics Faculty Publications - Archive

Neurodegenerative diseases and traumatic brain injury, whose hallmark features are the presence of focal axonal swellings (FAS), are leading causes of cognitive dysfunction. By leveraging biophysical observations of FAS statistics, we develop a theoretical model of functional neural network activity driven by adaptive changes from plasticity. Based upon the FORCE model of Sussillo and Abbott [1], our innovations highlight the role of plasticity in overcoming injuries and degeneration of neurons in a network architecture. We provide a quantitative measure, on a network level, of cognitive deficits arising from injury. We demonstrate that plasticity is capable of overcoming mild injuries while …

Inference On Time-To-Event Distribution From Retrospective Data With Imperfect Recall., Sedigheh Salehabadi Dr.

Doctoral Theses

Time-to-event data arises from measurements of time till the occurrence of an event of interest. Such data are common in the fields of biology, epidemiology, pub- lic health, medical research, economics and industry. The event of interest can be the death of a human being (Klein and Moeschberger, 2003), failure of a machine (Zhiguo et al., 2007), onset of menarche in adolescent and young adult females (Bergsten-Brucefors, 1976; Chumlea et al., 2003; Mirzaei, Sengupta and Das, 2015), onset (or relapse) of a disease (Klein and Moeschberger, 2003), dental develop- ment (Demirjian, Goldstien and Tanner, 1973; Eveleth and Tanner, 1990), breast …

Introduction To The Early Development Of Mathematics (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: An Introduction to the Early Development of Mathematics by Michael K. J. Goodman. Wiley, 2016. 233 pp. ISBN: 9781119104971.

Sources And Characteristics Of Medium-Scale Traveling Ionospheric Disturbances Observed By High-Frequency Radars In The North American Sector, N. A. Frissell, J. B. H. Baker, J. M. Ruohoniemi, R. A. Greenwald, A. J. Gerrard, E. S. Miller, M. L. West

Department of Mathematics Faculty Scholarship and Creative Works

Medium-scale traveling ionospheric disturbances (MSTIDs) are wave-like ionospheric perturbations routinely observed by high-frequency radars. We focus on a class of MSTIDs observed during the winter daytime at high latitudes and midlatitudes. The source of these MSTIDs remains uncertain, with the two primary candidates being space weather and lower atmospheric processes. We surveyed observations from four high-latitude and six midlatitude Super Dual Auroral Radar Network radars in the North American sector from November to May 2012 to 2015. The MSTIDs observed have horizontal wavelengths between ∼150 and 650 km and horizontal velocities between ∼75 and 325 m s−1. In local fall …

Gut Microbial Metabolite Tmao Enhances Platelet Hyperreactivity And Thrombosis Risk, Weifei Zhu, Jill C. Gregory, Elin Org, Jennifer A. Buffa, Nilaksh Gupta, Zeneng Wang, Lin Li, Xiaoming Fu, Yuping Wu, Margarete Mehrabian, R. Balfour Sartor, Thomas M. Mcintyre, Roy L. Silverstein, W.H. Wilson Tang, Joseph A. Didonato, J. Mark Brown, Aldons J. Lusis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Normal platelet function is critical to blood hemostasis and maintenance of a closed circulatory system. Heightened platelet reactivity, however, is associated with cardiometabolic diseases and enhanced potential for thrombotic events. We now show gut microbes, through generation of trimethylamine N-oxide (TMAO), directly contribute to platelet hyperreactivity and enhanced thrombosis potential. Plasma TMAO levels in subjects (n > 4,000) independently predicted incident (3 years) thrombosis (heart attack, stroke) risk. Direct exposure of platelets to TMAO enhanced sub-maximal stimulus-dependent platelet activation from multiple agonists through augmented Ca2+ release from intracellular stores. Animal model studies employing dietary choline or TMAO, germ-free mice, and microbial …

Generalized Phase Retrieval: Isometries In Vector Spaces, Josiah Park

USF Tampa Graduate Theses and Dissertations

In this thesis we generalize the problem of phase retrieval of vector to that of multi-vector. The identification of the multi-vector is done up to some special classes of isometries in the space. We give some upper and lower estimates on the minimal number of multi-linear operators needed for the retrieval. The results are preliminary and far from sharp.

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Resonant Solutions To (3+1)-Dimensional Bilinear Differential Equations, Yue Sun

USF Tampa Graduate Theses and Dissertations

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by D_p-operators with p = 5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p = 5.

Geometric Optimization, Analysis, And Design, Denise Halverson

Journal of Undergraduate Research

1. Evaluation of how well the academic objectives of the proposal were met

The goals for the mentoring environment were reached:

• Academic Development – Each student had the opportunity to work on a cutting edge research problem, as indicated below. Papers are in various stages of completion, a few submitted or accepted for publication, but all have drafted papers.
• Community Development – Several students were able to attend the MAA Math Fest in both 2014 and 2015. Most students gave presentations at the CPMS Student Research Conference. My students have been able to interact with engineering student working on similar …