Mathematics Commons^™

Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces (Corrected), Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Two Riemann surfaces S₁ and S₂ with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S₁ -> S₂ which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials H^q(S₁) and H^q(S₂). In this note we study the differences between topological equivalence and H^q equivalence of prime cyclic actions, where S₁/G and S₂/G have genus zero.

Partial Differential Equations And Function Spaces, Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc

Mathematical Sciences: Faculty Publications

It is well known that PDEs and the theory of function spaces have played a central role in the mathematical analysis of problems arising from mathematical physics, biology, and other branches of modern applied sciences. This special issue addresses the current advances in these two broad areas; in particular it focuses on the connections and interactions between them. We are happy that this issue has received the attention of active researchers with interesting and valuable contributions in the field. Topics cover areas from existence and nonexistence theorems for degenerate differential operators to multilinear fractional singular integral operators on weighted function …

Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application, Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard E. Piltner

Mathematical Sciences: Faculty Publications

Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM_2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM_2.5 refers to particles with a mean aerodynamic …

A Three-Fold Approach To The Heat Equation: Data, Modeling, Numerics, Kimberly R. Spayd, James G. Puckett

Math Faculty Publications

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components.

Mutation Selection On The Metabolic Pathway And The Effects On Protein Co-Evolution And The Rate Limiting Steps On The Tree Of Life, Katherine S. Porter

Mathematics Summer Fellows

Metabolic pathways are made of a series of reactions by enzymes at different speeds. These pathways include the rate limiting step, which is the slowest step that determines the rate of the overall reaction. To date, one study has examined the pathway of glycolysis and found no evidence of evolutionary stability of its rate limiting step. In addition, phylogenetic evidence has shown evolution in the pathway over time including gene duplication and positive selection within the pathway. This evidence suggests that there is coevolutionary selection on glycolysis. The evidence from this previous study is simulation-based. The Michaelis-Menten kinetics that describe …

Ciliate Codon Translator Program Manual, Quentin D. Altemose

Mathematics Summer Fellows

Understanding the evolutionary history of organisms allows us to better comprehend selective pressures and their effects on larger populations. In our study, we focused on analyzing the DNA of ciliate groups, which are single celled protozoans characterized by the presence of cilia on their outer membrane. We utilized the DNA of the organisms to analyze the changes in population genotype over time. We tested existing evolutionary models (designed to represent natural genetic variation over time in populations) against our data to identify the model with the best fit and likelihood. From the DNA and the evolutionary model with the highest …

Theorems On Boundedness Of Solutions To Stochastic Delay Differential Equations, Youssef Raffoul, Dan Ren

Mathematics Faculty Publications

In this report, we provide general theorems about boundedness or bounded in probability of solutions to nonlinear delay stochastic differential systems. Our analysis is based on the successful construction of suitable Lyapunov functionals. We offer several examples as application of our theorems.

From Exam To Education: The Math Exam/Education Resources, Carmen Bruni, Christina Koch, Bernhard Konrad, Michael R. Lindstrom, Iain Moyles, Will Thompson

School of Mathematical & Statistical Sciences Faculty Publications

The Math Exam/Education Resources (MER) is an open online learning resource hosted at The University of British Columbia (UBC), aimed at providing mathematics education resources for students and instructors at UBC. In this paper, there will be a discussion of the motivation for creating this resource on the MediaWiki platform, key features of the implementation that support student learning (including the evolution of the MER wiki from an exam database to a more-general learning resource), data on student use and response, potential for future development, and a brief description of how the project was implemented. Preliminary correlation data between wiki …

Efficient Algorithms And Applications In Topological Data Analysis, Junyi Tu

USF Tampa Graduate Theses and Dissertations

Topological Data Analysis (TDA) is a new and fast growing research field developed over last two decades. TDA finds many applications in computer vision, computer graphics, scientific visualization, molecular biology, and material science, to name a few. In this dissertation, we make algorithmic and application contributions to three data structures in TDA: contour trees, Reeb graphs, and Mapper. From the algorithmic perspective, we design a parallel algorithm for contour tree construction and implement it in OpenCL. We also design and implement critical point pairing algorithms to compute persistence diagrams directly from contour trees, Reeb graphs, and Mapper. In terms of …

Example Of An Order 16 Non Symplectic Action On A K3 Surface, Jimmy J. Dillies

Mathematical Sciences: Faculty Publications

We exhibit an example of a K3 surface of Picard rank 14 with a non-symplectic automorphism of order 16 which fixes a rational curve and 10 isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki's classification.

Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache

Mathematics Faculty Publications

Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. …

Kolmogorov’S Axioms For Probabilities With Values In Hyperbolic Numbers, Daniel Alpay, M. E. Luna-Elizarrarás, Michael Shapiro

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov’s system of axioms. We show that this new measure verifies the usual properties of a probability; in particular, we treat the conditional hyperbolic probability and we prove the hyperbolic analogues of the multiplication theorem, of the law of total probability and of Bayes’ theorem. Our probability may take values which are zero–divisors and we discuss carefully this peculiarity.

Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, Mudassar Imran

Mathematics Faculty Publications

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.

Anomalous Fluctuations In The Orientation And Velocity Of Swarming Bacteria, Shawn D. Ryan, Gil Ariel, Avraham Be’Er

Mathematics and Statistics Faculty Publications

Simultaneous acquisition of phase-contrast light microscopy and fluorescently labeled bacteria, moving within a dense swarm, reveals the intricate interactions between cells and the collective flow around them. By comparing wild-type and immotile cells embedded in a dense wild-type swarm, the effect of the active thrust generated by the flagella can be singled out. It is shown that while the distribution of angles among cell velocity, cell orientation, and the local flow around it is Gaussian-like for immotile bacteria, wild-type cells exhibit anomalous non-Gaussian deviations and are able to move in trajectories perpendicular to the collective flow. Thus, cells can maneuver …

Eccentricity Sum In Trees, Heather Smith, Laszlo A. Szekely, Hua Wang

Mathematical Sciences: Faculty Publications

The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.

How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary …

On A Desert Island With Unit Sticks, Continued Fractions And Lagrange, Victor J. Ricchezza, H. L. Vacher

Numeracy

GLY 4866, Computational Geology, provides an opportunity, welcomed by our faculty, to teach quantitative literacy to geology majors at USF. The course continues to evolve although the second author has been teaching it for some 20 years. This paper describes our experiences with a new lab activity that we are developing on the core issue of measurement and units. The activity is inspired by a passage in the 2008 publication of lectures that Joseph Louis Lagrange delivered at the Ecole Normale in 1795. The activity envisions that young scientists are faced with the need to determine the dimensions of a …

Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett

Analysis

No abstract provided.

Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett

Analysis

No abstract provided.

The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder

Geometry

No abstract provided.

Impartial Avoidance And Achievement Games For Generating Symmetric And Alternating Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben

Mathematics Faculty Publications

Anderson and Harary introduced two impartial games on finite groups. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.

Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett

Abstract Algebra

No abstract provided.

Department History, University Of Mississippi. Department Of Mathematics

Faculty and Student Publications

The Department of Mathematics has been a part of the University of Mississippi since the university opened its doors in 1848. Its graduates have gone on to successful careers in a variety of industries, and several of its faculty have become University administrators, including Chancellor.

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

The Problems Of Contemporariness And Voice: Review Of Literacy & Mathematics: A Contemporary Approach To Quantitative Literacy By Jay P. Abramson And Matthew A. Isom (2005), Gizem Karaali

Pomona Faculty Publications and Research

The book under review covers the traditional content of a typical mathematical literacy text. After a brief overview of the book contents, the review then focuses on two specific challenges that QL textbooks have to meet: the timeliness of the contexts used and the subjective author voice that inevitably colors any contextualized discussion. Both issues noticeably arise in the text reviewed. Nonetheless instructors may find it a helpful resource.

Nullification Of Torus Knots And Links, Zachary S. Bettersworth

Masters Theses & Specialist Projects

Knot nullification is an unknotting operation performed on knots and links that can be used to model DNA recombination moves of circular DNA molecules in the laboratory. Thus nullification is a biologically relevant operation that should be studied.

Nullification moves can be naturally grouped into two classes: coherent nullification, which preserves the orientation of the knot, and incoherent nullification, which changes the orientation of the knot. We define the coherent (incoherent) nullification number of a knot or link as the minimal number of coherent (incoherent) nullification moves needed to unknot any knot or link. This thesis concentrates on the study …

Why 3-D Space? Why 10-D Space? A Possible Simple Geometric Explanation, Vladik Kreinovich

Departmental Technical Reports (CS)

In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact, without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is known that for some physical quantities, the 3-D space model with point-wise particles leads to meaningless infinities. To avoid these infinities, physicists have proposed that particles are more adequately described not as 0-D points, but rather as 1-D strings …

Decrypting The Link Between Elliptic Primes And Twin Primes, John M. Elizarraras, Devin N. Ferri, Javier M. Hernandez Jr., Anthony Luo, Isabel F. Swafford, Liljana Babinkostova (Mentor), Robin M. Betcher (Mentor), Spencer Nelson (Mentor), Marion Scheepers (Mentor)

Idaho Conference on Undergraduate Research

From Caesar’s cipher to Germany’s enigma machine to modern day cryptosytems, cryptography spans throughout history. Methods of encryption have evolved over hundreds of years and continue to evolve as computational efficiency increases. Over 2.5 quintillion bytes of data are generated per day through online networks such as banking, shopping, and social media. More than 90% of the total data in the world has been generated in the past two years, thereby requiring more sophisticated cybersecurity systems and an increasing demand for research in the field of cryptography. A curve of the form y² = x³ + Ax + …

Steady State Configurations Of Cells Connected By Cadherin Sites, Jared Adam Mcbride

Theses and Dissertations

Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides …

Complex-Valued Time-Series Correlation Increases Sensitivity In Fmri Analysis, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.

Materials and Methods

The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform …