Mathematics Commons^™

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0

Review Paper: The Shape Of Phylogenetic Treespace, Katherine St. John

Publications and Research

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths.

On The Number Of Colors In Quandle Knot Colorings, Jeremy William Kerr

USF Tampa Graduate Theses and Dissertations

A major question in Knot Theory concerns the process of trying to determine when two knots are different. A knot invariant is a quantity (number, polynomial, group, etc.) that does not change by continuous deformation of the knot. One of the simplest invariant of knots is colorability. In this thesis, we study Fox colorings of knots and knots that are colored by linear Alexander quandles. In recent years, there has been an interest in reducing Fox colorings to a minimum number of colors. We prove that any Fox coloring of a 13-colorable knot has a diagram that uses exactly five …

Sticky Seeding In Discrete-Time Reversible-Threshold Networks, Gwen Spencer

Mathematics Sciences: Faculty Publications

When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of Sticky Interventions: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is Ω(ln(OP T ))-hard to approximate and that maximizing conversion subject to a budget is …

Hawking Radiation Screening And Penrose Process Shielding In The Kerr Black Hole, Eamon Mccaughey

Articles

The radial motion of massive particles in the equatorial plane of aKerr black hole is considered. Screening of the Hawking radiation and shielding of the Penrose process are examined (both inside and outside the ergosphere) and their effect on the evaporation of the black hole is studied. In particular, the locus and width of a classically forbidden region and their dependence on the particle’s angular momentum and energy is analysed. Tunneling of particles between the boundaries of this region is considered and the transmission coefficient determined.

Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu

Mathematical Sciences: Faculty Publications

In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desired numerical results with two different continuous higher order dynamical systems that exhibit chaotic behavior, the Lorenz equations and the Rössler attractor.

Periodicity In Quantum Calculus, Jeffrey T. Neugebauer

Mathematics Colloquium Series

After a brief introduction to time scales, we will explore periodic functions on time scales. We will discuss how periodicity is defined on time scales that are not periodic. In particular, we will look at periodicity in the quantum case. Two definitions of periodicity have recently been introduced. One definition is based on the equality of areas lying below the graph of the function at each period; the other regards a periodic function to be one that repeats its values after a certain number of steps. We will show a relation between these two definitions and then use this relation …

Oscillation Of Solution To Second-Order Half-Linear Delay Dynamic Equations On Time Scales, Hongwu Wu, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results.

On The Dynamics Of Boolean Gene Regulatory Networks With Stochasticity, Yuezhe Li

Theses and Dissertations

Genes are responsible for producing proteins that are essential to the construction of complex biological systems. The mechanisms by which this production is regulated have long been the center of wide spread research efforts. Deterministic Boolean gene regulatory models have been a particularly effective avenue of research in this field. However these models fall short of accounting for variations in the gene functionality due to the uncertain internal or external environmental conditions. One of the recent attempts to overcome this weakness is by (Murrugarra, 2012), in which a probabilistic component is introduced as the fixed activation/degradation propensities at the cellular …

Review: On Complex Symmetric Toeplitz Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Optimal Binomial, Poisson, And Normal Left-Tail Domination For Sums Of Nonnegative Random Variables, Iosif Pinelis

Department of Mathematical Sciences Publications

Exact upper bounds on the generalized moments E ƒ (S_n) of sums S_n of independent nonnegative random variables X_i for certain classes Ƒ of nonincreasing functions ƒ are given in terms of (the sums of) the first two moments of the X_i’s. These bounds are of the form Eƒ(η), where the random variable η is either binomial or Poisson depending on whether n is fixed or not. The classes Ƒ contain, and are much wider than, the class of all decreasing exponential functions. As corollaries of these results, optimal in a certain sense …

Expression Profiles Of Mirna Subsets Distinguish Human Colorectal Carcinoma And Normal Colonic Mucosa, Daniel F. Pellatt, John R. Stevens, Roger K. Wolff, Lila E. Mullany, Jennifer S. Herrick, Wade Samowitz, Martha L. Slattery

Mathematics and Statistics Faculty Publications

OBJECTIVES: MicroRNAs (miRNAs) are small, non-protein-coding RNA molecules that are commonly dysregulated in colorectal tumors. The objective of this study was to identify smaller subsets of highly predictive miRNAs.

METHODS: Data come from population-based studies of colorectal cancer conducted in Utah and the Kaiser Permanente Medical Care Program. Tissue samples were available for 1,953 individuals, of which 1,894 had carcinoma tissue and 1,599 had normal mucosa available for statistical analysis. Agilent Human miRNA Microarray V.19.0 was used to generate miRNA expression profiles; validation of expression levels was carried out using quantitative PCR. We used random forest analysis and verified findings …

Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees

National Youth Advocacy & Resilience Conference

This presentation targets a study in which four high school students with disabilities were taught to solve algebraic equations using iPads and video-based instruction. All students showed immediate increases in accurate responding following the introduction of the video-based intervention. This presentation provides practitioners with a flexible technology-based intervention for students with disabilities in need of grade-level academic instruction. The intervention could be used across a variety of subjects and academic tasks.

Cirrhosis And Advanced Fibrosis In Hispanics In Texas: The Dominant Contribution Of Central Obesity, Jingjing Jiao, Gordon P. Watt, Minjae Lee, Mohammad H. Rahbar, Kristina Vatcheva, Jen-Jung Pan, Joseph B. Mccormick, Susan P. Fisher-Hoch, Michael Fallon, Laura Beretta

School of Mathematical & Statistical Sciences Faculty Publications

Liver cirrhosis is a leading cause of death in Hispanics and Hispanics who live in South Texas have the highest incidence of liver cancer in the United States. We aimed at determining the prevalence and associated risk factors of cirrhosis in this population. Clinical and demographic variables were extracted for 2466 participants in the community-based Cameron County Hispanic Cohort in South Texas. Aspartate transaminase to Platelet Ratio Index (APRI) was used to predict cirrhosis in Cameron County Hispanic Cohort. The prevalence of cirrhosis using APRI≥2 was 0.94%, which is nearly 4-fold higher than the national prevalence. Using APRI≥1, the overall …

Leonard Systems And Their Friends, Jonathan Spiewak

USF Tampa Graduate Theses and Dissertations

Let $V$ be a finite-dimensional vector space over a field $\mathbb{K}$, and let

\text{End}$(V)$ be the set of all $\mathbb{K}$-linear transformations from $V$ to $V$.

A {\em Leonard system} on $V$ is a sequence

\[(\A ;\B; \lbrace E_i\rbrace_{i=0}^d; \lbrace E^*_i\rbrace_{i=0}^d),\]

where

$\A$ and $\B $ are multiplicity-free elements of \text{End}$(V)$;

$\lbrace E_i\rbrace_{i=0}^d$ and $\lbrace E^*_i\rbrace_{i=0}^d$

are orderings of the primitive idempotents of $\A $ and $\B$, respectively; and

for $0\leq i, j\leq d$, the expressions $E_i\B E_j$ and $E^*_i\A E^*_j$ are zero when $\vert i-j\vert > 1$ and

nonzero when $\vert i-j \vert = 1$.

%

Leonard systems arise in connection …

Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie

Professional Learning Day

How many of your students say that √9 = ±3? This may have to do with a lack of understanding of functions. This session will highlight some of the nuances of functions with less formal, non-formula driven examples with which students can expand their understanding.

Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio

Professional Learning Day

Most mathematics teachers are aware of the some of the more straightforward connections Pascal's Triangle has to mathematics. Come explore some of the lesser known connections that can be used to peak your students' interest and entice them into exploring the mathematics behind these connections.

Session F-1: Exploration Geometry: Hands-On Transformations, Lindsey Herlehy, David Hernandez, Karen Togliatti

Professional Learning Day

In this session, participants will engage in a series of hands-on, minds-on Geometry lessons designed to explore the four transformations. By completing several critical thinking challenges, teachers will use the Common Core Mathematical Practices and various manipulatives to investigate how figures rotate, dilate, translate, and reflect within a plane. Appropriate for multiple grade levels, teachers will leave the session with all instructional plans and various ways to adapt the lesson based on the needs of their students.

Session F-4: Developing Parametric Equations Using Mathematical Modeling, Mark Kammrath

Professional Learning Day

Designing project to develop student understanding of parametric equations and two modeling situations in which they are applied. No previous knowledge of parametrics is required by the students. The project requires two days of class time, with the remaining work done outside of class. This project is intended to be given three days into a unit on vectors.

Session A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez

Professional Learning Day

Investigate the concepts of surface area, measurement, ratio and proportion through a visual and kinesthetic mathematical investigation. Participants will be presented with the challenge of calculating how many sheets of toilet paper it would take to wrap one of their group members using a limited selection of tools. This session will provide teachers with a wonderful hands-on, minds-on activity that could easily be implemented into any classroom!

Session A-3: The Box Problem – An Introduction, Ruth Dover

Professional Learning Day

Create some simple boxes with paper and scissors. Then we'll measure the height, area of the base, and the volume. Find formulas, find regressions, and graph the functions. It's a simple activity to engage students and combine many different aspects of mathematics.

Session C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones

Professional Learning Day

Participants will work together using pi to try to open an ancient chest filled with treasure!! The chest is protected by a passcode that can only be determined through the activities within the lesson. Enjoy a progressive exposure to pi through this two-part lesson (total 110 minutes) offering a FUN storyline within the context of geometry and circles. With "pi-day" right around the corner, this hands-on, fun, inquiry-based lesson is sure to be a hit with your budding mathematicians.

Experimental Demonstration Of Topological Effects In Bianisotropic Metamaterials, Alexey P. Slobozhanyuk, Alexander B. Khanikaev, Dmitry S. Filonov, Daria A. Smirnova, Andrey E. Miroshnichenko, Yuri S. Kivshar

Publications and Research

Existence of robust edge states at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, a topological insulator. Such nontrivial states were originally predicted and discovered in condensed matter physics, but they find their counterparts in other fields of physics, including the physics of classical waves and electromagnetism. Here, we present the first experimental realization of a topological insulator for electromagnetic waves based on engineered bianisotropic metamaterials. By employing the near-field scanning technique, we demonstrate experimentally the topologically robust propagation of electromagnetic waves around sharp corners without backscattering effects.

Why Lp-Methods In Signal And Image Processing: A Fuzzy-Based Explanation, Fernando Cervantes, Bryan E. Usevitch, Vladik Kreinovich

Departmental Technical Reports (CS)

In signal and image processing, it is often beneficial to use semi-heuristic Lp-methods, i.e., methods that minimize the sum of the p-th powers of the discrepancies. In this paper, we show that a fuzzy-based analysis of the corresponding intuitive idea leads exactly to the Lp-methods.

Limitations Of Realistic Monte-Carlo Techniques, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Because of the measurement errors, the result Y = f(X1, ..., Xn) of processing the measurement results X1, ..., Xn is, in general, different from the value y = f(x1, ..., xn) that we would obtain if we knew the exact values x1, ..., xn of all the inputs. In the linearized case, we can use numerical differentiation to estimate the resulting difference Y -- y; however, this requires >n calls to an algorithm computing f, and for complex algorithms and large $n$ this can take too long. In situations when for each input xi, we know the probability distribution …

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

Ogden College of Science & Engineering Publications

No abstract provided.

Increased Mortality With Elevated Plasma Endothelin-1 In Acute Heart Failure: An Ascend-Hf Biomarker Substudy, Antonio L. Perez, Justin L. Grodin, Yuping Wu, Adrian F. Hernandez, Javed Butler, Marco Metra, Michael G. Felker, Adriaan A. Voors, John J. Mcmurray, Paul W. Armstrong, Randall C. Starling, Christopher M. O'Connor, W. H. Wilson Tang

Mathematics and Statistics Faculty Publications

Aims: Endothelin-1 (ET-1) is an endogenous vasoconstrictor implicated in pulmonary and systemic hypertension, as well as ventricular dysfunction, through effects on vascular smooth muscle, the kidneys, and cardiomyocytes. We aimed to determine the association between serial ET-1 levels and acute heart failure patient outcomes. Methods and results: We measured plasma ET-1 at baseline, 48–72 h, and 30 days in a cohort of 872 patients hospitalized with acute heart failure from the ASCEND-HF trial (randomized to nesiritide vs. placebo), and its association with 30-day mortality, 180-day mortality, in-hospital death or worsening heart failure, and 30-day mortality or rehospitalization. Median ET-1 was …

Matched Metrics And Channels, Marcelo Firer, Judy L. Walker

Department of Mathematics: Faculty Publications

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes.

A New 12-Puzzle, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

This puzzle is a continuation of the tribute to the magician Paul Swinford. The following 18 two-letter words use each of the 12 letters of PAUL SWINFORD exactly three times each. The words are to be placed on the nodes of the grid so that each hexagon and each of the three diagonals contain the 12 letters of our honoree's name.

The White Rabbit 12-Puzzle, Chris Morgan, Jeremiah Farrell

Scholarship and Professional Work - LAS

Martin Gardner's fondness for the characters and themes of Lewis Carroll's "Alice" is well-known and to honor Gardner we offer two word puzzles to be played on the 12-node diagram of the WHITE RABBIT.