FL-MAA
FL-MAA

MAA-FL/FTYCMA

JOINT CONFERENCES 2022

TALKS & ZOOM ROOMS

ALL TIMES ARE EST

Saturday, February 19, 2022

8:30–12:00

Room #8

Social Room (Faculty)

Everybody

Everybody

This is where you can meet up with old friends and make new friends, if you wanted to take a short break. Enjoy the Conference in this new and virtual way!

8:30–12:00

Room #9

Social Room (Students)

Everybody

Everybody

This is where you can meet up with old friends and make new friends, if you wanted to take a short break. Enjoy the Conference in this new and virtual way!

8:45–9:00

Main Room

Welcome Back

Joni Pirnot & Anthony Okafor

Welcome to Day Two!

Joni Pirnot & Anthony Okafor

Updates if necessary!

9:00–9:50

B/O Room #11

Hawkes Learning

Taylor Ireland - Hawkes Learning

Math Pathway Prep & Corequisite Support

Taylor Ireland

The math pathways initiative created a challenge to implement strategies that support and accelerate developmental-level learning while providing robust curricular content. Join this presentation to learn about successful corequisite implementation structures, newly enhanced course materials that offer contextualized review, and pre-pathway math literacy courses designed to prepare students for any future math pathway curriculum. Learn how to use data on class and individual student performance, commonly missed questions, and time-on-task activity to identify intervention points for at-risk students. Attend and be entered to win one of three $25 Amazon Gift Cards!

9:00–9:45

B/O Room #1

Project-Based Learning in College Algebra

Nancy Eschen & Amber Strickland - Florida State College at Jacksonville

Project-Based Learning in College Algebra

Nancy Eschen & Amber Strickland

The aim of this presentation/talk is to outline and discuss a term-long project in a College Algebra Honors class at Florida State College at Jacksonville (FSCJ). Mathematics Professor Nancy Eschen and Academic Librarian Professor Amber Strickland collaborated to create a project that combined the curriculum of the class with the requirement of using FSCJ academic student support services. This project required students to select and analyze a dataset relating to a topic of their choice; explore functions models for the data using Excel; write a literary review of their topic; and present a poster of their work. Students met the librarian to learn how to find academic sources for information and research plus consulted with FSCJ tutors in the areas of mathematics, computer (Excel), and writing. Several students were selected to present their posters at the FSCJ Math Mini-Conference.

9:00–9:45

B/O Room #2

Get Ready MAT 1033! An Initiative to Address Student Preparedness for Intermediate Algebra

Megan Cavanah & Kimberly Hess - Polk State College

Get Ready MAT 1033! An Initiative to Address Student Preparedness for Intermediate Algebra

Megan Cavanah & Kimberly Hess

Get Ready MAT 1033! An Initiative to Address Student Preparedness for Intermediate Algebra In response to the learning loss associated with the COVID-19 pandemic, mathematics faculty at Polk State College created a bootcamp course to help students practice essential, prerequisite material before starting Intermediate Algebra. The course, which comes at no cost to students, includes videos, practice and self-assessments to help students work through material prior to starting the credit-bearing course. In this session, the designers and coordinators for Get Ready MAT 1033 will share the course design, the implementation and marketing strategies used to launch the course, as well as lessons learned. In addition to discussing student outcomes, participants will reflect on how this model could be used at their colleges.

9:00–9:20

B/O Room #3

Representations of Lattice Vertex Algebras, Trace Functions, and Modular Transformations

Jason Elsinger - Florida Southern College

Representations of Lattice Vertex Algebras, Trace Functions, and Modular Transformations

Jason Elsinger

A lattice vertex algebra is an algebraic structure associated to an even lattice. Any group of automorphisms of the lattice naturally extends to a group of automorphisms of the lattice vertex algebra. An important problem is to classify the representations for the subalgebra of fixed points, known as an orbifold. In this talk I will describe an alternative approach to writing the irreducible orbifold characters using a combination of trace functions. It has been known that the set of irreducible characters for an orbifold is closed under modular transformations and I will discuss our method for calculating these transformations.

9:00–9:20

B/O Room #4

On the Equivalence of Statistical Distances for Isotropic Convex Measures

Puja Pandey - University of Florida

On the Equivalence of Statistical Distances for Isotropic Convex Measures

Puja Pandey

In convex geometry and its probabilistic aspects, many fundamental inequalities can be reversed up to universal constants in the presence of geometric properties, for instance reverse isoperimetric inequality for convex bodies. In this talk we will see that distances between probability measures are equivalent for convex measures, which extends a result of Meckes and Meckes (2014). The class of convex measures contains fundamental distributions in probability and statistics. Examples include Gaussian distributions, uniform distributions on a convex set and more general log-concave distributions, as well as heavy tailed distributions such as Cauchy distribution. We will see that the convergence in total variation of an isotropic s-concave probability measures is equivalent to convergence in bounded Lipschitz and is further equivalent to Rényi and Tsallis divergence with respect to Gaussian.

9:00–9:20

B/O Room #5

A spatial study of quality of life in the USA

Bradly Rivera-Muñiz & Raid Amin - University of West Florida

A spatial study of quality of life in the USA

Bradly Rivera-Muñiz & Raid Amin

This study’s main goal was to develop a comprehensive Quality of Life (QoL) Index based on 31 demographic variables for the 3108 counties in the contiguous USA. Counties were ranked worst in QoL to best, and spatial cluster analysis is used to identify counties with significant low/high QoL clusters. GIS-based mapping was used to create informative heat maps with significant clusters shown. The rate of African Americans, diversity in a race within counties, and upward mobility were studied in a regression analysis in which QoL was predicted from these three covariates. The QoL Index was adjusted for the covariates, and a new spatial heat map with clusters is obtained. It was concluded that as the rate of African Americans increases in a county, the QoL decreases, while the QoL increases when diversity or upward mobility increases.

9:00–9:20

B/O Room #6

Inverse Source Problems for Wave Propagation

Mozhgan Nora Entekhabi – Florida A & M University

Inverse Source Problems for Wave Propagation

Mozhgan Nora Entekhabi

Inverse source scattering problem and uniqueness of the source arises in many areas of science. It has numerous applications to surface vibrations, elasticity and acoustical and bio-medical industries and medical imaging. In particular, inverse source problem seeks the radiating source which produces the measured wave field. The study aims to provide a technique for recovering the source function of the classical elasticity system and the Helmholtz equation from boundary data at multiple wave numbers when the source is compactly supported in an arbitrary bounded C^2 - boundary domain, establish uniqueness for the source from the Cauchy data on any open non-empty part of the boundary for arbitrary positive K, and increasing stability when wave number K is getting large. Various studies showed that the uniqueness can be regained by taking multifrequency boundary measurement in a non-empty frequency interval (0, K) noticing the analyticity of wave-field on the frequency.

9:25–9:45

B/O Room #3

Lorentzian Peak Sharpening and Sparse Blind Source Separation for NMR Spectroscopy

Yuanchang Sun - Florida International University

Lorentzian Peak Sharpening and Sparse Blind Source Separation for NMR Spectroscopy

Yuanchang Sun

In this talk, we shall introduce a weighted peak sharping technique for NMR spectra separation. To achieve an optimal sharpening while preserving the data nonnegativity, we prove the existence of an upper bound of the weight parameter and propose a selection criterion. Numerical experiments on NMR spectroscopy data show satisfactory performance of our proposed method.

9:25–9:45

B/O Room #4

Examining the Riemann Hypothesis, and Ratios of Robin and Lagarias Inequalities

Caroline E. Johnson (U) - Davis Senior High School & Woodland Community College & Paul Johnson - Biostat Software

Examining the Riemann Hypothesis, and Ratios of Robin and Lagarias Inequalities

Caroline E. Johnson & Paul Johnson

This presentation examines the Riemann Hypothesis (RH), and the two ‘if and only if’ inequalities due to Robin (1984) and Lagarias (2002). Robin showed that RH ⇔ 𝜎(n)/n< 𝑒^𝛾log log(n) for n > 5040, where 𝜎(n) is the sum of the divisors of the positive integer n; 𝛾 is Euler’s constant. Lagarias showed that RH ⇔ 𝜎(n)< H(n)+ 𝑒H(n)∗log(H(n)) for all n; where H(n) is the harmonic sum. We examine the ratios of the two inequalities, ratio1 = 𝜎(n)/n/(𝑒^𝛾log log(n)) and ratio2 = 𝜎(n){H(n)+ 𝑒H(n)∗log(H(n))}. We examine their linear relationship. We comment on the pattern of the means of the two ratios as n increases. We choose an optimal cutoff point and demonstrate that the percentage of ratios exceeding this cutoff point decreases as we increase n; approaching zero for large n. We discuss the findings in context to Morrill and Platt’s (2020) extension of Robin’s inequality for 20-free integers.

9:25–9:45

B/O Room #5

Essential Course for Undergraduate Students

Bariaa Shatila - Flagler College

Essential Course for Undergraduate Students

Bariaa Shatila

Many students think Mathematics is an abstract subject and are afraid from taking a Mathematics course. I believe that the Essentials of Mathematics course that I teach at Flagler College is an essential course for all undergraduate students. This course is relevant for our students and will equip them with the quantitative skills to deal with real-world math problems. This math course helps students practice critical thinking and problem-solving skills. It covers the following independent topics: financial mathematics, systematic counting, probability, geometry, and analyzing statistics. Students who took this class reported that it was the best Mathematics course they ever took.

9:00–9:20

B/O Room #6

Classic Results on the Bounds of Ramsey Numbers

Ryan Farrell - University of North Florida (U)

Classic Results on the Bounds of Ramsey Numbers

Ryan Farrell

Ramsey’s theorem states that a sufficiently large complete graph with each edge colored in one of finitely many colors will always contain a monochromatic subgraph of a certain type. This presentation investigates what “sufficiently large” means in specific cases. We define Ramsey numbers and prove a number of classic results including the well-known party problem which asserts that any party of six or more people where each pair of people are either friends or enemies must have at least three mutual friends or three mutual enemies.

10:00–11:15

B/O Room #10

Modelling and teaching Mindfulness for Math anxiety

Manisha Ranade - Santa Fe College

Modelling and teaching Mindfulness for Math anxiety

Manisha Ranade

Among college students, Math anxiety is a major stumbling block to success. It affects learning of new concepts and retention of old material. During the pandemic, anxieties regarding health, family and jobs increased dramatically making it even tougher for students. Anxiety affects physical health via decreased immunity. Besides students, professors and college administrators also suffered from pandemic related stresses. Mindfulness is one way to relieve anxiety and is a secular, accessible and equitable practice. In this workshop, we will introduce practicing mindfulness for wellbeing, followed by resources to take it to the Math classroom. There will be a guided practice as well as an interactive portion with breakouts for small group discussion. At the end, we will come up with an action plan to implement these practices. The speaker is trained in Yoga therapy and is working on a project, “Mindfulness in the Math classroom”.

10:00–10:45

B/O Room #1

Course Coordination in the midst of Covid-19 and thereafter

Adebukola Adeyem, Carrie Grant & Kurt Sebastian - Flagler College

Course Coordination in the midst of Covid-19 and thereafter

Adebukola Adeyem, Carrie Grant & Kurt Sebastian

Course coordination describes coordination in the design, structure, and teaching of a course, to the extent that multiple instructors within a multi-section course have come to common agreement. COVID-19 has changed numerous things in higher education, it has forced educators to reinvent themselves and their classrooms. Even after being back to face-to-face teaching, things are not necessarily back to “normal.” Our goal to coordinate our Introductory Statistics course has become more important. In this presentation, we will share how our Statistics team continue to collaborate to create a learning environment that provides consistency to our students. Changes the global pandemic had on our course coordination model, if any. Based on our experience, we will make recommendations regarding course coordination that will provide those in attendance ideas to use in their own institutions. Our discussion will include our course coordination model and the outcomes experienced over the last four years.

10:00–10:20

B/O Room #2

Observations on Transfer Student Experience: A Learning Model between Two-Year and University Faculty

Joanne Kiriazes - Valencia College, Sidra Van De Car - Valencia College, Maria Capursi - UCF, & Lori Dunlop-Pyle - UCF

Observations on Transfer Student Experience: A Learning Model between Two-Year and University Faculty

Joanne Kiriazes, Sidra Van De Car, Maria Capursi & Lori Dunlop-Pyle

Valencia College partnered with the University of Central Florida to create a peer observation model between mathematics faculty. Because transfer students typically have lower success rates, faculty at the sister institutions created a program to allow faculty to observe one another’s classes, evaluate differences in pedagogy, and identify aspects of classroom culture unique to the sister institution. This presentation will discuss differences in success rates, describe the observation program, and review differences observed between the institutions that may affect transfer student success, as found in the initial offering of the program in Fall 2020. Plans for future observations and actions for student success will be discussed.

10:00–10:20

B/O Room #3

An Extension of D'Alembert's Solution for the One-Dimensional Wave Equation

Alfred "Ken" Mulzet - Florida State College at Jacksonville

An Extension of D'Alembert's Solution for the One-Dimensional Wave Equation

Alfred "Ken" Mulzet

In this presentation we will use D'Alembert's formula to solve a two-dimensional wave equation/initial value problem, with suitable restrictions on the initial conditions. This method can be generalized to higher dimensions as well. We then use this approach to solve initial value problems of the form 𝑢_𝑡𝑡=𝐴𝑢_𝑥𝑥+𝐵𝑢_𝑥𝑦+𝐶𝑢_𝑦𝑦 𝑢(𝑥,𝑦,0)=𝑓(𝑥,𝑦) 𝑢_𝑡(𝑥,𝑦,0)=𝑔(𝑥,𝑦) where the functions f(x, y) and g(x, y) are homogeneous polynomial functions of degree n.

10:00–10:20

B/O Room #4

STEM-Focused and Personalized for First-Term Calculus Students

Ala’ J. Alnaser, Abigail Bowers, Aaron Bardal & Jared Bunn - Florida Polytechnic University

STEM-Focused and Personalized for First-Term Calculus Students

Ala’ J. Alnaser, Abigail Bowers, Aaron Bardal & Jared Bunn

In this project we seek to improve success and retention of STEM majors by improving student motivation for problem solving in STEM applications. This is done through enhancing first year and second year Calculus courses by not only connecting the learned theory to real-life STEM examples, but moreover relating them to the students’ actual areas of interest. Many projects and assignments were designed for this purpose, with a basic structure of (i) watching a video with examples, (ii) choosing an area of interest such as Mechanical or Electrical Engineering, Computer Science or Data Analysis, (iii) solving a real-life application based on this choice, and (iv) filling out a short survey and discussing with peers. We believe that this project is an extension on previous results that show the positive effect of homework on student learning, with the added motivation that comes from the student’s personal interest.

10:00–10:20

B/O Room #5

Management of Epidemics through Governance

Lindsey Fox - Eckerd College

Management of Epidemics through Governance

Lindsey Fox

In this study, we consider a system of ODEs for a two-patch epidemiological model with various management strategies for outbreaks of two diseases: Cholera and Ebola. Optimal control theory is used on both models to minimize the cost of the strategies and the burden of the epidemic. We analyze whether the difference in disease transmission mechanisms affect the management strategies of two types of governance: one-size-fits-all management for both patches and customized management for each patch.

10:25–10:45

B/O Room #2

Get Started with LaTeX

Joseph Ours - State College of Florida

Get Started with LaTeX

Joseph Ours

Learn how to start using LaTeX. LaTeX is a document preparation system used for the communication and publication of scientific documents and is a wonderful tool for typing mathematical documents—especially exams. This presentation will cover the very basics and allow you to begin writing LaTeX exams and documents. This will be a hands-on presentation and you will have the opportunity to create your own LaTeX document. This will be accomplished via Overleaf—an online editor for documents written in the LaTeX markup language. Please sign up for a free Overleaf account at Overleaf before attending the presentation.

10:25–10:45

B/O Room #3

Exploratory research of Covid-19 Vaccination Effects on population in Florida

Kristina Zogovic, Marcus Green, Subhash Bagu, Jossy Uvah, Sikha Bagui - UWF & Robert Lamar - Warner University

Exploratory research of Covid-19 Vaccination Effects on population in Florida

Kristina Zogovic, Marcus Green, Subhash Bagu, Jossy Uvah, Sikha Bagui & Robert Lamar

We studied longitudinal COVID-19 vaccination data for the State of FL, from 01/19/21 till 04/2/21. For this analysis, the State of FL was divided into six geographic regions and the whole state was used as the control group. The project assessed whether there was any detectable reduction in the population prevalence of COVID-19 in FL, associated with the current early stages of vaccination. We compared the actual number of new COVID-19 cases and deaths as well as the changes in disease prevalence across sex and racial groups between the sub-regions. Analysis showed that the vaccination had different rates. The slope was significantly different in some regions and with respect to some categories. Finally, the analysis showed that the COVID-19 vaccination played an important role in reducing the number of new cases of COVID-19 and new deaths in the state and sub-regions of FL.

10:25–10:45

B/O Room #4

Tales from the Bootstrap

Brian Camp - Suncoast Credit Union

Tales from the Bootstrap

Brian Camp

An eclectic mix of stories from a recovering teacher - the job market for math people; bootstrapping, pi and phi; Excel isn’t really that bad; some quizzes on data visualization and the square root of two.

10:25–10:45

B/O Room #5

Applications of the Markov Method for Ranking and Recommendation Tasks

Matthew Kimm (G), Gary Marmon (G), Jay Kim & Anthony Okafor - University of West Florida

Applications of the Markov Method for Ranking and Recommendation Tasks

Matthew Kimm (G), Gary Marmon (G), Jay Kim & Anthony Okafor

We discuss the Markov rating method, which has found success in ranking sports teams, and describe its application to graph based ranking methods. Then, we describe the application of graph based ranking methods to recommendations problems, and the advantages of additionally using the Markov rating method. Finally, we present an application of the Markov method to a higher educational recommendation task.

11:00–11:45

B/O Room #1

Palindromic Polynomials, Unimodular Roots, and Trigonometric Equations

Michael Brilleslyper - Florida Polytechnic University & Beth Schaubroeck - U.S. Air Force Academy

Palindromic Polynomials, Unimodular Roots, and Trigonometric Equations

Michael Brilleslyper & Beth Schaubroeck

A polynomial with all its roots having modulus one in the complex plane is called unimodular. It is well known that a unimodular polynomial must have coefficients that form a palindrome or an anti-palindrome. The converse, however, is false. Here we discuss a one-parameter family of anti-palindromic polynomials of even degree and describe how changing the parameter value increases the number of roots of modulus one until the polynomial is unimodular. The unimodular condition on a polynomial seems very rigid and sensitive to small changes, but this is not the case. Indeed, there is a continuous range of the parameter that preserves this property. Translating the problem to an equivalent trigonometric setting provides a simple explanation for the observed behavior. This talk is accessible to undergraduates and will include numerous graphics and animations created using Mathematica.

11:00–11:45

B/O Room #2

First Semester to First Year in College: Factors Predicting Improvements in GPA among At-Risk Students

Jay Kim, Anthony Okafor, & Josaphat Uvah - University of West Florida

First Semester to First Year in College: Factors Predicting Improvements in GPA among At-Risk Students

Jay Kim, Anthony Okafor, & Josaphat Uvah

First semester GPA performance is the most significant predictor for college dropouts. Interventions among at-risk students need to target their efforts to improve first year GPA; i.e., second semester improvements. A small size university in the Southeast US found that 76% of students who underperformed (GPA < 2.0) in their first term went on to drop out in their first year. Improving GPA past the first term is critical to reducing the dropout rate among these students. This study considers which factors best predict improvement in GPA during second and summer terms for at-risk first year students. Factors considered include pre-college factors (high school GPA, test scores, etc.), demographic factors, and type of major (STEM vs. non-STEM).

11:00–11:20

B/O Room #3

Meshfree space-time method for solving two-dimensional wave equation

L. H. Kuo & Niranjan Warnakulasooriya Mahaguruge - University of West Florida

Meshfree space-time method for solving two-dimensional wave equation

L. H. Kuo & Niranjan Warnakulasooriya Mahaguruge

In recent years, the time-space technique has demonstrated the potential to solve time-dependent problems such as wave equations to a Poisson-type PDE. In this presentation, we utilize Kansa’s method with Radial Basis Functions (RBF) to solve the Wave equation as Poisson’s type of equation. To overcome the resultant ill-conditioned matrix, we further apply ghost points as center points for the RBF kernel. The numerical results demonstrate that the accuracy of the solution of the Wave equation can reach up to 1E-10, which is potential to be used for nano-scale simulation.

11:00–11:20

B/O Room #4

Kahoot! in Calculus vs a General Education Course

Kevin Murphy - Saint Leo University

Kahoot! in Calculus vs a General Education Course

Kevin Murphy

This talk will introduce the online quiz tool Kahoot! and how it can be used to stimulate interest and participation in a variety of courses. In the Fall I used Kahoot! for both a general Business Math general education course and for a Calculus 1 course. I will describe what I did including the successes and shortcomings.

11:00–11:20

B/O Room #5

Partially ordered sets and quandles

Hitakshi Lahrani (G) - University of South Florida

Partially ordered sets and quandles

Hitakshi Lahrani

We will review the basics of quandles which are algebraic structures coming from knot theory. Given a partially ordered set structure on a quandle, we will discuss compatibility of the order with the binary operations of the quandle. We will present many examples. The talk will be self-contained.

11:00–11:20

B/O Room #6

Planar Graphs and Embeddings

Benjamin Titera (U) - University of North Florida

Planar Graphs and Embeddings

Benjamin Titera

This presentation discusses planar graphs: graphs which can be drawn in the plane without any two edges crossing. We examine the properties such a graph must possess and consider examples of planar and nonplanar graphs. These observations are generalized to graphs drawn on any closed, connected, orientable surface.

11:25–11:45

B/O Room #3

SCOREH+: A High-Order Node Proximity Spectral Clustering on Ratios-of-Eigenvectors Algorithm for Community Detection

Yanhui Zhu, Fang Hu, Lei Hsin Kuo & Jia Liu - University of West Florida

SCOREH+: A High-Order Node Proximity Spectral Clustering on Ratios-of-Eigenvectors Algorithm for Community Detection

Yanhui Zhu, Fang Hu, Lei Hsin Kuo & Jia Liu

Complex network analysis has brought significant advances to uncover network mesoscopic properties. Community detection is one of the significant features of understanding real complex systems. This paper proposes a High-order node proximity Spectral Clustering on Ratios-of-Eigenvectors (SCOREH+) algorithm for community detection in complex networks.

11:25–11:45

B/O Room #4

Wildlife Tracking with Asynchronous Multiple Directional Antenna Readings

Channa Navaratna - Indiana University of Pennsylvania & Menaka Navaratna - Florida Gulf Coast University

Wildlife Tracking with Asynchronous Multiple Directional Antenna Readings

Channa Navaratna & Menaka Navaratna

While GPS tracking provide a location information with better accuracy, it requires a substantial financial investment. In comparison, VHF radio telemetry is a low-cost option with ease of maintenance. Therefore, it is still popular among scientists. Multiple antennas with triangulating techniques can be deployed to estimate the location of a radio tagged animal. Telemetry data from multiple antennas can significantly improve the accuracy of location. Wildlife telemetry, in most cases, involves collecting data under less than perfect weather/terrain condition. Often data from multiple antennas are not collected at specified times or time intervals. This may create complications in estimation process.

11:25–11:45

B/O Room #5

Generating Functions and The Catalan Numbers

Albert Hancock (U) - University of North Florida

Generating Functions and The Catalan Numbers

Albert Hancock

Abstract. Generating functions are a type of formal power series used to provide a closed-form solution for recurrence relations. We explore the procedures of using ordinary generating functions and products of generating functions, and in particular, their application in finding a closed-form expression of the Catalan sequence. After the base recursion of triangulations of a convex (n+2)-gon, further applications of the Catalan numbers are examined in Dyck paths and ballot sequences.

12:00–12:50

B/O Room #1

Modeling the Effects of Resistance to Disinfectants on the Transmission of Nosocomial Infections

Karin Ebey (U), Mariana Olivares-Cely (U), & Lindsey Fox - Eckerd College

Modeling the Effects of Resistance to Disinfectants on the Transmission of Nosocomial Infections

Karin Ebey, Mariana Olivares-Cely & Lindsey Fox

Antimicrobial resistance is a growing threat, increasing the rate and complications of hospital-acquired infections. This study explores how resistance to disinfectants affects the spread of nosocomial diseases. An ODE compartmental model was created to describe the transmission of two strains of a generalized pathogen, resistant and susceptible to disinfectants, throughout a hospital ward. Transmission occurs directly and through contact with an environmental reservoir of pathogen. Evolution of resistance occurs through mutation and horizontal gene transfer. Different selection pressure magnitudes, and the ratio of disinfectant efficacy on resistant and susceptible strains, were tested.

12:00–12:50

B/O Room #1

Mathematically Modeling the Role of Healthcare Workers in the Environmental Transmission of C. difficile

Isaac Blackburn (U), Kat Fillman (U), & Lindsey Fox - Eckerd College

Mathematically Modeling the Role of Healthcare Workers in the Environmental Transmission of C. difficile

Isaac Blackburn, Kat Fillman & Lindsey Fox

Clostridioides difficile is the leading cause of infectious diarrhea and one of the most common healthcare-acquired infections in United States hospitals. C. difficile persists well in healthcare environments because it forms spores that can survive for long periods of time and can be transmitted to susceptible patients through contact with contaminated hands and surfaces that can harbor infectious agents, called fomites. This study explores an alteration of a previous model to include healthcare workers as a transmission vector in conjunction with high-touch and low-touch fomites. The transmission is described by a system of ordinary differential equations representing four patient classes, two pathogen environmental reservoirs, and two healthcare worker groupings.

12:00–12:50

B/O Room #1

Computational and Linear Stability Studies of Damping Effects on Rogue Wave Formation

Evelyn Smith (U), Constance Schober - University of Central Florida, Lane Ellisor (U) & Annalisa Calini - College of Charleston

Computational and Linear Stability Studies of Damping Effects on Rogue Wave Formation

Evelyn Smith, Constance Schober, Lane Ellisor & Annalisa Calini

Inspired by the work of Schober and Strawn on the effects of damping on the formation and persistence of rogue waves in deep water, modeled by the nonlinear Schrödinger (NS) equation and its higher-order generalizations (HONS), we investigate two interesting scenarios. While Schober and Strawn study the effects of nonlinear damping, our study focuses on the effects of viscous damping. To this end, we present numerical realizations of rogue waves and stability calculations for background states in higher-order Nonlinear Schrödinger models with viscous damping terms.

12:00–12:50

B/O Room #1

Mathematically modeling the transmission of Koi herpesvirus in common carp

Payton Bivens (U), Kelsey Weeden (U), & Lindsey Fox - Eckerd College

Mathematically modeling the transmission of Koi herpesvirus in common carp

Payton Bivens, Kelsey Weeden & Lindsey Fox

Koi herpesvirus (KHV) is an extremely contagious virus that affects common carp. The virus is transmitted through direct contact with infected fish, contaminated fluids, or other contaminated vectors. In this study, we constructed an epidemiological model that uses a system of ordinary differential equations to describe the dynamics of transmission of KHV. Classes include susceptible, exposed, infectious, ailing, and recovered. Some parameters of the model fluctuate with water temperature. The rate of progression through both compartments exposed (E) and infected (I) are dependent on temperature. Between sixteen degrees Celsius and twenty-eight degrees Celsius, the progression rates are highest. The goal is to better understand the direct transmission of KHV before adding an environmental component to study transmission via contaminated water.

12:00–12:50

B/O Room #1

Security Systems and Location Numbers of Graphs

Brendan Chamberlain (U) - University of North Florida

Security Systems and Location Numbers of Graphs

Brendan Chamberlain

We discuss location numbers of graphs and their applications to security systems. Given some number of sensors that output the distance between the room which the sensors are placed in and the room which an intruder is in, the location number of a connected graph can be interpreted as the smallest number of such sensors required in order to uniquely determine which room the intruder is in. More specifically, the locating code of a vertex with respect to some set of vertices in the graph is a vector whose entries are the distances between the vertex and the vertices in the set. A set of vertices in the graph is a locating set if every vertex in the graph has a unique locating code with respect to that set. The cardinality of a minimum locating set is the location number of the graph.

1:00–1:50

Main Room

Plenary Session

Anastasia Chavez - Saint Mary's College of California, MAA AWM Speaker

Matroids, Positroids, and Beyond!

Anastasia Chavez

Matroids are a fundamental combinatorial object with connections to many areas of mathematics: algebraic geometry, cluster algebra, coding theory, polytopes, physics, ... just to name a few. Introduced in the 1930’s, Whitney defined matroids with the desire to abstract linear and graphical dependence. In fact, every graph is associated with a matroid and from every vector configuration arises a representable matroid over F. It has been shown that most matroids are neither graphical or representable, making these two matroid properties rare and highly desired. A particularly well-behaved family of representable matroids, called positroids, was introduced by Postnikov and shown to have deep connections to the totally nonnegative Grassmannian and particle physics. Moreover, he described several combinatorial objects in bijection with positroids that compactly ecodes matroidal data and have been shown to characterize many matroidal properties. With just a few definitions and examples revealing their connections to a variety of fields, you too can begin searching for the matroids living among us.

1:50–2:00

Main Room

Closing Remarks

Joni Pirnot & Anthony Okafor

Closing Remarks

Joni Pirnot & Anthony Okafor

The annual business meeting.

2:00–3:00

Main Room

Award Ceremony and FL-MAA Business Meeting

Anthony Okafor

Award Ceremony and FL-MAA Business Meeting

Anthony Okafor

The annual business meeting.


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