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Abstracts

 

Lori Alvin, University of West Florida, Endpoints and Inverse Limit Spaces
Given a unimodal map f, let denote the core and set  where  is the associated inverse limit space.  It is often useful to study the collection of endpoints of an inverse limit space, as they are a topological invariant.  We are interested in identifying when the collection of endpoints of   is exactly    and when the collection of endpoints is a proper subset of     in hopes of better understanding the topological structure of the inverse limit space.

Marie Byrne, University of South Alabama, Prisoner's Dilemma Applied to the Interaction of Black Flies and their Residents
In the prisoner's dilemma of game theory, two prisoners cooperate for the optimal outcome of lighter prison sentences, or one prisoner can defect for a lighter sentence at the expense of the other'. If a prisoner anticipates that the other will defect, that prisoner should also defect for the second most-optimal outcome. We explore the prisoner's dilemma in the context of the interaction of black flies and their resident fungi. It appears that black flies and their fungal residents have the potential for cooperation (fungi and flies exchange nutrient production for shelter) but are in a mutually defecting arrangement (black flies eject the fungi from their gut as they grow and the fungal parasites hijack the black fly ovaries for their own dispersion). We couple an ecological cost-benefit fitness model with a simple evolutionary model to explore the possibility that fully cooperative state of the prisoner's dilemma might also be stable.

Jane Caffrey, University of West Florida, Resolving Drivers of Variability in Estuarine Metabolism from Sustained Observations of Water Quality in the SE US
Understanding the role of climate change and other human impacts as well as physical processes on estuaries is essential to preserve and protect these highly productive and vibrant ecosystems. We examine trends in water quality data from long-term monitoring (10-15 y) at 5 estuarine systems of NOAA’s National Estuarine Research Reserve (NERR) program: Grand Bay, MS; Weeks Bay, AL; Apalachicola Bay, FL; Rookery Bay, FL, and Guana Tolomatos and Matanzas Rivers, FL. These estuaries vary in size, flow regime, watershed area, anthropogenic influence, and land use. Water quality variables (water temperature, salinity, dissolved oxygen, and pH) were measured with in-situ data sondes at multiple sites in each system as part of the NERR System Wide Monitoring Program. We describe seasonal and interannual patterns in these water quality data for temporal coherence both within and among the estuaries. Preliminary data analysis shows strong coherence among all systems in annual salinity anomaly, calculated as the deviation of annual mean salinity from the long term mean, with highest salinity anomalies observed during the droughts of 2000-2002 and 2006-2007. The frequency of hypoxia (DO < 2 mg/L), used as an index of potential eutrophication, occurred infrequently at some sites (<1% per anum) and regularly at others (e.g., up to 17% per anum in Weeks Bay). Dissolved oxygen data are used to calculate daily gross production, respiration and net ecosystem metabolism (NEM) parameters. We hypothesize that warmer temperatures or higher flow regimes will cause a decrease in NEM, while cooler temperatures or lower flow regimes will result in higher NEM. Consistent with this hypothesis, prior analyses of Apalachicola and Weeks Bays data showed that gross production decreased during flood periods, likely due to increased turbidity and reduced residence time. Analysis of long term monitoring data can provide insights into the relative importance of anthropogenic and external drivers on estuarine ecosystem function.

Angelo Christopher Conner, University of West Florida, A Statistical Analysis of “An Historical Approach to Physics Instruction”
In 2007-2008 I conducted research on Physics instruction for the completion of a thesis in partial fulfillment for the honors in the major program in education in the College of Education and the Burnett Honors College at the University of Central Florida.  Beginning with the idea that Physics is a highly “humanistic activity” (Gosslein, 1975, p.15), I utilized the philosophy and history of the science to teach a unit on gas laws to 10th and 11th grade Chemistry students at a mid-level socioeconomic Central Florida High School.     
Through this teaching I was interested in measuring two important metrics.  The first is the students’ epistemological expertise and the second is the students attitudes towards science courses.  In order to assess these two metrics, I utilized the Epistemological Beliefs Assessment for Physical Science (EBAPS) survey and the Maryland Physics Expectation (MPEX) survey pre and post-instruction.  At the time these assessments were given I was statistically naive having taken no Statistics courses, therefore I could only speak of their results qualitatively.
Through the course of my studies in the Mathematical Sciences program at the University of West Florida, I have gained much statistical sophistication. With my current knowledge I can rescore and conduct a statistical analysis of the assessments completed during my undergraduate thesis.  This analysis is quite appropriate as it will lend a greater understanding of the proposed benefits of utilizing an historic approach to physics instruction and lend credibility to my conclusions.

Tracy Fister, University of West Florida, A Study of Association Between Violent Crimes and Poverty
This paper presents a study of association between poverty and violent crimes in the contiguous United States.  Murder, rape (or sexual assault), robbery, and aggravated assault crimes were analyzed using multivariate cluster analysis (drugs were also included due to a proven association with violent crimes).  Two large clusters were observed in the southeast and the southwest, requiring a second round of multivariate analysis on this region to expose the most influential underlying violent crime centers. 
When considering covariates, linear regression revealed that poverty yielded a higher correlation with violent crimes than did median income.  A Poisson regression model was applied to each of the crimes and poverty.  A reduction in size of the clusters determined that a meaningful association exists between violent crime and poverty; however, some areas of violent crime are not driven by poverty.

Mathew Garvin, Florida A&M University, Using Stereo Vision to Control and calibrate a Robot manipulator
GPS works well tracking objects provided the line of sight between the object and satellite is unobstructed. GPS becomes a challenge if objects are indoors or in obstructed areas. This work is motivated by the goal of tracking an unmanned ground vehicle (UGV) using a hexicopter.  The hexicopter, equipped with a stereo camera, will track the UGV in obstructed areas, assist the UGV’s end-effector in accomplishing certain task and reduce the mental fatigue of the operator.  The hexicopter will do this tracking through the use of shaped markers atop the UGV.
The first part of the research project uses a stereo camera to track the location of a colored circle positioned on a white background, akin to the tracking of markers atop the UGV. The position of the circle in the camera’s image frame is translated to a robot, such that, as the camera moves, the robot moves likewise. The Circular Hough Transformation Method (CHTM) is employed to track these markers.
Additionally, this work focuses on increasing the accuracy in calculations of the spatial position of the robot’s end-effector by combining feedback from the CHTM algorithm and the Least Squares Method. The stereo camera is used to track the robot’s end-effector as it moves along the path of a leminscate. Due to changes in physical attributes of the robot over time, there is a disparity in the actual and calculated position of the manipulator.  New physical parameters are determined for the robot, numerically.  These new parameters are then used by the robot to calculate more accurate spatial positions.
This research project yielded near real time response and accurate position translation between the movements of the stereo camera and the robot along with improved calculations of the robot’s end-effector position.

Hannah Hinojosa, North West Florida State College, Avoiding Latin Squares Simultaneously
"Chetwynd and Rhodes proved that two partial latin squares of order 4k are avoidable simultaneously if k > 3250. We improve their result to k > 35."

Wanwan Huang, Florida State University, Variance Reduction for Monte Carlo Simulation in the Coupled Additive-Multiplicative Noise Model
We propose a variance reduction method for Monte Carlo computation of option prices in the context of the CAM stochastic volatility model. This method selects control variates which are martingales in order to reduce the variance of unbiased option price estimators. Numerical  results for European call option are presented to illustrate the effectiveness and robustness of this martingale control variate method.

Martin Klein, U.S. Census Bureau Statistical Analysis based on Physiologically-based Pharmacokinetic Models.
Physiologically-based pharmacokinetic (PBPK) models are highly relevant for risk assessments arising out of exposure to various pollutants.
Typically we evaluate the risk for animals and use allometric scaling to extrapolate to humans.  Such evaluations are necessary from the EPA’s point of view to set thresholds or standards for some chemicals.  While PBPK modeling has reached considerable sophistication in its application, mature methodologies for making statistical inferences have not been routinely incorporated in these applications except in a few data-rich cases. In this talk, we present two important applications of PBPK modeling for which we study and conduct a rigorous statistical analysis. We explore both Bayesian and frequentist methods.
In the first application, we work with a previously developed PBPK model for the formation and disposition of DNA-protein cross-links formed by inhaled formaldehyde in the nasal lining of rats and rhesus monkeys.  We purposefully choose this model because it is based on sparse time course data. The second application considers a well established PBPK model developed for inhalation and metabolism of dichloromethane. In this application we work with time dependent, serially correlated data combined from several experiments.

Bill Leonard, Pearson Publishing  What's new in MyMathLab?
"What's new in MyMathLab? Using Show Work, Assign Questions from other
books, Lockdown Browsers, and other new features to enhance your Math
courses."

Christopher Li, University of West Florida, Latin Transversals and Completion Numbers for Complete Quin-Partite Graphs Let G be a graph and let Ik denote the graph on k isolated vertices. The competition number of a graph G, denoted k(G), is the minimum k such that  is the competition graph of an acyclic digraph. A complete quin-partite graph,  , is a complete 5-partite graph where each partite set contains n vertices. We show that if is odd, then .

Jia Liu, University of West Florida, An alternative Hermitian and Skew-Hermitian Preconditioning Technique for the Unsteady Oseen Problem
We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the the Krylov subspace iterative method. Numerical experiments show the robustness of the preconditioned iterative
methods with respect to the mesh size, Reynolds numbers, time step and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.

Tapiwa Maruni, Florida A&M University, Torque Determination and Simulation of 3-Degree of Freedom Manipulator
In this work, the appropriate motor torque needed to add rotation to the base of a 2-degree of freedom robot is bounded. A generalized method for determining an adequate torque to enable this third degree of freedom is developed using the governing equation of torque along with dynamic and kinematic analysis of the robot. This requires the analysis of the acceleration, which is based on the system’s dynamic capabilities and derived from one or more of the already present motors. An acceleration that contributes to the third motor is determined and this acceleration is then used to calculate a bound on the torque needed for the third motor.
Once an appropriate torque has been determined, various tasks are simulated on the robotic system to determine its usefulness and accuracy.  In order to simulate the calculated torques, a self-controlling feedback robotic simulated system is constructed. The system takes into consideration the robot’s kinematics and dynamics and uses second order differential equations to direct the robot. Torque usage data for each simulation is collected and compared to ideally calculated torques.

Morris Marx, University of West Florida, Revisiting Two-Sample Hypothesis Testing of Equality of Means
Two-sample testing of equality of means is considered a necessary topic for elementary or applied statistics courses. B. L. Welch is generally credited with deriving the test statistic for two-sample hypothesis testing of means when the variances are not assumed equal. The goal of this paper is to revisit his work and to provide some pedagogical suggestions based on his results

Madhuri  Mulekar, University of South Alabama, Improving Oral Communication Skills of Statistics Students
Good written and oral communication skills are essential for statisticians to succeed in their careers, whether it is in industry, government, or educational institutions. The time available to students for developing oral communication skills at an undergraduate level is typically limited to one or two courses in communications that include general information about different communication methods without any emphasis on communicating statistical information. Recently there has been an increased emphasis on including oral reports in student evaluations. This presentation will discuss the need for oral reports, instructors’ responsibilities in using oral reports as an evaluation tool, and merits and concerns of using student oral reports for evaluation in undergraduate statistics courses.

Nabendu Pal, University of Louisiana, Estimating the Sperm Whale Population Density in the Gulf of Mexico to Study the Effect of BP Oil Spill There has been a lot of interest in the Gulf of Mexico marine biology due to the disastrous British Petroleum (BP)'s Deep Horizon Oil Rig explosion and the subsequent oil spill for nearly five months. Attention is being focused on studying marine creatures to see how the oil spill has affected the surrounding ecosystem. As a part of this investigation we are looking into the passive acoustic data obtained by submerged sensors to estimate certain marine mammal populations, particularly sperm whales and beaked whales. The acoustic data obtained after the oil spill is used to estimate the population density of each species, and then compared with those available from the historical data. In this talk we will discuss the estimation method along with the model assumptions.

Katrina Palmer, Appalachian State University, NC, Using SmartPens to Facilitate Math Communication Online
This presentation will demonstrate how smartpens were used for an online computational math course. The instructor used smartpens to create mini lectures and to show students examples and thorough solutions.  In addition, each student was provided a smartpen and expected to use their smartpen to post solutions and comment on other student solutions.  Examples shown will be related to root-finding methods and Taylor polynomials.  The focus of the talk, however, will be how smartpens were used in an online course.  Student feedback about the course and smartpens will be given.

Amy Ramnarine, Florida A&M University, Asymptotic Dynamic of Action Potential and Related Phenomena in neuron activity.
The human nervous system is composed of billions of neurons and neurological cells. Neurons are able to respond and conduct impulses due to the membrane potential across the cell membrane. The unequal distribution of sodium and potassium ions contributes to this membrane potential. The action potential represents the rapid phases of change of depolarization and repolarization in the cell membrane. The Fitzhugh-Nagumo model, the simplified version of the action potential model developed by Hodgkin and Huxley will be utilized to assess the stability by the potential as well as the sodium and potassium channels created when the cell is stimulated. Application of nonlinear systems of ordinary differential equations with parameters will be employed to model the dynamics of the action potential. Using analytical and numerical methods, we assess the stability of the system. The system is said to be stable when it is at  a neutral state where no sodium and potassium channels are created. The effects of model parameters and the initial conditions on the long term behavior of the solutions will be studied without solving the differential equation.

Megan Schwab, Hawkes Publishing, Mastering Math, Not the System
You know the scenario: Students seem to be doing well on homework, yet are performing poorly on exams. With Hawkes, students cannot “cheat the system” to get through assignments. Instead, they are held accountable for mastering the material without relying on learning aids. Discover how Hawkes motivates students to succeed!

 

Emilee Schuck, University of West Florida, Minimal Surfaces
The purpose of this report is to explain the basics of minimal surfaces and area-minimizing surfaces and apply that knowledge to soap films.  Surfaces are described parametrically, and calculations are computed using first and second form notation.  The definition of a minimal surface requires that the mean curvature of the surface is equal to zero.  We will explore four surfaces: the sphere, the helicoid, Enneper’s surface, and the torus.  We will also discuss area-minimizing surfaces.  The minimal surface equation, by the use of Monge parametrization and Green’s Theorem, can be derived from the area formula.  Using a technique from the calculus of variation, it is proved that area-minimizing surfaces must also be minimal surfaces.  The physics of soap films and soap bubble clusters is based on the concept of surface tension, which accounts for soap films’ ability to enclose and separate volumes in a manner that minimizes the surface area of the enclosing surface.  Soap films are a physical manifestation of area-minimizing surfaces, and are thus minimal surfaces.  Soap bubble clusters contain regions of air enclosed by the bubbles.  The interfaces between separate regions are soap films.  Depending on how the cluster separates the volumes of air, soap bubble clusters may or may not be an area-minimizing surface or minimal surface.

Carol St. Dennis, Northwest Florida State College, NWFSC Math Prescription (Rx) Program
The Math Rx program  is targeted at developmental math students, specifically those in College Preparatory Algebra.  The idea is to provide instructors a way to “prescribe” work in areas where students may be struggling and to require that students complete the work in the MathLab with tutor help. The program includes a list of specific topics (modules) where students may require help, a prescription form and worksheets for a majority of the topic areas, as well as a web site for MathLab and Academic Success Center (ASC) use. 
I plan to cover the process of prescribing work, and some different ways to apply the program that I have used since its inception in 2009.

Christopher Stanley, University of West Florida, A Geospatial Study of Violent Crimes in the USA: The Race Factor Is there a relationship between race populations and violent crime? In my study, A Geospatial Study of Violent Crimes in the USA: The Race Factor, I examine this in detail. The study defined a violent crime as murder, rape, robbery, assault, and drugs. To begin the study, I collected all violent crime rates per county, percent of population per county, percent of population of whites and blacks per county from years 2000-2008.
After collecting the data, my first round analysis consisted of determining cluster locations in the United States where the likelihood of a crime was higher.  This process is done using the statistical software program SatScan. The first round analysis consisted of maps that took in consideration the space and time-space.
The first maps had many clusters in the United States; the most likely cluster was located in Baltimore Maryland. There also were large secondary clusters in the California and Florida regions.
The second round analysis consisted of determining if the percent of African Americans was related to the crimes in these clusters. Using SAS to determine the predicted murders for each county considering this covariate, I found that many of the murder rates in the counties were not associated to the percent of African Americans in each county.  The most likely cluster in the county of Baltimore was not shown in the second round analysis map.  This may provide evidence that murders may not be associated with the percent of black population.

Elizabeth Stanwyck, University of Maryland, A Meta-Analytical Approach for Examining the Effect of Ambient Air Pollution on Children's HealtThere have been numerous studies seeking to establish an association between air pollution and children's adverse health outcomes, and the ultimate findings are often varied. Some studies find a statistically significant association between an increase in a specific pollutant and an adverse health effect in children, while other studies find non-significant association between the same pair of variables.
Because of the conflicting results of these studies, one often wonders about the final conclusions, and this leads naturally to a novel application of the so-called statistical meta-analysis whose primary objective is to integrate or synthesize the findings from independent and comparable studies.  We first review a very recent statistical meta-analysis paper by Weinmayr et al. (2010) dealing with studies on the effects of NO2 and PM10 on some aspects of children's health. Next we conduct our own meta-analysis focusing on the association between children's (binary) health outcomes (such as cough and respiratory symptoms) and four pollutants: PM10, NO2, SO2, and O3.  While we find a statistically significant association in the case of every pollutant,

Emmanuel Taylor, Center to Reduce Cancer Health Disparities (CRCHD) National Cancer Institute (NCI), The Uses/ Utility of Mathematics and Biostatistics in Improving Public Health
Efforts to improve public health and quality of life globally are driven by reliable and accurate information for planning, monitoring and evaluation of public health programs. The information needed as well as the assessment of the quality of such information are based on the application of mathematical techniques in real-life situations, hence bio-statistics. The speech will present how mathematical techniques and biostatistics are used for disease surveillance; needs assessment; program planning; monitoring and evaluation of the effectiveness of public health strategies; and policy formulation. The audience will be informed of current efforts within the U.S. Department of Health (DHHS) and the National Cancer Institute (NCI) as well as the challenges to ensure systematic collection, analysis and interpretation of reliable data for these purposes.

David Turner, Faulkner University, An Induction Formula Generator
Students are often introduced to mathematical induction with expressions such as 1 + 2 + ... + n = n(n + 1)/2.  Homework problems consist of proving such relationships by induction and sometimes also require the student to conjecture a formula for the sum before providing the induction proof.  This talk will consider sums of the type where the general term is a polynomial.  The formula for any such sum will be shown to be a linear combination of a particular subcollection of all such formulas.

Sheryl Zavertnik, University of West Florida, Homicide-Suicide in the State of Florida - A Cluster Analysis Using SaTScan
A homicide which is followed by a suicide is a rare and deadly event in which a person kills

another and then commits suicide shortly after the homicide.  Currently, Dr. F. Stephen Bridges, Professor of Community Health Education at The University of West Florida, is conducting an extensive study on homicide-suicide in the state of Florida for the 1990-2007 time period.  This ground-breaking research will provide the first detailed study of this phenomenon in the state.  This proseminar study is the initial statistical analysis of the data which Dr. Bridges has compiled thus far in his study. The homicide-suicide data consists of 457 total cases in the 67 counties in Florida during the 18 year period from 1990–2007.   Using SaTScan, software which analyzes spatial, temporal and space-time data using the spatial, temporal, or space-time scan statistics, the existence of statistical clusters of homicide-suicide was examined.  The purely spatial analysis revealed a twelve county cluster in Central Florida for the period 1990-2007. The relative risk for this cluster of 1.47 indicates that the likelihood of a homicide-suicide in this region is 47% higher than the regions in Florida outside this cluster for this time period.  The twelve counties within the cluster were then compared with the counties outside the cluster to explore differences in median income, population density and percent population over age 65.

Zhoggang Zeng, Northeastern Illinois University, Designing Numerical Algorithms for Algebraic Computations
Algebraic computation is fundamental in scientific computing, where a cleverly designed algorithm can have a profound impact. There are many challenges and opportunities in developing numerical algorithms for solving algebraic problems.  Particularly, numerical computation in polynomial algebra emerges as a fast growing area of studies in recent years. This talk presents case studies and some successful strategies in numerical algebraic computations.

Chenhua Zhang, University of Southern Mississippi, Heavy Tail Distribution with Application in Shot Noise Sequence
Heavy tail distribution is used to study systems whose behavior is mainly governed by large values. This is different with many stable systems whose behavior is determined largely by an averaging effect. Shot noise processes are flexible models, which are capable of capturing stochastic features for a variety of natural phenomena. The asymptotic property of a shot noise sequence are considered, where the marginal distribution of the generating sequence is regularly varying at infinity with negative index.