Mathematics Commons^™

Merging Peg Solitaire In Graphs, John Engbers, Ryan Weber

Mathematics, Statistics and Computer Science Faculty Research and Publications

Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. The goal of the game is to reduce the number of pegs to one.

We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices x and z (with a hole on y) and merges them to …

High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus

Mathematics & Statistics ETDs

Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, …

A Perspective On The Challenges And Issues In Developing Biomarkers For Human Allergic Risk Assessments, Ying Mu, Dianne E. Godar, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran

Mathematics & Statistics ETDs

We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, …

Quantitative Skills And Reasoning (Armstrong), Patricia Brown, Joshua Lambert

Mathematics Grants Collections

This Grants Collection for Quantitative Skills and Reasoning was created under a Round Five ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

A Privacy Preserving Framework For Rfid Based Healthcare Systems, Farzana Rahman, Anwarul A. Bhuiyan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID (Radio Frequency IDentification) is anticipated to be a core technology that will be used in many practical applications of our life in near future. It has received considerable attention within the healthcare for almost a decade now. The technology’s promise to efficiently track hospital supplies, medical equipment, medications and patients is an attractive proposition to the healthcare industry. However, the prospect of wide spread use of RFID tags in the healthcare area has also triggered discussions regarding privacy, particularly because RFID data in transit may easily be intercepted and can be send to track its user (owner). In a …

Failure Of Care Acquisition: Identifying Risk Factors In American Health Disparities, Nicholas Downing, Mamunur Rashid

Student Research

We examined the effects of various demographic and socioeconomic risk factors that influence an adult's decision not to obtain medical care in the United States utilizing data from the 2015 National Health Interview Survey (NHIS). Bivariate analysis and multivariate logistic regression revealed that family income, insurance status and whether one worries about paying medical bills make individuals nearly 80% less likely to obtain care than their counterparts. This study provides evidence that certain risk factors, especially those directly related to one's socioeconomic status, may put individuals at greater risk for failure to obtain care. Interventions in policy may be needed …

Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.

Cybersecurity: Probabilistic Behavior Of Vulnerability And Life Cycle, Sasith Maduranga Rajasooriya

USF Tampa Graduate Theses and Dissertations

Analysis on Vulnerabilities and Vulnerability Life Cycle is at the core of Cybersecurity related studies. Vulnerability Life Cycle discussed by S. Frei and studies by several other scholars have noted the importance of this approach. Application of Statistical Methodologies in Cybersecurity related studies call for a greater deal of new information. Using currently available data from National Vulnerability Database this study develops and presents a set of useful Statistical tools to be applied in Cybersecurity related decision making processes.

In the present study, the concept of Vulnerability Space is defined as a probability space. Relevant theoretical analyses are conducted and …

A Direct D-Bar Method For Partial Boundary Data Electrical Impedance Tomography With A Priori Information, Melody Alsaker, Sarah J. Hamilton, Andreas Hauptmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges …

Symptom Levels In Care-Seeking Bangladeshi And Nepalese Adults With Advanced Cancer, Richard Love, Tahmina Ferdousy, Bishnu D. Paudel, Shamsun Nahar, Rumana Dowla, Mohammad Adibuzzaman, Golam Mushih Tanimul Ahsan, Miftah Uddin, Reza Selim, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Three-fourths of patients with advanced cancer are reported to suffer from pain. A primary barrier to provision of adequate symptom treatment is failure to appreciate the intensity of the symptoms patients are experiencing. Because data on Bangladeshi and Nepalese patients’ perceptions of their symptomatic status are limited, we sought such information using a cell phone questionnaire.

Methods

At tertiary care centers in Dhaka and Kathmandu, we recruited 640 and 383 adult patients, respectively, with incurable malignancy presenting for outpatient visits and instructed them for that single visit on one-time completion of a cell phone platform 15-item survey of questions …

Comparing Grounded Theory And Topic Modeling: Extreme Divergence Or Unlikely Convergence?, Eric P.S. Baumer, David Mimno, Shion Guha, Emily Quan, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Researchers in information science and related areas have developed various methods for analyzing textual data, such as survey responses. This article describes the application of analysis methods from two distinct fields, one method from interpretive social science and one method from statistical machine learning, to the same survey data. The results show that the two analyses produce some similar and some complementary insights about the phenomenon of interest, in this case, nonuse of social media. We compare both the processes of conducting these analyses and the results they produce to derive insights about each method's unique advantages and drawbacks, as …

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Physiological Health Parameters Among College Students To Promote Chronic Disease Prevention And Health Promotion, David R. Black, Daniel C. Coster, Samantha R. Paige

Mathematics and Statistics Faculty Publications

This study aimed to provide physiologic health risk parameters by gender and age among college students enrolled in a U.S. Midwestern University to promote chronic disease prevention and ameliorate health. A total of 2615 college students between 18 and 25 years old were recruited annually using a series of cross-sectional designs during the spring semester over an 8-year period. Physiologic parameters measured included body mass index (BMI), percentage body fat (%BF), blood serum cholesterol (BSC), and systolic (SBP) and diastolic (DBP) blood pressure. These measures were compared to data from NHANES to identify differences in physiologic parameters among 18-25 year …

Cox Processes For Visual Object Counting, Yongming Ma

Student Research Symposium

We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product …

Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

Weighted Distributions: A Brief Review, Perspective And Characterizations, Aamir Saghir, Gholamhossein G. Hamedani, Sadaf Tazeem, Aneeqa Khadim

Mathematics, Statistics and Computer Science Faculty Research and Publications

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship …

Joint Modelling Of Longitudinal Measurements And Time-To-Event Data : Application To Hiv Study, Mirna Walid Halawani

Theses, Dissertations and Culminating Projects

Longitudinal and survival data are frequently collected in biomedical studies. The research questions of interest in these studies often require separate analysis of the outcomes. But in many occasions interest also lies in studying their association structures, such as in biomarker research, where the clinical studies are designed to identify biomarkers with strong prognostic capabilities for event time outcomes. In the separate analyses, a linear mixed-effects model is used for modeling the longitudinal data to study the changing trend of the response overtime when controlling some covariates and a survival model is used to model the time-to-event data. A common …

Peptide Identification: Refining A Bayesian Stochastic Model, Theophilus Barnabas Kobina Acquah

Electronic Theses and Dissertations

Notwithstanding the challenges associated with different methods of peptide identification, other methods have been explored over the years. The complexity, size and computational challenges of peptide-based data sets calls for more intrusion into this sphere. By relying on the prior information about the average relative abundances of bond cleavages and the prior probability of any specific amino acid sequence, we refine an already developed Bayesian approach in identifying peptides. The likelihood function is improved by adding additional ions to the model and its size is driven by two overall goodness of fit measures. In the face of the complexities associated …

Eit Imaging Of Admittivities With A D-Bar Method And Spatial Prior: Experimental Results For Absolute And Difference Imaging, Sarah J. Hamilton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a …

Combinatorial Games On Graphs, Trevor K. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Combinatorial Games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games and some educational tools are presented which were developed by the author in the pursuit of the solution of these games.

Irrational Eigenvalues Of The Discrete Laplacian: A Study Of Simplical Complexes, Brian Bollen

Psychology

We study the behavior of eigenvalues of the discrete Laplacian of an abstract simplicial complex K when subdividing a single face of K . We show that if K is a simplex, performing this kind of restricted subdivision twice on a single face produces irrational eigenvalues for the discrete Laplacian.

Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding

Mathematics & Statistics ETDs

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …

Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado

Mathematics & Statistics ETDs

Cancer is a disease caused by mutations in normal cells. According to the National Cancer Institute, in 2016, an estimated 1.6 million people were diagnosed and approximately 0.5 million people died from the disease in the United States. There are many factors that shape cancer at the cellular and organismal level, including genetic, immunological, and environmental components. In this thesis, we show how mathematical modeling can be used to provide insight into some of the key mechanisms underlying cancer dynamics. First, we use mathematical modeling to investigate optimal homeostatic cell renewal in tissues such as the small intestine with an …

Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang

Mathematics & Statistics ETDs

Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. …

The Value Of A Win: Analysis Of Playoff Structures, Matthew Orsi

Honors Projects in Mathematics

The purpose of this Senior Capstone project is to analyze the distinctions between existing playoff systems. In particular, we are looking to analyze the differences between the standard single-elimination tournament (which the NCAA has used since the inception of the tournament) and other potential options: double-elimination and multiple game series. Popular sports such as Major League Baseball and the National Basketball Association all use multiple game series for their playoffs. This project will use probability theory and simulation to determine the likelihood of different seeds winning a championship as well as the expected number of victories by seed in each …

Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.

Regime Switching In Cointegrated Time Series, Bradley David Zynda Ii

Undergraduate Honors Capstone Projects

Volatile commodities and markets can often be difficult to model and forecast given significant breaks in trends through time. To account such breaks, regime switching methods allow for models to accommodate abrupt changes in behavior of the data. However, the difficulty often arises in beginning the process of choosing a model and its associated parameters with which to represent the data and the objects of interest. To improve model selection for these volatile markets, this research examines time series with regime switching components and argues that a synthesis of vector error correction models with regime switching models with ameliorate financial …

Deriving A Provisional Tolerable Intake For Intravenous Exposure To Silver Nanoparticles Released From Medical Devices, Laura C. Savery, Rene Vinas, Amber M. Nagy, Prachi Pradeep, Stephen Merrill, Subhas G. Malghan, Peter L. Goering, Ronald P. Brown

Mathematics, Statistics and Computer Science Faculty Research and Publications

Silver nanoparticles (AgNP) are incorporated into medical devices for their anti-microbial characteristics. The potential exposure and toxicity of AgNPs is unknown due to varying physicochemical particle properties and lack of toxicological data. The aim of this safety assessment is to derive a provisional tolerable intake (pTI) value for AgNPs released from blood-contacting medical devices. A literature review of in vivo studies investigating critical health effects induced from intravenous (i. v.) exposure to AgNPs was evaluated by the Annapolis Accords principles and Toxicological Data Reliability Assessment Tool (ToxRTool). The point of departure (POD) was based on an i. v. 28-day …