Mathematics Commons^™

Modeling Mortality Rates For Leukemia Between Men And Women In The United States, Blessed Quansah

UNLV Theses, Dissertations, Professional Papers, and Capstones

Leukemia related deaths increased dramatically over the last forty years. Leukemia is a malignant disease or cancer of the bone marrow and blood. It is characterized by the uncontrolled accumulation of blood cells. Leukemia is divided into two categories: myelogenous or lymphocytic, each of which can be acute or chronic. The terms, myelogenous or lymphocytic denote the cell type involved.

In this thesis, the proposed modeling techniques are applied to leukemia deaths data from the Surveillance Epidemiology and End Results (SEER). In particular, annual deaths data from 1969 to 2007 are used in the data analysis, which includes three major …

Monitoring Radiation Use In Cardiac Fluoroscopy Imaging Procedures, Nathaniel Stevens, S H. Steiner, I R. Smith, R J. Mackay

Mathematics

Objective: Timely identification of systematic changes in radiation delivery of an imaging system can lead to a reduction in risk for the patients involved. However, existing quality assurance programs involving the routine testing of equipment performance using phantoms are limited in their ability to effectively carry out this task. To address this issue we propose the implementation of an ongoing monitoring process that utilizes procedural data to identify unexpected large or small radiation exposures for individual patients, as well as to detect persistent changes in the radiation output of imaging platforms.

Methods: Data used in this study were obtained from …

2011-2012 Unlv Mcnair Journal, Cyndy Anang, Sajar Camara, Pamela Cornejo, Carla Antonieta Farcello, Ilse Anahi Garcia, Natiera Magnuson, William L. Mccurdy, Lorena Munoz, Maxym V. Myroshnychenko, Ricardo Rios, Theodore Waldeck, Barbara Wallen, Ana Zuniga, Brenda M. Aguilar, Tiffany Alexandra Alvarez, Daniel N. Erosa, Paige C. Espinosa, Carla Antonieta Farcello, Julienne Jochel Paraiso, Nathaniel Derek Phillipps, Carmen Vallin, Jacent N. Wamala, Ernesto Zamora-Ramos

McNair Journal

Journal articles based on research conducted by undergraduate students in the McNair Scholars Program

Table of Contents

Biography of Dr. Ronald E. McNair

Statements:

Dr. Neal J. Smatresk, UNLV President

Dr. Juanita P. Fain, Vice President of Student Affairs

Dr. William W. Sullivan, Associate Vice President for Retention and Outreach

Mr. Keith Rogers, Deputy Executive Director of the Center for Academic Enrichment and Outreach

McNair Scholars Institute Staff

The Dynamics Of Integrate-And-Fire: Mean Vs. Variance Modulations And Dependence On Baseline Parameters, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

The leaky integrate-and-fire (LIF) is the simplest neuron model that captures the essential properties of neuronal signaling. Yet common intuitions are inadequate to explain basic properties of LIF responses to sinusoidal modulations of the input. Here we examine responses to low - and moderate-frequency modulations of both the mean and variance of the input current and quantify how these responses depend on baseline parameters. Across parameters, responses to modulations in the mean current are low pass, approaching zero in the limit of high frequencies. For very low baseline firing rates, the response cutoff frequency matches that expected from membrane integration. …

Optimal Control Applied To A Discrete Time Influenza Model, Paula Andrea Gonzalez Parra

Open Access Theses & Dissertations

For the last decades, mathematical epidemiological models have been used to understand the dynamics of infectious diseases and guide public health policy.

In particular, several continuous models have been considered to study influenza outbreaks and their controls policies. However, most epidemiological data is discrete; therefore, a discrete formulation is more convenient to compare collected data with the output of the model. We introduce a discrete time model in order to study optimal control strategies for influenza transmission.

In our model, we divide the population into four classes: susceptible, infectious, treated, and recovered individuals.

In particular, we evaluate the potential effect …

Volume 03, Cheryl Peck, Charles Hoever, Longwood Theater Department, Brittany Anderson, J. Ervin Sheldon, Richard Hayden, Yuri Calustro, Candice Fleming, Rebecca Franklin, Ashley Yocum, Danielle M. Jagoda, Cristina M. Valdivieso, Jameka Jones, Amy Ellis, Ashley Maser, Erikk Shupp, Jamie Yurasits, Joshua Davis, Alexander Leonhart, Kenny Wolfe, Sally Meadows, J. Haley, Amy Jackson, Morgan Howard, Adrienne Heinbaugh, Melissa Dorton, Ciarra Stalker

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Little Shop of Horrors by Longwood Theater Department

Who Has the Hottest Hotsauce in Farmville: A Quantitative Comparison of Sauces from Local Restaurants by Cheryl Peck and Charles Hoever

Precipitation Effects on the Growth of White Oaks and Virginia Pines on the Mt. Vernon Plantation by Brittany Anderson

Design and Synthesis of Novel Ion Binding Molecules for Self-Assembly and Sensing Applications by J. Ervin Sheldon

A Statistical Analysis of Algorithms for Playing SameGame by Richard Hayden

Intersecting Cylinders at Arbitrary Angles by Yuri Calustro

Putting a Foot in the Revolving Door: Strategies for Reducing …

Modeling Super-Spreading Events For Sars, Thembinkosi P. Mkhatshwa

Theses, Dissertations and Capstones

One of the intriguing characteristics of the 2003 severe acute respiratory syndrome (SARS) epidemics was the occurrence of super spreading events (SSEs). Super-spreading events for a specific infectious disease occur when infected individuals infect more than the average number of secondary cases. The understanding of these SSEs is critical to under- standing the spread of SARS. In this thesis, we present a modification of the basic SIR (Susceptible - Infected - Removed) disease model, an SIPR (Susceptible - Regular Infected - Super-spreader - Removed) model, which captures the effect of the SSEs.

An Examination Of The Association Of Selected Toxic Metals With Total And Central Obesity Indices: Nhanes 99-02, Miguel A. Padilla, Mai Elobeid, Douglas M. Ruden, David B. Allison

Psychology Faculty Publications

It is conceivable that toxic metals contribute to obesity by influencing various aspects of metabolism, such as by substituting for essential micronutrients and vital metals, or by inducing oxidative stress. Deficiency of the essential metal zinc decreases adiposity in humans and rodent models, whereas deficiencies of chromium, copper, iron, and magnesium increases adiposity. This study utilized the NHANES 99-02 data to explore the association between waist circumference and body mass index with the body burdens of selected toxic metals (barium, cadmium, cobalt, cesium, molybdenum, lead, antimony, thallium, and tungsten). Some of the associations were significant direct relationships (barium and thallium), …

Operations Research Methods For Optimization In Radiation Oncology, M Ehrgott, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

Operations Research has a successful tradition of applying mathematical analysis to a wide range of applications, with one of the burgeoning areas of growth being in medical physics. The original application was in the optimal design of the influence map for a radiotherapy treatment, a problem that has continued to receive attention. However, operations research has been applied to other clinical problems like patient scheduling, vault design, and image alignment. The overriding theme of this article is to present how techniques in operations research apply to clinical problems, which we accomplish in three parts. First, we present the perspective from …

A Clustering Approach For Optimizing Beam Angles In Imrt Planning, Gino J. Lim, Allen Holder, Josh Reese

Mathematical Sciences Technical Reports (MSTR)

In this paper we introduce a p-median problem based clustering heuristic for selecting efficient beam angles for intensity-modulated radiation therapy. The essence of the method described here is the clustering of beam angles according to probability that an angle will be observed in the final solution and similarities among different angles and the selection of a representative angle from each of the p resulting cluster cells. We conduct experiments using several combinations of modeling parameters to find the conditions where the heuristic best performs. We found a combination of such parameters that outperformed all other parameters on three of the …

Confidence Intervals For The Ratio Of Two Exponential Means With Applications To Quality Control, James Albert Polcer,Iii

Student Research Conference Select Presentations

We considered the problem of statistical quality control based on the ratio of two population means. We restrict the discussion for two exponential rates, which are commonly used for modeling failure times of components, machines, or systems. Closed form expressions via the moment generation function (MGF) technique will be presented, and numerical examples will be shown using engineering data sets.

Volume 02, Joseph A. Mann, Kathryn J. Greenly, Scott E. Jenkins, Andrew E. Puckette, Daniel M. Honey, Jeffery P. Ravenhorst, Jamie Elizabeth Mesrobian, Thomas Scott, Jay Crowell, Sarah Spangenberg, Amy S. Eason, Kenny Wolfe, Liz Hale, Rachel Bouchard, Will Semonco, Carley York, Ryan Higgenbothom, Adrienne Heinbaugh, Melissa Dorton, Madeline Hunter, June Ashmore, Clark Barkley, Jay Haley

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Mike's Nite: New Jazz for an Old Instrument by Joseph A. Mann

Investigation of the use of Cucumis Sativus for Remediation Of Chromium from Contaminated Environmental Matrices: An Interdisciplinary Instrumental Analysis Project by Kathryn J. Greenly, Scott E. Jenkins, and Andrew E. Puckette

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Scott Jenkins

Building and Measuring Scalable Computing Systems by Daniel M. Honey and Jeffery P. Ravenhorst

Nomini Hall: A Case Study in the Use of Archival Resources as Guides for Excavation at An Archaeological Site by …

Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker

Pomona Faculty Publications and Research

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of a drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of a partial differential equations. The predictions of both models show good qualitative …

An Analysis Of Drug Dissolution Rates In The Usp 24 Type 2 Apparatus, David Mcdonnell, Brendan Redmond, Deirdre M. D'Arcy, Anne Marie Healy, Owen Corrigan

Articles

This paper applies boundary layer theory to the process of drug dissolution in the USP 24, Type 2 Apparatus. The mass transfer rate from the top flat surface of a compact in various positions within the device is evaluated by means of a Pohlhausen integral method.

Health Literacy In The Mathematics Classroom: The Iowa Core Curriculum As An Opportunity To Deepen Students’ Understanding Of Mathematics, Elana Joram, Susan Roberts-Dobie, Nadene Davidson

Faculty Publications

By 2012, all high schools in Iowa will be required to incorporate the new Iowa Core Curriculum, followed by elementary and middle schools in 2014 (Iowa Department of Education, 2009). The Iowa Core Curriculum addresses the question: "How is Iowa's educational system preparing our youth for successful lives in the 21st-century global environment?" (Davidson, 2009). It consists of core content standards, and identifies essential concepts and skills for content areas. The Iowa Core Curriculum also includes the ―21st Century Skills‖ of ―health, financial, technology, and civic literacy, and employability skills. These skills are to be infused into existing subject matter …

Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance …

Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter

Mathematical Sciences Technical Reports (MSTR)

Optimally designing radiotherapy and radiosurgery treatments to increase the likelihood of a successful recovery from cancer is an important application of operations research. Researchers have been hindered by the lack of academic software that supports head-to-head comparisons of different techniques, and this article addresses the inherent difficulties of designing and implementing an academic treatment planning system. In particular, this article details the algorithms and the software design of Radiotherapy optimAl Design (RAD).

Quasigeometric Distributions And Extra Inning Baseball Games, Darren B. Glass, Philip J. Lowry

Math Faculty Publications

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and …

Volume 01, Jessica Fields, Stephanie Neeley, Derek W. Hambright, Mary E. Lehman, Andrew R. Grzankowski, Zachary Johnson, Boone M. Prentice, Ashley M. Swandby, Victoria Morgan, Katie Williamson, Kristine G. Bender, Katelyn N. Romaine, D. Nicole Swann, Jessica Fox, Mike Mcateer, Alex Grabiec, Laura Nodtvedt, Nick Costa, Rachel Wolfe, Zack Dalton

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Three Decades of Digging: Undergraduate Archeology at Longwood by Jessica Fields and Stephanie Neeley

Interactions of Allelopathy and Heat Stress in Plants by Derek W. Hambright and Mary E. Lehman

Inertial Electrostatic Confinement D-D Fusion Device: Construction and Simulation by Andrew R. Grzankowski

Shackled Nim by Zachary Johnson

Development of GC-MS and Chemometric Methods for the Analysis of Accelerants in Arson Cases by Boone M. Prentice

A Comparison of Image Analysis Methods in cDNA Microarrays by Ashley M. Swandby

Perceived Sexual Activity of Short and Long-Term Relationships by Victoria Morgan and Katie Williamson

Elderly …

A Comparison Of Different Methods For Predicting Cancer Mortality Counts At The State Level, Corinne Wilson

Virginia Journal of Science

Cancer is a major health issue in the United States. Reliable estimates of yearly cancer mortality counts are essential for resourcing and planning. The American Cancer Society has used several methods of forecasting to estimate the future cancer burden and researchers are continually working to develop new methods with improved performance. There have been studies comparing different models for predicting the US cancer mortality counts. This study explores and compares several different models for cancer mortality count predictions at the state level, principally for the state of Virginia. Results of the comparisons appear to show the final improved model to …

A Spatial Sirs Boolean Network Model For The Spread Of H5n1 Avian Influenza Virus Among Poultry Farms, Alexander Kasyanov, Leona Kirkland, Mihaela Teodora Matache

Mathematics Faculty Proceedings & Presentations

To predict the spread of Avian Influenza we propose a synchronous Susceptible-Infected-Recovered-Susceptible (SIRS) Boolean network of poultry farms, using probabilistic Boolean rules. Gravity models from transportation theory are used for the probability of infection of a node in one time step, taking into account farm sizes, distances be- tween farms, and mean distance travelled by birds. Basic reproduction numbers are computed analytically and numerically. The dynamics of the network are analyzed and various statistics considered such as number of infected nodes or time until eradication of the epidemic. We conclude that mostly when large farms (eventually) become infected the epidemic …

Spatial Tumor-Immune Modeling, Lisette G. De Pillis, D G. Mallet, Ami E. Radunskaya

All HMC Faculty Publications and Research

In this paper, we carry out an examination of four mechanisms that can potentially lead to changing morphologies in a growing tumor: variations in nutrient consumption rates, cellular adhesion, excessive consumption of nutrients by tumor cells and immune cell interactions with the tumor. We present numerical simulations using a hybrid PDE-cellular automata (CA) model demonstrating the effects of each mechanism before discussing hypotheses about the contribution of each mechanism to morphology change.

Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore

All HMC Faculty Publications and Research

In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …

Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in …

Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 2, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence.

Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm …

Introduction To N-Adaptive Fuzzy Models To Analyze Public Opinion On Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

“AIDS is not simply a physical malady, it is also an artifact of social and sexual transgression, violated taboo, fractured identity—political and personal projections. Its key words are primarily the property of the powerful. AIDS: Keywords – is my attempt to identify and contest some of the assumptions underlying our current ‘knowledge’. In this effort I am joined by many AIDS activists including people living with AIDS— Acquired Immuno Deficiency Syndrome. “A syndrome is a pattern of symptoms pointing to a “morbid state” which may or may not be caused by infectious agents; a disease, on the other hand is, …

Interdependency Of Pharmacokinetic Parameters: A Chicken-And-Egg Problem? Not!, Reza Mehvar

Pharmacy Faculty Articles and Research

Pharmacokinetic (PK) software packages are widely used by scientists in different disciplines to estimate PK parameters. However, their use without a clear understanding of physiological parameters affecting the PK parameters and how different PK parameters are related to each other may result in erroneous interpretation of data. Often, mathematical relationships used for the estimation of PK parameters obscure the true physiological relationships among these parameters, prompting a discussion of which parameter came first and giving the appearance of the-chicken-and-the-egg dilemma. In this article, the author attempts to show how different PK parameters are related to physiological parameters and each other …

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

Convergence Analysis Of Mcmc Method In The Study Of Genetic Linkage With Missing Data, Diana Fisher

Theses, Dissertations and Capstones

Computational infeasibility of exact methods for solving genetic linkage analysis problems has led to the development of a new collection of stochastic methods, all of which require the use of Markov chains. The purpose of this work is to investigate the complexities of missing data in pedigree analysis using the Monte Carlo Markov Chain (MCMC) method as compared to the exact results. Also, we attempt to determine an association between missing data in a familial pedigree and the convergence to stationarity of a descent graph Markov chain implemented in the stochastic method for parametric linkage analysis.

In particular, we will …

I Don't Care If I Ever Get Back: Marathons Lasting 20 Or More Innings, Phil Lowry, Darren B. Glass

Math Faculty Publications

This article looks at marathon games of baseball. For purposes of this article, a marathon is defined as a game lasting 20 or more innings. In my research I have discovered 341 marathons. These games are hard to find. Leagues either keep no records, or keep track only of their longest game; only the Texas League keeps records on all marathons. Nobody has ever before explored such questions as: What is the probability a game will go x number of innings? How often should we expect a marathon of 20 or more innings, or 40 or more innings? What is …