Mathematics Commons^™

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 …

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 …

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.

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 …

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 …

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, …

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 …

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 …

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 …

Advances And Applications Of Dezert-Smarandache Theory (Dsmt), Vol. 1, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning is a natural extension of the classical Dempster-Shafer Theory (DST) but includes fundamental differences with the DST. DSmT allows to formally combine any types of independent sources of information represented in term of belief functions, but is mainly focused on the fusion of uncertain, highly conflicting and imprecise quantitative or qualitative sources of evidence. DSmT is able to solve complex, static or dynamic fusion problems beyond the limits of the DST framework, especially when conflicts between sources become large and when the refinement of the frame of the problem under consideration …

Stage Based Interventions For Low Fat Diet With Middle School Students, Marilyn Frenn, Shelly Malin, Naveen K. Bansal

College of Nursing Faculty Research and Publications

Preventing obesity and cardiovascular disease at early ages is important; however, few effective interventions for early adolescents have been reported. In this study, low-income, culturally diverse students from an urban middle school (n = 60) received four classroom interventions with the use of a combined Health Promotion/Transtheoretical Model to control fat in diet and increase physical activity. A control group (n = 57) received the usual classroom education. Pretest percentage fat in diet was regressed on demographics, access to low-fat foods, perceived self-efficacy, benefits/barriers, and stage of change with results as proposed by the model [F(9,64) …

A Mathematical Model Of Immune Response To Tumor Invasion, Lisette De Pillis, Ami Radunskaya

All HMC Faculty Publications and Research

Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand expression create a significant barrier to tumor establishment in the mouse. Additionally, ligand transduced tumor cells stimulate protective immunity to tumor rechallenge. Based on the results of the Diefenbach experiments, we have developed a mathematical model of tumor growth to address some of the questions …

A Contrast-Based Neural Control System For Ant Navigation, Joanna R. Wares, Predrag-Peter Ilich, Daniel P. Dougherty

Department of Math & Statistics Faculty Publications

A mathematical model for a neural control system of ant locomotion was developed. Contrast-based detectors using excitation and inhibition were tuned to specific contrast orientations. A control system using multiple orientation contrast detectors was then developed and optimized for a model ant, which could move via a biased random walk. The system allowed sufficient control to guide the ant through various mazes.

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan

Department of Math & Statistics Faculty Publications

This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …