Mathematics Commons^™

A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao

Mathematics & Statistics Faculty Publications

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R₀ = 1 for the combined human-environment epidemiological …

An Epidemiological Model Of Rift Valley Fever With Spatial Dynamics, Tianchan Niu, Holly D. Gaff, Yiannis E. Papelis, David M. Hartley

Biological Sciences Faculty Publications

As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of …

The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance

A Mathematician Weighs In On The Evolution Debate, Kris H. Green

Journal of Humanistic Mathematics

There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.

Mathematical Modeling And Dynamical Analysis Of The Operation Of The Hypothalamus - Pituitary - Thyroid (Hpt) Axis In Autoimmune (Hashimoto's) Thyroiditis, Balamurugan Pandiyan

Dissertations (1934 -)

This thesis is a mathematical modeling study of the operation of the negative feedback control through the hypothalamus-pituitary- thyroid (HPT) axis in autoimmune (Hashimoto's) thyroiditis. Negative feedback control through the HPT axis is a mechanism in which the high levels of thyroid hormone; free thyroxine (FT4) in the blood inhibits the secretion of the pituitary hormone, thyroid stimulating hormone (TSH) into the blood. Similarly, the low levels of free thyroxine (FT4) sensed by the pituitary gland and then it secretes thyroid stimulating hormone (TSH) into the blood. Autoimmune (Hashimoto's) thyroiditis is a disease in which the immune system turns against …

Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.

A Predictive Model Which Uses Descriptors Of Rna Secondary Structures Derived From Graph Theory., Alissa Ann Rockney

Electronic Theses and Dissertations

The secondary structures of ribonucleic acid (RNA) have been successfully modeled with graph-theoretic structures. Often, simple graphs are used to represent secondary RNA structures; however, in this research, a multigraph representation of RNA is used, in which vertices represent stems and edges represent the internal motifs. Any type of RNA secondary structure may be represented by a graph in this manner. We define novel graphical invariants to quantify the multigraphs and obtain characteristic descriptors of the secondary structures. These descriptors are used to train an artificial neural network (ANN) to recognize the characteristics of secondary RNA structure. Using the ANN, …

Analysis Of Biological Features Associated With Meiotic Recombination Hot And Cold Spots In Saccharomyces Cerevisiae, Loren Hansen, Nak-Kyeong Kim, Leonardo Mariño-Ramírez, David Landsman

Mathematics & Statistics Faculty Publications

Meiotic recombination is not distributed uniformly throughout the genome. There are regions of high and low recombination rates called hot and cold spots, respectively. The recombination rate parallels the frequency of DNA double-strand breaks (DSBs) that initiate meiotic recombination. The aim is to identify biological features associated with DSB frequency. We constructed vectors representing various chromatin and sequence-based features for 1179 DSB hot spots and 1028 DSB cold spots. Using a feature selection approach, we have identified five features that distinguish hot from cold spots in Saccharomyces cerevisiae with high accuracy, namely the histone marks H3K4me3, H3K14ac, H3K36me3, and H3K79me3; …

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

Weighted Scores Method For Regression Models With Dependent Data, Aristidis K. Nikoloulopoulos, Harry Joe, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a "weighted scores method", which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our …

Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam

Mathematics & Statistics Faculty Publications

(First Paragraph) Charles Darwin's 1859 work On the Origin of the Species contained no equations. But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart's new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) …

Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod

All Graduate Theses, Dissertations, and Other Capstone Projects

The purpose of the knowledge-based system is to predict the rehabilitation timeline of a patient in physical therapy for a total knee replacement. All patients have various attributes that contribute to their rehabilitation rate such as: weight, gender, smoking habit, medications, physical ability, or other medical problems. A combination of any one or several of these attributes will affect the recovery process. The proposed FRTP (Fuzzy Rehabilitation Timeline Predictor) is a fuzzy data mining model that can predict the recovery length of a patient in physical therapy for a total knee replacement and provide feedback to experts for revision of …

Class Discovery And Prediction Of Tumor With Microarray Data, Bo Liu

All Graduate Theses, Dissertations, and Other Capstone Projects

Current microarray technology is able take a single tissue sample to construct an Affymetrix oglionucleotide array containing (estimated) expression levels of thousands of different genes for that tissue. The objective is to develop a more systematic approach to cancer classification based on Affymetrix oglionucleotide microarrays. For this purpose, I studied published colon cancer microarray data. Colon cancer, with 655,000 deaths worldwide per year, has become the fourth most common form of cancer in the United States and the third leading cause of cancer - related death in the Western world. This research has been focuses in two areas: class discovery, …

Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.

"Toward Integration: From Quantitative Biology To Mathbio-Biomath?", Pat Marsteller, Lisette G. De Pillis, Ann Findley, Karl Joplin, John Pelesko, Karen Nelson, Katerina Thompson, David Usher, Joseph Watkins

All HMC Faculty Publications and Research

In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Department of Math & Statistics Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Biology Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

"Beyond Bio2010: Celebration And Opportunities" At The Intersection Of Mathematics And Biology, John R. Jungck, Holly D. Gaff, Adam P. Fagen, Jay B. Labov

Biological Sciences Faculty Publications

With this special edition of CBE-LSE, which focuses on connections between and integration of the biological and mathematical sciences, it is especially fitting that we report on an important symposium, Beyond BIO2010: Celebration and Opportunities,1 which was held at the National Acad- emy of Sciences (NAS) in Washington, D.C. on May 21–22, 2010. This symposium was organized to assess what progress has been made in addressing the challenges and recommendations in the National Research Council’s (NRC) report: BIO2010: Transforming Undergraduate Education for Future Research Biologists (NRC, 2003a). Most of the presen- tations and posters at this event emphasized the increasing …

Mathematical Manipulative Models: In Defense Of "Beanbag Biology", John R. Jungck, Holly Gaff, Anton E. Weisstein

Biological Sciences Faculty Publications

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational …

Bioinformatics Across The Sciences, Nigel Yarlett

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

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 …

Mathematical Biology At An Undergraduate Liberal Arts College, Stephen C. Adolph, Lisette G. De Pillis

All HMC Faculty Publications and Research

Since 2002 we have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper we describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities we have experienced.

Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, Jan Holly, Scott Wood, Gin Mccollum

Mathematics and Statistics Faculty Publications and Presentations

Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both the OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravito-inertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA …

A Decomposition Of The Pure Parsimony Problem, Allen Holder, Thomas M. Langley

Mathematical Sciences Technical Reports (MSTR)

We partially order a collection of genotypes so that we can represent the problem of inferring the least number of haplotypes in terms of substructures we call g-lattices. This representation allows us to prove that if the genotypes partition into chains with certain structure, then the NP-Hard problem can be solved efficiently. Even without the specified structure, the decomposition shows how to separate the underlying integer programming model into smaller models.

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 …

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen

Faculty Publications

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the …

At Least Four Distinct Circadian Regulatory Mechanisms Required For All Phases Of Rhythms In Mrna Amount, Sigrid Jacobshagen, Bruce Kessler, Claire Rinehart

Mathematics Faculty Publications

Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA abundance have been reported. These rhythms generally differ in amplitude and phase. First studies on circadian rhythms of transcription on a large scale are also emerging. We investigated to what extent the same circadian regulatory mechanism of transcription can give rise to rhythms in RNA amount that differ in phase solely based on a parameter that is not regulated by the circadian clock. Using a discrete-time approach, we modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. We …