Mathematics Commons^™

17. Psychology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

19. Zoology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

06. Computer Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

03. Biology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

05. Chemistry, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

10. Forensic Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

12. Kinesiology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

15. Pharmacy, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

18. Statistics, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

Social Aggregation In Pea Aphids: Experiment And Random Walk Modeling, Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Matthew Lam '15, Andrew J. Bernoff, Chad M. Topaz

All HMC Faculty Publications and Research

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. …

Creating An Interdisciplinary Research Course In Mathematical Ecology, Glenn Ledder, Brigitte Tenhumberg

School of Biological Sciences: Faculty Publications

An integrated interdisciplinary research course in biology and mathematics is useful for recruiting students to interdisciplinary research careers, but there are difficulties involved in creating and implementing it. We describe the genesis, objectives, design policies, and structure of the Research Skills in Theoretical Ecology course at the University of Nebraska–Lincoln and discuss the difficulties that can arise in designing and implementing interdisciplinary courses.

An Interdisciplinary Research Course In Theoretical Ecology For Young Undergraduates, Glenn Ledder, Brigitte Tenhumberg, G. Travis Adams

School of Biological Sciences: Faculty Publications

As part of an interdepartmental effort to attract promising young students to research at the interface between mathematics and biology, we created a course in which groups of recent high school graduates and first-year college students conducted a research project in insect population dynamics. The students set up experiments, collected data, used the data to develop mathematical models, tested their models against further experiments, and prepared their results for dissemination. The course was self-contained in that the lecture portion developed the mathematical, statistical, and biological background needed for the research. A special writing component helped students learn the principles of …

Identifying Requirements For The Invasion Of A Tick Species And Tick-Borne Pathogen Through Ticksim, Holly Gaff, Robyn Nadolny

Biological Sciences Faculty Publications

Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the success of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and …

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Biology Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Department of Math & Statistics Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Volume 04, Matt Szemborski, Phillip Van Ness, Sarah Croughwell, Sarah Mayfield, Alyssa Strackbein, Marley Kimmel, Stephanie Skipp, Jamie Yurasits, Katherine Taggart, Alex Leonhart, Kristen Rawls, Andrew Armes, Amanda Haymens, Allison Paqlowski, Erica May, Stephanie Lane, Luke Acree, Cassandra L. Wilson, Stephanie Pishock, Erica Hopson, K. Juston Osborne, Katheryn Grayson, Kyle Fowlkes, Jessica Cox, Kaity Byrum, John-Harwood Scott, Ashley Johnson, Samantha Hockman, Emily Staskiel, Nancy Macdonald, R. Kruger Bressin, Benjamin P. Bilodeau, Andrea Irby, Kristin Macquarrie, Sarah Bietsch, Elizabeth Bednar

Incite: The Journal of Undergraduate Scholarship

Please note that part of pages 92-95 are redacted, in the digital copy, due to a misprint of the original printed article.

Introduction from Dean Dr. Charles Ross

The Internal Other: Transculturation and Postcolonial Magical Realism in Rushdie’s Midnight’s Children by Matt Szemborski

Photography by Phillip Van Ness

Photography “Waterfall” by Sarah Croughwell

Romancing the Bite: Statistical Analysis of Young Adult Vampire Novels by Sarah Mayfield

Photography by Alyssa Strackbein

Photography by Marley Kimmel

Wine and Society in the Viceroyalty of Peru by Stephanie Skipp

Analysis of Claud Monet’s Impression, Sunrise by Jamie Yurasits

Exploring Meaning: The Lindisfarne Gospels by …

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

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.

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; …

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 …