Mathematics Commons^™

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 …

Foundations And Interpretations Of Quantum Mechanics, Cory Johnson

Honors Theses

The first famous thought experiment of Einstein gives rise to his theories of relativity, the bedrock of modern astrophysics and cosmology. His second famous thought experiment begins the investigation into the foundations of quantum mechanics. It leads to a paradox, inspiring various 'no-go' theorems proven by Bell, Kochen, and Specker. Physicists and philosophers worldwide become increasingly dissatisfied with the probabilistic complementarity interpretation (Born-Bohr) and eventually offer their own accounts of the theory. By the end of the 20th century two alternative approaches stand out as the best candidates: Both the hidden variables interpretation (de Broglie-Bohm) and the many worlds interpretation …

Effects Of Context Of Natural And Artifactual Objects On Categorization, Linsey Walker

Honors Theses

Categorization of animals and vehicles in different contexts was investigated in three experiments using event related potentials (ERPs). The presence of a background and congruency of the background in relation to the object were both manipulated in order to determine the effects of context on visual processing. In Experiment 1, adults were presented with images of animals and vehicles in two conditions: situated in a congruent context (e.g. an animal in a field) and in the absence of a context (an animal in a white homogeneous background). In experiment 2, adults were presented with images of animals and vehicles in …

The Shapley Value Of Phylogenetic Trees, Claus-Jochen Haake, Akemi Kashiwada '05, Francis E. Su

All HMC Faculty Publications and Research

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space …

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 …

Modeling Algae Self-Replenishment, V. S. Manoranjan, Miguel A. Olmos Gomez, R. Corban Harwood

Faculty Publications - Department of Mathematics

This paper presents a sunlight-dependent algae growth model. Driven by the circumstances surrounding Lake Chapala, Mexico, this theoretical model is an endeavor to understand the resilient sustainability of algae that threatens the area’s ecosystem. In this paper, free-floating algae (phytoplankton) are treated as two distinct populations according to their location in the body of water: the vibrant sunlit upper region and the stagnate lower region where photosynthesis is not possible. The numerical solution for the model is analyzed and results are discussed in light of previous studies and the state of Lake Chapala.

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 …

Improved Constrained Global Optimization For Estimating Molecular Structure From Atomic Distances, Terri Marie Grant

Mathematics & Statistics Theses & Dissertations

Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance …

Ua66 2007 Student Awards Ceremony, Wku Ogden College Of Science & Engineering

WKU Administration Documents

Program recognizing Ogden College students with brief list of activities for each student.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

A Proposal For Robust Temperature Compensation Of Circadian Rhythms, Christian I. Hong, Emery D. Conrad, John J. Tyson

Dartmouth Scholarship

The internal circadian rhythms of cells and organisms coordinate their physiological properties to the prevailing 24-h cycle of light and dark on earth. The mechanisms generating circadian rhythms have four defining characteristics: they oscillate endogenously with period close to 24 h, entrain to external signals, suffer phase shifts by aberrant pulses of light or temperature, and compensate for changes in temperature over a range of 10°C or more. Most theoretical descriptions of circadian rhythms propose that the underlying mechanism generates a stable limit cycle oscillation (in constant darkness or dim light), because limit cycles quite naturally possess the first three …

Strokes Of Existence: The Connection Of All Things, Mari Gorman

Graduate Student Publications and Research

Acted or real—and all life is real whether one is acting or not—the common denominator and consistent, ubiquitous reality of life and all behavior is that it manifests in the form of relationships on all scales. But what is a relationship? Until now, the answer to this question has not been sufficiently known. As a result of many years of empirical research that began with the aim of discovering what is going on in a gifted actor when s/he is playing a character that can be observed and experienced as a living, intuitive being, and based on the knowledge that …

A Model Of Dna Knotting And Linking, Erica Flapan, Dorothy Buck

Pomona Faculty Publications and Research

We present a model of how DNA knots and links are formed as a result of a single recombination event, or multiple rounds of (processive) recombination events, starting with an unknotted, unlinked, or a (2,m)-torus knot or link substrate. Given these substrates, according to our model all DNA products of a single recombination event or processive recombination fall into a single family of knots and links.

A Robust Measure Of Correlation Between Two Genes On A Microarray, Johanna S. Hardin, Aya Mitani '06, Leanne Hicks, Brian Vankoten

Pomona Faculty Publications and Research

Background

The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing …

World Bank -Cpa Conflict: The Struggle To Define Human Rights And Development In The Philippines, Adam B. Robbins

Honors Theses

This thesis analyzes the interactions between the World Bank (hereafter, the Bank) and the Cordillera Peoples Alliance (CPA), an indigenous and environmental advocacy group based in the Cordillera region of Luzon, in the Philippines. Using data gathered through both text-based and participatory research methods, I analyze the discursive relationship and violent confrontations between the two organizations. Conflicting development and human rights values cause the majority of these conflicts. I focus on how each organization enacts development and human rights, and how this leads to conflict. Ultimately, I intend for this thesis to offer practical guidance for the reader involved in …

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Analyzing Dna Microarrays With Undergraduate Statisticians, Johanna S. Hardin, Laura Hoopes, Ryan Murphy '06

Pomona Faculty Publications and Research

With advances in technology, biologists have been saddled with high dimensional data that need modern statistical methodology for analysis. DNA microarrays are able to simultaneously measure thousands of genes (and the activity of those genes) in a single sample. Biologists use microarrays to trace connections between pathways or to identify all genes that respond to a signal. The statistical tools we usually teach our undergraduates are inadequate for analyzing thousands of measurements on tens of samples. The project materials include readings on microarrays as well as computer lab activities. The topics covered include image analysis, filtering and normalization techniques, and …

The Stepping Stone Model, Ii: Genealogies And The Infinite Sites Model, Submitted, Iljana Zähle, J. Theodore Cox, Richard Durrett

Mathematics - All Scholarship

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman’s coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by …

A High -Order Finite Difference Method For Solving Bioheat Transfer Equations In Three-Dimensional Triple -Layered Skin Structure, Haofeng Yu

Doctoral Dissertations

Investigations on instantaneous skin burns are useful for an accurate assessment of burn-evaluation and for establishing thermal protections for various purposes. Meanwhile, hyperthermia with radiation is important in the treatment of cancer, and it is essential for developers and users of hyperthermia systems to predict, and interpret correctly the biomass thermal and vascular response to heating. In this dissertation, we employ the well-known Pennes' bioheat transfer equation to predict the degree of skin burn and the temperature distribution in hyperthermia cancer treatment.

A fourth-order compact finite difference scheme is developed to solve Pennes' bioheat transfer equation in a three-dimensional single …