Mathematics Commons^™

Cross Faculty Collaboration In The Development Of An Integrated Mathematics And Science Initial Teacher Education Program, Sharon P. Fraser, Kim Beswick, Margaret Penson, Andrew Seen, Robert Whannell

Australian Journal of Teacher Education

This paper describes a collaborative project involving mathematicians, scientists and educators at an Australian university where an innovative initial teacher education (ITE) degree in mathematics/science was developed. The theoretical frameworks of identity theory and academic brokerage and their use in understanding the challenges associated with the early stages of collaborative projects is described. Data from reflections and interviews of the participants after involvement in the project from one to three years are presented to illustrate these challenges. The paper concludes with a description of the importance of the academic broker in overcoming identity challenges and facilitating cultural change for academics …

Aligning Best Practices In Student Success And Career Preparedness: An Exploratory Study To Establish Pathways To Stem Careers For Undergraduate Minority Students, Kimberly D. Kendricks, Anthony A. Arment, K. V. Nedunuri, Cadance A. Lowell

Journal of Research in Technical Careers

Undergraduate minority retention and graduation rates in STEM disciplines is a nationally recognized challenge for workforce growth and diversification. The Benjamin Banneker Scholars Program (BBSP) was a five-year undergraduate study developed to increase minority student retention and graduation rates at an HBCU. The program structure utilized a family model as a vehicle to orient students to the demands of college. Program activities integrated best K-12 practices and workforce skillsets to increase academic preparedness and career readiness. Findings revealed that a familial atmosphere improved academic performance, increased undergraduate research, and generated positive perceptions of faculty mentoring. Retention rates among BBSP participants …

Developmental Parameters Of A Southern Mountain Pine Beetle (Coleoptera: Curculionidae) Population Reveal Potential Source Of Latitudinal Differences In Generation Time, Anne E. Mcmanis, James A. Powell, Barbara J. Bentz

Mathematics and Statistics Faculty Publications

Mountain pine beetle (Dendroctonus ponderosae, Hopkins) is a major disturbance agent in pine ecosystems of western North America. Adaptation to local climates has resulted in primarily univoltine generation time across a thermally diverse latitudinal gradient. We hypothesized that voltinism patterns have been shaped by selection for slower developmental rates in southern populations inhabiting warmer climates. To investigate traits responsible for latitudinal differences we measured lifestage-specific development of southern mountain pine beetle eggs, larvae and pupae across a range of temperatures. Developmental rate curves were fit using maximum posterior likelihood estimation with a Bayesian prior to improve fit stability. …

Genome-Wide Association Study For Variants That Modulate Relationships Between Cerebrospinal Fluid Amyloid-Beta 42, Tau, And P-Tau Levels, Taylor J. Maxwell, Chris Corcoran, Jorge L. Del-Aguila, John P. Budde, Yuetiva Deming, Carlos Cruchaga, Alison M. Goate, John S. K. Kauwe, Alzheimer's Disease Neuroimaging Initiative

Mathematics and Statistics Faculty Publications

Background: A relationship quantitative trait locus exists when the correlation between multiple traits varies by genotype for that locus. Relationship quantitative trait loci (rQTL) are often involved in gene-by-gene (G×G) interactions or gene-by-environmental interactions, making them a powerful tool for detecting G×G.

Methods: We performed genome-wide association studies to identify rQTL between tau and Aβ42 and ptau and Aβ42 with over 3000 individuals using age, gender, series, APOE ε2, APOE ε4, and two principal components for population structure as covariates. Each significant rQTL was separately screened for interactions with other loci for each trait in the rQTL model. Parametric bootstrapping …

Using Computational Bayesian Statistics To Analyze Parameters In A Differential Equation Model, Jacob Menix

Mahurin Honors College Capstone Experience/Thesis Projects

The purpose of this project is to use Bayesian statistics to analyze values of parameters for a previously developed system of differential equations which describes the healing process of diabetic foot ulcers. The model describes the relationships between matrix metalloproteinases (MMPs), their inhibitors (TIMPs), and extracellular matrix (ECM). A Bayesian approach is used when the availability of data is sparse, as it is in this case. Delayed Rejection Adaptive Metropolis (DRAM), a MATLAB implementation of a Metropolis-Hastings algorithm, is used to estimate parameters. This approach with the individual patient data allows us to estimate and compare parameters and their pairwise …

Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, Emily Horton

Undergraduate Theses and Capstone Projects

This research investigates the native Virginia orchid, Cyprepedium pubescens, or the large yellow lady-slipper. Researchers at Lynchburg College, located in central Virginia, collected orchid activity data over the span of nine years from 2006-2014. This data included the following information: when the first sprout appeared, the number of leaves, the number of flowers, and the number of flowers per each plant. Using collected data about nine orchids on the campus of Lynchburg College as a basis, we wanted create a model that would predict when we might see flowering on a yearly basis. Flowering is important because researchers are investigating …

Effect Of A Pre-Dinner Walnut Snack On Nutrient Intake Among University Students, Michelle E. Lacasse, Mackenzie J. Weis, Lauren S. Devaan, Gabrielle L. Schnellman, Elizabeth M. Gile, Molly D. Ahmann, Ted Wilson, Tisha L. Hooks

Undergraduate Research Celebration 2018

No abstract provided.

Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, Emily Horton

Student Scholar Showcase

No abstract provided.

Volume 10, Taylor Hogg, Tiffany Carter, Brandyn Johnson, Haleigh James, Josh Baker, Tyler Cernak, Kirsten Bauer, Allie Snavely, Mary Zell Galen, Eric Powell, Thomas Wise, Katie Kinsey, Beth Barbolla, Maeleigh Ferlet, Rebecca Morra, Michala Day, Alexandra Evangelista, Max Flores, Harley Hodges, Clardene Jones, Harrison Samaniego, Jamesha Watson, Abby Gargiulo, Heather Green, Haley Klepatzki, Juan Guevara, Dani Bondurant, Michael Joseph Link Jr., Pamela Dahl, Maeve Losen, Charlotte Murphey

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Roger A. Byrne

An Analysis of Media Framing in Cases of Violence Against Women by Taylor Hogg

Writing in the Discipline of Nursing by Tiffany Carter

Photography by Brandyn Johnson

The Hidden Life of Beef Cattle: A Study of Cattle Welfare on Traditional Ranches and Industrial Farms by Haleigh James

Bloodworth's by Josh Baker and Tyler Cernak

Prosimians: Little Bodies, Big Significance by Kirsten Bauer

Skinformed by Allie Snavely

Coopertition and Gracious Professionalism: The Effects of First Robotics Folklore and Culture on the Stem Community by Mary Zell Galen

Tilt by Eric Powell And Thomas Wise

The Millennial …

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.

Using Mixed Effects Modeling To Quantify Difference Between Patient Groups With Diabetic Foot Ulcers, Rachel French

Mahurin Honors College Capstone Experience/Thesis Projects

When diabetes progresses, many patients suffer from chronic foot ulcers. In a study described in Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008), sixteen patients with diabetic foot ulcers were examined throughout a twelve week healing period. During this period, levels of matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and the extracellular matrix in a wound area were measured at distinct time intervals for each patient. The ratios of these healing components are vital in determining whether a wound will heal or become chronic and never properly heal. Connecting Local and Global Sensitivities in a Mathematical Model for Wound …

Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour

Mathematics and Statistics Faculty Publications

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x′ = P(t)∇f(x) which arise as critical points of f, under the assumption that P(t) is positive semi-definite. It is shown that the condition ∫^∞λ₁(P(t)) dt = ∞, where λ₁(P(t)) is the smallest eigenvalue of P(t), plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami

Dissertations

We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. …

Methodological Approach To The Ex Vivo Expansion And Detection Of T. Cruzi-Specific T Cells From Chronic Chagas Disease Patients, Gonzalo R. Acevedo, Silvia A. Longhi, Alcinette Bunying, Nazila Sabri, Augusto Atienza, Maria P. Zago, Radleigh Santos, Valeria A. Judkowski, Clemencia Pinilla, Karina A. Gomez

Mathematics Faculty Articles

The discovery of T cell epitopes is essential not only for gaining knowledge about host response to infectious disease but also for the development of immune-intervention strategies. In Chagas disease, given the size and complexity of the Trypanosoma cruzi proteome and its interaction with the host’s immune system, the fine specificity of T cells has not been extensively studied yet, and this is particularly true for the CD4+ T cell compartment. The aim of the present work was to optimize a protocol for the generation of parasite-specific memory T cell lines, representative of their in vivo precursor populations and capable …

Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill

Dialogue & Nexus

Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.

Attraction-Repulsion Forces Between Biological Cells: A Theoretical Explanation Of Empirical Formulas, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Biological calls attract and repulse each other: if they get too close to each other, they repulse, and if they get too far away from each other, they attract. There are empirical formulas that describe the dependence of the corresponding forces on the distance between the cells. In this paper, we provide a theoretical explanation for these empirical formulas.

Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …

Sensitivity Analysis Of Wolf Restoration In Yellowstone Nation Park Using Omnivory Models, Derek Fields

Theses, Dissertations and Capstones

In the ever-changing world of ecology, species survival often depends on approximations and measurements taken by biologists. These approximations help to ensure and predict the future of that given species. Our ecological community of interest involves wolves, elk, and berry producing shrubs within Yellowstone National Park. We use two different systems of ordinary differential equations, each increasing in complexity to model our community. In each model the predator (wolves) and consumers (elk) compete for a common resource, berry producing shrubs. We call this consumption of resources, from more than one trophic level, omnivory. We approximate each system with parameter values …

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

Introducing A Theory Of Neutrosophic Evolution: Degrees Of Evolution, Indeterminacy, And Involution, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

During the process of adaptation of a being (plant, animal, or human), to a new environment or conditions, the being partially evolves, partially devolves (degenerates), and partially is indeterminate i.e. neither evolving nor devolving, therefore unchanged (neutral), or the change is unclear, ambiguous, vague, as in neutrosophic logic. Thank to adaptation, one therefore has: evolution, involution, and indeterminacy (or neutrality), each one of these three neutrosophic components in some degree. The degrees of evolution/indeterminacy/involution are referred to both: the structure of the being (its body parts), and functionality of the being (functionality of each part, or inter-functionality of the parts …

Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou

Mathematics and Statistics Faculty Research & Creative Works

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …

Effects Of Cell Cycle Noise On Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, William Ott

Mathematics Faculty Publications

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.

Territorial Movement Game, Jan Rychtar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Designing And Mentoring In A Research Experience For Undergraduates, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Grnsight: A Web Application And Service For Visualizing Models Of Small- To Medium-Scale Gene Regulatory Networks, Kam D. Dahlquist, John David N. Dionisio, Ben G. Fitzpatrick, Nicole A. Anguiano, Anindita Varshneya, Britain J. Southwick, Mihir Samdarshi

Biology Faculty Works

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of …

Mutation Selection On The Metabolic Pathway And The Effects On Protein Co-Evolution And The Rate Limiting Steps On The Tree Of Life, Katherine S. Porter

Mathematics Summer Fellows

Metabolic pathways are made of a series of reactions by enzymes at different speeds. These pathways include the rate limiting step, which is the slowest step that determines the rate of the overall reaction. To date, one study has examined the pathway of glycolysis and found no evidence of evolutionary stability of its rate limiting step. In addition, phylogenetic evidence has shown evolution in the pathway over time including gene duplication and positive selection within the pathway. This evidence suggests that there is coevolutionary selection on glycolysis. The evidence from this previous study is simulation-based. The Michaelis-Menten kinetics that describe …

Ciliate Codon Translator Program Manual, Quentin D. Altemose

Mathematics Summer Fellows

Understanding the evolutionary history of organisms allows us to better comprehend selective pressures and their effects on larger populations. In our study, we focused on analyzing the DNA of ciliate groups, which are single celled protozoans characterized by the presence of cilia on their outer membrane. We utilized the DNA of the organisms to analyze the changes in population genotype over time. We tested existing evolutionary models (designed to represent natural genetic variation over time in populations) against our data to identify the model with the best fit and likelihood. From the DNA and the evolutionary model with the highest …

Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper

Senior Honors Projects, 2010-2019

The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …

Volume 08, Meghan Enzinna, Casey Dawn Gailey, Raven Collins, Chiara Enriquez, Amelia Mcconnell, Alexander Morton, Emma Beckett, Leah G. Parr, Briana Adhikusuma, Taylor Embrey, Rowan Davis, Danielle Sisson, Bianca Cherry, Melissa Cacho, Chloe Woodward, Catherine Rollins, Carson Reeher, Landon Cooper, Haley Vasquez, Marlisha Stewart, Eric Whitehead, Sabrina Walker, James Bates

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Indigenous Peoples and the Modern Era by Meghan Enzinna

"Who Says": How Selena Gomez and the Scene Attempt to Subvert the Popular Standards of Beauty by Casey Dawn Gailey

Art by Raven Collins

Meltdown on Social Media: Amy's Baking Company Meets Kitchen Nightmares by Nathena Haddrill

Art by Chiara Enriquez

Design by Amelia Mcconnell

Worth More Than a Thousand Words: A Visual Rhetorical Discussion of Virtual Reality by Examining "Clouds Over Sidra" by Alexander Morton

Design by Emma Beckett

The Sonata: An Analysis of Piano Sonata No. 14 in C Minor, K. …

Volume 07, Rachel C. Lombardi, Ben Osterhout, Lindsay Graybill, Rebecca E. Dey, Skyler T. Carpenter, Emma Beckett, Jason Ware, Mollie Andrews, James Bates, Landon Cooper, Tiffani Jeffries, Maria Wheaton, Dallas Price, Laura Kahler, Sarah Charlton, Anna Bultrowicz, Emily Spittle, Erin Godwin, Eamon Brokenbrough

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Spatial Analysis of Potential Risk Factors Associated with Addition of Atlantic Coast Pipeline Through Virginia by Rachel C. Lombardi

"Delicate Matters with No Speaking," "Hope and Nothing," "Mono Duality" by Ben Osterhout

"Connect" Graphic Design Senior Project by Lindsay Graybill

Phenolic Acids in Brassicaceae Plants: Ovipositional Stimulants or Deterrents for Cabbage White Butterfly, Pieris Rapae? by Rebecca E. Dey And Skyler T. Carpenter

"Abecedarian Cards" by Emma Beckett, Jason Ware, And Mollie Andrews

Helvetica: A Type Specimen Book by James Bates, Landon Cooper, Tiffani Jeffries, And Maria Wheaton

“Things Left Behind” by Dallas …