Mathematics Commons^™

Third Voices Conference On Teaching Stem With Music, September 22-23, 2019, Lawrence M. Lesser

Journal of Humanistic Mathematics

The third annual VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song; https://www.causeweb.org/voices/) conference will be held online September 22-23, 2019. Chaired by Tiffany Getty, this conference will explore the use of song to teach STEM (science, technology, engineering, and mathematics) at the postsecondary (or secondary) level.

Applied Scientific Demiurgy I – Entrance Examination Information Sheet, Mario Daniel Martín

Journal of Humanistic Mathematics

This document provides all the required information needed by aspiring demiurges to sit the entrance examination for the foundation course Applied Scientific Demiurgy I in the scientific stream of the Bachelor of Applied Demiurgy at the Topological Hyper-university of Technological Cosmology.

Differential Equations Of Love And Love Of Differential Equations, Isaac Elishakoff

Journal of Humanistic Mathematics

In this paper, simple ordinary differential equations are discussed against the background of William Shakespeare’s Romeo and Juliet. In addition, a version of this relationship in a somewhat opposite setting is considered. It is proposed that engineering mathematics courses include this topic in order to promote additional interest in differential equations. In the final section it is shown that vibration of a single-degree-of-freedom mechanical system can be cast as a love-hate relationship between its displacement and velocity, and dynamic instability identified as a transition from trigonometric love to hyperbolic.

Using Hidden Markov Modeling For Biogeographical Ancestry Analysis, Melvin R. Currie

Journal of Humanistic Mathematics

This paper describes a methodology for analyzing X-chromosome data to establish biogeographical contributions to the author’s X chromosome. We present an exposition of how Hidden Markov Modeling (HMM) can be used as a black box for ancestry analysis and focus on a set of conditions that are not universal but fairly common. The first condition is that the ancestral populations are drawn from regions that have had very little or no contact with each other since prehistoric times. The second condition is that the number of possible ancestral populations is small. In this analysis, we assume that the ancestral populations …

Large And Small Data Blow-Up Solutions In The Trojan Y Chromosome Model, Rana D. Parshad, Matthew Beauregard, Eric M. Takyi, Thomas Griffin, Landrey Bobo

Faculty Publications

The Trojan Y Chromosome Strategy (TYC) is an extremely well investigated biological control method for controlling invasive populations with an XX-XY sex determinism. In [35, 36] various dynamical properties of the system are analyzed, including well posedness, boundedness of solutions, and conditions for extinction or recovery. These results are derived under the assumption of positive solutions. In the current manuscript, we show that if the introduction rate of trojan fish is zero, under certain large data assumptions, negative solutions are possible for the male population, which in turn can lead to finite time blow-up in the female and male populations. …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Network Analyses Of Glomerular Capillaries, Jason Cory Brunson, Justin Sardi, Mark Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Control Theory And Estimation Of Parameters In A Differential Equation Model For Patients With Lupus, Peter Agaba

Masters Theses & Specialist Projects

System Lupus Erythematosus (SLE) is a chronic inflammatory autoimmune disorder that affects many parts of the body including skin, joints, kidneys, brains and other organs. Lupus Nephritis (LN) is a disease caused by SLE. Given the complexity of LN, we establish an optimal treatment strategy based on a previously developed mathematical model.For our thesis work, the model variables are: Immune Complexes (I), Pro-inflammatory mediators (P), Damaged tissue (D), and Anti-inflammatory mediators (A). The analysis in this research project focuses on analyzing therapeutic strategies to control damage using both parameter estimation techniques (integration of data to quantify any uncertainties associated with …

Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

Rose-Hulman Undergraduate Mathematics Journal

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code C can be represented by its neural ideal J_C. In turn, the polynomials in J_C can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were …

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

COBRA Preprint Series

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards …

Ua84 Sigma Chi, Wku Archives

WKU Archives Collection Inventories

Records created by and about the WKU chapter of Sigma Xi.

Effective Plant Discrimination Based On The Combination Of Local Binary Pattern Operators And Multiclass Support Vector Machine Methods, Vi N T Le, Beniamin Apopei, Kamal Alameh

Research outputs 2014 to 2021

Accurate crop and weed discrimination plays a critical role in addressing the challenges of weed management in agriculture. The use of herbicides is currently the most common approach to weed control. However, herbicide resistant plants have long been recognised as a major concern due to the excessive use of herbicides. Effective weed detection techniques can reduce the cost of weed management and improve crop quality and yield. A computationally efficient and robust plant classification algorithm is developed and applied to the classification of three crops: Brassica napus (canola), Zea mays (maize/corn), and radish. The developed algorithm is based on the …

Volume 11, Jacob Carney, Ryan White, Joseph Hyman, Jenny Raven, Megan Garrett, Ibrahim Kante, Summer Meinhard, Lauren Johnson, William "Editha" Dean Howells, Laura Gottschalk, Christopher Siefke, Pink Powell, Natasha Woodmancy, Katharine Colley, Abbey Mays, Charlotte Potts

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Synthesis of 3,5-substituted Parabens and their Antimicrobial Properties, Jacob Coarney, Ryan White

Chernobyl: Putting "Perestroika" and "Glasnot" to the Test, Joseph Hyman

Art by Jenny Raven

Watering Down Accessibility: The Issue with Public Access to Alaska's Federal Waterways, Meagan Garrett

Why Has the Democratic Republic of the Congo outsourced its Responsibility to Educate its Citizens? Ibrahim Kante

Art by Summer Meinhard

A Computational Study of Single Molecule Diodes, Lauren Johnson

Satire of …

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 …

New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/ Under-/ Off Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This international collective massive book, edited by Florentin Smarandache, has 716 pages, and represents the special issue on neutrosophic environment at SYMMETRY international journal (Scopus, Web of Science, IF: 2.143). The book contains 37 published papers, by 73 authors and coauthors, from 13 countries from around the world, in alphabetical order: China, Cuba, Ecuador, Egypt, India, Jordan, Korea, Malaysia, Pakistan, Romania, Saudi Arabia, United Kingdom, and United States of America.

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

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. …

Spatial Factor Models For High-Dimensional And Large Spatial Data: An Application In Forest Variable Mapping, Daniel Taylor-Rodríguez, Andrew O. Finley, Abhirup Datta, Chad Babcock, Hans-Erik Andersen, Bruce D. Cook, Douglas C. Morton, Sudipto Banerjee

Mathematics and Statistics Faculty Publications and Presentations

Gathering information about forest variables is an expensive and arduous activity. As such, directly collecting the data required to produce high-resolution maps over large spatial domains is infeasible. Next generation collection initiatives of remotely sensed Light Detection and Ranging (LiDAR) data are specifically aimed at producing complete-coverage maps over large spatial domains. Given that LiDAR data and forest characteristics are often strongly correlated, it is possible to make use of the former to model, predict, and map forest variables over regions of interest. This entails dealing with the high-dimensional (∼10² ) spatially dependent LiDAR outcomes over a large number …

Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

With-In Host Dynamics Of L. Monocytogenes And Thresholds For Distinct Infection Scenarios, Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

The case fatality and illness rates associated with L. monocytogenes continue to pose a serious public health burden despite the significant efforts and control protocol administered by private and public sectors. Due to the advance in surveillance and improvement in detection methodology, the knowledge of sources, transmission routes, growth potential in food process units and storage, effect of pH and temperature are well understood. However, the with-in host growth and transmission mechanisms of L. monocytogenes, particularly within the human host, remain unclear, largely due to the limited access to scientific experimentation on the human population. In order to provide insight …

Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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 …

Advancing Risk Assessment: Mechanistic Dose-Response Modelling Of Listeria Monocytogenes Infection In Human Populations, Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. The utility of characterizing the effects of strain variation and individual/subgroup susceptibility on dose-response outcomes has motivated the search for new approaches beyond the popular use of the exponential dose-response model for listeriosis. While descriptive models can account for such variation, they have limited power to extrapolate beyond the details of particular outbreaks. By contrast, this study exhibits dose-response relationships from a mechanistic basis, quantifying key biological factors involved in pathogen-host dynamics. An …

United States Population Future Estimates And Long-Term Distribution, Sean P. Brogan

DePaul Discoveries

The population of the United States has always increased year over year. Even now with decreasing birth rates, the overall population continues to grow when looking at conventional models. The present study specifically examines what would happen to the U.S. population if we were to maintain the current birth and survival rates into the future. By 2050, our research shows that the U.S. population will become much older and cease to grow at all.

Feasibility Of Predicting Vietnam’S Autumn Rainfall Regime Based On The Tree-Ring Record And Decadal Variability, Yan Sun, Shih-Yu (Simon) Wang, Rong Li, Brendan M. Buckley, Robert R. Gilies, Kyle G. Hansen

Mathematics and Statistics Faculty Publications

We investigate the feasibility of developing decadal prediction models for autumn rainfall ( R_A ) over Central Vietnam by utilizing a published tree-ring reconstruction of October–November (ON) rainfall derived from the earlywood width measurements from a type of Douglas-fir (Pseudotsuga sinensis). Autumn rainfall for this region accounts for a large percentage of the annual total, and is often the source of extreme flooding. Central Vietnam’s R_A along with its notable autocorrelation and significant cross-correlation with basin-wide Pacific sea surface temperature (SST) variability, to develop four discrete time-series models. The sparse autoregressive model, with Pacific SST as …

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 …