Mathematics Commons^™

Hydra Effects In Stable Communities And Their Implications For System Dynamics, Michael H. Cortez, Peter A. Abrams

Mathematics and Statistics Faculty Publications

A hydra effect occurs when the mean density of a species increases in response to greater mortality. We show that, in a stable multispecies system, a species exhibits a hydra effect only if maintaining that species at its equilibrium density destabilizes the system. The stability of the original system is due to the responses of the hydra-effect species to changes in the other species’ densities. If that dynamical feedback is removed by fixing the density of the hydra-effect species, large changes in the community make-up (including the possibility of species extinction) can occur. This general result has several implications: (1) …

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. …

Review Paper: The Shape Of Phylogenetic Treespace, Katherine St. John

Publications and Research

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths.

Approximating Optimal Release In A Deterministic Model For The Sterile Insect Technique, Sergio Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Cost/benefit analyses are essential to support management planning and decisions before launching any pest control program. In particular, applications of the sterile insect technique (SIT) are often prevented by the projected economic burden associated with rearing processes. This has had a deep impact on the technique development and its use on insects with long larval periods, as often seen in beetles. Under the assumptions of long adult timespan and multiple mating, we show how to find approximate optimal sterile release policies that minimize costs. The theoretical framework proposed considers the release of insects by pulses and finds approximate optimal release …

Atypical Visual And Somatosensory Adaptation In Schizophrenia-Spectrum Disorders, Gizely Andrade, John Butler, Gregory Peter, Sophie Molholm, John J. Foxe

Articles

Neurophysiological investigations in patients with schizophrenia consistently show early sensory processing deficits in the visual system. Importantly, comparable sensory deficits have also been established in healthy first-degree biological relatives of patients with schizophrenia and in first-episode drug-naive patients. The clear implication is that these measures are endophenotypic, related to the underlying genetic liability for schizophrenia. However, there is significant overlap between patient response distributions and those of healthy individuals without affected first-degree relatives. Here we sought to develop more sensitive measures of sensory dysfunction in this population, with an eye to establishing endophenotypic markers with better predictive capabilities. We used …

Application Of Virtual Reality Head Mounted Display For Investigation Of Movement: A Novel Effect Of Orientation Of Attention, Brendan Quinlivan, John Butler, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard Reilly

Articles

Objective. To date human kinematics research has relied on video processing, motion capture and magnetic search coil data acquisition techniques. However, the use of head mounted display virtual reality systems, as a novel research tool, could facilitate novel studies into human movement and movement disorders. These systems have the unique ability of presenting immersive 3D stimulus while also allowing participants to make ecologically valid movement-based responses. Approach. We employed one such system (Oculus Rift DK2) in this study to present visual stimulus and acquire head-turn data from a cohort of 40 healthy adults. Participants were asked to complete head movements …

A Model For Spheroid Versus Monolayer Response Of Sk-N-Sh Neuroblastoma Cells To Treatment With 15-Deoxy-Pgj2, Dorothy I. Wallace, Ann Dunham, Paula X. Chen, Michelle Chen, Milan Huynh, Evan Rheingold, Olivia F. Prosper

Mathematics Faculty Publications

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ₂ and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ₂. The monolayer …

Unraveling The Dose-Response Puzzle Of L. Monocytogenes: A Mechanistic Approach, S. M.Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

Food-borne disease outbreaks caused by Listeria monocytogenes continue to impose heavy burdens on public health in North America and globally. To explore the threat L. monocytogenes presents to the elderly, pregnant woman and immuno-compromised individuals, many studies have focused on in-host infection mechanisms and risk evaluation in terms of dose-response outcomes. However, the connection of these two foci has received little attention, leaving risk prediction with an insufficient mechanistic basis. Consequently, there is a critical need to quantifiably link in-host infection pathways with the dose-response paradigm. To better understand these relationships, we propose a new mathematical model to describe the …

The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm

Articles

Young children are often hyperreactive to somatosensory inputs hardly noticed by adults, as exemplified by irritation to seams or labels in clothing. The neurodevelopmental mechanisms underlying changes in sensory reactivity are not well understood. Based on the idea that neurodevelopmental changes in somatosensory processing and/or changes in sensory adaptation might underlie developmental differences in somatosensory reactivity, high-density electroencephalography was used to examine how the nervous system responds and adapts to repeated vibrotactile stimulation over childhood. Participants aged 6–18 yr old were presented with 50-ms vibrotactile stimuli to the right wrist over the median nerve at 5 blocked interstimulus intervals (ranging …

Apply Data Clustering To Gene Expression Data, Abdullah Jameel Abualhamayl Mr.

Electronic Theses, Projects, and Dissertations

Data clustering plays an important role in effective analysis of gene expression. Although DNA microarray technology facilitates expression monitoring, several challenges arise when dealing with gene expression datasets. Some of these challenges are the enormous number of genes, the dimensionality of the data, and the change of data over time. The genetic groups which are biologically interlinked can be identified through clustering. This project aims to clarify the steps to apply clustering analysis of genes involved in a published dataset. The methodology for this project includes the selection of the dataset representation, the selection of gene datasets, Similarity Matrix Selection, …

Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz

Mathematics Colloquium Series

An appealing hypothesis suggests that neurons represent inputs in a coordinate system that is matched to the statistical structure of images in the natural environment. I discuss theoretical work on unsupervised learning of statistical regularities in natural images. In the model, Bayesian inference amounts to a generalized form of divisive normalization, a canonical computation that has been implicated in many neural areas. In our framework, divisive normalization is flexible: it is recruited only when the image is inferred to contain dependencies, and muted otherwise. I particularly focus on recent work in which we have applied this approach to understanding spatial …

Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston

Mathematics Colloquium Series

Simulating marine invaded systems requires broad consideration of physical oceanographic processes, such as ocean circulation patterns and temperature, and biological traits of the invader, such as their reproductive strategy and tolerances to their environment. Through this understanding of baseline biological and oceanographic function, models can be developed in order to forecast the incursion patterns of marine invasive species - helpful both to predict their spread as well as forewarn of impacts. To facilitate this understanding, computer simulation is useful in order to quickly and efficiently assimilate large biological and oceanographic datasets into digestible products. Data derived from such simulations are …

Age-Related Sexual Dimorphism In Temporal Discrimination And In Adult-Onset Dystonia Suggests Gabaergic Mechanisms, John Butler, Ines M. Beiser, Laura Williams, Eavan Mcgovern, Fiona Molloy, Timothy Lynch, Dan G. Healy, Helena Moore, Richard Walsh, Richard B. Reilly, Sean O'Riordan, Cathal Walsh, Michael Hutchinson

Articles

Background: Adult-onset isolated focal dystonia (AOIFD) presenting in early adult life is more frequent in men, whereas in middle age it is female predominant. Temporal discrimination, an endophenotype of adult-onset idiopathic isolated focal dystonia, shows evidence of sexual dimorphism in healthy participants. Objectives: We assessed the distinctive features of age-related sexual dimorphism of (i) sex ratios in dystonia phenotypes and (ii) sexual dimorphism in temporal discrimination in unaffected relatives of cervical dystonia patients. Methods: We performed (i) a meta-regression analysis of the proportion of men in published cohorts of phenotypes of adult-onset dystonia in relation to their mean age of …

The Integration Of Kinesthetic Learning Through The Math & Movement Program: Pilot Study 2015, Benjamin Ferder

Master's Theses

Purpose: The primary purpose of this pilot study was to verify that the use of kinesthetic learning (Math & Movement Program) in the classroom increases retention of multiplication facts at a greater rate than traditional drill and practice. The Math & Movement Program uses a kinesthetic learning-based approach for practicing, learning, and memorizing mathematics through the incorporation of bodily movement(s). Participants: The directors of the research project for the participating school district selected the sample of convenience. The population size of this study included 213 third and fourth grade students during the second half of the 2011-2012 school years. Data …

Evaluation Of Control Strategies For The Spread Of Citrus Greening, Vicente Valle Martinez

Theses and Dissertations - UTB/UTPA

Huanglongbing, also known as citrus greening, is a vector-based disease in citrus (with no cure known to date) that has drastically affected the citrus production in Florida in less than a decade and has been recently detected in Texas and California. In this paper, an epidemic model of the spatial spread of the disease is implemented among commercial and residential groves by taking into consideration the diffusion patterns of the psyllid vectors. A system of differential equations resembling one for malaria infection in humans is derived to evaluate different control methods such as quarantine, treatment, removal, foliar treatment, and pest …

Zernike Moments And Genetic Algorithm: Tutorial And Application, Oluleye Babatunde, Leisa Armstrong, Jinsong Leng, Dean Diepeveen

Grain and Other Field Crops Research Articles

Aims/ objectives: To demontrate effectiveness of Zernike Moments for Image Classification. Zernike moment(ZM) is an excellent region-based moment which has attracted the attentions of many image processing researchers since its first application to image analysis. Many papers have been published on several works done on ZM but no single paper ever give a detailed information of how the computation of ZM is done from the time the image is captured to the computation of ZM. This work showed how to effectively apply ZM on RGB images. We have demonstrated the effectiveness of Zernike moment in image classification system. A neuro-genetic …

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

Department of Mathematics: Dissertations, Theses, and Student Research

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to …

Manipulating The Mass Distribution Of A Golf Putter, Paul J. Hessler Jr.

Senior Honors Projects

Putting may appear to be the easiest but is actually the most technically challenging part of the game of golf. The ideal putting stroke will remain parallel to its desired trajectory both in the reverse and forward direction when the putter head is within six inches of the ball. Deviation from this concept will cause a cut or sidespin on the ball that will affect the path the ball will travel.

Club design plays a large part in how well a player will be able to achieve a straight back and straight through club head path near impact; specifically the …

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

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 …

Exploring The Unknown: Electrophysiological And Behavioural Measures Of Visuospatial Learning, Brendan Quinlivan, John Butler, Abdur R. Ridwan, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard B. Reilly

Articles

Visuospatial memory describes our ability to temporarily store and manipulate visual and spatial information, and is employed for a wide variety of complex cognitive tasks. Here, a visuospatial learning task requiring fine motor control is employed to investigate visuospatial learning in a group of typically developing adults. Electrophysiological and behavioural data are collected during a target location task under two experimental conditions: Target Learning and Target Cued. Movement times (MTs) are employed as a behavioural metric of performance, while dynamic P3b amplitudes and power in the alpha band (approximately 10 Hz) are explored as electrophysiological metrics during visuospatial learning. Results …

2015 Oklahoma Research Day Full Program, Northeastern State University

Oklahoma Research Day Abstracts

This document contains all abstracts from the 2015 Oklahoma Research Day held at Northeastern State University.

Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov

Department of Mathematics: Faculty Publications

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …

Mathematical Model For Bone Mineralization, Svetlana V. Komarova, Lee Safranek, Jay Gopalakrishnan, Miao-Jung Yvonne Ou, Marc D. Mckee, Monzur Murshed, Frank Rauch, Erica Zuhr

Mathematics and Statistics Faculty Publications and Presentations

Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively …

A Robust Deep Model For Improved Classification Of Ad/Mci Patients, Feng Li, Loc Tran, Kim-Han Thung, Shuiwang Ji, Dinggang Shen, Jiang Li

Electrical & Computer Engineering Faculty Publications

Accurate classification of Alzheimer's disease (AD) and its prodromal stage, mild cognitive impairment (MCI), plays a critical role in possibly preventing progression of memory impairment and improving quality of life for AD patients. Among many research tasks, it is of a particular interest to identify noninvasive imaging biomarkers for AD diagnosis. In this paper, we present a robust deep learning system to identify different progression stages of AD patients based on MRI and PET scans. We utilized the dropout technique to improve classical deep learning by preventing its weight coadaptation, which is a typical cause of overfitting in deep learning. …

Long Wavelength Analysis Of A Model For The Geographic Spread Of A Disease, Layachi Hadji

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the temporal and spatial evolution of the spread of an infectious disease by performing a long-wavelength analysis of a classical model for the geographic spread of a rabies epidemic in a population of foxes subject to idealized boundary conditions. We consider twodimensional and three-dimensional landscapes consisting of an infinite horizontal strip bounded by two walls a finite distance apart and a horizontal region bounded above and below by horizontal walls, respectively. A nonlinear partial differential evolution Equation for the leading order of infectives is derived. The Equation captures the space and time variations of the spread of the …

Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean

Ogden College of Science & Engineering Publications

No abstract provided.

Citizen Science Reveals Widespread Negative Effects Of Roads On Amphibian Distributions, Bradley J. Cosentino, David M. Marsh, Kara S. Jones, Joseph J. Apodaca, Christopher Bates, Jessica Beach, Karen H. Beard, Kelsie Becklin, Jane Margaret Bell, Christopher Crockett, George Fawson, Jennifer Fjelsted, Elizabeth A. Forys, Kristen S. Genet, Melanie Grover, Jaimie Holmes, Katherine Indeck, Nancy E. Karraker, Eran S. Kilpatrick, Tom A. Langen, Stephen G. Mugel, Alessandro Molina, James R. Vonesh, Ryan J. Weaver, Anisha Willey

Wildland Resources Faculty Publications

Landscape structure is important for shaping the abundance and distribution of amphibians, but prior studies of landscape effects have been species or ecosystem-specific. Using a large-scale, citizen science-generated database, we examined the effects of habitat composition, road disturbance, and habitat split (i.e. the isolation of wetland from forest by intervening land use) on the distribution and richness of frogs and toads in the eastern and central United States. Undergraduates from nine biology and environmental science courses collated occupancy data and characterized landscape structure at 1617 sampling locations from the North American Amphibian Monitoring Program. Our analysis revealed that anuran species …

Generalized Theoretical Criteria For Annihilation Of Hiv-1 Virions During Haart, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

Aims: This paper is an elaborate and quantitative attempt to construct medically applicable mathematical models and derive criteria for efficacious Highly Active Anti-Retroviral Therapy (HAART) protocol for an AIDS patient. The patho-physiological dynamics of Human Immuno-deficiency Virus type 1 (HIV-1) induced AIDS during HAART is modeled by a system of non-linear deterministic differential equations. The physiologically relevant and clinically plausible equations depict the dynamics of uninfected CD4+ T cells (x1), HIV-1 infected CD4+ T cells (x2), HIV-1 virions in the blood plasma (x3), HIV-1 specific CD8+ T cells (x4), and the concentration of HAART drug molecules (x5). The major objective …

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …