Physical Sciences and Mathematics Commons^™

Glucose Regulation Using An Intelligent Pid Controller, Parker Willmon

Mathematics Senior Capstone Papers

Type 1 diabetes is a condition characterized by a lack of insulin production. This lack of insulin causes glucose concentration in the blood to increase after meals. In order to maintain blood glucose levels, diabetics must inject insulin using needles or an insulin pump. Additionally, the lack of insulin can cause glucose levels to decrease overnight. This project uses a proportional integral derivative (PID) controller to modify the rate of insulin and glucagon infusion when glucose levels are increasing or decreasing, respectively. A system of 13 differential equations were used to anticipate changes in glucose concentration as insulin and glucagon …

A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang

Mathematics Theses and Dissertations

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating …

The Boundary Element Method For Parabolic Equation And Its Implementation In Bem++, Sihao Wang

Mathematics Theses and Dissertations

The goal of this work is to develop a fast method for solving Galerkin discretizations of boundary integral formulations of the heat equation. The main contribution of this work is to devise a new fast algorithm for evaluating the dense matrices of the discretized integral equations.

Similar to the parabolic FMM, this method is based on a subdivision of the matrices into an appropriate hierarchical block structure. However, instead of an expansion of the kernel in both space and time we interpolate kernel in the temporal variables and use of the adaptive cross approximation (ACA) in the spatial variables.

The …

Spreading Mechanics And Differentiation Of Astrocytes During Retinal Development, Tracy Stepien, Timothy W. Secomb

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parallel-In-Time Simulation Of Biofluids, Weifan Liu, Minghao Rostami

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model-Based Investigation Of The Role Of Density Dependence In Juvenile Mosquito Development And Survival, Melody Walker Ms, Lauren M. Childs, Michael A. Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mathematical Framework To Augment Metrics Of Small Intestinal Health, Cara J. Sulyok, Judy Day, Suzanne Lenhart

Biology and Medicine Through Mathematics Conference

No abstract provided.

Eco-Evolutionary Dynamics Of Microbial Communities, Lihong Zhao

Biology and Medicine Through Mathematics Conference

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of The Car T-Cell Therapy, Emek Kose, Elizabeth Zollinger, Samantha Elliott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Tympanal Asymmetry In A Parasitoid Fly: Small Asymmetries Produce Big Gains, Max Mikel-Stites, Anne E. Staples

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mathematical Model To Study The Crime Dynamics Spread Within Minority Communities, Maila Brucal-Hallare, Beatriz Cuartas, Anne Fernando, Ana Vivas-Barber

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parameter Estimation For Tear Film Thinning, Rayanne Luke

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Role Of Variation In Mate Choice And Wolbachia Infection On Aedes Aegypti Population Dynamics, Bernardo Ameneyro

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce

Biology and Medicine Through Mathematics Conference

No abstract provided.

Exploring The Effect Of The Nestling Recruitment Curve On Enzootic West Nile Virus Transmission, Emily B. Horton

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multilevel Asymptotic Parallel-In-Time Techniques For Temporally Oscillatory Pdes, Nicholas Abel

Mathematics & Statistics ETDs

As the clock speeds of individual processors level off and the amount of parallel resources continue to increase rapidly, further exploitation of parallelism is necessary to improve compute times. For time-dependent differential equations, the serial computation of time-stepping presents a bottleneck, but parallel-in-time integration methods offer a way to compute the solution in parallel along the time domain. Parallel-in-time methods have been successful in achieving speedup when computing solutions for parabolic problems; however, for problems with large hyperbolic terms and no strong diffusivity, parallel-in-time methods have traditionally struggled to offer speedup. While work has been done to understand why parallel-in-time …

Predicting And Comparing The Stock Value Of Chick-Fil-A, Mark Yates

Mathematics Senior Capstone Papers

This project focuses on estimating the stock value of Chick-fil-A as if it were a publicly traded company using a comparable analysis method or CAM. We begin by obtaining financial information from Chick-fil-A as well as the amount of locations there are chain-wide. Next we find two publicly traded fast food companies, one that is larger, and one that is smaller than Chick-fil-A and obtain the same information from them. The idea is that Chick-fil-A will lie between theses two companies and we can use the CAM to estimate their stock value. The CAM gives us a multiple of the …

On The Properties Of Solutions Of A Cross-Diffusion System With Nonlinear Boundary Flux, Zafar Rakhmonov, Jasur Urunbaev, Bobur Allaberdiyev

Scientific Journal of Samarkand University

In this paper, based on a self-similar analysis and the method of standard equations, the properties of a nonlinear cross-diffusion system coupled via nonlocal boundary conditions are studied. We are investigated the qualitative properties of solutions of a nonlinear system of parabolic equations of cross-diffusion in a medium coupled with nonlinear boundary conditions. It is proved that for certain values of the numerical parameters of the nonlinear cross-diffusion system of parabolic equations coupled via nonlinear boundary conditions, they may not have global solutions in time. Based on a self-similar analysis and the principle of comparing solutions, a critical exponent of …

Laser Beam Propagation Over Long Distances In Turbulent Media, Justyna O. Sotiris

Mathematics & Statistics ETDs

The propagation of lasers through different media is a broad topic of study and falls under the larger topic of wave propagation. The focus of this thesis is the development and analysis of a numerical computational model of laser beam propagation through a turbulent atmosphere over a long distance. When a beam propagates through a turbulent atmosphere over a distance exceeding several kilometers it is a strong fluctuation propagation. There exist fewer robust methods to demonstrate how strong fluctuations affect the beam. Beam propagation can be described by the Linear Schr\"{o}dinger Equation (LSE). The fluctuations in the refractive index are …

The Axiom Of Choice And Related Topics, Bryan Mccormick

Mathematics Senior Capstone Papers

In this paper I will be discussing the Axiom of Choice and its equivalent statements. The Axiom of Choice is an axiom of Zermelo-Fraenkel set theory that states that given a collection of non-empty sets, there exists a choice function which selects one element from each set to form a new set. The equivalents of the Axiom of Choice that I will be discussing include Zorn’s Lemma, which states that a partially ordered set with every chain being bounded above contains a maximal element, and the Well-Ordering Theorem, which states that every set has a well ordering. In addition to …

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

Undergraduate Research and Scholarship Symposium

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three …

Shallow Water Equations And Floor Topography Affect On Sea Surface, Chase Jones

Mathematics Senior Capstone Papers

For this research project, we have been doing research on the shallow water equations: a set of hyperbolic partial differential equations. These equations exist as a set of three primary equations [2]. However, there is another version of the shallow water equations called the Saint Venant’s equations. These equations are similar to the standard shallow water equations, but these equations have been reduced to one-dimension. The primary goal of our research has been to investigate the behavior and mathematical construction of the Saint Venant’s equations and model these equations using COMSOL. Regardless of the equation type, standard or Saint Venant’s, …

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

Undergraduate Research and Scholarship Symposium

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three …

A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh

Mathematics & Statistics ETDs

The NSF-funded FACETS (Formation of Accomplished Chemical Engineers for Transforming Society, NSF Award 1623105) grant aims to transform the undergraduate engineering experience in the Department of Chemical and Biological Engineering at the University of New Mexico to address attrition within engineering majors, especially among underserved populations (Brainard & Carlin, 1998). The UNM FACETS Design Identity & Beliefs survey, an assessment tool used as part of the research of the grant, generated the dataset used in this study. I performed several different statistical analyses on the dataset, including confirmatory factor analysis (CFA), principal component analysis (PCA), and cluster analysis. The …

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.