Applied Mathematics Commons^™

Impact Of Vaccine Supplies And Delays On Optimal Control Of The Covid-19 Pandemic: Mapping Interventions For The Philippines, Carlo Delfin S. Estadilla, Joshua Uyheng, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Jay Michael R. Macalalag, Ma. Regina Justina E. Estuar

Mathematics Faculty Publications

Background

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and …

Development Of Synthetic Coal Char Simulant For Microwave Conversion Studies: A Computationally-Driven Approach, Kevin A. Hager

Graduate Theses, Dissertations, and Problem Reports (ETD)

Recent experimental demonstration of new reaction windows for coal char/methane reactions that are less energy-intensive, provides innovation for modular reactors. However, the correlation of the exact mechanism for the enhancement of these reaction windows is not certain. This study investigates the simplification of these experimental studies by developing a well-characterized coal char simulant. The approach involves using a computational approach to screen macroscopic composition to replicate the dielectric and compositional response of actual char. This study is focused on PRB coal char. A discrete element method (DEM) technique was used to simulate the packing of coal chars to give the …

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …

New Results On Cyclic Compositions And Multicompositions, Silvana Ramaj

College of Graduate Studies: Theses & Dissertations

Integer compositions, cyclic compositions, and lately k-compositions, are an important topic in combinatorics and number theory. In this paper, we will explain, the general approach of using generating functions to study number sequences involving compositions, cyclic compositions, k-compositions, and the number of parts in each of them. After generating the data, some properties are observed and proved. Also, some interesting bijections involving Pell numbers and the Jacobsthal sequence are given.

Arnold Transformations As Applied To Data Encryption, Haley N. Anderson

College of Graduate Studies: Theses & Dissertations

As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples …

A New Mathematical Theory For The Dynamics Of Large Tumor Populations, A Potential Mechanism For Cancer Dormancy & Recurrence And Experimental Observation Of Melanoma Progression In Zebrafish, Adeyinka A. Lesi

Dissertations and Theses

Cancer, a family of over a hundred disease varieties, results in 600,000 deaths in the U.S. alone. Yet, improvements in imaging technology to detect disease earlier, pharmaceutical developments to shrink or eliminate tumors, and modeling of biological interactions to guide treatment have prevented millions of deaths. Cancer patients with initially similar disease can experience vastly different outcomes, including sustained recovery, refractory disease or, remarkably, recurrence years after apparently successful treatment. The current understanding of such recurrences is that they depend on the random occurrence of critical mutations. Clearly, these biological changes appear to be sufficient for recurrence, but are they …

Modeling And Simulation Techniques Used In High Strain Rate Projectile Impact, Derek G. Spear, Anthony N. Palazotto, Ryan A. Kemnitz

Faculty Publications

A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison …

Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik

Williams Honors College, Honors Research Projects

In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …

An Enumeration Of Nested Networks, Nathan Cornelius

Williams Honors College, Honors Research Projects

Nested networks have several applications in phylogenetics and electrical circuit theory. In many cases, there may exist more than one distinct network which correctly models a given data set. This proposes a combinatorial problem to determine all possible network solutions. In this paper, we partially solve this problem by developing exponential generating functions which enumerate all 1-nested and 2-nested unicyclic networks. We also describe our procedure to directly count all 1-nested and 2-nested networks and provide all 1-nested networks with 7, 8, and 9 terminal nodes.

Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo

Williams Honors College, Honors Research Projects

In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

No abstract provided.

Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen

Articles

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …

Implementing A Neural Network For Supervised Learning With A Random Configuration Of Layers And Nodes, Kane A. Phillips

College of Graduate Studies: Theses & Dissertations

Deep learning has a substantial amount of real-life applications, making it an increasingly popular subset of artificial intelligence over the last decade. These applications come to fruition due to the tireless research and implementation of neural networks. This paper goes into detail on the implementation of supervised learning neural networks utilizing MATLAB, with the purpose being to generate a neural network based on specifications given by a user. Such specifications involve how many layers are in the network, and how many nodes are in each layer. The neural network is then trained based on known sample values of a function …

Application Of Optimal Control Theory To A Malaria Model, Cassidy Hill

Murray State Theses and Dissertations

With malaria still prevalent and considered to be one of the most devastating infectious diseases in the world, many scientific efforts have been made to reduce its impact. One such effort includes the construction of mathematical models. Mathematical models can be used to analyze malaria transmission dynamics in the human population. The development of these models allows researchers to consider the control measures necessary to reduce the prevalence of malaria infection and possibly eliminate it.

The model presented in this thesis will provide the relationship of female Anopheles mosquitoes and insecticide treated paint acting as the control. A deterministic system …

Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith

Williams Honors College, Honors Research Projects

The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …

Extending Critical Infrastructure Element Longevity Using Constellation-Based Id Verification, Christopher M. Rondeau, Michael A. Temple, J. Addison Betances, Christine M. Schubert Kabban

Faculty Publications

This work supports a technical cradle-to-grave protection strategy aimed at extending the useful lifespan of Critical Infrastructure (CI) elements. This is done by improving mid-life operational protection measures through integration of reliable physical (PHY) layer security mechanisms. The goal is to improve existing protection that is heavily reliant on higher-layer mechanisms that are commonly targeted by cyberattack. Relative to prior device ID discrimination works, results herein reinforce the exploitability of constellation-based PHY layer features and the ability for those features to be practically implemented to enhance CI security. Prior work is extended by formalizing a device ID verification process that …

New Numerical Approximations Of Geological Processes In Heterogeneous Systems Using Radial Basis Functions, Nadun Lakshitha Dissanayake Kulasekera Mudiyanselage

Dissertations, Master's Theses and Master's Reports

This dissertation includes four chapters. A brief description of each chapter is organized as follows. The first chapter provides an introduction to the RBF method. The chapter follows the historical progression of the Radial Basis Function (RBF) method while outlining the method’s advantages and disadvantages. A brief introduction about RBF interpolation, the RBF-FD method, and how to use it to solve PDEs is provided. Chapter 2 introduces a novel computationally efficient RBF-FD algorithm to solve the groundwater flow equation in the presence of an active well. We show that our method analytically handles the singularities in the PDE caused by …

Optimal Construction Of A Layer-Ordered Heap And Its Applications, Jake Pennington

Graduate Student Theses, Dissertations, & Professional Papers

The layer-ordered heap (LOH) is a simple data structure used in algorithms that perform optimal top-$k$ on $X+Y$, algorithms with the best known runtime for top-$k$ on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotopologue peaks in a chemical compound. In the analysis of these algorithms, the rank, $\alpha$, has been treated as a constant and $n$, the size of the array, has been treated as the sole parameter. Here, we explore the algorithmic complexity of LOH construction with $\alpha$ as a parameter, introduce a few algorithms for constructing LOHs, analyze their complexity in both …

Inference Of Surface Velocities From Oblique Time Lapse Photos And Terrestrial Based Lidar At The Helheim Glacier, Franklyn T. Dunbar Ii

Graduate Student Theses, Dissertations, & Professional Papers

Using time dependent observations derived from terrestrial LiDAR and oblique
time-lapse imagery, we demonstrate that a Bayesian approach to glacial motion es-
timation provides a concise way to incorporate multiple data products into a single
motion estimation procedure effectively producing surface velocity estimates with
an associated uncertainty. This approach brings both improved computational effi-
ciency, and greater scalability across observational time-frames when compared to
existing methods. To gauge efficacy, we apply these methods to a set of observa-
tions from the Helheim Glacier, a critical actor in contemporary mass loss trends
observed in the Greenland Ice Sheet. We find that …

Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.

Thermodynamic Entropy Of A Magnetized Ree-Eyring Particle-Fluid Motion With Irreversibility Process: A Mathematical Paradigm, M. M. Bhatti, Sara I. Abdelsalam

Basic Science Engineering

This article deals with the entropy generation and irreversibility process under the effects of partial slip on magnetic dusty liquid induced by peristaltic wave through a porous channel. The Ree-Eyring fluid model has been used for a governing flow. Mathematical modelling is based on Ohm's law, continuity equation, Darcy law and momentum equation. Analytical solutions are presented for fluid and particle phase. The effects of different pertinent parameters are considered for Newtonian and non-Newtonian cases. Numerical integration has been carried out using a computational software to analyse the pumping characteristics. The behaviour of velocity profile, trapping mechanism, entropy generation, Bejan …

Leveraging Elasticity To Uncover The Role Of Rabinowitsch Suspension Through A Wavelike Conduit: Consolidated Blood Suspension Application, Sara I. Abdelsalam, A. Z. Zaher

Basic Science Engineering

The present work presents a mathematical investigation of a Rabinowitsch suspension fluid through elastic walls with heat transfer under the effect of electroosmotic forces (EOFs). The governing equations contain empirical stress-strain equations of the Rabinowitsch fluid model and equations of fluid motion along with heat transfer. It is of interest in this work to study the effects of EOFs, which are rigid spherical particles that are suspended in the Rabinowitsch fluid, the Grashof parameter, heat source, and elasticity on the shear stress of the Rabinowitsch fluid model and flow quantities. The solutions are achieved by taking long wavelength approximation with …

Stability Theory Of Nonlinear Differential Equations, Jiaxiao Wei

Graduate Theses/Dissertations

Nonlinear differential equations are often effective tools in modeling some important phenomena in nature. However, most of the nonlinear ordinary differential equation cannot be solved by analytical methods. A more effective way is to explore the prop- erties of critical point and the trajectory around it. In this study, I will focus on sys- tems of autonomous differential equations, linear as well as nonlinear. I will not only focus on the stability of equilibria but also the orbital stability of nonlinear differential equations. I will introduce various approaches to the study of equilibrium points of the system in terms of …