Applied Mathematics Commons^™

Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia

Physics

Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating …

Consensus Model Of Families Of Images Using Tensor-Based Fourier Analysis, Joel A. Shelton

Electronic Theses and Dissertations

A consensus model is a statistical approach that uses a family of signals or in our case, a family of images to generate a predictive model. In this thesis, we consider a family of images that are represented as tensors. In particular, our images are (2,0)-tensors. The consensus model is produced by utilizing the quantum Fourier transform of a family of images as tensors to transform images to images. We write a quantum Fourier transform in the numerical computation library for Python, known as Theano to produce the consensus spectrum. From the consensus spectrum, we produce the consensus model via …

Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)

Rose-Hulman Undergraduate Research Publications

Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …

Aberrant Dna Methylation: Implications In Racial Health Disparity, Xuefeng Wang, Ping Ji, Yuanhao Zhang, Joseph F. Lacomb, Xinyu Tian, Ellen Li, Jennie L. Williams

Department of Biomedical Engineering Faculty Publications

Background Incidence and mortality rates of colorectal carcinoma (CRC) are higher in African Americans (AAs) than in Caucasian Americans (CAs). Deficient micronutrient intake due to dietary restrictions in racial/ethnic populations can alter genetic and molecular profiles leading to dysregulated methylation patterns and the inheritance of somatic to germline mutations. Materials and Methods Total DNA and RNA samples of paired tumor and adjacent normal colon tissues were prepared from AA and CA CRC specimens. Reduced Representation Bisulfite Sequencing (RRBS) and RNA sequencing were employed to evaluate total genome methylation of 5’-regulatory regions and dysregulation of gene expression, respectively. Robust analysis was …

Drawing Numbers And Listening To Patterns, Loren Zo Haynes

Honors College Theses

The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …

Theoretical Modeling Of The Effect Of Polymer Chain Immobilization Rates On Holographic Recording In Photopolymers, Dana Mackey, Paul O'Reilly, Izabela Naydenova

Articles

This paper introduces an improved mathematical model for holographic grating formation in an acrylamide-based photopolymer, which consists of partial differential equations derived from physical laws. The model is based on the two-way diffusion theory of \cite{izabela}, which assumes short polymer chains are free to diffuse, and generalizes a similar model presented in \cite{josab} by introducing an immobilization rate governed by chain growth and cross-linking. Numerical simulations were carried out in order to investigate the behaviour of the photopolymer system for short and long exposures, with particular emphasis on the effect of recording parameters (such as illumination frequency and intensity), as …

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

Honors College Theses

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …

Locally Convex Words And Permutations, Christopher Coscia, Jonathan Dewitt

Dartmouth Scholarship

We introduce some new classes of words and permutations characterized by the second difference condition pi(i - 1) + pi(i + 1) - 2 pi(i)

The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares

Department of Math & Statistics Faculty Publications

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and sub-optimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …

The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares

Department of Math & Statistics Faculty Publications

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and suboptimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …

Flesch-Kincaid Reading Grade Level Re-Examined: Creating A Uniform Method For Calculating Readability On A Certification Exam, Emily Neuhoff, Kristiana M. Feeser, Kayla Sutherland, Thomas Hovatter

Online Journal for Workforce Education and Development

Abstract

Objective: This study attempted to establish a consistent measurement technique of the readability of a state-wide Certified Nursing Assistant’s (CNA) certification exam. Background: Monitoring the readability level of an exam helps ensure all test versions do not exceed the maximum reading level of the exam, and that knowledge of the subject matter, rather than reading ability, is being assessed. Method: A two part approach was used to specify and evaluate readability. First, two methods (Microsoft Word^® (MSW) software and published readability formulae) were used to calculate Flesch Reading Ease (FRE) and Flesch-Kincaid Reading Grade Level (FKRGL) for multiple …

Variance Of Clusterings On Graphs, Thomas Vlado Mulc

Mathematical Sciences Technical Reports (MSTR)

Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.

The Evaluation Of Rhode Island Public High School Teachers: The Impact On Students, Stephen Lamontagne

Honors Projects in Mathematics

In 2012, the state of Rhode Island began the full implementation of a high-stakes teacher evaluation system. Its purpose is to increase teacher accountability and to improve student performance. However, a significant amount of literature casts doubt about the effectiveness and validity of teacher evaluation. This paper utilizes statistical methods including regression and decision trees in order to determine whether or not there is a relationship between teacher evaluation in Rhode Island and student performance, using RI Department of Education Data for each school from 2008-2015. Furthermore, this presentation investigates other factors that affect schools, to see if changes in …

Using Odes To Model Drug Concentrations Within The Field Of Pharmacokinetics, Andrea Mcnally

Mathematics: Student Scholarship & Creative Works

No abstract provided.

What Is The True Cost To Stay In The Hospital?, Samantha Alicandro

Honors Projects in Mathematics

Currently, the unfortunate reality that receiving diverse health procedures can be extremely expensive is widely acknowledged and woefully accepted. However, have you inquired or been curious about the specific factors that influence the cost per day expensed by a hospital? Through examination, investigation, and evaluation operating SAS Enterprise Guide, SAS Enterprise Miner and Tableau I have attempted to arrive at a conclusion for this very question. Utilizing a 1.5 million row data set provided by Rhode Island, for the years 2003-2013, I analyzed the assorted elements conceivably bearing impact on the cost per day at a hospital. Regressions, decision trees, …

Catching Card Counters, Sarah French

Honors Projects in Mathematics

The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. …

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

University Faculty Publications and Creative Works

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

Coding Strategies, The Choquet Game And Domain Representability, Lynne Yengulalp

Mathematics Faculty Publications

We prove that if the NONEMPTY player has a winning strategy in the strong Choquet game on a regular space X then NONEMPTY has a winning coding strategy in that game (a strategy that only depends on the previous 2 moves). We also prove that any regular domain representable space is generalized subcompact.

Regularity Of Solutions And The Free Boundary For A Class Of Bernoulli-Type Parabolic Free Boundary Problems With Variable Coefficients, Thomas H. Backing

Open Access Dissertations

In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact …

Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …

Cutting Triangles, Nghia Nguyen, Jane Long

Undergraduate Research Conference

The idea of this project began with a question: Draw any triangle on a piece of paper, is it possible to fold the paper so that the triangle can be cut out in one slice?

A Logistic Regression And Markov Chain Model For The Prediction Of Nation-State Violent Conflicts And Transitions, Nicholas Shallcross

Theses and Dissertations

Using open source data, this research formulates and constructs a suite of statistical models that predict future transitions into and out of violent conflict and forecasts the regional and global incidences of violent conflict over a ten-year time horizon. A total of thirty predictor variables are tested and evaluated for inclusion in twelve conditional logistic regression models, which calculate the probability that a nation will transition from its current conflict state, either In Conflict or Not in Conflict, to a new state in the following year. These probabilities are then used to construct a series of nation-specific Markov chain models …

Diagnosing Autism Spectrum Disorder Through Brain Functional Magnetic Resonance Imaging, Kyle A. Palko

Theses and Dissertations

Autism spectrum disorder (ASD) is a neurodevelopmental condition that can be debilitating to social functioning. Previous functional Magnetic Resonance Imaging (fMRI) classification studies have included only small subject sample sizes (n 50) and have seen high classification accuracy. The recent release of the Autism Brain Imaging Data Exchange (ABIDE) provides fMRI data for over 1,100 subjects. In our research, we derive a subject's functional network connectivity (FNC) from their fMRI data and develop a regularized logistic classifier to determine whether a subject has autism. We obtained up to 65% classification accuracy, similar to other studies using the ABIDE dataset, suggesting …

Radial Basis Function Based Quadrature Over Smooth Surfaces, Maloupu L. Watts

Theses and Dissertations

The numerical approximation of denite integrals, or quadrature, often involves the construction of an interpolant of the integrand and subsequent integration of the interpolant. It is natural to rely on polynomial interpolants in the case ofone dimension; however, extension of integration of polynomial interpolants to two or more dimensions can be costly andunstable. A method for computing surface integrals on the sphere is detailed in the literature (Reeger and Fornberg,Studies in Applied Mathematics, 2016). The method uses local radial basis function (RBF) interpolation to reducecomputational complexity when generating quadrature weights for the particular node set. This thesis expands upon thesame …

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0

On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0

Oscillation Of Solution To Second-Order Half-Linear Delay Dynamic Equations On Time Scales, Hongwu Wu, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results.

Matched Metrics And Channels, Marcelo Firer, Judy L. Walker

Department of Mathematics: Faculty Publications

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes.

How Much Should You Pay For A Financial Derivative?, Boyan Kostadinov

Publications and Research

We explain some key mathematical ideas behind the no-arbitrage pricing of financial derivatives by replication, starting from a simple coin toss model and ending with the continuous-time limit of a multi-step coin-toss model using a geometric random walk model. In the limit, we obtain the classical Black-Scholes-Merton formula for pricing European call and put options.