Digital Commons Network^™

An Analysis Of Major League Baseball Sabermetrics, Zack O. Fuller

Research & Creative Achievement Day

With baseball becoming an increasingly competitive sport, professional baseball teams are looking to the statistical side of the sport to find ways to win more games. With my analysis, I studied baseball statistics to look for interesting patterns and relationships. For example, I investigated the effect of a trade on a player's performance (both batters and pitchers) and analyzed the relationship between a player's performance and salary. My analysis also determined the statistics teams should utilize to win more games. To effectively analyze these patterns and relationships, visualizations were made in Tableau, and linear models were fit with R. Overall, …

Nviz: Unraveling Neural Networks Through Visualization, Kevin Hoffman

Mathematics, Computer Science & Statistics Presentations

The growing utility of artificial intelligence (AI) is attributed to the development of neural networks. These networks are a class of models that make predictions based on previously observed data. While the inferential power of neural networks is great, the ability to explain their results is difficult because the underlying model is automatically generated. The AI community commonly refers to neural networks as black boxes because the patterns they learn from the data are not easily understood. This project aims to improve the visibility of patterns that neural networks identify in data. Through an interactive web application, NVIZ affords the …

Cie Text Analysis: Narrative Of The Life Of Frederick Douglass, The Declaration Of Independence, And The Declaration Of Sentiments, Arianna Knipe

Mathematics, Computer Science & Statistics Presentations

Our STAT-451 class has worked with analyzing the words from CIE texts and assigning them to a sentiment or feeling and comparing them with one another using RStudio. This project analyzes texts from three sources: The Narrative of the Life of Frederick Douglass, The Declaration of Independence and the Declaration of Sentiments.

Translation Of: Sur Des Familles D’Hypersurfaces Isoparamétriques Des Espaces Sphériques À 5 Et À 9 Dimensions, Revista Univ. Tucuman, Serie A, 1 (1940), 5–22, By Elie Cartan, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

English title: On Families of Isoparametric Hypersurfaces in Spherical Spaces of 5 and 9 Dimensions

This is an English translation of the article "Sur des familles d'hypersurfaces isoparamétriques des espaces sphériques à 5 et à 9 dimensions" which was originally published in Revista Univ. Tucuman, Serie A, 1, pp. 5-22 (1940), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

Mathematics Subject Classification Numbers: 53B25, 53C40, 53C42

Mth 125 - Modeling With Exponential Functions, Stivi Manoku

Open Educational Resources

The file includes a variety of problems that emphasize the importance of modeling exponential growth and/or radioactive decay. Through different exercises and problems, the assignment goal is to improve their comprehension of exponential functions and hone their problem-solving abilities.

Volume 14, Ireland Seagle, Dalton C. Whitby, Cassandra Poole, Rachel Cannon, Heidi Parker-Combes, Devon G. Shifflett, Antonio Harvey

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

• Introduction: Dr. Amorette Barber
• From the Editor: Dr. Larissa "Kat" Tracy
• From the Designers: Rachel English, Rachel Hanson
• Hungry Like the Wolf: The Wolf as Metaphor in Paramount Network’s Yellowstone: Ireland Seagle
• “Floating Cities”: Illustrating the Commercial and Conservation Conflict of Alaskan Cruise Ship Tourism: Dalton C. Whitby
• What Can You Do When Your Genes are the Enemy? Current Applications of Gene Manipulation and the Associated Ethical Considerations: Cassandra Poole
• La doble cara: un tema romántico en las obras de Larra y Hawthorne: Rachel Cannon
• Resolving a Conflict: How to …

The Mceliece Cryptosystem As A Solution To The Post-Quantum Cryptographic Problem, Isaac Hanna

Liberty University Research Week

Undergraduate

Theoretical Proposal

Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks, Adam Wagenknecht

Dissertations

Convolutional Neural Networks (CNNs) have become one of the most commonly used tools for performing image classification. Unfortunately, as with most machine learning algorithms, CNNs suffer from a lack of interpretability. CNNs are trained by using a training data set and a loss function to tune a set of parameters known as the layer weights. This tuning process is based on the classical method of gradient descent, but it relies on a strong stochastic component, which makes the weight behavior during training difficult to understand. However, since CNNs are governed largely by the weights that make up each of the …

Translation Of: Sur Quelque Familles Remarquables D’Hypersurfaces, C.R. Congrès Math. Liège, 1939, Pp. 30–41, By Élie Cartan., Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

English title: On some remarkable families of hypersurfaces

This is an English translation of the article "Sur quelque familles remarquables d’hypersurfaces" which was originally published in C.R. Congrès Math. Liège, pp. 30–41 (1939), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

Mathematics Subject Classification Numbers: 53B25, 53C40, 53C42

Identity Development And Empathy Among Pre-Health Students: A Longitudinal Study Employing Latent Class Analysis, Bergen Johnson, Gabe Deyoung, Matthew Stafford

22nd Annual Celebration of Undergraduate Research and Creative Activity (2023)

Pre-health students endure rigorous education to prepare for treating patients, but potentially not for every aspect of patient care. Beyond medical knowledge, successful patient interactions often include moral decision making and the possession of traits such as empathy. There is little research on early physician and nurse development, with a substantial gap at the undergraduate level. This is significant as the trend toward a decrease in empathy could begin sooner. We explore this using latent class analysis to categorize participants based upon survey response patterns regarding numerous indicators, the most dominant class indicators being religion and political views.

Classification Of Land Cover On Sand Dunes, Heleyna Tucker, Micah Sterk

22nd Annual Celebration of Undergraduate Research and Creative Activity (2023)

As members of the Hope College Coastal Research Group, we have studied the mechanisms for and effects of sand transport. In particular, we have worked to model vegetation coverage in West Michigan sand dune complexes in order to better understand how sand movement and resident vegetation affect one another. We use aerial drone imagery to develop machine learning algorithms for creating ground cover classification mappings in an automated way. Our team collected drone imagery ranging from high-resolution, low-altitude photographs to high-altitude stitched and rectified orthomosaics. We developed accurate ground cover classification methods for the low-altitude imagery and then explored ways …

Area Activity, Admin Stem For Success

STEM for Success Showcase

Lesson plan to teach students about area including an activity plan, activity description, activity video, and additional activity materials

Liouville Soliton Surfaces Obtained Using Darboux Transformations, S. C. Mancas, K. R. Acharya

Publications

We construct parametric Liouville surfaces corresponding to parametric soliton solutions of the Liouville equation and Darboux-transformed counterparts. We also use a modified variation of parameters method together with the elliptic functions method to obtain the traveling wave solutions to Liouville equation and express the centroaffine invariant in terms of the soliton Hamiltonian.

I-Optimal Or G-Optimal: Do We Have To Choose?, Stephen J. Walsh, Lu Lu, Christine M. Anderson-Cook

Mathematics and Statistics Faculty Publications

When optimizing an experimental design for good prediction performance based on an assumed second order response surface model, it is common to focus on a single optimality criterion, either G-optimality, for best worst-case prediction precision, or I-optimality, for best average prediction precision. In this article, we illustrate how using particle swarm optimization to construct a Pareto front of non-dominated designs that balance these two criteria yields some highly desirable results. In most scenarios, there are designs that simultaneously perform well for both criteria. Seeing alternative designs that vary how they balance the performance of G- and I …

Tuning Random Forests For Interpretability, Kelvyn Bladen

Student Research Symposium

Random Forests are a widely used predictive technique in the modern data analyst’s toolkit. As with other machine learning methods, Random Forests have hyper-parameters that should be tuned for getting the best predictive accuracy and for interpretation. Variable importance measures give users valuable insights regarding which features are most informative for prediction. The subject of my research is the commonly used permutation importance algorithm with Random Forests. Key results of my research are: 1. When predictive features are highly correlated, importance values can be misleading. 2. The best choice of the Random Forests hyper-parameter mtry for importances may be quite …

Using Particle Swarm Optimization To Generate Optimal Experimental Designs With Replication Structures, Thomsen Bolton

Student Research Symposium

The modern dominant approach to planning experiments in industrial engineering and manufacturing is optimal design. This is a popular design paradigm because it 1) requires specification of an optimality criterion which incorporates practical objectives as definition of a design with high quality and 2) yields a design via high-dimensional optimization that gives the researcher ‘the most bang for the buck’ for a fixed sample/experimental run size. We aim to adapt the state-of-the-art meta-heuristic optimization algorithm, the Particle Swarm Optimization (PSO), to generating optimal designs with user-specified replication structure. Recently, PSO has been demonstrated to be highly effective at generating candidate …

Generating Optimal Space-Filling Designs With Particle Swarm Optimization, Rebekah Scott

Student Research Symposium

In 1935, Ronald Fisher published The Design of Experiments, establishing classical designs for various types of experiments. With the rise of computing power came optimal design, where statisticians can better customize designs according to the needs of the researchers running the experiment. This research focuses on generating optimal MaxMin space-filling designs with particle swarm optimization using various distance metrics (Manhattan, Euclidean, etc). Interestingly, changing the distance metric in the objective function had a minimal effect on the design, except for Aitchison geometry on the simplex. Space-filling designs are optimal for supporting high-order models with only a small sacrifice in prediction …

Optimal Control Problems For Stochastic Processes With Absorbing Regime, Yaacov Kopeliovich

Journal of Stochastic Analysis

No abstract provided.

Bounds For The Augmented Zagreb Index, Ren Qingcuo, Li Wen, Suonan Renqian, Yang Chenxu

Theory & Applications of Graphs

The augmented Zagreb index (AZI for short) of a graph G, introduced by Furtula et al. in 2010, is defined as AZI(G)= Σ v_iv_j ∈ E(G)} (d(v_i)d(v_j)} {d(v_i)+d(v_j)-2)³, where E(G) is the edge set of G, and d(v_i) denotes the degree of the vertex v_i. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs.

New Diagonal Graph Ramsey Numbers Of Unicyclic Graphs, Richard M. Low, Ardak Kapbasov

Theory & Applications of Graphs

Grossman conjectured that R(G, G) = 2 ⋅ |V(G)| - 1, for all simple connected unicyclic graphs G of odd girth and |V(G)| ≥ 4. In this note, we prove his conjecture for various classes of G containing a triangle. In addition, new diagonal graph Ramsey numbers are calculated for some classes of simple connected unicyclic graphs of even girth.

Ts-Reconfiguration Of K-Path Vertex Covers In Caterpillars For K \Geq 4, Duc A. Hoang

Theory & Applications of Graphs

A k-path vertex cover (k-PVC) of a graph G is a vertex subset I such that each path on k vertices in G contains at least one member of I. Imagine that a token is placed on each vertex of a k-PVC. Given two k-PVCs I, J of a graph G, thek-Path Vertex Cover Reconfiguration (k-PVCR)} under Token Sliding (TS) problem asks if there is a sequence of k-PVCs between I and J where each intermediate member is obtained from its predecessor by sliding a token from some …

Ramsey Numbers For Connected 2-Colorings Of Complete Graphs, Mark Budden

Theory & Applications of Graphs

In 1978, David Sumner introduced a variation of Ramsey numbers by restricting to 2-colorings in which the subgraphs spanned by edges in each color are connected. This paper continues the study of connected Ramsey numbers, including the evaluation of several cases of trees versus complete graphs.

Over-Determined Control Systems On Time Scales, Danian Castillo, Drew Barnes, Nick Wintz

2023 Student Academic Showcase

Control theory is a branch of mathematics focused on observing or controlling a process governed by a dynamic equation. We use state-space notation to represent all meaningful information about our process. This means our processes are expressed in vector form. Typically, the state matrix is square. In this project, we consider a control system where the corresponding state is over-determined, meaning there are more rows than columns. In addition, our state equation is on a time scale T, which allows us to consider discrete, continuous, or hybrid measurements. Here, we offer two methods to solve the dynamic system. Finally, we …

Fast Computation Of Friction Stir Welding Process With Model Order Reduction And Machine Learning, Joshua Kay

Student Research Symposium

Joining aluminum alloys and other metal workpieces is a typical manufacturing process, which can be accomplished by various welding techniques. Friction stir welding (FSW), a relatively new technology patented in 1991, has many advantages over conventional welding processes. For the FSW process, it is desirable to determine an optimal set of parameters to avoid product defects in the joints. Modeling and simulating the FSW process is computationally expensive which creates a bottleneck in searching for optimal operating parameters. Reduced order modeling techniques will be used to significantly reduce computation time for FSW models while maintaining accuracy. In addition, machine learning …

How Daily Movement Impacts Elementary Students In Math, Lesley Mcmahan Lawson

Morehead State Theses and Dissertations

A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the Ernst and Sara Lane Volgenau College of Education at Morehead State University by Lesley McMahan Lawson on April 11, 2023.

Generalized Spherical Aluthge Transforms And Binormality For Commuting Pairs Of Operators, Slaviša Djordjević, Jaewoong Kim, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set …

A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin

Honors College Theses

Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …

Arma Model Development And Analysis For Global Temperature Uncertainty, Mahmud Hasan, Gauree Wathodkar, Mathias Muia

Faculty and Student Publications

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time-series temperature uncertainty model, which is the autoregressive moving average (ARMA) (1,1) model. The model was developed for an observed annual mean temperature anomaly X(t), which is a combination of a true (latent) global anomaly Y(t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t), which was divided into land surface temperature (LST) uncertainty, sea surface temperature (SST) uncertainty, and the corresponding source of uncertainty. The ARMA …

Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra

Mathematics & Statistics ETDs

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …

Nash Blowups Of Toric Varieties In Prime Characteristic, Daniel Duarte, Jack Jeffries, Luis Núñez-Betancourt

Department of Mathematics: Faculty Publications

We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially.