Mathematics Commons^™

Identity Development Among Pre-Health Students During The Covid-19 Pandemic, Anya Kapitula, Anna Tyshka

23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024)

Many sociology studies have been published regarding the experiences and development of medical school students, but there is a gap in research observing undergraduate students on pre-health professions tracks. Specifically, studies have been published noting a significant decrease in the empathy of medical school students during their third year, but no research has been conducted to identify development patterns of these students during their undergraduate years. This study aims to identify groups of undergraduate students on pre-health professions tracks based on typologies formed from longitudinal survey responses, and also to identify any significant transitions between these groups over time. Because …

Numerical Studies On Bose-Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

Gender And The Billboard Top 40 Charts Between 1958 And 2023, Brileigh Cates, Justin W. Pope

Undergraduate Research Conference at Missouri S&T

Is there an inherent bias towards male artists in the music industry? Evidence has been shown in previous studies, the most recent being from 2017, that there may be bias towards male artists appearing in Billboard Magazine s Hot 100 list. This study not only updates previous data to include 2017 through 2023, but also looks at the top 40 charts on a week-by-week bias as opposed to the year-end charts that other studies used for their data. We coded each song so as to indicate the gender of the artist(s) as well as whether or not the artists appeared …

Numerical Studies On Bose–Einstein Condensates, Megan Benkendorf

Undergraduate Research Conference at Missouri S&T

Bose-Einstein condensate (BEC) is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent "super-wave". The superfluidity of BEC has been the focus of active research since the first experimental realization of BEC in 1995. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018, has once again drawn spotlights to these fascinating properties of BEC. In this project, we will carry out numerical studies to understand the behavior of exciton-polariton BECs. A modified Gross-Pitaevskii equation is used to model the dynamics …

The History Of The Billboard Hot 100 And Its Process, Brileigh Cates

Undergraduate Research Conference at Missouri S&T

The Billboard Hot 100 has been around for decades, and it is believed without much accreditation. What really is Billboard, and why is it so popular? Why have other charting companies not taken up as much popularity? How does Billboard determine the popularity of artists? How has this changed with the introduction of the internet? This research project addresses all of these question, allowing the validity of the data collection to be addressed.

How Generative Ai Models Such As Chatgpt Can Be (Mis)Used In Spc Practice, Education, And Research? An Exploratory Study, Fadel M. Megahed, Ying-Ju (Tessa) Chen, Joshua A. Ferris, Sven Knoth, L. Allison Jones-Farmer

Mathematics Faculty Publications

Generative Artificial Intelligence (AI) models such as OpenAI's ChatGPT have the potential to revolutionize Statistical Process Control (SPC) practice, learning, and research. However, these tools are in the early stages of development and can be easily misused or misunderstood. In this paper, we give an overview of the development of Generative AI. Specifically, we explore ChatGPT's ability to provide code, explain basic concepts, and create knowledge related to SPC practice, learning, and research. By investigating responses to structured prompts, we highlight the benefits and limitations of the results. Our study indicates that the current version of ChatGPT performs well for …

Variable-Order Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, Yixuan Wu, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variable-order Laplacian (-Δ) α (x) / 2 with 0 < α (x) ≤ 2, which will also be referred as the variable-order fractional Laplacian if α(x) is strictly less than 2. We present a class of hypergeometric functions whose variable-order Laplacian can be analytically expressed. Building on these analytical results, we design the meshfree methods based on globally supported radial basis functions (RBFs), including Gaussian, generalized inverse multiquadric, and Bessel-type RBFs, to approximate the variable-order Laplacian (-Δ) α (x) / 2. Our meshfree methods integrate the advantages of both pseudo-differential and hypersingular integral forms of the variable-order fractional Laplacian, and thus avoid numerically approximating the hypersingular integral. Moreover, our methods are simple and flexible of domain geometry, and their computer implementation remains the same for any dimension d ≥ 1. Compared to finite difference methods, our methods can achieve a desired accuracy with much fewer points. This fact makes our method much attractive for problems involving variable-order fractional Laplacian where the number of points required is a critical cost. We then apply our method to study solution behaviors of variable-order fractional PDEs arising in different fields, including transition of waves between classical and fractional media, and coexistence of anomalous and normal diffusion in both diffusion equation and the Allen–Cahn equation. These results would provide insights for further understanding and applications of variable-order fractional derivatives.

Thermal Performance Of Forced Convection Of Water- Nepcm Nanofluid Over A Semi-Cylinder Heat Source, Xiaoming Wang, Rassol H. Rasheed, Babak Keivani, Dheyaa J. Jasim, Abbas J. Sultan, Sajad Hamedi, Hamed Kazemi-Varnamkhasti, Soheil Salahshour, Davood Toghraie

Mathematics and Statistics Faculty Research & Creative Works

1) Background: Phase change materials (PCMs) have been used statically, which has caused the use of these materials to face challenges. Encapsulating PCMs and combining them with the base fluid can significantly solve the problem of using PCMs in BTM systems. In the present study, based on computational fluid dynamics, forced convection heat transfer of nano-encapsulated phase change materials (NEPCM) in a BTM system are simulated. The main aim of the present research is to reduce the temperature at the surface of the hot cylinder. 2) Methods: In this research, we simulated lithium battery thermal management systems in both steady …

Optimizing Buying Strategies In Dominion, Nikolas A. Koutroulakis

Rose-Hulman Undergraduate Mathematics Journal

Dominion is a deck-building card game that simulates competing lords growing their kingdoms. Here we wish to optimize a strategy called Big Money by modeling the game as a Markov chain and utilizing the associated transition matrices to simulate the game. We provide additional analysis of a variation on this strategy known as Big Money Terminal Draw. Our results show that player's should prioritize buying provinces over improving their deck. Furthermore, we derive heuristics to guide a player's decision making for a Big Money Terminal Draw Deck. In particular, we show that buying a second Smithy is always more optimal …

A Causal Inference Approach For Spike Train Interactions, Zach Saccomano

Dissertations, Theses, and Capstone Projects

Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the …

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.

Time Scale Theory On Stability Of Explicit And Implicit Discrete Epidemic Models: Applications To Swine Flu Outbreak, Gülşah Yeni, Elvan Akın, Naveen K. Vaidya

Mathematics and Statistics Faculty Research & Creative Works

Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs, or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the …

On A Multivalued Prescribed Mean Curvature Problem And Inclusions Defined On Dual Spaces, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This article addresses two main objectives. First, it establishes a functional analytic framework and presents existence results for a quasilinear inclusion describing a prescribed mean curvature problem with homogeneous Dirichlet boundary conditions, involving a multivalued lower order term. The formulation of the problem is done in the space of functions with bounded variation. The second objective is to introduce a general existence theory for inclusions defined on nonreflexive Banach spaces, which is specifically applicable to the aforementioned prescribed mean curvature problem. This problem can be formulated as a multivalued variational inequality in the space of functions with bounded variation, which, …

Classification In Supervised Statistical Learning With The New Weighted Newton-Raphson Method, Toma Debnath

Electronic Theses and Dissertations

In this thesis, the Weighted Newton-Raphson Method (WNRM), an innovative optimization technique, is introduced in statistical supervised learning for categorization and applied to a diabetes predictive model, to find maximum likelihood estimates. The iterative optimization method solves nonlinear systems of equations with singular Jacobian matrices and is a modification of the ordinary Newton-Raphson algorithm. The quadratic convergence of the WNRM, and high efficiency for optimizing nonlinear likelihood functions, whenever singularity in the Jacobians occur allow for an easy inclusion to classical categorization and generalized linear models such as the Logistic Regression model in supervised learning. The WNRM is thoroughly investigated …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractional Differential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Mathematics and Statistics Faculty Research & Creative Works

Using the Coincidence Degree Theory of Mawhin and Constructing Appropriate Operators, We Investigate the Existence of Solutions to Hadamard Fractional Differential Equations (FRDEs) at Resonance

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Open Diameter Maps On Suspensions, Hussam Abobaker, Włodzimierz J. Charatonik, Robert Paul Roe

Mathematics and Statistics Faculty Research & Creative Works

It is shown that if X is a metric continuum, which admits an open diameter map, then the suspension of X, admits an open diameter map. As a corollary, we have that all spheres admit open diameter maps.

Modeling The Development & Expression Of Political Opinion: A Zallerian Approach, Avery C. Ellis

Honors Projects

Research focused on John Zaller's famous RAS model of political opinion formation and change from "The Nature and Origins of Mass Opinion" (1992). Analyzed the mathematical and psychological underpinnings of the model, the first paper to do so in over fifteen years and the first to do so through an analysis of motivated reasoning and Bayesian reasoning. Synthesized existing critiques of Zaller's model and other literature to suggest ways to build on Zaller, utilizing fundamental reunderstandings of opinions and messages from political and mathematical perspectives. Found verification for Zaller's model, confirming its value, but also found support for the proposed …

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

Refining The Inverse Lipschitz Constant For Injective Relu Networks, Cole Rausch

Electronic Theses and Dissertations

In this thesis, we study the Inverse Lipschitz Constant (ILC) of injective ReLU layers. We study the tightness of the ILC lower bound established in Puthawala et al. Our approach has three components. First, we find that the conditions for injectivity on lines yield a weaker condition than the general condition given in Puthawala et al. Second, we perform numerical experiments to judge the tightness of the existing ILC lower bound and find that bound is overly conservative. Third, we identify the source of the potential slack in the proof of the existing ILC bound, and perform further numerical experiments …

A Copula Discretization Of Time Series-Type Model For Examining Climate Data, Dimuthu Fernando, Olivia Atutey, Norou Diawara

Mathematics & Statistics Faculty Publications

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

On A Fully Coupled Nonlocal Multipoint Boundary Value Problem For A Dual Hybrid System Of Nonlinear Q -Fractional Differential Equations, Ahmed Alsaedi, Martin Bohner, Bashir Ahmad, Boshra Alharbi

Mathematics and Statistics Faculty Research & Creative Works

A new class of nonlocal multipoint boundary value problems involving a dual hybrid system of nonlinear Riemann-Liouville-type q-fractional differential equations is studied in this paper. Existence and uniqueness results for the given problem are derived by applying the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle. Examples are presented for illustrating the obtained results. The work established in this paper is a useful contribution to the existing literature on q-fractional differential equations. Some interesting special cases are also discussed.

Critical Point Approaches To Nonlinear Square Root Laplacian Equations, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, Amjad Salari

Mathematics and Statistics Faculty Research & Creative Works

This work is devoted to the study of multiplicity results of solutions for a class of nonlinear equations involving the square root of the Laplacian. Indeed, we will use variational methods for smooth functionals, defined on reflexive Banach spaces, in order to achieve the existence of at least three solutions for the equations. Moreover, assuming that the nonlinear terms are nonnegative, we will prove that the solutions are nonnegative. Finally, by presenting an example, we will ensure the applicability of our results.

An Unsupervised Machine Learning Algorithm For Clustering Low Dimensional Data Points In Euclidean Grid Space, Josef Lazar

Senior Projects Spring 2024

Clustering algorithms provide a useful method for classifying data. The majority of well known clustering algorithms are designed to find globular clusters, however this is not always desirable. In this senior project I present a new clustering algorithm, GBCN (Grid Box Clustering with Noise), which applies a box grid to points in Euclidean space to identify areas of high point density. Points within the grid space that are in adjacent boxes are classified into the same cluster. Conversely, if a path from one point to another can only be completed by traversing an empty grid box, then they are classified …

Contrastive Learning, With Application To Forensic Identification Of Source, Cole Ryan Patten

Electronic Theses and Dissertations

Forensic identification of source problems often fall under the category of verification problems, where recent advances in deep learning have been made by contrastive learning methods. Many forensic identification of source problems deal with a scarcity of data, an issue addressed by few-shot learning. In this work, we make specific what makes a neural network a contrastive network. We then consider the use of contrastive neural networks for few-shot learning classification problems and compare them to other statistical and deep learning methods. Our findings indicate similar performance between models trained by contrastive loss and models trained by cross-entropy loss. We …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

Graduate Theses, Dissertations, and Problem Reports

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Computation Of Separate Ratio And Regression Estimator Under Neutrosophic Stratified Sampling: An Application To Climate Data, Abhishek Singh, Hemant Kulkarni, Florentin Smarandache, Gajendra K. Vishwakarma

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we introduce a novel approach by presenting separate ratio and regression estimators in the context of neutrosophic stratified sampling for the very first time, incorporating auxiliary variables. We have conducted a thorough analysis to estimate these newly proposed estimators' bias and mean square error (MSE) up to the first-order approximation. Theoretically using efficiency comparison criteria, our findings demonstrate the superior performance of these estimators compared to traditional unbiased estimators. Also, numerically based on real-life and artificial data, we have shown the supremacy of the neutrosophic stratified sampling over neutrosophic simple random sampling along with the supremacy of …

Row-Column Designs: A Novel Approach For Analyzing Imprecise And Uncertain Observations, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Classical row-column designs cannot be applied when the underlying data set contains some imprecise, uncertain, or undetermined observations. In this paper, we discuss row-column design under a neutrosophic statistical framework. A significant contribution of our study is to propose a novel approach to analyzing row-column designs using neutrosophic data. This approach involves calculating the neutrosophic analysis of variance (NANOVA) table for the proposed design and using it to derive the FN -test in an uncertain environment. Two numerical examples have been used to assess the proposed design’s performance. Results from the study indicated that a row column design under …