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 …

Maximizing The Number Of H-Colorings Of Graphs With A Fixed Minimum Degree, John Engbers

Mathematical and Statistical Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency-preserving map from the vertex set of G to the vertex set of H.

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 …

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 …

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 …

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 …

Extremal Graphs For Widom–Rowlinson Colorings In K-Chromatic Graphs, John Engbers, Aysel Erey

Mathematical and Statistical Science Faculty Research and Publications

The Widom–Rowlinson graph, H_WR , is the fully looped path on three vertices. Let hom(G,H_WR) be the number of graph homomorphisms from G to H_WR or, equivalently, the number of H_WR-colorings of G. We investigate extremal graphs for hom(G,H_WR) for G in the family of k-chromatic graphs subject to various connectivity requirements. In particular, we determine the graphs G maximizing hom(G,H_WR) in the families of n-vertex k-chromatic graphs, n-vertex connected k-chromatic graphs, n-vertex k-chromatic graphs with c components, n …

Gwid: An R Package And Shiny Application For Genome-Wide Analysis Of Ibd Data, Soroush Mahmoudiandehkordi, Mehdi Maadooliat, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Summary

Genome-wide identity by descent (gwid) is an R package developed for the analysis of identity-by-descent (IBD) data pertaining to dichotomous traits. This package offers a set of tools to assess differential IBD levels for the two states of a binary trait, yielding informative and meaningful results. Furthermore, it provides convenient functions to visualize the outcomes of these analyses, enhancing the interpretability and accessibility of the results. To assess the performance of the package, we conducted an evaluation using real genotype data derived from the SNPs to investigate rheumatoid arthritis susceptibility from the Marshfield Clinic Personalized Medicine Research Project.

Availability …

A Journey From Univariate To Multivariate Functional Time Series: A Comprehensive Review, Hossein Haghbin, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time-dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high-dimensional data. We …

Cryptographic Algorithms, Cryptocurrencies, And A Predictive Model Of Bitcoin Value By Pls Regression, Paul Kenneth O'Connor

Masters Theses

"With the invention of Bitcoin in 2009, as a seemingly timed response to the ongoing financial crisis, the popularity of the cryptocurrency has since continued to grow. Just this year, the Security Exchange Commission approved Bitcoin for exchange traded funds, allowing major investment firms to begin product trading. With this approval, and during this very moment of writing, Bitcoin has entered a bull market and reached a record value of over 72,000 USD. In addition, the Bitcoin halving event in April of 2024 is expected to increase demand even further. It has been anticipated that Bitcoin and other cryptocurrencies will …

Univariate Extreme Value Analysis Of Quantitative Investment Management, George Agbenyega Zumanu

Graduate Research Theses & Dissertations

The evolution of product development within the variable annuity (VA) business have sparked interest in quantitative investment management, particularly as most VA issuers have integrated volatility-controlled funds into their annuity portfolios. Despite the existence of empirical research on statistical analysis of extreme values in conventional investments, there has been a notable gap in research focus towards risk modeling in volatility-controlled funds.

This study contributes by analyzing and modeling the extreme values of investments in volatility-controlled funds, comparing them to conventional equity funds. The financial returns of S&P Dow Jones Indices (SPDJI) indices - SPXTR, risk control SPXT18UT, and managed risk …

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

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.

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

College of Graduate Studies: Theses & 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 …

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

Graduate Theses, Dissertations, and Problem Reports (ETD)

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 …

Development Of Probabilistic Dynamic Model Building And Bayesian Machine Learning Approaches, Samuel Oladayo Adeyemo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Abstract

Development of Probabilistic Dynamic Model Building and Bayesian Machine Learning Approaches

Samuel Adeyemo

The recent years have seen a tremendous increase in the use of artificial intelligence (AI) and machine learning (ML) for the development of data-driven mathematical models needed for performing real-time optimization, model-based control, performance optimization, dynamic data reconciliation, and process performance monitoring. However, the development of data-driven models is faced with some challenges including lack of model interpretability, sensitivity of algorithm to noise in training data, limited extrapolation capabilities and violation of conservation laws. Drawing motivation from these existing gaps, this work aims to develop robust …

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 …

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 …

Generating Neutrosophic Random Variables Based Gamma Distribution, Maissam Ahmad Jdid, Florentin Smarandache, Khalifa Al Shaqsi

Branch Mathematics and Statistics Faculty and Staff Publications

In practical life, we encounter many systems that cannot be studied directly, either due to their high cost or because some of these systems cannot be studied directly. Therefore, we resort to the simulation method, which depends on applying the study to systems similar to real ones and then projecting these results if they are suitable for the real system. The simulation process requires a good understanding of probability distributions and the methods used to transform random numbers that follow a regular distribution in the field [0,1] into random variables that follow them, so that we can achieve the greatest …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Self-Exciting Point Processes In Real Estate, Ian Fraser

Theses and Dissertations (Comprehensive)

This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …

L∞ Bounds For Transient Growth In Repetitive And Iterative Learning Control Systems, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Optimal Stopping And Related Topics, Jackson Scott Hebner

Honors Scholar Theses

Suppose we are observing a randomly evolving system and have the ability to freeze it at any time. If we want to maximize some function of the state of the system, how can we determine the best time to freeze the system based on observations only up until the present moment? That is, without seeing the future, how can we form a rule for stopping the system such that we optimize the expected value of the function of interest to us? This is an informal statement of the concept of optimal stopping, a topic with deep theory and numerous applications. …

A Nonparametric Test For Comparing Survival Functions Based On Restricted Distance Correlation, Quinyang Zhang

Mathematical Sciences Faculty Publications and Presentations

In this article, we propose an omnibus test for comparing two survival functions under non-proportional hazards. The test statistic is based on a product-limit estimate of the restricted distance correlation, which is closely related to the L₂ distance between survival curves. The strong consistency is established under mild regularity conditions. Our simulation studies show that the new test has satisfactory power under proportional hazard and various non-proportional hazards settings including delayed treatment effect, diminishing effect, and crossing survival curves; therefore, it can be a competitive alternative to the existing omnibus tests such as Kolmogorov-Smirnov test, Cramer-von Mises test, two-stage …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

LSU New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.