Statistics and Probability Commons^™

A Longitudinal Study Of Achilles Tendon Adaptation In Ncaa Division I Female Gymnasts: Associations With Menstrual Status, Birth Control Use, Pain, Limb Dominance, And Training Exposure, Mattie Jane Hyde

Electronic Theses and Dissertations

This longitudinal study evaluated Achilles tendon (AT) thickness in 22 NCAA Division I (DI) female gymnasts across three consecutive seasons in relation to menstruation, birth control use, pain, limb dominance, training week, and year of collegiate competition. Weekly ultrasound and athlete survey data were analyzed using mixed-effects models for absolute AT thickness and change in thickness from baseline measurements. Associations were primarily characterized by interactions rather than uniform effects of individual predictors. A Pain × Limb Dominance × Week × Year interaction was associated with both thickness outcomes across season-specific and combined analyses, with relationship directions varying by limb, season …

Predicting Remaining Useful Life Using Multivariate Time-Series Data, Anayah Smith, Victoria Gaibor

Discovery Day - Daytona Beach

Accurate prediction of Remaining Useful Life (RUL) is critical for enabling predictive maintenance, improving system reliability, and reducing operational costs in degrading systems. This project addresses the problem of modeling and predicting RUL using multivariate time-series sensor data from the NASA CMAPSS turbofan engine dataset, with a focus on understanding how predictive performance changes across datasets of varying complexity. The objective is to develop a reproducible machine learning pipeline that captures degradation patterns and produces reliable time-to-failure predictions. The approach includes data preprocessing, exploratory data analysis, feature engineering, dimensionality reduction, and model evaluation. RUL values are computed and capped to …

Predicting Passenger Demand On National Flights Departing From Hartsfield-Jackson Atlanta International Airport (Atl) In 2024, Brooklyn Gossett, Ana Yu Wen

Discovery Day - Daytona Beach

The aviation industry relies heavily on accurate demand forecasting to guide critical decisions regarding route planning, capacity management, and pricing strategy. Misjudging passenger demand can result in significant revenue loss and operational inefficiency, making it essential for airlines and analysts to identify the key drivers of flight patronage. This study investigates the factors that most significantly predict the number of passengers on domestic flights departing from Hartsfield-Jackson Atlanta International Airport (ATL) during the 2024 calendar year. Using passenger and route data sourced from the Bureau of Transportation Statistics (BTS) and the U.S. Department of Transportation (DOT), a multiple regression analysis …

A Compact Representation Of Oscillatory Limits Via Asymptotic Value Distributions, Ibrahim Arnous, Eric M. Rodarte, Chirag Kumar

Discovery Day - Daytona Beach

Classical limits describe asymptotic behavior through convergence to a single value, but many important oscillatory functions do not converge in this sense. Standard examples such as sin(𝑥) as 𝑥→∞ and sin(1/x) as x→0 instead display stable distributions of values over time. This project examines how such behavior can be described using a measure-theoretic framework, particularly through occupation measures and, in sequence-based settings, Young measures. The objective is to present this perspective in a clear and accessible way while introducing the Ansatz representation, a compact notation for recording the support and density of an asymptotic value distribution when the limiting measure …

Bounded Thunderstorm Tracking Of Lightning Events With Muon Detection, Skylar Wardlaw, Ainsley Helgerson, Maria Kaminska, Logan Velvet, Georgii Dubrov, Jackson Stewart, Aaron Jung, Nathaniel O’Hara, Amelia Koth, Nash Mcleod, Emaleth Wyckoff

Discovery Day - Daytona Beach

The muon is a high-energy particle that can be produced by cosmic rays and trigger upper-atmospheric particle cascades and energetic processes. It has been hypothesized that such cascades are at the onset of lightning. As such, muons serve as a valuable probe for investigating the underlying mechanisms of its initiation, whose full governing dynamics remain vastly unknown despite extensive research. Traditional approaches to lightning research involve simulations and observations of the discharge itself, but the role of high-energy particle interactions has yet to be fully constrained. The CosmicWatch Muon Detector design enables the detection of atmospheric muons through scintillation events, …

Statistical Methodologies For Count Time Series Analysis And Topological Data Analysis Of Medical Images, Yuhyeong Jang

Statistical Science Theses and Dissertations

This dissertation addresses two distinct topics related to count time series analysis and topological medical image analysis, respectively. The first part of the dissertation comprises an application of a count time series model to analysis of US monthly sex trafficking data and development of a new model for multivariate count data that exhibits serial dependence and overdispersion. By imposing a family of multivariate mixed Poisson distributions on the count random vector, the proposed model can accommodate a broad range of overdispersion as well as positive contemporaneous correlations. For maximum likelihood estimation, a computationally feasible EM-type algorithm is derived based on …

Algebraic And Topological Methods In Computational Neuroscience, Trong-Thuc Trang

Electronic Theses and Dissertations 2020 - Present

Neural data is incredibly rich in combinatorial, topological, and geometrical information, reflecting the intricate shape and connectivity of neural firing patterns. To decipher these structures, neuroscience increasingly relies on advanced mathematical tools to analyze neural activity. Here we study (1) neural codes within the poset P_Code of neural codes and (2) the connectivity of neural population activity within the insular cortex when responding to interoceptive information. In (1), we establish combinatorial constructions for all upward covering relations based on what we call “isolated subsets” with supporting theorems and give a slight modification of the existing downward covering relations. We …

Ground To Roof Snow Load Ratio (Gr) Data Release, Brennan Bean, Cooper Nelson, Jesse Wheeler, Scout Jarman, Salam Adil Al-Rubaye, Marc Maguire

Browse all Datasets

This data release provides historical ground-to-roof snow load ratio (GR) datasets used for snow load research and model development. The release includes original referenced datasets, cleaned country specific datasets, and a master dataset that combines Canadian and United States datasets into a standardized format for research and engineering applications.

A Semantic Data Management Framework For Uncertainty Quantification In Synchrotron Diffraction Pattern Analysis, Ayorinde E. Olatunde, Ozan Dernek, Erika I. Barcelos, Roger H. French, Anirban Mondal

Student Scholarship

Advancements in technology have enabled scientists and engineers in the synchrotron science domain to generate high-dimensional data. To conduct a machine learning study on these data, an analyst undergoes multiple analytical stages, including dimensionality reduction, predictive modelling, and uncertainty quantification (UQ).

To ensure reproducibility in science, it is necessary to document the semantic relationships among the stages of the analysis to enable provenance, interoperability, and knowledge reuse. In this work, we present a Semantic Data Management (SDM) framework rooted in FAIR principles that provides ontologies for UQ workflows. We illustrate the application of UQ ontology in synchrotron diffraction pattern analyses …

Wavelet-Based Multiscale Analysis Of Cave Co₂ Concentration In Response To Short-Term High-Intensity Tourism Activities: Spatiotemporal Heterogeneity And Lag Characteristics, Mingda Cao, Wenwen Song, Yan Zhang, Jie Zhang, Zhiqiang Yao

International Journal of Speleology

High-intensity tourism activities can cause a significant increase in cave air CO₂ concentration, thereby affecting the cave micro-environment and secondary carbonate deposition. During the 2023 National Day Golden Week, high-frequency continuous monitoring of cave air CO₂ partial pressure (PCO_2(A)) and visitor numbers was conducted in Dawang Cave, Anhui Province. Wavelet transform and cross-correlation analyses were used to reveal the multi-scale response characteristics of CO₂ concentration to tourism activities. The results show that: (1) PCO_2(A) exhibited clear diurnal variations (higher during the day, lower at night) and decreased spatially with enhanced ventilation, controlled jointly by …

Community Detection In Bipartite Networks Using Bipartite Stochastic Block Models With Node-Level Covariates, Geraldine Elaine Percival

Dissertations

In this age, monumental webs of data demands for perpetual cultivation of ways to untangle these webs of information. One of the many curiosities is how to systematically group entities. When clustering, one avenue to take is ascertaining the interconnectedness between the data points, and gauging their influence to each other. This perspective is programmed to model the relationships between the data presented as a network. Many of the methods being used today are algorithm-based, which may pose limitations in understanding and explaining the uncertainty revolving around the data. Hence, it is proposed to steer towards a model-based approach that …

Improving Tensorsketch Using Complex Random Variables, Amit Sharma, Mohammad Azhar Khan, Rameshwar Pratap, Keegan Kang

Faculty Conference Papers and Presentations

TensorSketch by Pham and Pagh [2013], Kar and Karnick [2012] provides efficient sketching algorithms for highdimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. Kar and Karnick [2012] uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, whereas Pham and Pagh [2013] extends the sparse CountSketch [Charikar et al., 2024] algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\left(p(\nnz{\vec{x}} + D \log D)\right)$. However, the variance of both estimators grows exponentially with the polynomial degree $p$, scaling as $3^{p}/D$, where $D$ denotes the sketch dimension. Recent work by Wacker et al. [2023] showed that using complex-valued distribution reduces …

Laplace Factor Models In High-Dimensional Data, Siqi Liu, Xuerong Meggie Wen, Akim Adekpedjou, Guangbao Guo

Mathematics and Statistics Faculty Research & Creative Works

Laplace factor models (LFMs) provide a heavy-tailed alternative to Gaussian factor models by representing high-dimensional observations through a low-rank common component and Laplace-distributed idiosyncratic errors. This paper develops an assumption-consistent finite-sample analysis of matrix concentration, covariance estimation, and Monte Carlo integration under this model. We first formulate the model with explicit dimensional, independence, covariance, and identifiability conditions. Standard matrix Laplace-transform and matrix Bernstein inequalities are then recalled with their precise applicability conditions. Because untruncated Laplace variables are neither almost surely bounded nor strongly log-concave, these standard results cannot be applied directly in the forms commonly used for bounded or Gaussian-like …

Fixed Points For Fitted Lines, David L. Farnsworth

Articles

For many fitting methods for lines in the plane, each observation possesses an associated point in the plane, or at infinity for particular observations. These associated points are called “fixed points,” because properly chosen replacement points for the originally selected observation create other fitted lines that contain the same fixed point. Simple linear regression and orthogonal least-squares regression are investigated as examples. The phenomenon has been previously noted for simple regression, where the properly selected replacement points are related to regression diagnostics and the determination of outliers. Orthogonal regression lines are fundamental to principal component analysis. Mechanical devices for simple …

Some Results About Orthogonal Least-Squares Lines, Steven J. Kilner, David L. Farnsworth

Articles

A set of quantitative bivariate data is augmented with one additional point. Orthogonal least-squares fitting is used for the original set and the augmented set. The possible locations of the two lines, the points of means of the two sets, and the augmenting point are examined.

Physics-Guided Deep Learning For Predictive Modeling Of Spatiotemporal Dynamical Systems, Niharika Deshpande

Engineering Management & Systems Engineering Theses & Dissertations

Many physical and networked systems evolve under continuously changing spatial and temporal conditions. Transportation networks respond to fluctuating demand, atmospheric fields reorganize as storms intensify, and coastal response depends on localized forcing pathways. Modeling such systems requires learning formulations that adapt to evolving structure, operate on irregular geometries, and provide interpretable measures of predictive uncertainty. This dissertation develops a physics-guided spatiotemporal learning framework designed for structured dynamical systems whose governing interactions are neither static nor Euclidean. The central premise is that spatial relationships in these systems are dynamic and geometry-dependent. To represent this behavior, system states are modeled on time-varying …

Spatial Prediction Under Uncertainty: Methodological And Computational Advances In Bayesian Maximum Entropy, Kinspride K. Duah

All Graduate Theses and Dissertations, Fall 2023 to Present

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that …

The Impact Of State Insulin Copayment Caps On Diabetics In The United States, Ryan C. Meyer

All Theses

Insulin is a life-saving medication for people with diabetes that helps regulate blood glucose levels throughout the body. A Type 1 diabetic cannot survive without insulin, and a Type 2 diabetic’s quality of life greatly diminishes without access and use of this drug. Currently, many diabetics skip, ration, or abstain from insulin due to financial barriers. As of June 2026, 29 states have enacted insulin copayment caps for state-regulated commercial health insurance plans to reduce the financial burden of insulin costs. This study examines the impact of these caps on all commercially insured diabetics in the United States, particularly on …

Criticality In A Heterogeneous Neutron Transport Rod Model, Samuel Kaleb Crowford

All Graduate Reports and Creative Projects, Fall 2023 to Present

This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the …

Physics Model Calibration Via Functional Kernel Regression, Kwesi Appau Ohene-Obeng

Open Access Theses & Dissertations

Physics based computational simulators encode the governing equations of complex physical phenomena through parameters that must be inferred from empirical observations, and the observational record in modern experimental campaigns is increasingly a high dimensional functional response rather than a scalar summary. The canonical treatment of this calibration problem through the additive discrepancy decomposition of Kennedy and O'Hagan incurs O(N^3obs) Gaussian process inversion costs at functional resolution, sensitivity to discrepancy prior specification, and the confounding identifiability between the calibration parameter and the discrepancy function; scalar reduction strategies bypass the cost but discard the morphological information that the functional response carries about …