Numerical Analysis and Scientific Computing Commons^™

Muon Lifetime: Theory, Experiment, And Simulation, Soren Agustin Munoz

Physics

This senior project investigates the muon lifetime through three complementary approaches: theoretical calculation, laboratory measurement, and computational simulation. The theoretical component develops the necessary background from relativistic field theory to the effective weak interaction, culminating in the leading-order Fermi-theory prediction of τ ≈ 2.2 μs, which explains why the muon lifetime lies on the microsecond scale.

The experimental component measures the lifetime of stopped cosmic-ray muons using a plastic scintillator, photomultiplier tube, and analog timing electronics. A binned Poisson likelihood fit to the primary 15-day acquisition run τ = 2.17^+0.03_-0.09 μs, consistent with the accepted value within the …

Pyspqr: A Python Package For Density Estimation Using Deep Learning, Cameron Eddy, Reetam Majumder

Electrical Engineering and Computer Science Undergraduate Honors Theses

Splines are used for representing complex functions. In statistics, splines can be used for distributional shapes that are difficult to model by traditional parametric approaches. Ramsay (1) uses M-Spline bases to estimate continuous distributions. Semi-Parametric Quantile Regression (SPQR), developed by Xu and Reich (2), models conditional distributions where a neural network is used to estimate the basis function weights that depend on covariates. (3) implements a package for SPQR in R. We build on this by implementing a version of SPQR in Python with PyTorch. By using PyTorch, we can use more sophisticated deep learning architectures than those available in …

Maddenlite, Sergio Pena

Presentations - 2026

Problem •“What If” scenarios impossible to test accurately •Commercial games rely on arcade physics •Spreadsheets lack visual engagement

Motivation •Passion for football analytics •Desire to simulate cross-era matchups •Apply math models to real-world sports data

Solution •Python based simulation engine using historical play-by-play data •Simulates outcomes based on probability

Swimming In Uncertainty: Filling Data Gaps And Providing An Educational Platform For Beach Water Quality At Tybee Island, Georgia, Lukas Roberson

College of Graduate Studies: Theses & Dissertations

@font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-536870145 1107305727 0 0 415 0;}p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0in; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman",serif; mso-fareast-font-family:"Times New Roman";}.MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; mso-font-kerning:0pt; mso-ligatures:none;}div.WordSection1 {page:WordSection1;}

Swimming in beaches water contaminated with high levels of bacteria can make you sick. Current monitoring at the public beaches on Tybee Island consists of weekly monitoring and enumeration of fecal indicator bacteria that takes 24 hours for results. If the number of bacteria exceed regulatory limits, a public health advisory is issued, and affected waters are retested until …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

How’S It Growing? Tools For Observing Snow And Sea Ice In A Changing Arctic Ocean, Ian Alexander Raphael

Dartmouth College Ph.D Dissertations

September Arctic sea ice extent has diminished by roughly 50% in the 45 years since satellite observations began. The Arctic Ocean may experience ice-free summers within the next decade, with implications for habitat, resource extraction, geopolitics, and local and global climate change. To predict how Arctic sea ice will change in the future, we need to understand its behavior in the present. In situ sea ice mass balance measurements (snow accumulation, ice growth, snow and ice surface melt, and bottom melt) are essential for studying the processes driving rapid changes in the ice pack, and for validating remote sensing measurements …

A Comparative Study Of Neural Networks And Xgboost Models For Flight Time Prediction, Ioannis Paraschos, Taryn E. Trimble, Eshna Bhargava, Jake Klingler, Benjamin R. Nicolai

Beyond: Undergraduate Research Journal

Flight time prediction plays a crucial role in modern air travel, benefiting airlines and passengers alike. Accurate predictions enable airlines to optimize schedules, allocate resources effectively, and ensure passenger safety and satisfaction. In recent years, machine learning models, such as neural networks and XGBoost, have gained popularity for predicting flight times. This study aims to compare the performance of neural network and XGBoost models in predicting flight times, considering factors such as weather conditions, air traffic control, and aircraft performance. The results indicate that both models are effective, with XGBoost achieving slightly higher accuracy. However, neural networks offer advantages in …

Using Gaussian Process Regression To Learn Thermodynamic Equations Of State With Uncertainty Quantification, Austen T. Lee

Chemical Engineering Undergraduate Honors Theses

This study investigates the use of derivative-informed Gaussian Process (GP) models to estimate thermodynamic behavior across temperature and density by building a Helmholtz-based equation of state. Argon, a stable monatomic gas, was chosen as a case study within the vapor region. The GP model was trained using values of experimentally measurable properties found by taking first and second derivatives of the original potential function. Results show that while the GP model offered uncertainty quantification and informed thermodynamic behavior, it predicted values that deviated from the ground truth depending on the property. The model exhibited high confidence in regions with substantial …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

The Presence Of Outer Giant Planets And Their Role In Inner Planet Formation With And Without Their Influence, Mateo E. Guerra Toro

Graduate Theses/Dissertations

We performed dynamical simulations of the giant impact phase of planet formation to investigate the formation of inner terrestrial planets under the influence of 4 solar system-like outer giant planets. We developed a new code using the N-body simulation suite REBOUND and REBOUNDx (Rein et al. (2019) and Tamayo et al. (2019)) to simulate 2 stages of planetary formation: a residual gaseous protoplanetary disk phase and subsequent dynamical evolution after the disk photoevaporates. The initial conditions for the inner planetary embryos were taken by Morrison et al. (2020) based on a range of solid surface densities that produced Super-Earth terrestrial …

Linking Empirical Data And Numerical Simulation To Characterize Dynamic Fire Behavior Associated With Interacting Firelines, Marta Sergeevna Jerebets

Graduate Student Theses, Dissertations, & Professional Papers

Understanding fuel pattern-fire process relationships is key for predicting fire behavior and effects with follow-on benefits to proactive fire management and model validation. To characterize dynamic fire behavior, this thesis leverages empirical data and numerical simulation through two complementary studies.

In the first study, longwave thermal sensors aboard unmanned aerial systems (UAS) were used to capture fine-scale fire behavior in two experimental grass burns. A novel paired design was used to quantify the effects of fuel arrangement on fire behavior with 3.66 m diameter treatments cut to a height of 0.15 m. The treatments ephemerally reduced fire rate of spread …

Impact Of Urban Development On Uv Exposure: A Clustering And Machine Learning Assessment, Taufik Roni Sahroni Mr., Verdi Yasin, Lulut Alfaris, Reza Ariefka, Ruben Cornelius Siagian, Mohammad Alfin Karim, Nana Rahdiana, Ade Suhara

Journal of Environmental Science and Sustainable Development

The relocation of Indonesia's capital city is anticipated to promote inclusive economic growth while embracing cultural diversity. However, this transition may affect ultraviolet (UV) radiation exposure patterns. The study investigated variations in UV exposure in the IKN region, focusing on urban development factors such as land use and population density that affect public health, sun protection, and skin cancer prevention. The research hypothesized that UV radiation is significantly correlated with these factors. UV Index data from 2010-2023, a hierarchical clustering method, identifies complex data patterns without determining the number of clusters. XGBoost, a machine learning model, was used for handling …

Calculation And Statistical Analysis Of Wins Above Replacement, Joshua Taylor

Departmental Honors & Graduate Capstone Projects

The Wins Above Replacement (WAR) statistic in Major League Baseball is a prominent metric used to estimate player value by quantifying all aspects of play in terms of wins added to a baseball team. We will use R to calculate WAR for all players from 1871 to 2012 and use data from those years to construct multivariate predictive models to attempt to estimate WAR for players from 2013 to 2024. We find strong correlations between predicted and actual WAR values for most models, with the exception of the polynomial predictive model for non-qualified pitchers.

Gradient Wild Bootstrap For Instrumental Variable Quantile Regressions With Weak And Few Clusters, Wenjie Wang, Yichong Zhang

Research Collection School Of Economics

We study the gradient wild bootstrap-based inference for instrumental variable quantile regressions in the framework of a small number of large clusters in which the number of clusters is viewed as fixed, and the number of observations for each cluster diverges to infinity. For the Wald inference, we show that our wild bootstrap Wald test, with or without studentization using the cluster-robust covariance estimator (CRVE), controls size asymptotically up to a small error as long as the parameter of endogenous variable is strongly identified in at least one of the clusters. We further show that the wild bootstrap Wald test …

Multi-Case Study Of Left-Flank Boundaries Within Supercells, Peyton B. Stevenson

Department of Earth and Atmospheric Sciences: Dissertations, Theses, and Student Research

This study investigates the prevalence and significance of forward-flank convergence boundaries (FFCBs) and left-flank convergence boundaries (LFCBs) in shaping the structure and intensity of supercells, using observational data from various field projects. Unlike previous research focusing on individual cases, this study examines a diverse range of cases to provide comprehensive insights into the relationship between these boundaries and supercell characteristics such as intensity, longevity, and tornadogenesis. By analyzing high-resolution surface data, the research addresses the frequency, location, and intensity of these boundaries, and their impact on pseudo vertical vorticity, pseudo convergence, and density gradients. A total of 228 boundary identifications …

Stock Market Volatility In The United Kingdom: Simulating Post-Covid-19 Recovery, Bala A. Dahiru, Mohammed Shuaibu, Najibullah Hassanov

CBN Journal of Applied Statistics (JAS)

This paper investigates the time it would take for the FTSE-100 index to reach its post-COVID-19 peak. The paper utilises an exponential generalised autoregressive conditional heteroscedasticity (EGARCH) model that accounts for leverage effect and asymmetries. The preferred models amongst competing variants was the Autoregressive Moving Average (ARMA)-EGARCH(2,1) specification and was used to predict daily FTSE-100 data from 5th January 2000 to 21st June 2024. The empirical exercise showed that the COVID-19-induced financial crisis negatively affected the United Kingdom’s stock market performance. The results show that the FTSE100 index could reach its post-pandemic peak around 27th August, 2024 (two months after …

Physician-Patient Interactions In Online Healthcare Communities: The Effects Of Preconsultation On Service Delivery And Patient Satisfaction, Qian Tang, Anqi Zhao

Research Collection School Of Computing and Information Systems

Preconsultation by medical professionals is a common practice in offline healthcare services to improve consultation efficiency but is rarely adopted for online healthcare services. In a noteworthy departure from this trend, a Chinese online healthcare community (OHC) has instituted preconsultation by assistant physicians prior to online consultations. Using comprehensive service data from this OHC, this study scrutinizes the effects of preconsultation on online healthcare services from both the physician and patient perspectives. The findings reveal that preconsultation by the assistant physician can significantly increase the attending physician’s response speed, length, and provision of informational support, while maintaining a consistent level …

Code For Care: Hypertension Prediction In Women Aged 18-39 Years, Kruti Sheth

Electronic Theses, Projects, and Dissertations

The longstanding prevalence of hypertension, often undiagnosed, poses significant risks of severe chronic and cardiovascular complications if left untreated. This study investigated the causes and underlying risks of hypertension in females aged between 18-39 years. The research questions were: (Q1.) What factors affect the occurrence of hypertension in females aged 18-39 years? (Q2.) What machine learning algorithms are suited for effectively predicting hypertension? (Q3.) How can SHAP values be leveraged to analyze the factors from model outputs? The findings are: (Q1.) Performing Feature selection using binary classification Logistic regression algorithm reveals an array of 30 most influential factors at an …

Mathematically Rigorous Deep Learning Paradigms For Data-Driven Scientific Modeling, Owen Nicholas Davis

Mathematics & Statistics ETDs

This dissertation explores the crucial role of data-driven modeling in science and engineering, with a focus on developing surrogate models to accelerate large-scale computational tasks, aiding in both outer-loop functions like uncertainty quantification and expensive inner-loop tasks within broader computational frameworks. Challenges arise with increased problem dimension and sparse, noisy training data, particularly significant when constructing surrogates for very expensive computational models where acquiring sufficient high-fidelity training data is unfeasible. In such scenarios, training surrogates from an ensemble of multifidelity information sources of varying accuracy and cost becomes essential. We emphasize neural network-based modeling paradigms, which are flexible in integrating …

External Debt Pass-Through To Inflation In Nigeria, Emmanuel A. Asue, James V. Ikyaator

CBN Journal of Applied Statistics (JAS)

This study examines external debt pass-through to inflation in Nigeria using annual data from 1981 to 2020 based on structural vector autoregressive (SVAR) model. The results reveal that an increase in external debt service leads to a significant depreciation of the exchange rate, which leads to a contemporaneous increase in inflation, while the direct response of inflation to external debt is statistically not significant. The impulse response confirms these results. The forecast error variance decomposition depicts that future values of official exchange rate depend on external debt, inflation and external debt service. The study recommends that the Nigerian government should …

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Forecasting Stock Indices With The Covid-19 Infection Rate As An Exogenous Variable, Mohammad Saha A. Patwary

School of Computing and Informatics

Forecasting stock market indices is challenging because stock prices are usually nonlinear and non- stationary. COVID-19 has had a significant impact on stock market volatility, which makes forecasting more challenging. Since the number of confirmed cases significantly impacted the stock price index; hence, it has been considered a covariate in this analysis. The primary focus of this study is to address the challenge of forecasting volatile stock indices during Covid-19 by employing time series analysis. In particular, the goal is to find the best method to predict future stock price indices in relation to the number of COVID-19 infection rates. …

Improving The Efficiency Of Exponential Ratio-Type Estimator For Population Median: A Calibration Weight Adjustment Approach, Mathew J. Iseh, Kufre J. Bassey

CBN Journal of Applied Statistics (JAS)

This paper modifies the Bahl and Tuteja exponential ratio-type estimator for population median under simple random and stratified sampling schemes using calibration weight adjustment technique with supplementary information to vary the stratum weights. The bias and mean square error of the modified estimator were obtained up to the second-order approximation, which satisfies the necessary conditions for efficiency. The findings show that the new estimator surpasses existing estimators in efficiency gain. This suggests the appropriateness of calibration weight modification in boosting the efficiency of a population parameter estimator under stratified random sampling especially where the population parameter of the auxiliary variable …

Statistical Methods To Generate Artificial Slot Floor Data For The Advancement Of Casino Related Research, Courtney Bonner, Anastasia (Stasi) D. Baran, Jason D. Fiege, Saman Muthukumarana

International Conference on Gambling & Risk Taking

Abstract:

A common difficulty when researching gambling topics is the availability of high-quality data sets for development and testing. Due to the high level of secrecy within the gambling industry, if data is obtained for research purposes it is often prohibitively obfuscated, incomplete, or aggregated. Although these data have allowed for advancement in academic work, it leaves both the researchers and readers left wondering about what would be possible if more detailed data sets were available. To mitigate the paucity of data available to researchers, we present a Markov chain-based statistical process for producing artificial event data for a simulated …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Quantification Of Various Types Of Biases In Large Language Models, Sudhashree Sayenju

Doctor of Data Science and Analytics Dissertations

Natural Language Processing (NLP) systems are included everywhere on the internet from search engines, language translations to more advanced systems like voice assistant and customer service. Since humans are always on the receiving end of NLP technologies, it is very important to analyze whether or not the Large Language Models (LLMs) in use have bias and are therefore unfair. The majority of the research in NLP bias has focused on societal stereotype biases embedded in LLMs. However, our research focuses on all types of biases, namely model class level bias, stereotype bias and domain bias present in LLMs. Model class …

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 …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

Doctoral Dissertations and Master's Theses

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

Application Of Probabilistic Ranking Systems On Women’S Junior Division Beach Volleyball, Cameron Stewart, Michael Mazel, Bivin Sadler

SMU Data Science Review

Women’s beach volleyball is one of the fastest growing collegiate sports today. The increase in popularity has come with an increase in valuable scholarship opportunities across the country. With thousands of athletes to sort through, college scouts depend on websites that aggregate tournament results and rank players nationally. This project partnered with the company Volleyball Life, who is the current market leader in the ranking space of junior beach volleyball players. Utilizing the tournament information provided by Volleyball Life, this study explored replacements to the current ranking systems, which are designed to aggregate player points from recent tournament placements. Three …

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil

Electronic Theses and Dissertations

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features …