Numerical Analysis and Computation Commons^™

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 …

(R2072) A Method To Sample From Transition Densities Of Diffusion Processes With Unknown Densities, Yasin Kikabi, Juma Kasozi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a reliable method that can be used to sample paths of a diffusion process described by a system of stochastic differential equations. These are types of processes whose transition density is not known in closed form. This reliable method involves solving a partial differential equation of the Fokker-Planck type by rejection sampling techniques applied to the associated densities. We then use the novel method to sample from the Ornstein-Uhlenbeck (OU) process whose transition density is known and has unbounded drift. The results obtained compare excellently with the analytical results, thus rendering the method reliable and …

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

Complex Systems Mapping Of Fiscal Growth Dynamics At Strategic Maritime Chokepoints Using Time-Series Slopes, Rahul Balamurugan, Preethi Nanjundan, Avichal Sharma

Northeast Journal of Complex Systems (NEJCS)

This study examines how maritime and trading states allocate public resources between defence, health, and economic growth around three strategic chokepoints the Strait of Malacca, the Strait of Hormuz, and the Suez Canal. The analysis extends the classic “guns versus butter” framing by treating defence and health spending as co-evolving components of an interconnected fiscal-growth system. Using World Development Indicators data (1999-2024), trend slopes are estimated for military spending (% of GDP), healthcare spending (% of GDP), and GDP growth (annual %). Two derived indicators are computed, a defence-to-health slope ratio (military slope/health slope) and a fiscal-balance proxy (health slope …

Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski

Mathematical Modelling and Numerical Simulation with Applications

The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …

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 …

Coupled Machine Learning Models: Combining Observations And Numerical Analysis In A Physics-Regularized Approach, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

This dissertation investigates surrogate modeling for fixed-location environmental forecasting using novel data-combination techniques. The work surveys the landscape of observational measurements and numerically generated data, identifying similar research and gaps in current methodologies. The ratio-coupled training framework is introduced to combine two data sources per predicted feature through a tunable parameter that weights training signal strength. An optimization scheme is developed to simultaneously tune surrogate weights and the coupled signal ratio, allowing relative influence between signals to act as an explicit regularizer. Three case studies demonstrate the methodology and approach in a variety of contexts. The first study is based …

The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up, Nysa Vedwan, Shane Carey

LASER Journal

In Adam McKay’s 2021 satirical sci-fi movie Don’t Look Up, two astronomers discover a comet heading directly toward Earth. Despite overwhelming evidence and near-certainty of global extinction, their warnings are ignored and ridiculed. This paper discusses the mathematical and scientific foundations of the movie’s social and political reception, and specifically focuses on orbital prediction and probabilistic modeling as they relate to public understanding of risk. This paper shows how data is often undermined by political and social dynamics, by connecting the fictional events of the movie with real-world crises like the COVID-19 pandemic and the climate emergency. In Don’t Look …

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

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 …

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …

Analysis Of Systematic Trade-Offs Between Military And Healthcare Expenditure Alongside Gdp Growth Of Select Asian And Western Exporting Economies In The 21st Century, Rahul Balamurugan, Carlos Gershenson, Preethi Nanjundan, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study explores the complexity in the trade-offs between military expenditure, healthcare expenditure, and GDP growth across select Asian nations and major weapon-exporting countries, examining how nations allocate finite resources between national security and human well-being over the past two decades. Using a systems science approach, the research integrates Granger causality testing to analyze temporal and directional relationships among GDP growth, military expenditure, and healthcare expenditure, uncovering their dynamic interdependencies. The methodology includes trend and slope analysis, Granger causality testing, outlier detection, and clustering to identify heterogeneity in resource allocation strategies. Developed, weapon-exporting nations exhibit complementary trends, with strong causality …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Predicting Real Estate Prices Using Deep Learning Regression Models On Socio Spatial Data, Gentle Engworo

Graduate Theses/Dissertations

ABSTRACT

Cities keep their own kind of ledger. Every block, bus stop, corner store, and year that slips by leaves a small entry about what homes are worth. That ledger is what we call socio-spatial data: simple facts about what a home is (its age), where it sits (latitude/longitude), how easy it is to get around (distance to the nearest MRT station), what’s nearby (number of convenience stores), and when it sold (transaction date). This thesis asks a practical question in that everyday language: given these common clues, can we predict home prices more accurately and explain why? Using 414 …

Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

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 …

A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, Krishna Kumar Gupta, Suneet Saxena

Applications and Applied Mathematics: An International Journal (AAM)

Probabilistic fuzzy set is used to model the non-probabilistic and probabilistic uncertainties simultaneously in the system. This study proposes a cumulative probability-based discretization and probabilistic fuzzy set based novel fuzzy time series forecasting method. It also proposes a novel discretization approach based on cumulative probability to tackle the probabilistic uncertainty in partitioning of datasets. Gaussian probability distribution function has been used to construct probabilistic fuzzy set. The advantage of the proposed work is that it addresses the uncertainties due to randomness and fuzziness simultaneously and also improves accuracy rate in time series forecasting. A proposed forecasting method is applied on …

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 …

A Comparative Analysis Of A Family Of Advanced Iterative Optimization Methods In Nonlinear Regression, Tanmoy Kumar Debnath

College of Graduate Studies: Theses & Dissertations

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in …

Optimizing Sports Outcome Prediction Through Feature Engineering And Machine Learning, Vitor S. Freitas

Graduate Theses/Dissertations

The challenge of predicting the outcome of a team game lies in the high complexity and dynamics of the sports data. This thesis focuses on the aspect of using feature engineering and the genetic algorithm to predict the winner and the score of various sports events. Generally, it deals with how machine learning algorithms are combined with state-of-the-art feature engineering techniques in sports datasets derived from various sports disciplines. In this thesis, five different machine learning models have been applied, classification and regression trees (CART), random forest (RF), stochastic gradient boosting (SGB), eXtreme gradient boosting (XGBoost), and extreme learning machine …

Simulation Of Wave Propagation In Granular Particles Using A Discrete Element Model, Syed Tahmid Hussan

College of Graduate Studies: Theses & Dissertations

The understanding of Bender Element mechanism and utilization of Particle Flow Code (PFC) to simulate the seismic wave behavior is important to test the dynamic behavior of soil particles. Both discrete and finite element methods can be used to simulate wave behavior. However, Discrete Element Method (DEM) is mostly suitable, as the micro scaled soil particle cannot be fully considered as continuous specimen like a piece of rod or aluminum. Recently DEM has been widely used to study mechanical properties of soils at particle level considering the particles as balls. This study represents a comparative analysis of Voigt and Best …

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 …

Mathematical Modeling Of The Impact Of Lobbying On Climate Policy, Andrew Jacoby, Claire Hannah, James Hutchinson, Jasmine Narehood, Aditi Ghosh, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Departmental Research

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Brief Review: Low Frequency Event Charts (G-Charts) In Healthcare, James Espinosa, David Ho, Alan Lucerna, Henry Schuitema

Rowan-Virtua Research Day

The ability to determine if a change in a system is actually an improvement—or worsening in function—is one of the essential desiderata of quality improvement efforts. There are many ways to look at the issue. A special problem occurs when the event being studied is low frequency by nature. By way of example, patient falls in a given hospital or division of a hospital may occur in a way that is low frequency—yet each event is important. Process engineering has developed an approach to low frequency events. Part of this approach may involve specialized charts that look at the “time-between-events”—as …

National Residency Matching Program: Looking At The Data Through Linear Regressions, Jacklyn Tellez

Undergraduate Theses

The National Residency Matching Program (NRMP) oversees the process of medical school graduates being matched to a residency program. The NRMP determines both the hospital and residency program for medical students. Prior to matching, both hospital programs and students rank each other. The NRMP uses these lists to determine the matches. Four distinct models using data from hospitals and applicants were used to determine what characteristics lead to a chance of being matched. Each model went through multiple rounds of testing to determine the importance of the different independent variables. In each data set, the dependent variable is either the …

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 …

Novel Bayesian Neural Networks And Uncertainty Quantification Of Computational Mechanics Models, Ponkrshnan Thiagarajan

Dissertations, Master's Theses and Master's Reports

Computational and data-driven models suffer from a wide range of uncertainties that impact the reliability of such models. Given the exponential proliferation of machine learning models in real-world systems, establishing a degree of confidence in their predictions becomes paramount. Reliability in predictions takes on utmost significance in domains such as autonomous driving, medical image analysis, etc., where human lives are involved, and inaccuracies in predictions could lead to disastrous outcomes. For these reasons, comprehending and quantifying uncertainties in computational and data-driven models is of utmost importance. A number of techniques have been developed to quantify uncertainties in machine learning models. …

Efficient Hierarchical Space-Time Models For Large Areal Datasets With Application To Forest Inventory Mapping Using Remote Sensing Imagery, Md Kamrul Hasan Khan

Graduate Theses and Dissertations

The focus of this dissertation is development of a novel hierarchical framework, that can be used for predictive modeling of Forest Inventory and Analysis (FIA) data over large regions. This dissertation has two significant contributions. Based on a study region in north-central Wisconsin, we analyze satellite imagery, along with a sample of national forest inventory field plots, to monitor and predict changes in forest conditions over time. The auxiliary data from the satellite imagery of this region are relatively dense in space and time, and can be used to learn how forest conditions changed over that decade. However, these records …