Mathematics Commons^™

Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett

CODEE Journal

As data-driven methods are increasingly used in science and engineering, students benefit from learning to integrate machine learning techniques with traditional mathematical modeling. We present a hands-on extra-credit assignment for an undergraduate ordinary differential equations (ODE) course that enables students to compare classical analytical methods with data-driven approaches on the same physical system. Using a coupled-pendulum system---two pendulums connected by a spring---with real experimental data acquired via video tracking of a real physical setup, students work through three models in a guided Jupyter notebook with all code provided. First, they fit a neural network with Fourier features as a purely …

Differential-Geometric Methods For Neural Signed Distance Fields: Parameterized Surface Extraction And Curvature Regularization For Cad Models, Haotian Yin

Dissertations

Neural signed distance fields have emerged as a powerful framework for representing three-dimensional geometry through continuous and differentiable neural functions. Their flexibility, resolution independence, and compatibility with gradient-based optimization make them especially attractive for surface reconstruction and geometric learning. However, despite these advantages, two fundamental challenges remain for engineering-grade applications. First, higher-order geometric properties such as curvature are difficult to model reliably during training and often require computationally expensive second-order differentiation. Second, while neural signed distance fields provide implicit surface representations, they do not directly yield a globally consistent forward map or parameterization for downstream geometric processing.

This dissertation addresses …

Data Driven Monitoring And Control Of Laser Powder Bed Fusion Process, Jose De Jesus Galarza

Theses and Dissertations

The Laser Powder Bed Fusion Process (LPBF) has been one of the main processes of additive manufacturing, enabling the manufacturing of complex geometries, customization, and lightweight parts. Modern LPBF processes have integrated monitoring systems that capture the light emissions per layer for quality assurance. However, standard defect detection algorithms have not yet achieved the high precision required due to the inherently variable nature of the signal, insufficient data for model training, and the confounding effects of the print.

The processes still have some challenges, such as characterizing the roughness from the build parameters alone, improving the pore detection using the …

A Computer Vision Approach To Analyzing Taxane Effects On Prostate Cancer Cells, Diana Elizabeth Dancea

Electronic Theses and Dissertations

Actin is a family of proteins that help create the structure of the cytoskeleton, which gives shape to the cell. In many chemotherapy treatments, researchers target actin because it controls the cell division process. Therefore, if they are able to understand the actin fibers, that may help in formulating methods to stop or slow down cancer cells from reproducing. Another important protein is PAK6, which regulates actin. In our research, a collaborative effort with Prof. Michael Lu’s lab at Florida Atlantic University, we use machine learning techniques to analyze cells which had their PAK6 protein knocked out, and compare them …

Comparative Machine Learning Models For Disease Risk Prediction, Mercy Mawusi Agbley

Theses, Dissertations and Capstones

Accurate prediction of disease outcomes is crucial for improving clinical decision-making and enabling early intervention. This study compares the performance of various statistical and machine learning models for clinical risk prediction using two healthcare datasets: diabetic retinopathy and heart disease. The models assessed include Logistic Regression, LASSO, k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Neural Networks, Random Forests, Gradient Boosting Machines (GBM), and a stacked ensemble model. Prior to modeling, datasets were split into train and test sets. Standardization was applied to numeric features whilst categorical features were one-hot encoded. These transformations were later applied to the test set. Principal …

Sugar: A Sequence Unfolding Based Transformer Model For Group Activity Recognition, Yash U. Gondkar

Graduate Masters Theses

Large Language Models have improved significantly in the past couple of years due to the adoption of transformers. However, transformers still find it challenging to process videos due to limited context size caused by their quadratic computing cost. Therefore, we studied a booming field in machine learning which powers applications like social scene analysis and video surveillance systems called Group Activity Recognition (GAR). We found that recent models were able to achieve more than 90% accuracy on popular datasets like the Volleyball dataset, however, it turned out that even they relied on transformers.

Therefore, in this work, we developed a …

Exploring System Identification Of Non-Linear Dynamics Using The Weighted Composition Operator And The Liouville Operator, Chukwuebuka Amagwula

USF Tampa Graduate Theses and Dissertations

System identification is the process of determining mathematical models that describe the dynamics of a system from data. Dynamic Mode Decomposition (DMD) and Sparse Identification of Nonlinear Dynamical Systems (SINDy) are two distinct approaches used for this purpose.

DMD identifies dominant spatiotemporal modes and eigenvalues that describe the evo lution of a system. It assumes a near-linear representation of dynamics and is closely linked to the Koopman operator, making it ideal for analyzing fluid flows, oscillatory systems, and modal structures. The DMD method uses time series data where each data point is referred to as a snapshot and represents the …

Machine Learning: Neural Networking With Relu And Optimization, Aidan Redmond Brownell

Undergraduate Theses, Capstones, and Recitals

At its core, learning is an algorithmic process: it begins with input data, undergoes a series of transformations or computations, and yields an output intended to solve a specific task. This output is then compared against a target or desired result, and the internal mechanisms are updated based on how well the output aligns with expectations. While this feedback-driven process occurs almost effortlessly in humans, it is a far more structured, deliberate, and computationally intensive undertaking for machines.

Data-Driven Survival Modeling For Breast Cancer Prognostics: A Comparative Study With Machine Learning And Traditional Survival Modeling Methods, Theophilus Gyedu Baidoo, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Background This investigation delves into the potential application of data-driven survival modeling approaches for prognostic assessments of breast cancer survival. The primary objective is to evaluate and compare the ability of machine learning (ML) models and conventional survival analysis techniques, to identify consistent key predictors of breast cancer survival outcomes.

Methods This study employs data-driven survival modeling approaches to predict breast cancer survival, including survival-specific methods such as the Cox Proportional Hazards (CPH) model, Random Survival Forests (RSF), and Cox Proportional Deep Neural Networks (DeepSurv), as well as machine learning models like Random Forests (RF), XGBoost, Support Vector Machines (SVM) …

Supplementary Files For: "Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake", Ben Shaw, Haley Burger, Brennan Bean, Kevin Moon

Browse all Datasets

This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis revealed that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This suggests that the structure observed in the water …

Enhancement Of Mechanical, Structural, And Electrical Properties In Advanced Composites And Vat Photopolymerized 3d Printing Nanocomposites, Poom Narongdej

CGU Theses & Dissertations

Advanced composites have gained significant attention across various industries, including aerospace, automotive, clean energy, and healthcare, owing to their exceptional mechanical properties and versatility. Fiber-reinforced polymer (FRP) composites, particularly those reinforced with carbon fibers, are extensively used as structural materials in spacecraft, aircraft, high-performance vehicles, and wind turbines due to their high strength-to-weight ratios, stiffness, durability, and tailorable mechanical characteristics. In healthcare, the advent of additive manufacturing (3D printing) has expanded the utility of advanced composites, enabling precise customization of components to meet patient-specific needs while offering design flexibility and ease of fabrication. Despite these advantages, several challenges hinder the …

Logarithmic Number System Is Optimal For Ai Computations: Theoretical Explanation Of Empirical Success, Olga Kosheleva, Vladik Kreinovich, Christoph Lauter, Kristalys Ruiz-Rohena

Departmental Technical Reports (CS)

Everyone knows the success story of machine-learning AI. However, the current AI tools are not perfect. We know how to make them better: every time we increase the amount of computations by the order of magnitude, we get a drastic improvement in the performance of the resulting machine learning tools. Training modern AI system requires a tremendous amount of computations -- that already take a lot of time. So, to increase the number of computations, we need to make each computation step faster. One way to do that is to use low-precision arithmetic operations, e.g., with 1 byte per real …

Machine Learning Methods For Quantification Of Glacier Variations Through Satellite Imagery, Robert D. Breininger

Theses and Dissertations

Glaciers around the world have experienced a trend of recession within the past century. Quantification of glacier variations using satellite imagery is of great interest due to the importance of glaciers as freshwater resources and as indicators of climate change. The potential methods to quantify glacier variations with increasing complexity include detecting the terminus location, quantifying the glacier surface area, and measuring glacier volume. Although there are methods in literature designed purposefully for glacier area segmentation that have achieved acceptable results, they are often localized to the region where their training data were acquired and further rely on training sets …

Decoding Neural Networks: An Information-Theoretic Guide To Interpretability, Error Analysis And Efficiency, Mackenzie J. Meni

Theses and Dissertations

This dissertation addresses critical challenges in neural network design by leveraging entropy-based techniques to improve model efficiency, interpretability, and bias reduction. Focusing on the unique demands of computer vision applications, particularly object detection and classification for real-time systems, this work introduces a series of innovative methods centered on information theory. At the core of these methods is the Probabilistic Explanations of Entropic Knowledge (PEEK) framework, a tool developed to analyze and visualize entropy distributions across feature maps. PEEK offers insights into information flow within neural networks, making it possible to pinpoint layers that contribute meaningfully to decision-making or identify those …

A Staged Approach Using Machine Learning And Uncertainty Quantification To Predict The Risk Of Hip Fracture, Anjum Shaik, Kristoffer A. Larsen, Nancy E. Lane, Chen Zhao, Kuan Jui Su, Joyce H. Keyak, Qing Tian, Qiuying Sha, Hui Shen, Hong Wen Deng, Weihua Zhou

Michigan Tech Publications

Hip fractures present a significant healthcare challenge, especially within aging populations, where they are often caused by falls. These fractures lead to substantial morbidity and mortality, emphasizing the need for timely surgical intervention. Despite advancements in medical care, hip fractures impose a significant burden on individuals and healthcare systems. This paper focuses on the prediction of hip fracture risk in older and middle-aged adults, where falls and compromised bone quality are predominant factors. The study cohort included 547 patients, with 94 experiencing hip fracture. To assess the risk of hip fracture, clinical variables and clinical variables combined with hip DXA …

How To Propagate Uncertainty Via Ai Algorithms, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Any data processing starts with measurement results. Measurement results are never absolutely accurate. Because of this measurement uncertainty, the results of processing measurement results are, in general, somewhat different from what we would have obtained if we knew the exact values of the measured quantities. To make a decision based on the result of data processing, we need to know how accurate is this result, i.e., we need to propagate the measurement uncertainty through the data processing algorithm. There are many techniques for uncertainty propagation. Usually, they involve applying the same data processing algorithm several times to appropriately modified data. …

How To Make Ai More Reliable, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the reasons why the results of the current AI methods (especially deep-learning-based methods) are not absolutely reliable is that, in contrast to more traditional data processing techniques which are based on solid mathematical and statistical foundations, modern AI techniques use a lot of semi-heuristic methods. These methods have been, in many cases, empirically successful, but the absence of solid justification makes us less certain that these methods will work in other cases as well. To make AI more reliable, it is therefore necessary to provide mathematical foundations for the current semi-heuristic techniques. In this paper, we show that …

Robust Prediction Of Charpy Toughness Of Additively Manufactured Kovar Using Deep Convolutional Neural Networks, Nathan R. Bianco

Mathematics & Statistics ETDs

Understanding the reason for mechanical failures of manufactured parts in their operating environments is critical to prevention of future failures. However, in-situ post-mortem evaluation of physical properties, such as fracture toughness, is time consuming and alters the condition of the material, leading to potentially misleading findings. In this study, additively manufactured test coupons were produced over a wide range of process conditions to test the impact toughness of a material. The Charpy V-Notch toughness was measured on over 200 samples alongside corresponding optical images of both sides of the fracture surface. Convolutional neural network models were trained to correlate fracture …

Coarctation Duration And Severity Predict Risk Of Hypertension Precursors In A Preclinical Model And Hypertensive Status Among Patients, Arash Ghorbannia, Hilda Jurkiewicz, Lith Nasif, Abdillahi Ahmed, Jennifer Co-Vu, Mehdi Maadooliat, Ronald K. Woods, John F. Ladisa Jr.

Mathematical and Statistical Science Faculty Research and Publications

BACKGROUND:

Coarctation of the aorta (CoA) often leads to hypertension posttreatment. Evidence is lacking for the current >20 mm Hg peak-to-peak blood pressure (BP) gradient (BPGpp) guideline, which can cause aortic thickening, stiffening, and dysfunction. This study sought to find the BPGpp severity and duration that avoid persistent dysfunction in a preclinical model and test if predictors translate to hypertension status in patients with CoA.

METHODS:

Rabbits (n=75; 5–12/group) were exposed to mild, intermediate, or severe CoA (≤12, 13–19, ≥20 mm Hg BPGpp) for ≈1, 3, or 22 weeks using dissolvable and permanent sutures with thickening, stiffening, contraction, and endothelial …

Influence Of Parsimony And Work-Related Psychological Constructs In Predicting Turnover Intention When Using Machine Learning Vs Regression, Diego Figueiras

Theses, Dissertations and Culminating Projects

This dissertation explores the ongoing debate between traditional statistical regression models and machine learning (ML) algorithms in predictive modeling, focusing on the impact of sample size and the number of variables. Study 1 investigates the relationship between sample size and predictive accuracy, proposing hypotheses regarding the advantages of ML over regression as sample size increases. Additionally, the study examines the influence of the number of variables on predictive accuracy, emphasizing the trade-off between ML and regression models. Using data from the Federal Employee Viewpoint Survey, the research aims to contribute insights into the conditions favoring each modeling approach. Study 2 …

A Statistical Look Into How Common Soccer Metrics Influence Expected Goal Measures In The Professional Game, Tristan George Rumsey

Undergraduate Honors Thesis Collection

The advent of sports analytics has ignited a fervor across all sporting disciplines, particularly soccer, where clubs are sprinting to harness vast data reserves to elevate team performance, spearhead effective marketing endeavors, and bolster financial gains crucial for club expansion. Much like Billy Beane's transformative "Moneyball" approach, soccer clubs are in pursuit of innovative strategies to transcend financial limitations and achieve triumph. In soccer, where goals are scarce commodities, heightened offensive efficacy becomes imperative. Presently, one metric stands out as pivotal in gauging a team's goal-scoring success: expected goals (xG). This metric quantifies the likelihood of a given shot or …

Examining Course Achievement In An Undergraduate Psychology Statistics Course Through The Lens Of Machine Learning Techniques, Sunny Nguyet Le

CGU Theses & Dissertations

The Introductory to Psychology Statistics course stands as a notable challenge for psychology majors, often acting as a gatekeeper course. This study embarks on two primary objectives using machine learning techniques: (1) to identify the determinants of overall course achievement, specifically course grade, and (2) to investigate the influence of statistics anxiety and statistics self-efficacy, when both are present, on overall course grade. Employing a machine-learning approach, both objectives were effectively addressed. The study involved the development of a self-reported questionnaire consisting of perceptions of statistics anxiety and statistics self-efficacy, along with other demographic and academic background variables. Conducted at …

Platform-Independent Estimation Of Human Physiological Time From Single Blood Samples, Yitong Huang, Rosemary Braun

Mathematics Sciences: Faculty Publications

Abundant epidemiological evidence links circadian rhythms to human health, from heart disease to neurodegeneration. Accurate determination of an individual's circadian phase is critical for precision diagnostics and personalized timing of therapeutic interventions. To date, however, we still lack an assay for physiological time that is accurate, minimally burdensome to the patient, and readily generalizable to new data. Here, we present TimeMachine, an algorithm to predict the human circadian phase using gene expression in peripheral blood mononuclear cells from a single blood draw. Once trained on data from a single study, we validated the trained predictor against four independent datasets with …

Infusing Machine Learning And Computational Linguistics Into Clinical Notes, Funke V. Alabi, Onyeka Omose, Omotomilola Jegede

Mathematics & Statistics Faculty Publications

Entering free-form text notes into Electronic Health Records (EHR) systems takes a lot of time from clinicians. A large portion of this paper work is viewed as a burden, which cuts into the amount of time doctors spend with patients and increases the risk of burnout. We will see how machine learning and computational linguistics can be infused in the processing of taking clinical notes. We are presenting a new language modeling task that predicts the content of notes conditioned on historical data from a patient's medical record, such as patient demographics, lab results, medications, and previous notes, with the …

Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ₀ norm. Specifically, the ℓ₀ model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ₀ norm regularization term. Such an ℓ₀ model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this …

A Review Of Cyber Attacks On Sensors And Perception Systems In Autonomous Vehicle, Taminul Islam, Md. Alif Sheakh, Anjuman Naher Jui, Omar Sharif, Md Zobaer Hasan

School of Mathematical & Statistical Sciences Faculty Publications

Vehicle automation has been in the works for a long time now. Automatic brakes, cruise control, GPS satellite navigation, etc. are all common features seen in today's automobiles. Automation and artificial intelligence breakthroughs are likely to lead to an increase in the usage of automation technologies in cars. Because of this, mankind will be more reliant on computer-controlled equipment and car systems in our daily lives. All major corporations have begun investing in the development of self-driving cars because of the rapid advancement of advanced driver support technologies. However, the level of safety and trustworthiness is still questionable. Imagine what …

Explainable Machine Learning Reveals The Relationship Between Hearing Thresholds And Speech-In-Noise Recognition In Listeners With Normal Audiograms, Jithin Raj Balan, Hansapani Rodrigo, Udit Saxena, Srikanta K. Mishra

School of Mathematical & Statistical Sciences Faculty Publications

Some individuals complain of listening-in-noise difficulty despite having a normal audiogram. In this study, machine learning is applied to examine the extent to which hearing thresholds can predict speech-in-noise recognition among normal-hearing individuals. The specific goals were to (1) compare the performance of one standard (GAM, generalized additive model) and four machine learning models (ANN, artificial neural network; DNN, deep neural network; RF, random forest; XGBoost; eXtreme gradient boosting), and (2) examine the relative contribution of individual audiometric frequencies and demographic variables in predicting speech-in-noise recognition. Archival data included thresholds (0.25–16 kHz) and speech recognition thresholds (SRTs) from listeners with …

Longboard Classification Using Machine Learning, Tuan (Kevin) Le, Evans Sajtar, Mckenzie Lamb

Annual Student Research Poster Session

There are several techniques a rider can choose from that they can perform being distributed along the long-board ride. This research aims to create a machine-learning model that can efficiently classify these techniques at different periods of time using raw acceleration data. This paper presents the complete workflow of the application. This application involves analytical geometry, multidimensional calculus, and linear algebra and can be used to visualize and normalize time-invariant object paths. This model focuses on displacement data calculated from raw acceleration data and gyro sensor data from a smartphone application called "Physics Toolbox Sensor Suite". We extracted features from …

Compatibility Of Clique Clustering Algorithm With Dimensionality Reduction, Ug ̆Ur Madran, Duygu Soyog ̆Lu

Applied Mathematics & Information Sciences

In our previous work, we introduced a clustering algorithm based on clique formation. Cliques, the obtained clusters, are constructed by choosing the most dense complete subgraphs by using similarity values between instances. The clique algorithm successfully reduces the number of instances in a data set without substantially changing the accuracy rate. In this current work, we focused on reducing the number of features. For this purpose, the effect of the clique clustering algorithm on dimensionality reduction has been analyzed. We propose a novel algorithm for support vector machine classification by combining these two techniques and applying different strategies by differentiating …

Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams, Benjamin F. Akers

Faculty Publications

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse …