Numerical Analysis and Computation Commons^™

Analyzing Fungal Growth Dynamics Under Different Environmental Conditions Using A Lotka–Volterra Competition System, Maria Ordonez, Fabrio Araujo

Discovery Day - Daytona Beach

Fungi play a critical role in ecosystems as decomposers that recycle nutrients and maintain environmental balance. Their populations are influenced by multiple environmental factors such as temperature, humidity, nutrient availability, and interactions with other organisms. In this project, the Lotka–Volterra model is used to analyze how competing fungal species interact and how these interactions influence population dynamics over time. By modeling two fungal populations competing for the same limited resources, the equations illustrate how environmental conditions and competition coefficients determine whether one species dominates; both species coexist, or one species becomes extinct. The model provides insight into how changes in …

Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore

Discovery Day - Daytona Beach

This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional …

A Multiscale Computational Framework Coupling Pulmonary Arterial Blood Flow And Lung Tissue Perfusion, Nigar Sultana, Hangjie Ji, Mette Sofie Olufsen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Stochastic Universal Differential Equations For Epidemiological Modeling: Uncertainty Quantification In Disease Transmission Dynamics, Alice Menaya Armah-Bonney

Electronic Theses and Dissertations

Epidemic forecasting requires not only predictions of expected case counts, but also quantification of uncertainty, although existing surrogate modeling frameworks for agent-based models remain fundamentally deterministic. In this thesis a Stochastic Universal Differential Equation framework is presented that extends the deterministic Universal Differential Equation approach by incorporating a learnable stochastic diffusion term, enabling calibrated probabilistic forecasts while preserving the mechanistic interpretability and computational efficiency of the deterministic baseline. In doing so, a two-phase training algorithm is introduced to ensure stable convergence and the framework is validated against the ensemble output from ExaEpi, an exascale agent-based model of a COVID-19 outbreak …

Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner

Dissertations, Master's Theses and Master's Reports

Background: Microgravity exposure alters cardiovascular loading, yet its impact on left atrial flow dynamics and thrombotic risk remains poorly understood. This study investigates how spaceflight-relevant microgravity-induced changes in cardiac outflow affect left atrial hemodynamics in healthy individuals and patients with atrial fibrillation.

Methods: Patient-specific left atrial models were generated for three healthy individuals and three AF patients. Computational fluid dynamics (CFD) simulations were performed using each patient’s baseline mitral outflow waveform and two modified waveforms representing short- and long-duration post-flight cardiac loading changes derived from echocardiographic observations. Hemodynamic metrics included left atrial velocity, time averaged wall shear stress, oscillatory shear …

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

Analysis And Numerical Investigation Of A Breast Cancer Treatment Model Incorporating Ketogenic Diet And Immune Boosters Via Optimal Control Theory, Kunnisai Muniroh, Ummu Habibah, Wuryansari Muharini Kusumawinahyu, Nur’Izzati Hamdan

Mathematical Modelling and Numerical Simulation with Applications

This paper develops a mathematical model to investigate breast cancer dynamics by incorporating tumor–immune interactions, ketogenic diet effects, and medical treatment. The model is formulated as a system of nonlinear ordinary differential equations and analyzed within an optimal control framework. Time-dependent control variables are introduced to represent treatment strategies aimed at minimizing tumor progression while reducing therapeutic costs. The model’s well-posedness is established through positivity and boundedness analysis. The necessary conditions for optimality are derived using Pontryagin’s Minimum Principle, resulting in a coupled system of state and adjoint equations. Numerical solutions are obtained using the fourth-order Runge–Kutta method combined with …

Mathematical Analysis And Numerical Simulation Of A Fractional-Order Sir-Si Model For Malaria Transmission Dynamics, Gassan A. M. O. Farah, Abdulaziz Y. A. Mukhtar, Kailash C. Patidar

Mathematical Modelling and Numerical Simulation with Applications

This study investigates the complex transmission dynamics of malaria, a critical global health challenge, with a focus on the African continent. We introduce a novel approach that employs Fractional Differential Equations (FDEs) to advance the understanding of malaria spread and control. Specifically, we develop a new SIR-SI model using the Caputo fractional operator, which captures the memory effects and time-delay characteristics inherent in real-world epidemiological systems. A detailed analysis of the model's solvability and uniqueness is conducted using fixed-point theory. To obtain an analytical solution, the system is solved via the Laplace transform method, with solutions expressed in closed form …

Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions., Archana Neupane Timsina

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling, Analysis, And Prediction Of Covid-19 Dynamics With Interacting Subpopulations And Implicit Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

In this paper, we consider an extended SEIR compartmental model that incorporates young and old interacting subpopulations, allowing for cross-group transmission dynamics. Implicit behavioral changes are included to determine the influence of social behavior on coronavirus transmission dynamics. The basic reproduction number, the average number of secondary cases of infection produced by a single primary case, is derived for both the explicit and implicit model using the next-generation matrix method. We solve the associated differential equation systems and estimate useful parameters in the explicit model using physics-informed neural networks (PINNs). Our results point to how the PINNs approach offers an …

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 …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations and Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

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 …

Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein

Rose-Hulman Undergraduate Mathematics Journal

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …

Human System Composite Performance Measures: General Systems Performance Theory Insights, Lawrence Disalvi

Bioengineering Dissertations - Archive

Composite Performance Measures (CPMs) of human performance are widely employed in applications that range from mundane to life-changing, yet they are frequently presented without explanation or reference to theoretical underpinnings. The conceptual soundness of a widely used CPM approach, based on additive combination of constituent components, has been called into question by Kondraske. He argues the relevance of General Systems Performance Theory (GSPT) and performance capacity envelope concepts when applied to multidimensional CPM measures.

To obtain evidence-based answers to assertions regarding CPM types and rationale employed in medical and non-medical contexts, a Systematic Descriptive Review was conducted. Separately, the GSPT-based …

A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd

Mathematics Dissertations - Archive

In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …

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 …

Physics-Informed Neural Networks For Agent-Based Epidemiological Model Calibration, Alvan C. Arulandu, 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 …

Using Medicare Claims To Estimate Risk-Adjusted Performance Of Pennsylvania Trauma Centers, Alexis M Zebrowski, Phillipe Loher, David G Buckler, Isidore Rigoutsos, Brendan G Carr, Douglas J Wiebe

Computational Medicine Center Faculty Papers

Trauma centers use registry data to benchmark performance using a standardized risk adjustment model. Our objective was to utilize national claims to develop a risk adjustment model applicable across all hospitals, regardless of designation or registry participation. Patients from 2013-14 Pennsylvania Trauma Outcomes Study (PTOS) registry data were probabilistically matched to Medicare claims using demographic and injury characteristics. Pairwise comparisons established facility linkages and matching was then repeated within facilities to link records. Registry models were estimated using GLM and compared with five claims-based LASSO models: demographics, clinical characteristics, diagnosis codes, procedures codes, and combined demographics/clinical characteristics. Area under the …

Stochastic Gradient Descent Method For A Parameter Identification Problem In Elasticity Imaging, Basca Jadamba

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …

Head And Neck Tumor Histopathological Image Representation With Pre- Trained Convolutional Neural Network And Vision Transformer, Ranny Rahaningrum Herdiantoputri, Daisuke Komura, Tohru Ikeda, Shumpei Ishikawa

Journal of Dentistry Indonesia

Image representation via machine learning is an approach to quantitatively represent histopathological images of head and neck tumors for future applications of artificial intelligence-assisted pathological diagnosis systems. Objective: This study compares image representations produced by a pre-trained convolutional neural network (VGG16) to those produced by a vision transformer (ViT-L/14) in terms of the classification performance of head and neck tumors. Methods: W hole-slide images of five oral t umor categories (n = 319 cases) were analyzed. Image patches were created from manually annotated regions at 4096, 2048, and 1024 pixels and rescaled to 256 pixels. Image representations were …

Chatgpt As Metamorphosis Designer For The Future Of Artificial Intelligence (Ai): A Conceptual Investigation, Amarjit Kumar Singh (Library Assistant), Dr. Pankaj Mathur (Deputy Librarian)

Library Philosophy and Practice (e-journal)

Abstract

Purpose: The purpose of this research paper is to explore ChatGPT’s potential as an innovative designer tool for the future development of artificial intelligence. Specifically, this conceptual investigation aims to analyze ChatGPT’s capabilities as a tool for designing and developing near about human intelligent systems for futuristic used and developed in the field of Artificial Intelligence (AI). Also with the helps of this paper, researchers are analyzed the strengths and weaknesses of ChatGPT as a tool, and identify possible areas for improvement in its development and implementation. This investigation focused on the various features and functions of ChatGPT that …

Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Olfactory Bulb Processing Of Ortho Versus Retronasal Odors, Michelle F. Craft, Andrea Barreiro, Shree Gautam, Woodrow Shew, Cheng Ly

Biology and Medicine Through Mathematics Conference

No abstract provided.

Toward Suicidal Ideation Detection With Lexical Network Features And Machine Learning, Ulya Bayram, William Lee, Daniel Santel, Ali Minai, Peggy Clark, Tracy Glauser, John Pestian

Northeast Journal of Complex Systems (NEJCS)

In this study, we introduce a new network feature for detecting suicidal ideation from clinical texts and conduct various additional experiments to enrich the state of knowledge. We evaluate statistical features with and without stopwords, use lexical networks for feature extraction and classification, and compare the results with standard machine learning methods using a logistic classifier, a neural network, and a deep learning method. We utilize three text collections. The first two contain transcriptions of interviews conducted by experts with suicidal (n=161 patients that experienced severe ideation) and control subjects (n=153). The third collection consists of interviews conducted by experts …

A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury

Doctoral Dissertations and Master's Theses

The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless …