Applied Mathematics Commons^™

Multivariate Time-Series Forecasting Of 24-Hour Ambulatory Blood Pressure Using Long Short-Term Memory And Temporal Fusion Transformers, Sebastian Alejos Torres

Theses and Dissertations

Time series play a central role in healthcare by enabling continuous patient monitoring and forecasting of physiological and clinical measurements. Traditional models, such as autoregressive integrated moving average (ARIMA), are limited in capturing nonlinear dynamics and irregular sampling. In this study, we develop and evaluate Long Short-Term Memory (LSTM) networks and Temporal Fusion Transformers (TFTs) to forecast 24-hour ambulatory systolic and diastolic blood pressure (SBP and DBP) time series enriched with demographic and clinical features. Mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), and R² were used to evaluate predictive accuracy and temporal pattern …

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 …

Analysis Of Collective Behavior In Living And Nonliving Systems, Kaitlyn Cohan

Theses, Dissertations and Culminating Projects

This thesis aims at understanding the phenomenon of of self-organization in complex dissipative systems, living and nonliving. Dissipative systems are characterized by their search for energy, interactions with their surroundings and the production of entropy, all of which result in the creation of stable structures or patterns, which persist as long as the initial environmental conditions are maintained. The two specific models that we chose to study here are (a) Futbol (or Soccer) and (b) a chemical system involving free-floating menthol crystals floating on a fluid surface to represent nonliving systems. Using experiments and mathematical models, we will try to …

Pattern Dynamics And Stochasticity Of Brain Rhythms And Spike Trains In A Tauopathy Mouse Model Of Alzheimer’S Disease, Clarissa M. Hoffman

Dissertations and Theses (Open Access)

Systems neuroscience posits that every aspect of perceived physical reality, every aspect of animal and human behavior, and every cognitive phenomenon emerges from patterns of neuronal activity. While most researchers embrace this idea, there are major difficulties in describing and analyzing these complex neuronal dynamics—spike flows produced by cells ensembles, synchronized extracellular field oscillations, and other patterns—which limits our understanding of how the activity of individual neurons and the whole-animal cognition and behavior might be connected. In particular, we lack the approaches and even the semantics for connecting the individual cell outputs and the integrated results of their activity. Current …

Safe Control Design For Quadruped Locomotion In Unstructured Environments Using Linear Transfer Operators, Sriram Sundar Krishnamoorthy Shankara Narayanan

All Dissertations

Deploying quadruped robots in unstructured, obstacle-rich environments requires control and planning methods that remain safe and reliable despite complex terrain geometry, limited sensing, and inevitable modeling errors. This thesis develops operator-theoretic tools for safe control design of robotic systems using linear transfer operators, with a focus on quadruped locomotion in unstructured environments. The central goal is to develop a unified operator-theoretic framework for safe control design based on the Perron–Frobenius (P–F) and Koopman operators. In particular, the thesis leverages \emph{density functions} to develop safe navigation frameworks in the dual space of densities. In the operator-theoretic perspective, the P–F operator governs …

Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin

All Dissertations

Large-scale decision-making problems appear in many areas including long-range forecasting such as energy generation forecasting. Many such problems are subject to conflicting objectives and uncertain data, and can be modeled as linear optimization problems. We study novel theoretical results and algorithms for large-scale linear decision problems under conflict and uncertainty. First, we propose a parametric Benders decomposition algorithm for solving large-scale linear optimization problems with multiple objectives or deterministically uncertain objectives. Second, we extend the parametric Benders decomposition to a multi-stage setting, developing a parametric stochastic dual dynamic programming algorithm, which enables decision-making when conflicts and uncertainty have planning impacts …

Discrete-Event Simulation: A Leslie System Model For Transportation Demography, Md Zobaer Ahammad

Electronic Theses and Dissertations

Transportation systems are influenced by demographic change, household formation,and patterns of vehicle ownership. These factors affect long-run transportation demand and congestion levels within urban infrastructure. Understanding how demographic dynamics interact with transportation behavior is therefore important for analyzing the long-term evolution of transportation systems. This thesis develops a modeling framework that integrates discrete-event simulation with a Leslie-type matrix model to study transportation–demography interactions.Simulation outputs are aggregated to construct a transition matrix describing changes in transportation states. This matrix acts as a linear (or affine) transformation on the transportation state vector, allowing the system to be analyzed as a discrete linear …

Adaptive Artificial Potential Field Guidance And Control For Autonomous Docking With Uncooperative And Unknown Spacecraft, Steven Holmberg

Theses and Dissertations

The increasing demand for on-orbit servicing (OOS), active debris removal (ADR), and space domain awareness (SDA) missions has increased the need for autonomous spacecraft rendezvous and proximity operations (RPO) with uncooperative and unknown targets. Traditional guidance and control methods are typically designed for cooperative systems with known geometry and state information. This work builds on previous research to develop and evaluate an artificial potential field (APF)-based control framework capable of autonomous operation with minimal prior target knowledge and applicability to both relatively static and tumbling spacecraft.

The proposed APF formulation incorporates established safety constructs from cooperative docking systems, including an …

Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach

The Transdisciplinary STEAM+ Journal

In this paper, I explore how chaos theory can be used to design a new kind of synthesizer with the primary focus of producing glitchy, unpredictable sounds. Glitch music embraces abstract sound design, malfunctioning electronics, and randomness as the main compositional elements. However, most synthesizers rely on stable, repetitive oscillators that often sound too controlled. To challenge this, I developed FractSynth, a real-time synthesizer that uses chaotic attractors–including the Logistic Map, Henon Map, and Lorenz System–as modulation sources for frequency, amplitude, and tone. The software also features real-time Lyapunov Exponent Tracking, which gives users a direct visual of how …

Consistency-Based Computing Of Fuzzy Eigenvalues And Fuzzy Eigenvectors: Method And Application, Kamala. R. Aliyeva Prof., Nihad Mehdiyev, Shamil Mehdi

Chemical Technology, Control and Management

The computation of eigenvalues and eigenvectors under uncertainty is a fundamental problem in fuzzy linear algebra and decision analysis. When matrix elements are represented by fuzzy numbers, classical spectral methods cannot be directly applied due to nonlinearity, ambiguity in ordering, and the propagation of uncertainty. Moreover, in many practical applications, particularly those involving pairwise comparison matrices, the reliability of eigenvalue-based results strongly depends on the consistency of the underlying data. This paper proposes a consistency-based framework for computing fuzzy eigenvalues and fuzzy eigenvectors that explicitly integrates consistency analysis into the spectral derivation process. The proposed method preserves the fuzzy structure …

Intermediate-Scale Outflow Dynamics Of Eta Carinae, Edmund J. Garcia, Matthew C. Fleenor

Departmental Honors & Graduate Capstone Projects

η Carinae (η Car) is a binary system, with the larger star being an extremely massive, luminous blue variable (LBV) beyond the Eddington Limit. Surrounding the η Car system, numerous multi-wavelength imaging campaigns reveal axisymmetric structures with the expanding bipolar Homunculus Nebula (¡1 pc). In combination with the episodic eruptive history of the η Car system, our initial intermediate-scale imaging revealed further axisym- metric structures (1-5 pc). To gain a more expansive view of how the small scale structure connects to panoramic imaging of the η Car region, we constructed a deep, optical, narrowband mosaic of 189 images utilizing the …

Theory And Simulations Of Delayed Stochastic And Deterministic Models Of Prion Diseases, Gangadhara Boregowda, Omar Sharif, Daniel Gutierrez Iii, Allegra Simmons, Laurent Pujo-Menjouet, Tamer Oraby, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Neurodegenerative diseases (NDs), such as Alzheimer’s, Parkinson’s, and prion diseases, are characterized by the dynamical spread of toxic proteins through the brain. In prion diseases, cellular prion protein (PrPC), produced by neurons, misfolds into a toxic form, known as scrapie prion protein (PrPSc). PrPSc induces neuronal stress which ultimately leads to cell death. In this paper, we develop mathematical models for the progression of prion diseases, incorporating a cellular defense mechanism that introduces a delay term affecting protein translation and a volatility term accounting for unaccounted biological factors influencing the system. We also extend the model to capture the spatial …

A Computational Approach To Periodic Orbits Of State-Dependent Delay Differential Equations, Noah Corbett

Electronic Theses and Dissertations

The field of delay differential equations (DDEs) concerns the study of systems whose evolution depends on certain past states of the system. Of particular interest are the state-dependent DDEs, whose delay terms are non-constant and depend on the current state itself. In this thesis, we provide rigorous solution-finding techniques for a certain class of one-dimensional state-dependent DDEs, as well as a state-dependent delayed Van der Pol equation. This technique is inspired by the classical Picard-Lindelof theorem and is successful in proving the existence and uniqueness of orbits in such systems under certain reasonable restrictions. We then employ the Lagrange-Chebyshev interpolating …

The Digital Neuron: Neural Cellular Automata For Neural–Symbolic Translation, Nicole Assenza

SMU Data Science Review

A neural cellular automata (NCA) architecture, referred to as Pluto’s NCA, was developed to characterize bilateral communication and semantic reciprocity between symbolic representations and a spatially distributed update field. The architecture employs an encoder–automata–decoder pipeline that maps symbolic inputs into a multichannel state field and reconstructs them through agreement-driven attractor convergence within a stable semantic attractor landscape. System behavior was evaluated under controlled perturbations, including rhythmic desynchronization, graded ablations, correlated and independent noise, and percolation-based structural degradation. Quantities such as Agreement(t), internal coherence Aᵢ(t), the recovery time constant τ, and the critical percolation threshold pc were measured to assess stability, …

Emergent Dynamics In Multiplex Social Networks: Agent-Based Modeling Of Information Diffusion For Misinformation Control, Harshvardhan Prabhakar Ghongade, Anjali Ashokrao Bhadre, Shivani Agarwal, Harjitkumar Uttamrao Pawar, Harshal Subhash Rane

Northeast Journal of Complex Systems (NEJCS)

Information misrepresentation is widespread in multi-layered social networks which provide multiple avenues to communicate information. As such, it presents significant opportunities for both information integrity and public discourse to be undermined by disinformation. This paper outlines a new agent-based model, developed to capture emergent dynamics of multi-layered social networks and to help identify technical means to mitigate information misrepresentation in complex systems. A key component of this research includes a novel Multi-Layer Information Diffusion Model (MLIDM), integrating both cross-layer communication among agents, as well as heterogeneous agent behaviors and adaptive intervention strategies. Our methods employ a three-stage process to model …

Modeling Flood-Induced Cascading Disruptions In The Indian Electronics Supply Chain Using Influence Network Analysis, Surendra Orupalli, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study investigates flood induced disruptions in the Indian electronics supply chain using influence network analysis. Monsoon floods are recurring hazards that significantly impact economic activities, logistics, and industrial productivity. This study integrates district-level rainfall data (2020 to 2025) with supply chain network models to quantify cascading failures. The methodology applies rainfall thresholds (≥ 300 mm/month) to identify flood-prone districts and constructs a stochastic influence matrix representing inter-firm dependencies. Flood propagation dynamics are modeled iteratively with a propagation coefficient (α = 0.6) and convergence threshold (ε = 10⁻⁴). The resulting disruption profiles are mapped onto company-level revenues calibrated to India-specific …

Modeling Bitcoin Dynamics Using Differential Equations, Boone M. Fleenor

Departmental Honors & Graduate Capstone Projects

In this thesis, we develop and analyze two nonlinear systems of ordinary differential equations to model Bitcoin price dynamics. Analytical techniques are used to obtain exact or approximate solutions where possible. Then, numerical simulations using a fourth-order Runge–Kutta method are employed to explore system behavior beyond analytically tractable regimes. Finally, model outputs are compared to historical Bitcoin price data using normalized and resampled time series. These results suggest that deterministic models can provide meaningful insight into the structural behavior of Bitcoin markets, while highlighting the need for stochastic or time-dependent extensions for more realistic modeling.

Fractals Exploration Through Computer Visualization, Sihui Wei

SACAD: Scholarly Activities

This project explores the generation and visualization of fractals using computational methods. Several well-known fractal structures, including the Koch Snowflake, Sierpinski Triangle, Mandelbrot Set, and Julia Set, were implemented using C++ and the SFML graphics library.

The study focuses on how simple mathematical rules, when applied recursively or iteratively, can produce highly complex and self-similar structures. For geometric fractals, recursive algorithms were used to subdivide shapes and generate patterns. For complex-plane fractals, iterative formulas were applied pixel-by-pixel to determine set membership and visualize escape behavior.

The results demonstrate that small changes in parameters, such as recursion depth or iteration count, …

A Computational Study Of Taylor Approximation, Sihui Wei

SACAD: Scholarly Activities

This project investigates the accuracy of Taylor approximation using computational methods. Taylor polynomials of degree 1, 3, and 5 were applied to the functions e^x, sin x, and ln⁡(1+x), all centered at x=0.

Using C++, we generated both numerical data and graphical visualizations to analyze the absolute error∣f(x)−Tn(x)∣. The results show that higher-degree polynomials provide better approximation near the expansion point, while the error increases as the distance from the center grows.

In addition, the study reveals that the effectiveness of Taylor approximation depends not only on the polynomial degree but also on the structure of the function. In particular, …

A Dynamic Systems Framework For Customer Lifecycle Management: From Latent State Discovery To Robust Control Policy, Ali Nasirzonouzi

Northeast Journal of Complex Systems (NEJCS)

Traditional marketing often relies on static strategies that fail to capture dynamic customer behavior. This paper introduces an integrated framework to model and control the customer lifecycle, bridging the gap between empirical data and computational simulation. Using the Customer Personality Analysis dataset, we implemented a five-stage methodology. We first identified three distinct customer segments (At-Risk, Standard, High-Value) using Gaussian Mixture Models. To address the lack of longitudinal data, we calibrated a normative transition model based on customer inertia principles. Our analysis revealed that marketing effectiveness is highly state-dependent; notably, At-Risk customers exhibited a 33.5% lift when targeted with catalogs. Leveraging …