Dynamic Systems Commons^™

A Simulation Assessment Of The 'Law Of One Price', Caleb Wilkins

Computational and Data Sciences (MS) Theses

The ‘law of one price’ is an appealing notion regarding pricing of tradeable commodities that are priced in different currencies. It states that the prices of the same good in different markets should be equal after adjustment for exchange rates and that equality should persist through exchange rate fluctuations.

My research simulates the market conditions that should precipitate the ‘law of one price.’ Data was obtained from the simulated trade between algorithmic artificial intelligence agents that operated under induced boundedly rational market behaviors. Trade took place in two initially separate markets, a high-price market with a higher equilibrium price and …

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 …

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

An Analytical Framework For Quantifying Urban And Community Resilience To Natural Hazards From Cell-Phone Gps-Location And Traffic-Flow Data, Georgios Chatzikyriakidis

Civil and Environmental Engineering Theses and Dissertations

Urban areas are increasingly exposed to natural hazards while accommodating a growing share of the global population, yet a consistent science-based framework for quantifying urban and community resilience remains lacking. This dissertation develops a physics-based analytical framework grounded in statistical mechanics and the quantitative theory of Brownian motion. A city is conceptualized as a complex medium in which citizens move analogously to Brownian particles within a viscoelastic environment, influenced by socioeconomic interactions and infrastructure functionality.

A central premise is that urban resilience, interpreted as engineering resilience (an outcome), can be quantified through a single metric: the mean-square displacement MSD=⟨r²(t)⟩, of …

Welcome Tilly Norwood: Forecasting Hollywood’S Ai Policy Futures, Samuel P. Rooker

Senior Honors Projects, 2020-current

In late 2025, weekly trade publication Variety Magazine reported on the announcement of a new acting talent in Hollywood: Tilly Norwood. Norwood is an industry outsider and the pet project of Eline Van der Velden, who unveiled the actress’ existence to the world at the Zurich Film Festival. The announcement quickly gained media coverage while Van der Velden has since faced cyclical backlash from Hollywood trade unions, which does not seem entirely without reason. Tilly Norwood is a digital persona, a generative artificial intelligence (GenAI) program, designed by Van der Velden’s novel AI talent studio, Xicoia, to become the next …

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 …

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 …

A Stability Analysis Of The Phase-Lock Equations, Brian M. Sunguza

UNF Graduate Theses and Dissertations

Ginzburg and Landau have provided a set of equations that relate superconductivity to magnetic fields. Through a transformation process, Zhan has derived what are now called the phase-lock equations. A stability analysis of the spatially-independent phase-lock equations is the purpose of this presentation. This simplification is significant since it allowed for the analytical determination of equilibria, their stability, and the influence of a periodic forcing function. Through the use of an original code, numerical simulations are shown to corroborate the analytical results described above.

This analysis includes novel Lyapunov functions that allowed for the analytical determination of the instability region. …

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi

Electronic Theses & Dissertations (2024 - present)

In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …

Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris

All Dissertations

The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …

Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz

Dartmouth College Ph.D Dissertations

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …

Identifying And Characterizing Transition Cells In Developmental Processes From Scrna-Seq Data, Yuanxin Wang

Dissertations and Theses (Open Access)

During the development of multicellular organisms, individual cells make distinct decisions about their cell types and states. Understanding the molecular mechanisms underlying cellular state transitions at different developmental stages provides deep insights into physiology, morphology and the etiology of diseases. Single-cell RNA-sequencing (scRNA-seq), which is widely used to study complex cell states and dynamic gene expression patterns, enables us to investigate molecular mechanisms of cellular state transitions. Currently, however, computational tools available for identifying cellular states and state transitions remain limited.

Although trajectory-based methods such as Monocle and Slingshot assume that state transitions generate continuous expression profiles, they cannot distinguish …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …

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

Graduate Theses/Dissertations

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

Modeling The Impacts Of The Current And Projected Temperatures On Spongy Moth Population Dynamics, Adrienne B. Spring

Theses and Dissertations

The spongy moth (Lymantria dispar) is an invasive forest pest that has caused significant ecological damage across the United States. Its invasion front is shaped by a number of factors, including temperature in both the northern and southern regions. With ongoing climate change, areas that were previously uninhabitable may become increasingly favorable for moth population establishment and expansion, while other areas may experience thermal stress limiting persistence. This study develops a temperature-driven population model to analyze how temperature affects the spongy moth population dynamics along the invasion front. This model incorporates temperature effects on fecundity, stage-specific survival rates, …

Wave Reflections In A Biophysically Detailed Model Of Cardiac Tissue, Grace Moberg

Honors Theses

Regular heart rhythms are governed by the coordinated spread of action potentials through cardiac tissue. The interaction of an action potential with a tissue heterogeneity may lead to a reflection, where both a retrograde and an anterograde wave propagate off of the initial impulse. Reflections have been experimentally linked to cardiac arrhythmias, but their mechanisms of generation are not well-understood. Mathematically, reflections in phenomenological models of cardiac tissue have been linked to an unstable periodic orbit. These models typically sacrifice detail about the variety of ionic currents and processes involved in action potential propagation in favor of mathematical simplicity. Biophysically …

Dynamics Of Prey-Prey Mutualism With Varying Carrying Capacity And Herd Behavior In The Presence Of Predator, Felix Dela Djokoto

UNF Graduate Theses and Dissertations

This study investigates the dynamics of mutualistic relationships between two prey species in the presence of a predator, by taking into account herding in one species along with the influence of carrying capacities between two prey species. These mutualistic dynamics are presented by constructing two mathematical models, namely an indirect and direct mutualism model. As the strength of the symbiotic relationship increases the indirect model goes through transcritical bifurcation to Hopf bifurcation whereas in the direct mutualism model goes through saddle-node bifurcation to Hopf bifurcation.

Bound Preserving Discontinuous Galerkin Methods For Euler Equations And Nonequilibrium Flows, Fangyao Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation is composed of four chapters in which we will closely examine the high order bound preserving discontinuous Galerkin methods for solving partial differential equations, specifically non-equilibrium chemical reacting flows and Euler equations under gravitational fields. A shared requirement between the two is the necessity for positive values of both density and pressure. Due to this physical nature of the two systems, constructing a positivity preserving scheme become very essential in our research.

For non-equilibrium flows where multi-reactions and multi-species are involved, we are also required to keep the bounds of the mass fraction of each species in between …

Mathematical Modeling Of Lead Climbing Falls, Rosemary Christmas Evans

EWU Masters Thesis Collection

This thesis presents a force-based mathematical model for simulating dynamic falls in lead sport climbing, with an emphasis on physical realism and empirical validation. The system is modeled as a mass–spring–damper, incorporating gravity, nonlinear rope stiffness, internal damping, and Capstan-style friction at protection points. The goal is to predict peak forces and rope elongation while capturing the complex dynamics of real climbing ropes. Several novel features are introduced. Activation switches ensure forces only engage when the rope is tensioned, preventing premature response. A velocity-sensitive stiffness transition function allows the rope to stiffen smoothly with increasing fall speed, reflecting rate-dependent rope …

Quantized Average Agreement Algorithms With Error Correction For Digraphs, Shuaib A. Mughal

Honors Undergraduate Theses

Multi-agent systems have become more and more prevalent as technology increasingly gets integrated into our daily lives. Some of these technological systems are large in size; for example, the smart grid where multiple devices are used to monitor and control different aspects of the energy grid. Another example is a team of autonomous systems deployed for a specific task. When these systems are spatially distributed, an important component of distributed algorithms is the ability for the agents to reach consensus on the global state of the system. Reaching agreement enables the spatially distributed agent make decisions or determine the next …

Mathematical Contributions To The Study Of Chemotaxis And Cell Signaling, Hajr Zam

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents results from two mathematical projects concerned with the biology of cells. Chapter 1 provides biological background and places the two mathematical problems in the context of cell signaling. The larger project, with Prof. H. Hattori on a chemotaxis model is presented in Chapters 3 and 4. Work with Prof. \'{A}. Hal\'{a}sz on a chemical reaction network system with linear multimers and two types of labels is presented in Chapter 2. The chemotaxis system describes the one-dimensional dynamics of a species of cells with two chemical species, a chemo-attractant and chemo-repellent. The goal is to analyze the behavior …

Essays On Technological Change And Scientific Research, Max Mayca

Electronic Theses & Dissertations (2024 - present)

The primary objective of economic science has long been to understand and promote growth, as it contributes to a more prosperous civilization and improves individual well-being. The core drivers of growth—capital accumulation, human capital development, and technological progress—are well-established. While capital deepening enables scaling of production, and human capital enhances labor productivity, technological and scientific advancements remain the most critical, as they continually redefine the efficiency frontier. Given this centrality, it is essential to understand how technological progress affects labor markets, how research resources should be allocated, and how technology relates to human capital formation.

The first part of this …

Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox

McKelvey School of Engineering Graduate Student Theses & Dissertations

The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

Hitch Cart “Landing Gear”, Rebekah White, Jose Raygoza, Randy Hernandez, Brandon Leon

Mechanical Engineering

This report aims to allow our sponsor, to review our design process of the Hitch Cart Landing Gear Prototype. In the design overview section of this report, we discuss the primary design modifications we made to the wheel mechanism of the existing hitch cart prototype, including the addition of the ACME screws and the folding brackets. This allows our sponsor to see the intended improvements made to the past prototype and understand the primary goal of our project. Then, in the implementation section, we cover the entire manufacturing process to allow our sponsor to understand what manufacturing steps must be …

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Effects Of A Protection Zone In A Reaction-Diffusion Model With Shifting Bounded Habitat And Allee Effect., Davis Henderson

Electronic Theses and Dissertations

We consider a reaction-diffusion equation that models a population in a shifting bounded habitat with a protection zone and the Allee effect. We assume that the population growth function exhibits the strong Allee effect and has a positive integral within the protection zone (indicating population persistence) and a negative integral in the surrounding patches (indicating population decay). We prove that the existence of steady-state solutions to this system depends on the length of the protection zone. It is demonstrated that there exists some value H* such that, for a protection zone of size H*, there exists a solution and, for …

Frameworks For The Techno-Economic Assessment Of Membrane-Based Bioprocessing Platforms, Juan Jose Romero Conde

All Dissertations

This dissertation describes developing and implementing computational frameworks for simulating and optimizing purification processes in the biopharmaceutical industry. The framework performs techno-economic analyses to establish value propositions for new process alternatives, especially membrane technologies. Initially, the focus is developing a framework capable of simulating monoclonal antibody (mAb) capture using membrane and resin media in multi-column chromatography (MCC) platforms for continuous manufacturing. Subsequently, the impact of capture MCC is compared against other intensification strategies in established mAb manufacturing facilities. Finally, the framework application expands to simulate the purification of adeno-associated virus (AAV) vectors for gene therapy.

Chapter 2 details the framework …