Dynamical Systems Commons^™

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Uniform Stability Of Katyusha In Strongly-Convex Settings, Don Li

University Honors Theses

Acceleration of convergence and reduction of variance constitute a trade-off in the design of stochastic optimization machine learning algorithms. Katyusha was introduced to address this trade-off, synthesizing Nesterov Accelerated Gradient (NAG) and Stochastic Variance-Reduced Gradient (SVRG) into a single first-order optimizer with promising empirical performance. However, the generalization properties of Katyusha remain largely unexplored. We conjecture that, in the smooth quadratic regime (i.e., under assumptions of strong convexity and smoothness of the loss function, and boundedness of gradients), Katyusha is uniformly stable in the sense of Bousquet and Elisseeff. Instantiating our framework for NAG, we extend the use of Lyapunov …

Computational Insights Into Nucleosome Dynamics In Epigenetics Using Molecular Dynamics Simulations, Rutika Patel

Dissertations, Theses, and Capstone Projects

Nucleosome core particles (NCP) are the building blocks that form a highly organized and compact chromatin structure. Nucleosomes package DNA in the nucleus of eukaryotic cells. The NCP consists of about 147 base pairs of DNA wrapped around the histone octamer, with 1.65 superhelical turns in a left-handed manner. The histone octamer is composed of two copies of H3, H4, H2A, and H2B. Together with histone H1 and linker DNA, they further assemble into a higher-order chromatin structure. The nucleosome complex is stabilized by electrostatic interactions between positively charged histone residues and the negatively charged DNA backbone. To effectively access …

Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev

Honors Scholar Theses

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …

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, …

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Cancer Cell Growth Predictions Based On Classical Mathematical Models With Physics-Informed Neural Network, Widodo Samyono

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

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 …

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Applying Hallgren’S Algorithm For Solving Pell’S Equation To Finding The Irrational Slope Of The Launch Of A Billiard Ball, Sangheon Choi

Mathematical Sciences Technical Reports (MSTR)

This thesis is an exploration of Quantum Computing applied to Pell’s equation in an attempt to find solutions to the Billiard Ball Problem. Pell’s equation is a Diophantine equation in the form of x² − ny² = 1, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. We will be applying Hallgren’s algorithm for finding irrational periods in functions, in the context of billiard balls and their movement on a friction-less unit square billiard table. Our central research question has been the following: Given the cutting sequence of the billiard …

Time Evolution Is A Source Of Bias In The Wolf Algorithm For Largest Lyapunov Exponents, Kolby Brink, Tyler Wiles, Nicholas Stergiou, Aaron Likens

UNO Student Research and Creative Activity Fair

Human movement is inherently variable by nature. One of the most common analytical tools for assessing movement variability is the largest Lyapunov exponent (LyE) which quantifies the rate of trajectory divergence or convergence in an n-dimensional state space. One popular method for assessing LyE is the Wolf algorithm. Many studies have investigated how Wolf’s calculation of the LyE changes due to sampling frequency, filtering, data normalization, and stride normalization. However, a surprisingly understudied parameter needed for LyE computation is evolution time. The purpose of this study is to investigate how the LyE changes as a function of evolution time …

A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman

HMC Senior Theses

We can think of a pixel as a particle in three dimensional space, where its x, y and z coordinates correspond to its level of red, green, and blue, respectively. Just as a particle’s motion is guided by physical rules like gravity, we can construct rules to guide a pixel’s motion through color space. We can develop striking visuals by applying these rules, called dynamical systems, onto images using animation engines. This project explores a number of these systems while exposing the underlying algebraic structure of color space. We also build and demonstrate a Visual DJ circuit board for …

Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

Doctoral Dissertations and Master's Theses

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …

Knowing What We Know: Leveraging Community Knowledge Through Automated Text-Mining, Justin Gardner, Jonathan Tory Toole, Hemant Kalia, Garry Spink Jr., Gordon Broderick

Advances in Clinical Medical Research and Healthcare Delivery

No abstract provided.

Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai

Mathematical Sciences Spring Lecture Series

There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …

Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, Elizabeth Hunter, John D. Kelleher

Articles

Background

In order to be prepared for an infectious disease outbreak it is important to know what interventions will or will not have an impact on reducing the outbreak. While some interventions might have a greater effect in mitigating an outbreak, others might only have a minor effect but all interventions will have a cost in implementation. Estimating the effectiveness of an intervention can be done using computational modelling. In particular, comparing the results of model runs with an intervention in place to control runs where no interventions were used can help to determine what interventions will have the greatest …

An Update On The Computational Theory Of Hamiltonian Period Functions, Bradley Joseph Klee

Graduate Theses and Dissertations

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple …

A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, Elizabeth Hunter, Brian Mac Namee, John D. Kelleher

Articles

Both agent-based models and equation-based models can be used to model the spread of an infectious disease. Equation-based models have been shown to capture the overall dynamics of a disease outbreak while agent-based models are able to capture heterogeneous characteristics of agents that drive the spread of an outbreak. However, agent-based models are computationally intensive. To capture the advantages of both the equation-based and agent-based models, we create a hybrid model where the disease component of the hybrid model switches between agent-based and equation-based. The switch is determined using the number of agents infected. We first test the model at …

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

Emirates Journal for Engineering Research

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response …

Period Estimation And Noise In A Neutrally Stable Stochastic Oscillator, Kevin R. Sanft, Ben F. M. Intoy

Spora: A Journal of Biomathematics

The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

Optimal Control Of A Rumor Propagation Model With Different Propagation Degrees In Social Network, Yingfeng Tang

Student Works (2020-2029)

Rumor is a social interaction of information, and its development is of great significance to human beings. In this paper, by studying the D K model and a rumor model spreading with rumor latent period, deduces the rumor model with differe nt propagation degrees of the spreaders. The two equilibrium points in the system are found through derivation. In real life, enterprises often ignore the reasonable planning of the cost of rumor control. By means of public education and media technology u sing by the authorities to debunk rumors, an optimal control problem i s established. The Pontryagin’s maximum principle …

Remark On Artificial Intelligence, Humanoid And Terminator Scenario: A Neutrosophic Way To Futurology, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article is an update of our previous article in this SGJ journal, titled: On Gödel's Incompleteness Theorem, Artificial Intelligence & Human Mind [7]. We provide some commentary on the latest developments around AI, humanoid robotics, and future scenario. Basically, we argue that a more thoughtful approach to the future is "technorealism."

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch

Electronic Theses and Dissertations

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work …