Applied Mathematics Commons^™

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 …

Bringing Gans To Medieval Times: Manuscript Translation Models, Tonilynn M. Holtz

College of Graduate Studies: Theses & Dissertations

The Generative Adversarial Networks (GAN) recently emerged as a powerful framework for producing new knowledge from existing knowledge. These models aim to learn patterns from input data then use that knowledge to generate output data samples that plausibly appear to belong to the same set as the input data. Medieval manuscripts study has been an important research area in the humanities field for many decades. These rare manuscripts are often times inaccessible to the general public, including students in scholars, and it is of a great interest to provide digital support (including, but not limited to translation and search) for …

A Comparative Analysis Of A Family Of Advanced Iterative Optimization Methods In Nonlinear Regression, Tanmoy Kumar Debnath

College of Graduate Studies: Theses & Dissertations

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in …

Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain

College of Graduate Studies: Theses & Dissertations

As a promising clean energy carrier hydrogen has recently gained significant interest, but its efficient and safe storage is a major challenge. Compared to the gaseous state and liquid state, metal hydrides (MH) offer a potentially more effective storage approach for hydrogen. However, the main challenge in this approach is the low thermal conductivity of the MH bed that leads to low heat transfer and ultimately to higher charging and discharging times. The purpose of this work is to develop an in-house comprehensive heat and mass transfer model for hydrogen sorption in MH reactors to simulate the dynamic behavior of …

Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, Quintessa Hay

Theses and Dissertations

A variety of insults, including tissue injury and/or exposure to pathogen, elicit an immune response in many organisms. An improperly regulated immune response can result in deleterious effects to the organism. Here we present models for lung injury in young and old mice and models for wound healing in coral reefs.

It is well known that the immune response becomes less effective in older individuals. This is of particular interest in pulmonary insults such as ventilator induced lung injury (VILI) or lung infection. We extended a mathematical model for the inflammatory response to VILI and used experimental data to select …

Mathematical Analysis Of Eukaryotic Pericentromere, Puranjan Ghimire

Theses and Dissertations

The centromere is crucial for chromosomal stability and their proper segregation during cell division in eukaryotes. Surrounding the centromere are pericentromeres, made of repetitive DNA elements called pericentromeric repeats, varying from 10 in fission yeast to thousands in humans. These repeats form densely packed heterochromatin, where genes are usually silenced. The silencing mechanism across different pericentromeric repeats remains unclear.

Despite variations in sequence and length, pericentromeric repeats are conserved across eukaryotes, indicating their functional importance. This dissertation presents mathematical models to quantify gene silencing in fission yeast and humans. In fission yeast, my model predicts that silencing occurs only with …

Mathematical Modeling Of Phage-Bacteria Population Dynamics, John Lawrence D. Palacios

Theses and Dissertations

Bacteriophages are viruses that infect and replicate within bacteria. Lytic phages cause the bacterial cell to burst, killing the bacteria. These types of phages can be used to treat patients with antibiotic-resistant bacterial infections. As a step in developing successful treatment protocols, we aim to understand the population dynamics of phages and bacteria using an in vitro model. We model the dynamics using the Campbell model, which consists of a delay differential equation (DDE), as a base model. We extended the model by including the emergence of phage resistance. We then compared the DDE model with a parallel ordinary differential …

Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

Theses and Dissertations

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

Long-Wave Modeling Of Viscous Film Dynamics Inside A Tube With Time-Dependent Radius, Robert E. Hicks

Theses and Dissertations

Lung fluid dynamics is a well studied topic and relevant in the field of research surrounding patients with Chronic Obstructive Pulmonary Disease (COPD) and cystic fibrosis. However, the literature on the mathematical description of the net pulmonary fluid transport in the case of constricting and expanding airways is scarce. In this paper we aim to address how breathing contributes to airways clearance in patients with pulmonary diseases such as COPD and CF in which cilia do not function properly. We begin with the flow of a fluid-filled tube with rigid walls of fixed radius and the effects of gravity being …

Cryptographic Algorithms, Cryptocurrencies, And A Predictive Model Of Bitcoin Value By Pls Regression, Paul Kenneth O'Connor

Masters Theses

"With the invention of Bitcoin in 2009, as a seemingly timed response to the ongoing financial crisis, the popularity of the cryptocurrency has since continued to grow. Just this year, the Security Exchange Commission approved Bitcoin for exchange traded funds, allowing major investment firms to begin product trading. With this approval, and during this very moment of writing, Bitcoin has entered a bull market and reached a record value of over 72,000 USD. In addition, the Bitcoin halving event in April of 2024 is expected to increase demand even further. It has been anticipated that Bitcoin and other cryptocurrencies will …

A New Proper Orthogonal Decomposition Method With Second Difference Quotients For The Wave Equation, Andrew Calvin Janes

Masters Theses

"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and …

Explicit Proximal Gradient Methods: Bridging Theory And Practice In Optimization, Cassandra Mohr

Graduate Research Theses & Dissertations

Convex optimization problems are central to numerous fields, including machine learning, signal processing, and image reconstruction. The development and analysis of algorithms for solving splitting optimization problems constitutes a significant area of research. In particular, we investigate a proximal gradient splitting method (PGM) with an explicit linesearch for finding the solution of nonsmooth optimization problems, where the objective function is the sum of two convex functions.

We focus on cases where one of the functions is differentiable, without imposing any Lipschitz continuity assumption on its gradient. We establish the proper definition of the linesearch, and demonstrate that this version of …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

Artificial Intelligence- Driven Fvm-Ann Model For Entropy Analysis Of Mhd Natural Bioconvection In Nanofluid-Filled Porous Cavities, N. Elsedais, M. A. Mansour, A. M. Aly, Sara Abdelsalam

Basic Science Engineering

No abstract provided.

Characterizing Probabilities Of Outbreaks Of Dengue In Central Argentina Using A Temperature-Dependent Stochastic Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and dengue transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks of dengue can only occur due to new introductions of DENV from other regions. Due to the relationships between temperature and dengue, the risk of outbreak changes throughout the year.

We develop a stochastic model including temperature-dependent mosquito life history traits and transmission-related parameters. …

Sparse Representation Learning For Temporal Networks, Maxwell Mcneil

Electronic Theses & Dissertations (2024 - present)

Temporal networks arise in many domains including activity of social network users, sensor network readings over time, and time course gene expression within the interaction network of a model organism. Data of this type contains a wealth of prior information such as the connectivity among nodes (e.g., a friendship graph), and prior knowledge of expected temporal patterns (e.g., periodicity). Modeling these temporal and network patterns jointly is essential for state-of-the-art performance in temporal network data analysis and mining. Sparse dictionary encoding is one modeling approach for such underlying patterns. However, most classical approaches consider only one dimension of the data …

Hamiltonian Models For The Propagation Of Long Gravity Waves, Higher-Order Kdv-Type Equations And Integrability, Rossen Ivanov

Book chapter/book

A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation.

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

College of Graduate Studies: Theses & Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan

College of Graduate Studies: Theses & Dissertations

Lithium-ion batteries (LIBs) are central in numerous high-demand applications due to their high energy density and prolonged cycle life. Despite these advantages, their susceptibility to thermal runaway (TR) poses a significant safety risk, with the potential for catastrophic failures. This study focuses on the thermal behavior of prismatic lithium-ion cells, using a finite volume-based partial differential equation (PDE) solver developed in MATLAB and JULIA to model TR behavior. This solver accurately simulates transient behaviors, convection, diffusion, and source terms across various coordinate systems. By engaging in a series of increasing complex case studies, this research aims to identify the critical …

Optimizing Microbe-Infected Mosquito Release: A Stochastic Model For Malaria Prevention, Steeven Belvinos Affognon, Henri E.Z. Tonnang, Philip Ngare, Benard Kipchumba Kiplangat, Shirley Abelman, Jeremy K. Herren

All Peer-Reviewed Publications

Malaria remains a critical public health challenge in Africa, demanding innovative control strategies. This study introduces a novel approach using Microsporidia MB-infected mosquitoes and stochastic optimal control within a Lévy process framework to regulate mosquito release strategies. The primary goal is to optimize Microsporidia MB prevalence within mosquito populations to disrupt Plasmodium transmission to humans. By incorporating Lévy noise into the modeling process, we capture the inherent randomness of mosquito dynamics, improving intervention accuracy. The model, guided by the Hamilton–Jacobi–Bellman (HJB) equation, optimizes release protocols while accounting for key environmental factors like seasonality and temperature fluctuations. Results show that intervention …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

Quantitative Verification For Massive Linear Systems, Qing Liu

School of Computing: Dissertations, Theses, and Student Research

The verification of linear systems has been an active area of research for decades. Reachability analysis is a key component in verification problems. It involves computing the system’s reachable set, the set of reachable states in the state space from a given set of initial states. Most verification methods primarily focus on qualitative verification, which answers whether or not a system may violate specified safety conditions. This paper extends this qualitative verification to quantitative verification by introducing a novel approach, employing probabilistic stars (Probstars) to compute reachable sets, which augment traditional star sets by integrating Gaussian-distributed random variables with …

Determination Of Spore Viability In Concrete Across Several Factors Using Most Probable Number, Samuel Boyer

Williams Honors College, Honors Research Projects

To determine the lowest concentration of spore added to polyurethane-cement composite (PUCCO) particles that can still germinate after curing in concrete. This research project is a small addition to the larger research project being undertaken by Mirza Mohammed Rashiduzzaman for his Masters. The larger project involves the use of fungal spores added in concrete to act as a self-healing component when cracks form in the concrete structure over time. These spores are suspended in a protective oil and loaded into small, hardened sponge-like PUCCO cubes to act as growth points when water and air can reach the PUCCO in the …

Modeling Inflation Using A Fast Fourier Transform (Fft), Blake Smith

Williams Honors College, Honors Research Projects

This paper utilizes a Fast Fourier Transform (FFT) algorithm to construct a trigonometric interpolant for the Consumer Price Index (CPI), which is then differentiated and used to obtain a continuous function for “instantaneous” (i.e., month-wise) inflation, as opposed to a 12-month percent-change. Fourier coefficients are analyzed to investigate underlying periodicities in the newly constructed function. This metric does not hold significant predictive value but it may prove helpful in retroactive analysis of inflation trends.

Applications Of Physics-Informed Graph Neural Networks In Wind Farm Layout Optimization, Emma R. Martin

Theses and Dissertations

Rapid advancements in data-driven deep learning models have led to their increased usage in recent years. Highly-effective models for conducting complex decision-making tasks have been developed. Given their success, data-driven deep learning models are being developed and improved in a variety of areas, one of which is renewable energy. In this thesis, we discuss the development of data-driven, deep learning models for optimizing wind farm layouts for maximum power output. We include a background for wind energy, the physics of fluid flow and power production, and two types of neural networks: graph neural networks and physics-informed neural networks. Additionally, we …

Deterministic And Stochastic Dynamics Of Marine Food Webs, Julian A. Hernandez S.

Theses, Dissertations and Culminating Projects

Ecologists have long been concerned with understanding the behavior and evolutionary patterns exhibited within complex ecological communities. Under- standing the delicate balance that sustains ecosystems is crucial in determining how these communities evolve over time. Recently, researchers have combined deterministic Lotka-Volterra dynamics with different types of synthetic food webs (cascade, niche and generalized cascade models), and have analyzed the mechanisms behind primary extinction events and the ensuing secondary extinction cascade. These studies also enabled the exploration of the complex interplay of species loss to explain how food web structure influences primary and secondary extinction. We have extended these ideas to …

Many Extensions Of Coulomb’S Law: A Scoping Review, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, Coulomb’s Law is extended from two stationary charged particles, on linear trajectory, to: many charged particles, or quantum level particles, or objects on arbitrary motions (with velocity, acceleration, time delay), on non-linear trajectories, at even superluminal and instantaneous speeds.

Jonckheere Trend Test Under Indeterminacy With Applications, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The classical Jonckheere trend test is a non-parametric statistical tool usually employed to compare the medians of multiple independent groups, especially when there is a natural ordering or trend among the groups. This paper aims to develop a more comprehensive and adaptable version of the Jonckheere trend test, called the neutrosophic Jonckheere trend test (NJT), which can be used to analyze di_erent types of uncertainty data. This paper discusses neutrosophic hypotheses and decision rules pertaining to the NJT test. Furthermore, the practical uses of the NJT test have been discussed in the context of real-world applications with COVID-19 data. Lastly, …

Enhancing Set-Theoretic Research Methods With Neutrosophic Sets, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study employed the integration of neutrosophic set theory with set-theoretic methods and Qualitative Comparative Analysis (QCA) to examine intricate social phenomena. Participants' opinions and attitudes were captured using neutrosophic Likert scales, which reflected elements of truth, indeterminacy, and falsity. This proposal is illustrated in a case study facilitated a more comprehensive and subtle examination, emphasizing the significance of variables such as motivation, instructional excellence, and educational resources in achieving academic accomplishment. The results of the necessary condition analysis and set coincidence analysis indicated that motivation and teaching quality have the highest individual impact. Nevertheless, the convergence of scholarly resources, …

An Innovative Approach On Yao’S Three-Way Decision Model Using Intuitionistic Fuzzy Sets For Medical Diagnosis, Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Florentin Smarandache, Hamza Ghazanfar Toor, Faiza Asif

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a …