Applied Mathematics Commons^™

A Compact Exploration Of Turiyam Neutrosophic Competition Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory, a branch of mathematics, examines relationships between entities using vertices and edges. Within this field, Uncertain Graph Theory has emerged to model uncertainties in real-world networks. A notable concept in this area is the competition graph, which captures interactions by connecting vertices that “compete” for the same neighbor, represented by directed edges indicating common neighbors in a digraph. This brief paper introduces the concept of the Generalized Turiyam Neutrosophic Competition Graph and explores its relationships with other graph classes.

Numerical Solution Of Hybrid Nanofluid And Its Stability Over Permeable Wedge Sheet With Heat Transfer Analysis, Aisha M. Alqahtani, Zeeshan, Waris Khan, Florentin Smarandache, Nidhal Becheikh, Roobaea Alroobaea, Taseer Muhammad

Branch Mathematics and Statistics Faculty and Staff Publications

The inclusion of nanoparticles has the potential to improve the thermal efficiency of the base fluid. The field of nanofluid (NF) dynamics has attracted important attention due to its extensive range of practical uses like fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to scrutinize the impact of Lorentz force, thermal energy, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability inquiry is reported for the existing work in order to confirm the stable …

Analysis And Detection Of Cyber Attacks In Multi Vehicle Systems Using Macroscopic Models, Abhishek Kashyap

Mechanical and Aerospace Engineering Dissertations - Archive

The study of potential cyber-attacks in different domains is an active area of research. Given that systems are becoming more and more interconnected, cyber physical systems that operate infrastructure and/or plants can make these assets more vulnerable and open to different attack vectors. The primary focus of this research is the modeling, analysis and detection of cyber-attacks on platoons of autonomous cars and swarms of UAVs. In this work, we consider scenarios wherein an attacker may hack into a subset of vehicles in a multi-vehicle system and make subtle modifications in their parameters. Due to the interconnected nature of the …

A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe

Mathematics Dissertations - Archive

Models of glucose metabolism in the brain often focus on chemical exchanges and reactions that occur as part of the tricarboxylic acid cycle (TCA cycle). Experiments involving nuclear magnetic resonance (NMR) spectroscopy to detect and measure carbon-labeled isotopomers of metabolites such as glutamate in vivo inform kinetic, mechanistic models used to study metabolic pathways. In the present work, a new model with two compartments, astrocytic and neuronal, is developed using known biochemical processes and fit to experimental data coming from fully labeled glucose infusions. A gradient descent method is introduced and employed to obtain optimal flux parameter values involved in …

Uniform Regularity Estimates For The Stokes System In Perforated Domains, Jamison R. Wallace

Theses and Dissertations--Mathematics

We consider the Stokes equations in an unbounded domain $\omega_{\epsilon,\eta}$ perforated by small obstacles, where $\epsilon$ represents the minimal distance between obstacles and $\eta$ is the ratio between the obstacle size and $\epsilon$. We are able to obtain uniform $W^{1,q}$ estimates for solutions to the Stokes equations in such domains with bounding constants depending explicitly on $\epsilon$ and $\eta$.

Advancements In Elliptic Mesh Redistribution And Automated Overset Grid Generation For Computational Fluid Dynamics, Chase Ashby

Theses and Dissertations--Mathematics

Automated and robust structured curvilinear overset grid generation remains a significant challenge for the application of computational fluid dynamics. This thesis intro- duces a specialized anisotropic Mach cone aligned adaptation algorithm for low-boom simulations and an automated procedure for generating structured curvilinear overset grids for immersed boundary simulations. Results demonstrate that anisotropic mesh adaptation can reduce computational resource usage by over 50% while maintaining sonic boom prediction accuracy across the entire sonic boom domain compared to user-constructed Mach cone aligned grids. The proposed immersed overset grid gen- eration procedure eliminates the need for complex surface generation algorithms, producing grids suitable …

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

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 …

Batch Culture Models Of The Murine Gut Microbiome & The Impact Of Simple Dormancy On Dormancy-Capable Microorganisms Models, Ana C. Mendez

Mathematics Dissertations - Archive

The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy …

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 …

Adaptive Neh With Constrained Nearest Neighbor Subtours For The Electric Vehicle Routing Problem With Time Windows, Andrew Struthers

All Master's Theses

The development of electric vehicles is currently considered one of the most innovative areas in manufacturing. Largely driven by the desire to reduce greenhouse emissions, electric vehicles are seen as a viable alternative to internal combustion engine cars. Starting from consumer cars, a dedicated effort is being made to translate this into commercial vehicles for freight and delivery. This research introduces a novel adaptive Nawaz, Enscore, Ham (NEH) algorithm with constrained nearest neighbor subtour (NEH-NN). This algorithm is tested on the standard benchmark problems in literature and used as a seed solution for the Genetic Algorithm (GA). The performance and …

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.

Investigation Of Space Charge Effects On Co2 Electrocatalytic Reduction On Gd-Doped Ceria Via Scanning Kelvin Probe And Model-Based Bayesian Analysis, Alejandro Mejia

Graduate Theses, Dissertations, and Problem Reports (ETD)

In studying novel energy conversion and storage systems, such as high-temperature electrolysis, numerous underlying fundamental physical processes remain unclear or inadequately understood. Among these, the modeling and comprehension of surface reaction mechanisms, coupled with the intricate effects of space‑charge interfaces, remains an unclear and challenging area of research.

The work of this dissertation involves the development of a 2D finite element analysis model, leveraging the robust MOOSE framework from INL. This model, featuring inhomogeneous defect thermodynamics for near-surface chemistry, formulated through Poisson‑Cahn variational theory, has been exploited for studying the electrocatalytic reduction of CO₂ on gadolinia doped ceria. The …

Robot-Based 3d Printing, Aaron Hoffman

Williams Honors College, Honors Research Projects

Details of a large-format 3D printer created to print experimental materials, test multi-axis print techniques, and quickly print large objects. The printer consists of a 7-axis robotic arm and pellet extruder, which are controlled by a PC. Experimental materials such as recycled polymers or carbon-fiber reinforced materials can be easily tested with the pellet format of the extruder. The printer can perform different printing techniques and can be used to experiment with material properties when using these techniques with different polymers. The print surface is around 5 times larger than the average commercial 3D printer, and the robotic arm provides …

Estimating Modeling Parameters For Covid-19 Spread On Campus, Aviel S. Crigger

Honors Undergraduate Theses

Understanding the true burden of community transmission of communicable diseases like COVID-19 is crucial for effective public health response. Clinical cases, while important, only represent a fraction of the actual disease prevalence within a population. In this thesis, we investigate methods to estimate parameters that link clinical cases to the true disease prevalence using a modified compartmental model known as SICR (Susceptible, Infected, Cases, Recovered). We employ Bayesian inference and ensemble Markov chain Monte Carlo (MCMC) simulations to analyze clinical case data provided by the University of Central Florida Health Center from 2020 to 2022. Our goal is to estimate …

Uniform Convergence Of Deep Neural Networks With Lipschitz Continuous Activation Functions And Variable Widths, Yuesheng Xu, Haizhang Zhang

Mathematics & Statistics Faculty Publications

We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias vectors together with the Lipschitz constant are provided to ensure uniform convergence of DNNs to a meaningful function as the number of their layers tends to infinity. In the framework, special results on uniform convergence of DNNs with a fixed width, bounded widths and unbounded widths are presented. In particular, as convolutional neural networks are special DNNs with weight matrices of increasing widths, we put …

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

Theses and Dissertations

We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that …

New Method For Computing The Euclidean Condition Number With Rim-C, Cody Mccarthy

Dissertations, Master's Theses and Master's Reports

The condition number, being critical to solving linear systems, has many impor-
tant applications. Specifically for robust control analysis, the Euclidean norm has
widespread use over the 1-norm and ∞-norm such as determining a control system’s
stability to uncertainty [1]. Much work has been done with estimating the Euclidean
condition number, but current algorithms for computing said condition number, with
large matrices, tend to run slow as well as requiring a large amount of computa-
tional resources. This report seeks to provide a more time efficient algorithm that
utilizes MATLAB’s eigs, svds, and normest commands as well as the recently …

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 …