Applied Mathematics Commons^™

Modeling, Simulation And Control Of Microrobots For The Microfactory., Zhong Yang

Electronic Theses and Dissertations

Future assembly technologies will involve higher levels of automation in order to satisfy increased microscale or nanoscale precision requirements. Traditionally, assembly using a top-down robotic approach has been well-studied and applied to the microelectronics and MEMS industries, but less so in nanotechnology. With the boom of nanotechnology since the 1990s, newly designed products with new materials, coatings, and nanoparticles are gradually entering everyone’s lives, while the industry has grown into a billion-dollar volume worldwide. Traditionally, nanotechnology products are assembled using bottom-up methods, such as self-assembly, rather than top-down robotic assembly. This is due to considerations of volume handling of large …

Trajectory Analysis For Driving Safety Quantification, Michael I. Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

In order to evaluate the efficacy of the skid recovery exercise in the Driver’s Edge teenage driving program, a process is established to determine the trajectories of vehicles from recorded videos, compare them in terms of similarity through dynamic time warping (DTW), and then analyze the similarity measurements to assess whether the program has a significant effect on driving ability by repeated measures analysis of variance (rANOVA). The video is analyzed by Harris corner detection and Lucas-Kanade optical flow method to ascertain the vehicle trajectories. A homography is then estimated to translate coordinates from video into real-world. The instructor and …

Analysis And Application Of Finite Element And High-Order Finite Difference Methods For Maxwell’S Equations In Complex Media, Li Zhu

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Perfectly Matched Layer (PML) technique is an effective tool introduced by B´erenger [13] to reduce the unbounded wave propagation problem to a bounded domain problem. This dissertation focuses on two different PML models and their applications to wave propagation problems with Maxwell’s equation in complex media. We investigate these models using two popular numerical methods: the Finite Difference Method (FDM) in Chapters 2 and 3, and the Finite Element Method (FEM) in Chapters 4 and 5.In Chapter 2, we focus on analyzing the stability of a PML developed by B’ecache et al. [10] for simulating wave propagation in the …

Mathematical Modeling: Finite Element Analysis And Computations Arising In Fluid Dynamics And Biological Applications, Jorge Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is often the case when attempting to capture real word phenomena that the resulting mathematical model is too difficult and even not feasible to be solved analytically. As a result, a computational approach is required and there exists many different methods to numerically solve models described by systems of partial differential equations. The Finite Element Method is one of them and it was pursued herein.This dissertation focuses on the finite element analysis and corresponding numerical computations of several different models. The first part consists of a study on two different fluid flow models: the main governing model of fluid …

A Machine Learning Approach To Evaluate The Effect Of Sodium-Glucose Cotransporter-2 Inhibitors On Chronic Kidney Disease In Diabetes Patients, Solomon Eshun

Theses and Dissertations

Chronic kidney disease (CKD) is a significant complication that contributes to diabetes-related mortality in the United States, and there is growing evidence that sodium-glucose cotransporter 2 inhibitors (SGLT2i) can slow its progression. However, observational studies may suffer from confounding by indication, where patient characteristics and disease severity influence the decision to prescribe SGLT2i. This study utilized electronic health records of individuals with diabetes (from TriNetX) to investigate the effectiveness of SGLT2i on CKD progression. The database provided detailed information on patients’ CKD status, demographics, diagnosis, procedures, and medications, along with corresponding dates of diagnosis and prescription. The study comprised of …

Modeling And Simulation Of Ion-Induced Volume Phase Transitions In Chemically-Active Polyelectrolyte Gels, Bindi Mahesh Nagda

Theses and Dissertations

Ion-induced volume phase transitions in polyelectrolyte gels play an important role in physiological processes such as mucus storage and secretion in the gut, nerve tissue excitation, and DNA packaging. Biological experiments show that polyelectrolyte gels may swell or collapse rapidly due to changes in external conditions such as ionic composition. The volume phase transition is accompanied by a monovalent/ divalent ion exchange between the polymer network and the solvent that make up the gel. We propose a 2D computational method for simulating mucus swelling and deswelling with a two-fluid mixture model. The model includes electro-diffusive transport of ionic species, the …

Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

Theses

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …

Inference For Multiple Utility In Time-Dependent Choice Pairs Under Copula-Based Models, Sasanka Adikari

Mathematics & Statistics Theses & Dissertations

Models for discrete choice experiments (DCE) are frequently used to analyze consumer choices about products and services. A family of DCE, best-worst scaling experiments, offers more in-depth insights into consumer preferences by eliciting a best and worst choice from a set of options, rather than just a single preference. Traditional approaches often assume that choices are mutually exclusive over time, which may not always be the case. This dissertation proposes a novel model for DCE that takes into account the changing nature of consumer choices over time and the priority constraint of transition probabilities. The model introduces a copula combination …

Mathematical Modeling Of Egain Droplets Sliding Down An Inclined Plane, Shawn Koohy, Kathryn Massey, Luis Schneegans, Megan Vezzetti, Keith Hillaire, Souradip Chattopadhyay, Jessie Chen, Carmen Lee, Karen Daniels

Undergraduate Research Symposium

Eutectic Gallium-Indium (EGaIn) is a room-temperature liquid metal alloy that dramatically changes its surface tension and dynamics under an applied electric field. EGaIn has been used heavily in soft electronics engineering due to its high conductivity, malleability, and safety. However, the absence of mathematical modeling in the current literature makes its behavior difficult to understand and predict. In this study, we present a one-dimensional lubrication model for the dynamics of an EGaIn droplet moving along an inclined plane. Our model incorporates essential physical effects and parameters including oxidation, capillary action, diffusion, gravity, and Marangoni effects. In particular, we incorporate effects …

Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng

Department of Mathematics: Faculty Publications

Here we prove that the dynamics on any two center-manifolds of a fixed point of any C^k,1 dynamical system of finite dimension with k ≥ 1 are C^k-conjugate to each other. For pedagogical purpose, we also extend Perron’s method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions.

Developing Weak Galerkin Finite Element Methods, Ahmed Sallal Joudah Al-Taweel

Theses and Dissertations

The weak Galerkin finite element method is a flexible and effective numerical technique for solving partial differential equations (PDEs). The goal of this dissertation is to develop new weak Galerkin schemes for solving PDEs on uniform triangular partitions in 2D. These schemes will improve the efficiency of the weak Galerkin method and avoiding numerical locking. First, we investigate the lowest-order weak Galerkin finite element method for solving reaction-diffusion equations with singular perturbations. Then, we propose a weak Galerkin method for the Laplace equation using harmonic polynomial finite elements instead of the full polynomial space $P_k$ to achieve the same order …

Head And Neck Tumor Histopathological Image Representation With Pre- Trained Convolutional Neural Network And Vision Transformer, Ranny Rahaningrum Herdiantoputri, Daisuke Komura, Tohru Ikeda, Shumpei Ishikawa

Journal of Dentistry Indonesia

Image representation via machine learning is an approach to quantitatively represent histopathological images of head and neck tumors for future applications of artificial intelligence-assisted pathological diagnosis systems. Objective: This study compares image representations produced by a pre-trained convolutional neural network (VGG16) to those produced by a vision transformer (ViT-L/14) in terms of the classification performance of head and neck tumors. Methods: W hole-slide images of five oral t umor categories (n = 319 cases) were analyzed. Image patches were created from manually annotated regions at 4096, 2048, and 1024 pixels and rescaled to 256 pixels. Image representations were …

Electric Vehicle Uptake: What Factors Are Motivating The Shift For College-Aged And Older Groups?, Jake Cardines

Honors Projects in Mathematics

Electric vehicles (EVs) arguably are the most quickly expanding form of transportation as the world races toward a greener future with advanced technology and reduced reliance on fossil fuels. This study analyzes various expected inputs to motivating consumers of particular age groups to purchase EVs, including examination of how the idea of EV ownership is currently perceived and testing which factors influence it positively and negatively. Data collected from 113 survey respondents serves as the basis for determining the responsiveness of potential future EV owners to variables such as vehicle brand and charging availability, electric range, costs associated with purchase …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

Analysis Of An Seir Model With Non-Constant Population, Kylar Byrd, Tess Tracy, Sunil Giri, Swarup Ghosh

Student Research

Analysis of an SEIR model with Non-Constant Population
by Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh.

Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as …

The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall

Honors Theses

One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …

National Residency Matching Program: Looking At The Data Through Linear Regressions, Jacklyn Tellez

Undergraduate Theses

The National Residency Matching Program (NRMP) oversees the process of medical school graduates being matched to a residency program. The NRMP determines both the hospital and residency program for medical students. Prior to matching, both hospital programs and students rank each other. The NRMP uses these lists to determine the matches. Four distinct models using data from hospitals and applicants were used to determine what characteristics lead to a chance of being matched. Each model went through multiple rounds of testing to determine the importance of the different independent variables. In each data set, the dependent variable is either the …

A Closer Look At The Death Penalty In The United States, Anna L. Cardell

Research & Creative Achievement Day

The death penalty has always been a source of contention towards most people in the United States – some agree with it, some do not. No matter one's opinion on whether it should be allowed, this poster presentation will give an in-depth analysis and present various visualizations of information regarding the convicted felons that have been sentenced to capital punishment in the United States from 1976-2016. Variables such as gender, age, and race will be explored to create some insight on some of the most infamous killers in United States history. Though looking at the demographics of these individuals and …

Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson

Spora: A Journal of Biomathematics

Silver carp (Hypophthalmichthys molitrix) are planktivorous fish that were originally introduced to the United States for use in fish production ponds and have since escaped these enclosures and are invading the Mississippi River Basin. The silver carp invasion of the Illinois River has a myriad of negative effects on native ecosystems. In this paper, we introduce key dependencies that are likely important in the population dynamics of silver carp: length-dependent egg production and density-dependent growth. Using movement data between two adjacent pools of the Illinois River, we conduct numerical simulations to explore the theoretical effect of harvesting and …

A Mathematical Model For Mosquito Population Dynamics, Christian Evans, Jemal Mohammed-Awel, Andreas Lazari

Georgia Journal of Science

In this study, a deterministic mathematical model for mosquito population dynamics is presented. The use of chemical insecticide to control population is incorporated into the model. It is assumed that there is insecticide sensitive (sensitive-type) and insecticide resistant (resistant-type) mosquitoes in the environment. Conditions for the existence and stability of four equilibria of the model have been established. Numerical simulations are carried out to confirm the analytical results and the implications, in terms of mosquito control in the environment, are discussed.

Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks, Adam Wagenknecht

Dissertations

Convolutional Neural Networks (CNNs) have become one of the most commonly used tools for performing image classification. Unfortunately, as with most machine learning algorithms, CNNs suffer from a lack of interpretability. CNNs are trained by using a training data set and a loss function to tune a set of parameters known as the layer weights. This tuning process is based on the classical method of gradient descent, but it relies on a strong stochastic component, which makes the weight behavior during training difficult to understand. However, since CNNs are governed largely by the weights that make up each of the …

A Predator-Prey Biological Model With Combined Birth Rates, Self-Limitation And Competition Terms, Joon Hyuk Kang, Lucinda Ford

Faculty Publications

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rⁿ. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive …

Unraveling The Nature Of Nano‑Diamonds And Silica In A Catheterized Tapered Artery: Highlights Into Hydrophilic Traits, Sara I. Abdelsalam, M.M. Bhatti

Basic Science Engineering

No abstract provided.

A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin

Honors College Theses

Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …

Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra

Mathematics & Statistics ETDs

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …

Nash Blowups Of Toric Varieties In Prime Characteristic, Daniel Duarte, Jack Jeffries, Luis Núñez-Betancourt

Department of Mathematics: Faculty Publications

We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially.

Finite Element Methods For Elliptic Optimal Control Problems With General Tracking, Seonghee Jeong

LSU Doctoral Dissertations

This dissertation concerns a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of a domain.

First we explore the elliptic optimal control problem subject to pointwise control constraints. This problem is reduced into a problem that only involves the control. The solution of the reduced problem is characterized by a variational inequality. Then we introduce the elliptic optimal control problem with general tracking and pointwise state constraints. Here we reformulate the optimal control problem into a problem that only involves the state, …

First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang

LSU Doctoral Dissertations

Nonlinear optimization is a critical branch in applied mathematics and has attracted wide attention due to its popularity in practical applications. In this work, we present two methods which use first-order information to solve two typical classes of nonlinear structured optimization problems.

For a class of unconstrained nonconvex composite optimization problems where the objective is the sum of a smooth but possibly nonconvex function and a convex but possibly nonsmooth function, we propose a unified proximal gradient method with extrapolation, which provides unified treatment to convex and nonconvex problems. The method achieves the best-known convergence rate for first-order methods when …

Effects Of Topography On Tornado Paths Using Navier Stokes Equations, Kayleigh Smith

Mathematics Senior Capstone Papers

Tornadoes are relatively common in Louisiana with an average of 55 tornadoes per year. Predicting tornado paths has been extremely challenging due to the many factors that play into the formation of a tornado. According to NASA/ADS topography can have significant influence on tornado direction. The main goal of this research is to analyze tornado patterns and to determine if local topography has an effect on tornadic activity. Navier-Stokes partial differential equations will be used to model the data that is collected from the national weather service and a finite difference method will be used to solve the equations. Data …

Modeling Reverberant Chambers Used In Time-Reversal Cavities Using Time-Frequency Methods, Jordan Savoie

Mathematics Senior Capstone Papers

The signal processing technique of time-reversal is used for various purposes in electro-magnetic interference testing, radar, communication, sonar, and medicine. This paper models the impulse response of a reverberant chamber such as might be used for a time-reversal cavity (TRC) using time-frequency methods. Reverberant chambers have chaotic delaying phase responses that cause the majority of the distortion seen in their impulse response. Time-reversal cancels this, creating a focused signal from a disperse one. Most research modeling the behavior of TRCs is more concerned with their physics, so there is relatively little commented on the form of their signals. Data of …