Physical Sciences and Mathematics Commons^™

Boundary Vortex Formation In Polarization-Modulated Orthogonal Smectic Liquid Crystals, Carlos J. García-Cervera, Tiziana Giorgi, Sookyung Joo

Mathematics & Statistics Faculty Publications

We investigate the relaxation of an energy functional originated in the physics literature to study the bistability of polarization modulated orthogonal smectic phases (SmAP_Fmod) of bent-core molecules liquid crystals. We show that the interplay between the mixed boundary conditions and the shape of the sample results in boundary defects. We also analyze the bistable switching due to an applied electric field via gradient flow numerical simulations. Our computations reveal a novel dynamic scenario, where switching is achieved by the formation of two internal vortices.

How We Can Extend The Standard Deviation Notion With Neutrosophic Interval And Quadruple Neutrosophic Numbers, Victor Christianto, Florentin Smarandache, Muhammad Aslam

Branch Mathematics and Statistics Faculty and Staff Publications

During scientific demonstrating of genuine specialized framework we can meet any sort and rate model vulnerability. Its reasons can be incognizance of modelers or information mistake. In this way, characterization of vulnerabilities, as for their sources, recognizes aleatory and epistemic ones. The aleatory vulnerability is an inalienable information variety related with the researched framework or its condition. Epistemic one is a vulnerability that is because of an absence of information on amounts or procedures of the framework or the earth [7]. Right now, we examine fourfold neutrosophic numbers and their potential application for practical displaying of physical frameworks, particularly in …

A Short Remark On Vortex As Fluid Particle From Neutrosophic Logic Perspective, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a previous paper in this journal (IJNS), it is mentioned about a possible approach to re-describe QED without renormalization route. As it is known that in literature, there are some attempts to reconcile vortex-based fluid dynamics and particle dynamics. Some attempts are not quite as fruitful as others. As a follow up to previous paper, the present paper will discuss two theorems for developing unification theories, and then point out some new proposals including by Simula (2020) on how to derive Maxwell equations in superfluid dynamics setting; this could be a new alternative approach towards “fluidicle” or “vorticle” model …

Elucidating The Properties And Mechanism For Cellulose Dissolution In Tetrabutylphosphonium-Based Ionic Liquids Using High Concentrations Of Water, Brad Crawford

Graduate Theses, Dissertations, and Problem Reports

The structural, transport, and thermodynamic properties related to cellulose dissolution by tetrabutylphosphonium chloride (TBPCl) and tetrabutylphosphonium hydroxide (TBPH)-water mixtures have been calculated via molecular dynamics simulations. For both ionic liquid (IL)-water solutions, water veins begin to form between the TBPs interlocking arms at 80 mol % water, opening a pathway for the diffusion of the anions, cations, and water. The water veins allow for a diffusion regime shift in the concentration region from 80 to 92.5 mol % water, providing a higher probability of solvent interaction with the dissolving cellulose strand. The hydrogen bonding was compared between small and large …

Decoupled Finite Element Methods For General Steady Two-Dimensional Boussinesq Equations, Lioba Boveleth

Masters Theses

"This work presents two kinds of decoupled finite element methods for the steady natural convection problem in two dimensions. Firstly, the standard Galerkin finite element method is derived in detail stating algorithms needed for the realization in MATLAB. A numerical example verifies the error convergence. Secondly, using iteration, the Boussinesq equations are decoupled into the Navier-Stokes equations and a parabolic problem. The resulting problems are solved either in parallel or sequentially. Finally, the same numerical example as before is used to confirm the convergence and analyze the methods in terms of iteration performance. In addition to a higher flexibility and …

The Application Of Machine Learning Models In The Concussion Diagnosis Process, Sujit Subhash

Masters Theses

“Concussions represent a growing health concern and are challenging to diagnose and manage. Roughly four million concussions are diagnosed every year in the United States. Although research into the application of advanced metrics such as neuroimages and blood biomarkers has shown promise, they are yet to be implemented at a clinical level due to cost and reliability concerns. Therefore, concussion diagnosis is still reliant on clinical evaluations of symptoms, balance, and neurocognitive status and function. The lack of a universal threshold on these assessments makes the diagnosis process entirely reliant on a physician’s interpretation of these assessment scores. This study …

Novel Approaches For Constructing Persistent Delaunay Triangulations By Applying Different Equations And Different Methods, Esraa Habeeb Khaleel Al-Juhaishi

Doctoral Dissertations

“Delaunay triangulation and data structures are an essential field of study and research in computer science, for this reason, the correct choices, and an adequate design are essential for the development of algorithms for the efficient storage and/or retrieval of information. However, most structures are usually ephemeral, which means keeping all versions, in different copies, of the same data structure is expensive. The problem arises of developing data structures that are capable of maintaining different versions of themselves, minimizing the cost of memory, and keeping the performance of operations as close as possible to the original structure. Therefore, this research …

Pattern Selection Models: From Normal To Anomalous Diffusion, Hatim K. Khudhair

Doctoral Dissertations

“Pattern formation and selection is an important topic in many physical, chemical, and biological fields. In 1952, Alan Turing showed that a system of chemical substances could produce spatially stable patterns by the interplay of diffusion and reactions. Since then, pattern formations have been widely studied via the reaction-diffusion models. So far, patterns in the single-component system with normal diffusion have been well understood. Motivated by the experimental observations, more recent attention has been focused on the reaction-diffusion systems with anomalous diffusion as well as coupled multi-component systems. The objectives of this dissertation are to study the effects of superdiffusion …

Numerical Analysis And Gravity, Tyler D. Knowles

Graduate Theses, Dissertations, and Problem Reports

In this dissertation we apply techniques of numerical analysis to current questions related to understanding gravity. The first question is that of sources of gravitational waves: how can we accurately determine the intrinsic physical parameters of a binary system whose late inspiral and merger was detected by the Laser Interferometer Gravitational-Wave Observatory. In particular, state-of-the-art algorithms for producing theoretical waveforms are as many as three orders of magnitude too slow for timely analysis. We show that direct software optimization produces a two order of magnitude speedup. We also describe documentation efforts undertaken so that the software may be rewritten to …

Genetic Algorithms Used For Search And Rescue Of Vulnerable People In An Urban Setting, Shuhad Aljandeel

Graduate Theses, Dissertations, and Problem Reports

The main goal of this research is to design and develop a genetic algorithm (GA) for path planning of an Unmanned Aerial Vehicle (UAV) outfitted with a camera to efficiently search for a lost person in an area of interest. The research focuses on scenarios where the lost person is from a vulnerable population, such as someone suffering from Alzheimer or a small child who has wondered off. To solve this problem, a GA for path planning was designed and implemented in Matlab. The area of interest is considered to be a circle that encompasses the distance the person could …

Spectral Analysis Of Complex Dynamical Systems, Casey Lynn Johnson

CGU Theses & Dissertations

The spectrum of any differential equation or a system of differential equations is related to several important properties about the problem and its subsequent solution. So much information is held within the spectrum of a problem that there is an entire field devoted to it; spectral analysis. In this thesis, we perform spectral analysis on two separate complex dynamical systems. The vibrations along a continuous string or a string with beads on it are the governed by the continuous or discrete wave equation. We derive a small-vibrations model for multi-connected continuous strings that lie in a plane. We show that …

High Order Explicit Semi-Lagrangian Method For The Solution Of Lagrangian Transport And Stochastic Differential Equations, Hareshram Natarajan

CGU Theses & Dissertations

A semi-Lagrangian method is developed for the solution of Lagrangian transport equations and stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its local and boundary fitted properties and its high performance on parallel platforms for the concurrent semi-Lagrangian and Eulerian solution of a class of time-dependent problems that can be described by coupled Eulerian-Lagrangian formulations. Such formulations include the probabilistic models used for the simulation of chemically reacting turbulent flows or particle-laden flows. Motivated by the high-fidelity simulation …

Iot Based Virtual Reality Game For Physio-Therapeutic Patients, K. Martin Sagayam, Shibin D, Helen Dang, Mohd Helmy Abd Wahab, Radzi Ambar

Faculty Works: MCS (1984-2023)

Biofeedback therapy trains the patient to control voluntarily the involuntary process of their body. This non-invasive and non-drug treatment is also used as a means to rehabilitate the physical impairments that may follow a stroke, a traumatic brain injury or even in neurological aspects within occupational therapy. The idea behind this study is based on using immersive gaming as a tool for physical rehabilitation that combines the idea of biofeedback and physical computing to get a patient emotionally involved in a game that requires them to do the exercises in order to interact with the game. This game is aimed …

Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher

Mahurin Honors College Capstone Experience/Thesis Projects

A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual …

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda

Theses, Dissertations and Culminating Projects

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …

Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

Dissertations

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between …

Topics On High Dimensional Selective Inference, Yan Zhang

Dissertations

In such applications as identifying differentially expressed genes in micro-array experiments or assessing safety and efficacy of drugs in clinical trials, researchers often report confidence intervals (CIs) and p-values only for the selected parameters, which is called selective inference. While constructing multiple CIs for the selected parameters, it is common practice to ignore issue of selection and multiplicity. Although protection against the effect of selection is sufficient in some cases, simultaneous coverage should be also needed in real applications. For example, in clinical trials, multiple endpoints are considered to assess effects of a drug and the ultimate decision often depends …

Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk

Department of Mathematics: Faculty Publications

One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

Near-To-Far Field Signal Propagation For The Wave And Maxwell Equations, Alhassan Ahmed

Mathematics & Statistics ETDs

The Maxwell equations may be viewed as evolution equations which develop an initial state of the electromagnetic field forward in time. Such evolution can be simulated numerically, that is modeled on a computer, in which case the domain of simulation is typically finite in extent. Nonetheless, one is often interested in the electromagnetic waves which reach infinity (of course which is outside of the simulation domain). Thus we are interested in near-to-far field signal propagation, that is a mathematical process where a signal or solution recorded at a finite radius r = r1 can be converted to a signal at …

Algorithms For Mappings And Symmetries Of Differential Equations, Zahra Mohammadi

Electronic Thesis and Dissertation Repository

Differential Equations are used to mathematically express the laws of physics and models in biology, finance, and many other fields. Examining the solutions of related differential equation systems helps to gain insights into the phenomena described by the differential equations. However, finding exact solutions of differential equations can be extremely difficult and is often impossible. A common approach to addressing this problem is to analyze solutions of differential equations by using their symmetries. In this thesis, we develop algorithms based on analyzing infinitesimal symmetry features of differential equations to determine the existence of invertible mappings of less tractable systems of …

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, Jacquelyn Cheun Phd, Luay Dajani, Quentin B. Thomas

SMU Data Science Review

In the age of hyper-connectivity, 24/7 news cycles, and instant news alerts via social media, mental health researchers don't have a way to automatically detect news content which is associated with triggering anxiety or depression in mental health patients. Using the Associated Press news wire, a semantic network was built with 1,056 news articles containing over 500,000 connections across multiple topics to provide a personalized algorithm which detects problematic news content for a given reader. We make use of Semantic Network Analysis to surface the relationship between news article text and anxiety in readers who struggle with mental health disorders. …

A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

SMU Data Science Review

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and gas …

On Improving Performance Of The Binary Logistic Regression Classifier, Michael Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Logistic Regression, being both a predictive and an explanatory method, is one of the most commonly used statistical and machine learning method in almost all disciplines. There are many situations, however, when the accuracies of the fitted model are low for predicting either the success event or the failure event. Several statistical and machine learning approaches exist in the literature to handle these situations. This thesis presents several new approaches to improve the performance of the fitted model, and the proposed methods have been applied to real datasets.

Transformations of predictors is a common approach in fitting multiple linear and …

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

High Strain Dynamic Test On Helical Piles: Analytical And Numerical Investigations, Mohammed Fahad Alwalan

Electronic Thesis and Dissertation Repository

Helical piles are currently considered a preferred foundation option in a wide range of engineering projects to provide high compressive and uplift resistance to static and dynamic loads. In view of the large capacity of large diameter helical piles, there is a need to determine their capacity using accurate and economically feasible testing techniques. The capacity of piles is usually determined by conducting a Static Load Test (SLT). However, the SLT can be costly and time consuming, especially for large capacity piles. The High Strain Dynamic Load Test (HSDT) evaluates the pile capacity using dynamic measurements generated through subjecting the …

Intermediate C∗-Algebras Of Cartan Embeddings, Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let A be a C*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C*-algebra such that D B A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C*-algebras B, and a class of open subgroupoids of the groupoid G, where ! G is the twist …

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …