Numerical Analysis and Computation Commons^™

Automatic Numerical Methods For Enhancement Of Blurred Text-Images Via Optimization And Nonlinear Diffusion, Aaditya Kharel

Honors Theses

In this paper, we propose an automatic numerical method for solving a nonlinear partialdifferential- equation (PDE) based image-processing model. The Perona-Malik diffusion equation (PME) accounts for both forward and backward diffusion regimes so as to perform simultaneous denoising and deblurring depending on the value of the gradient. One of the limitations of this equation is that a large value of the gradient for backward diffusion can lead to singularity formation or staircasing. Guidotti-Kim-Lambers (GKL) came up with a bound for backward diffusion to prevent staircasing, where the backward diffusion is only limited to a specific range beyond which backward diffusion …

Hydrodynamic Instability Simulations Using Front-Tracking With Higher-Order Splitting Methods, Dillon Trinh

Mathematical Sciences Undergraduate Honors Theses

The Rayleigh-Taylor Instability (RTI) is an instability that occurs at the interface of a lighter density fluid pushing onto a higher density fluid in constant or time-dependent accelerations. The Richtmyer-Meshkov Instability (RMI) occurs when two fluids of different densities are separated by a perturbed interface that is accelerated impulsively, usually by a shock wave. When the shock wave is applied, the less dense fluid will penetrate the denser fluid, forming a characteristic bubble feature in the displacement of the fluid. The displacement will initially obey a linear growth model, but as time progresses, a nonlinear model is required. Numerical studies …

Modeling Drought, Drought Teleconnection, And Its Effect On Groundwater Level Dynamics In The Biscayne Aquifer, Anteneh Z. Abiy

FIU Electronic Theses and Dissertations

Developing a self-sufficient water supply system in Southeast Florida is one input to the success of the ongoing restoration effort in the Everglades. Maintaining a high groundwater level in the urban side of the Biscayne Aquifer (BA) is important to sustain the urban water supply. However, the long-term groundwater table condition in the Biscayne Aquifer (BA) is threatened by a combination of drought, groundwater pumping, and sea-level rise. Further, the long-term drought pattern, drought drivers, and the aquifer’s response to drought and other stress conditions are not well known. As a result, options that would help to maintain a high …

Modeling Fico Score And Loan Amount, Ashleigh Romer

Georgia College Student Research Events

In this research, we use Lending Club data from Kaggle to analyze FICO scores and loan amounts funded using multiple predictors. Lending Club is a US peer-to-peer lending company, headquartered in San Francisco, California. First, we cleaned our big data with 1,048,575 rows and 97 columns and then performed exploratory data analysis. We also used feature engineering and subset selection methods to build a linear model to predict FICO score and amount funded of customers loan requests. Overall, we found that FICO score is best modeled using backward regression which gives an exponential function with the predictors being grade, title, …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Non-Uniform Haar Wavelet Method For Solving Singularly Perturbed Differential Difference Equations Of Neuronal Variability, Akmal Raza, Arshad Khan

Applications and Applied Mathematics: An International Journal (AAM)

A non-uniform Haar wavelet method is proposed on specially designed non-uniform grid for the numerical treatment of singularly perturbed differential-difference equations arising in neuronal variability.We convert the delay and shift terms using Taylor series up to second order and then the problem with delay and shift is converted into a new problem without the delay and shift terms. Then it is solved by using non-uniform Haar wavelet. Two test examples have been demonstrated to show the accuracy of the non-uniform Haar wavelet method. The performance of the present method yield more accurate results on increasing the resolution level and converges …

D-Vine Copula Model For Dependent Binary Data, Huihui Lin, N. Rao Chaganty

College of Sciences Posters

High-dimensional dependent binary data are prevalent in a wide range of scientific disciplines. A popular method for analyzing such data is the Multivariate Probit (MP) model. But the MP model sometimes fails even within a feasible range of binary correlations, because the underlying correlation matrix of the latent variables may not be positive definite. In this research, we proposed pair copula models, assuming the dependence between the binary variables is first order autoregressive (AR(1))or equicorrelated structure. Also, when Archimediean copula is used, most paper converted Kendall Tau to corresponding copula parameter, there is no explicit function of Pearson’s correlation coefficient …

Improved Filtering Of Electron Tomography Edx Data, Kelsey M. Larkin

Senior Theses

Electron microscopy is a very exciting field, which has shown huge developments in the last few decades. There is a continuous development of new methods which feature atomic level resolution. One of these methods is the energy dispersive X-ray (EDX) spectroscopy, which allows the researchers to understand the chemical make-up of the sample. It is particularly exciting that we are able to make EDX tomographic reconstructions and view the 3D structure of a nano-object.

This thesis is focused on developing a new methodology for EDX tomography. In a typical EDX set-up, one detects X-rays from the sample with different energies, …

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …

Wilson Sensor Footballs: Consistency Metric, Kenneth Eaton

Honors Capstone Enhancement Presentations

No abstract provided.

Numerical Analysis Of Three-Dimensional Mhd Flow Of Casson Nanofluid Past An Exponentially Stretching Sheet, Madhusudan Senapati, Kharabela Swain, Sampad Kumar Parida

Karbala International Journal of Modern Science

The convective three dimensional electrically conducting Casson nanofluid flow over an exponentially stretching sheet embedded in a saturated porous medium and subjected to thermal as well as solutal slip in the presence of externally applied transverse magnetic field (force-at-a-distance) is studied. The heat transfer phenomenon includes the viscous dissipation, Joulian dissipation, thermal radiation, contribution of nanofluidity and temperature dependent volumetric heat source. The study of mass diffusion in the presence of chemically reactive species enriches the analysis. The numerical solutions of coupled nonlinear governing equations bring some earlier reported results as particular cases providing a testimony of validation of the …

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

Emirates Journal for Engineering Research

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.

Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an …

A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the …

Informal Professional Development On Twitter: Exploring The Online Communities Of Mathematics Educators, Jaymie Ruddock

SMU Journal of Undergraduate Research

Professional development in its most traditional form is a classroom setting with a lecturer and an overwhelming amount of information. It is no surprise, then, that informal professional development away from institutions and on the teacher's own terms is a growing phenomenon due to an increased presence of educators on social media. These communities of educators use hashtags to broadcast to each other, with general hashtags such as #edchat having the broadest audience. However, many math educators usethe hashtags #ITeachMath and #MTBoS, communities I was interested in learning more about. I built a python script that used Tweepy to connect …

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 …

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, Kyle Eric Helfrich

Theses and Dissertations--Mathematics

Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this work we describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue, and derive update schemes for each architecture. Another portion of this work focuses on the often used technique of batch normalization. Although found to be successful …

Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals, Barry Farmer

Theses and Dissertations--Physics and Astronomy

Quasicrystals have been shown to exhibit physical properties that are dramatically different from their periodic counterparts. A limited number of magnetic quasicrystals have been fabricated and measured, and they do not exhibit long-range magnetic order, which is in direct conflict with simulations that indicate such a state should be accessible. This dissertation adopts a metamaterials approach in which artificial quasicrystals are fabricated and studied with the specific goal of identifying how aperiodicity affects magnetic long-range order. Electron beam lithography techniques were used to pattern magnetic thin films into two types of aperiodic tilings, the Penrose P2, and Ammann-Beenker tilings. SQUID …

Zero-Inflated Longitudinal Mixture Model For Stochastic Radiographic Lung Compositional Change Following Radiotherapy Of Lung Cancer, Viviana A. Rodríguez Romero

Theses and Dissertations

Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture …

Higher Accuracy Methods For Fluid Flows In Various Applications: Theory And Implementation, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on several topics related to Defect-deferred correction (DDC) method applying to CFD problems. First, we want to improve the error due to temporal discretization for the problem of two convection dominated convection-diffusion problems, coupled across a joint interface. This serves as a step towards investigating an atmosphere-ocean coupling problem with the interface condition that allows for the exchange of energies between the domains.

The main diffuculty is to decouple the problem in an unconditionally stable way for using legacy code for subdomains. To overcome the issue, we apply the Deferred Correction (DC) method. The DC method …

Unitary And Symmetric Structure In Deep Neural Networks, Kehelwala Dewage Gayan Maduranga

Theses and Dissertations--Mathematics

Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well-known difficulty in using RNNs is the vanishing or exploding gradient problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN), which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the …

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 …

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 …

Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, Gregory Allen Riggs

Graduate Theses, Dissertations, and Problem Reports

The application of bicoherence analysis to plasma research, particularly in non-linear, coupled-wave regimes, has thus far been significantly belied by poor resolution in time, and/or outright destruction of frequency information. Though the typical power spectrum cloaks the phase-coherency between frequencies, Fourier transforms of higher-order convolutions provide an n-dimensional spectrum which is adept at elucidating n-wave phase coherence. As such, this investigation focuses on the utility of the normalized bispectrum for detection of wave-wave coupling in general, with emphasis on distinct implications within the scope of non-linear plasma physics. Interpretations of bicoherent features are given for time series from …

An Exploration Of 5g Wireless Network Attenuation Using Finite Element Analysis In Comsol Multiphysics, Matthew Johnson

CMC Senior Theses

5G, ultra-high frequency wireless networks face numerous hurdles due to significant signal attenuation in materials and large path loss. Empirical research on signal attenuation has been limited to low frequencies or very select high frequencies. This paper utilizes Finite Element Analysis in COMSOL Multiphysics to analyze signal attenuation in materials over a range of the frequency spectrum, from 100Mhz to 40Ghz, which is inclusive of 5G wireless frequencies. The focus of this paper is on glass and dry wood, as well as wet wood (representative of trees), as these materials are some of the most likely to stand in the …