Informal Professional Development On Twitter: Exploring The Online Communities Of Mathematics Educators, 2020 Southern Methodist University

#### 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 ...

Elucidating The Properties And Mechanism For Cellulose Dissolution In Tetrabutylphosphonium-Based Ionic Liquids Using High Concentrations Of Water, 2020 West Virginia University

#### 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 ...

A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, 2020 Southern Methodist University

#### A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang

*Mathematics Theses and Dissertations*

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating ...

Desarrollo De Una Aplicación Móvil Para La Resolución De Problemas De Optimización Del Cálculo Diferencial, 2020 Universidad de La Salle, Bogotá

#### Desarrollo De Una Aplicación Móvil Para La Resolución De Problemas De Optimización Del Cálculo Diferencial, Julián David Arévalo García, Camilo Sebastián Guerrero Briceño

*Ingeniería en Automatización*

El presente trabajo consiste en el desarrollo de una aplicación móvil que facilite la comprensión de un problema de optimización en los estudiantes de cálculo diferencial, y a su vez de soporte al proyecto de investigación “Aprendiendo a solucionar problemas de optimización del cálculo diferencial a través de tecnología móvil”. Este trabajo es efectuado por los autores como auxiliares del proyecto de investigación. Las actividades que se tendrán en cuenta en el desarrollo incluyen un levantamiento de requerimientos en bases de datos sobre las aplicaciones móviles existentes en el mercado y un análisis en el aprendizaje de las matemáticas, en ...

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, 2020 Murray State University

#### 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 ...

An Exploration Of 5g Wireless Network Attenuation Using Finite Element Analysis In Comsol Multiphysics, 2020 Claremont Colleges

#### 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 ...

Numerical Analysis And Gravity, 2020 West Virginia University

#### 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 ...

Unitary And Symmetric Structure In Deep Neural Networks, 2020 University of Kentucky

#### 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 ...

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, 2020 University of Kentucky

#### 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 ...

Higher Accuracy Methods For Fluid Flows In Various Applications: Theory And Implementation, 2020 Michigan Technological University

#### 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 ...

Interpretations Of Bicoherence In Space & Lab Plasma Dynamics, 2020 West Virginia University

#### 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 ...

A Fully-Coupled Framework For Solving Cahn-Hilliard Navier-Stokes Equations: Second-Order, Energy-Stable Numerical Methods On Adaptive Octree Based Meshes, 2020 Iowa State University

#### A Fully-Coupled Framework For Solving Cahn-Hilliard Navier-Stokes Equations: Second-Order, Energy-Stable Numerical Methods On Adaptive Octree Based Meshes, Makrand A. Khanwale, Kumar Saurabh, Milinda Fernando, Victor M. Calo, James A. Rossmanith, Hari Sundar, Baskar Ganapathysubramanian

*Mechanical Engineering Publications*

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et al. [{\it Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes}, J. Comput. Phys. (2020)], to a fully-coupled, provably second-order accurate scheme in time, while maintaining energy-stability. The new method requires fewer matrix assemblies in each Newton iteration resulting in faster solution time. The method is based on a fully-implicit Crank-Nicolson scheme in time and a pressure stabilization for an equal order ...

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, 2019 Southern Methodist University

#### 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 ...

A Data Driven Approach To Forecast Demand, 2019 Southern Methodist University

#### 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 ...

High Strain Dynamic Test On Helical Piles: Analytical And Numerical Investigations, 2019 The University of Western Ontario

#### 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 ...

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, 2019 University of Nebraska - Lincoln

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

*Dissertations, Theses, and Student Research Papers in Mathematics*

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 ...

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, 2019 CUNY New York City College of Technology

#### Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

*Publications and Research*

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.

Multi-Point Flux Approximations Via The O-Method, 2019 University of Southern Mississippi

#### Multi-Point Flux Approximations Via The O-Method, Christen Leggett

*Master's Theses*

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients ...

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, 2019 University of Missouri-St. Louis

#### Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

*Dissertations*

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic ...

A Parallel Direct Method For Finite Element Electromagnetic Computations Based On Domain Decomposition, 2019 University of Massachusetts Amherst

#### A Parallel Direct Method For Finite Element Electromagnetic Computations Based On Domain Decomposition, Javad Moshfegh

*Doctoral Dissertations*

High performance parallel computing and direct (factorization-based) solution methods have been the two main trends in electromagnetic computations in recent years. When time-harmonic (frequency-domain) Maxwell's equation are directly discretized with the Finite Element Method (FEM) or other Partial Differential Equation (PDE) methods, the resulting linear system of equations is sparse and indefinite, thus harder to efficiently factorize serially or in parallel than alternative methods e.g. integral equation solutions, that result in dense linear systems. State-of-the-art sparse matrix direct solvers such as MUMPS and PARDISO don't scale favorably, have low parallel efficiency and high memory footprint. This work ...