Mathematics Commons^™

Solutions For Fermi Questions, May 2019: Question 1: Graduation Speeches; Question 2: Fan Propulsion, Larry Weinstein

Physics Faculty Publications

[Introduction] How many person-hoursare spent listening to graduation speeches each year? How long is this in lifetimes?

Answer: Just about everyone graduates high school and goes to their graduation, usually with guests. Only about 30% of Americans (more than 10% and less than 100% graduate college, so we will ignore those graduates. Therefore we need to estimate the number of graduating high school seniors, the number of guests per senior, and the length of the graduation speeches.

Cronbach’S Alpha Under Insufficient Effort Responding: An Analytic Approach, Stephen W. Carden, Trevor R. Camper, Nicholas S. Holtzman

Psychology: Faculty Publications

Surveys commonly suffer from insufficient effort responding (IER). If not accounted for, IER can cause biases and lead to false conclusions. In particular, Cronbach’s alpha has been empirically observed to either deflate or inflate due to IER. This paper will elucidate how IER impacts Cronbach’s alpha in a variety of situations. Previous results concerning internal consistency under mixture models are extended to obtain a characterization of Cronbach’s alpha in terms of item validities, average variances, and average covariances. The characterization is then applied to contaminating distributions representing various types of IER. The discussion will provide commentary on previous simulation-based investigations, …

Leibniz Algebras As Non-Associative Algebras, Jorg Feldvoss

University Faculty and Staff Publications

In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs but several results seem to be new.

Robust Statistical Inference For The Gaussian Distribution, Andrews Tawiah Anum

Open Access Theses & Dissertations

The aim of robust statistics is to develop statistical procedures which are not unduly influenced by outliers or observations that are not representative of the underlying "true" data generating process. This thesis focuses on an estimator with this characteristic. The divergence function is introduced in Chapter 2 with the sole aim of taking the function f to be the univariate normal distribution and α - [0, 1]. The estimator fails when we rely on the classic Newton's method to converge to the minimum of the density power divergence (MDPD) function. There is a tendency of such estimator never to approach …

Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

A neural network is a system of hardware and/or software patterned after the operation of neurons in the human brain. Neural networks,- also called Artificial Neural Networks - are a variety of deep learning technology, which also falls under the umbrella of artificial intelligence, or AI. Recent studies shows that Artificial Neural Network has the highest coefficient of determination (i.e. measure to assess how well a model explains and predicts future outcomes.) in comparison to the K-nearest neighbor classifiers, logistic regression, discriminant analysis, naive Bayesian classifier, and classification trees. In this work, the theoretical description of the neural network methodology …

Earthquake Magnitude Prediction Using Support Vector Machine And Convolutional Neural Network, Esther Amfo

Open Access Theses & Dissertations

A deep learning-based method Convolutional Neural Network (CNN) and Support Vector Machine (SVM) for earthquake prediction is proposed. Large-magnitude earthquakes triggered by earthquakes can kill thousands of people and cause millions of dollars worth of economic losses. The accurate prediction of large-magnitude earthquakes is a worldwide problem.

In recent years, deep learning technology that can automatically extract features from mass data has been applied in image recognition, natural language processing, object recognition, etc., with great success. We explore to apply deep learning technology to earthquake prediction, we propose a deep learning method for continuous earthquake prediction using historical seismic events. …

Towards Analytical Techniques For Systems Engineering Applications, Griselda Valdepeñas Acosta

Open Access Theses & Dissertations

One of the main objectives of systems engineering is to design, maintain, and analyze systems that help the users. To design an appropriate system for an application domain, we need to know: what are the users' desires and preferences (so that we know in what direction we should aim to change this domain), what is the current state and what is the dynamics of this application domain, and how to use all this information to select the best alternatives for the system design and maintenance. Designing a system includes selecting numerical values for many of the parameters describing the corresponding …

Inverse Gaussian Ornstein-Uhlenbeck Applied To Modeling High Frequency Data, Emmanuel Kofi Kusi

Open Access Theses & Dissertations

With about 226050 estimated deaths worldwide in 2010, an earthquake is considered as one of the disasters that records a great number of deaths. This thesis develops a model for the estimation of magnitude of future seismic events.

We propose a stochastic differential equation arising on the Ornstein-Uhlenbeck processes driven by IG(a,b) process. IG(a,b) Ornstein-Uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory

behavior. The stochastic differential equation is applied to geophysics and financial stock markets by fitting the superposed IG(a,b) Ornstein-Uhlenbeck model to earthquake and financial time series.

Cantor Sets, Cantorvals, And Their Topological Structure, Ángel Adrián Agüero

Open Access Theses & Dissertations

With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.

Formulation And Implementation Of Iterative Method For Generating Spatially-Variant Lattices, Manuel Fernando Martinez

Open Access Theses & Dissertations

The use of a matrix-free, memory-efficient approach to generate large-scale spatially variant lattices (SVL) was explored. A matrix-free iterative SVL generation algorithm was formulated and then implemented with a tremendous memory reduction observed. The algorithm consists of solving first-order central finite-differences along the entirety of the problem space point-by-point to obtain the grating phase function Φ(𝑠⃗) to which all desired spatially variant lattice properties are applied to. The algorithm was studied to identify key areas of data and task parallelism to exploit in heterogeneous computing systems consisting of clusters of central processing units (CPU) and graphics processing units (GPU) combinations. …

Upper Dimension And Bases Of Zero-Divisor Graphs Of Commutative Rings, S. Pirzada, M. Aijaza, Shane Redmond

EKU Faculty and Staff Scholarship

For a commutative ring R with non-zero zero divisor set Z∗(R), the zero divisor graph of R is Γ(R) with vertex set Z∗(R), where two distinct vertices x and y are adjacent if and only if x y = 0. The upper dimension and the resolving number of a zero divisor graph Γ(R) of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs …

Cross Faculty Collaboration In The Development Of An Integrated Mathematics And Science Initial Teacher Education Program, Sharon P. Fraser, Kim Beswick, Margaret Penson, Andrew Seen, Robert Whannell

Australian Journal of Teacher Education

This paper describes a collaborative project involving mathematicians, scientists and educators at an Australian university where an innovative initial teacher education (ITE) degree in mathematics/science was developed. The theoretical frameworks of identity theory and academic brokerage and their use in understanding the challenges associated with the early stages of collaborative projects is described. Data from reflections and interviews of the participants after involvement in the project from one to three years are presented to illustrate these challenges. The paper concludes with a description of the importance of the academic broker in overcoming identity challenges and facilitating cultural change for academics …

Finite Integration Method With Chebyshev Expansion For Finding Numerical Solution Of Nonlinear And Fractional Order Differential Equations, Ampol Duangpan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we develop the finite integration method by using Chebyshev polynomial expansion (FIM-CPE) for solving one- and two-dimensional nonlinear differential equations. The developed FIM-CPE can be used on any domains. Then, we utilize our FIM-CPE to deal with the spatial variable and the forward difference quotient to handle the derivative involving temporal variable. Thus, the numerical algorithms based on this idea are devised to overcome three nonlinear problems including one-dimensional Burgers' equation with shock wave, time-fractional Benjamin-Bona-Mahony-Burgers' equation and two-dimensional nonlinear Poisson equation over irregular domains. Moreover, we examine our algorithms with several experimental examples by comparing the …

Adjustment Of Maximum Likelihood Method For Multivariate Fay-Herriot Model, Annop Angkunsit

Chulalongkorn University Theses and Dissertations (Chula ETD)

The most widely used area-level model in small area estimation is the Fay-Herriot model, proposed by Fay and Herriot. It was used first to estimate average per capita income for small places (population less than 1,000) of the USA. In the context of the Fay-Herriot model, the traditional method in obtaining estimation of the population mean is the empirical best linear unbiased prediction (EBLUP) estimator. The estimate can be expressed as a weighted sum of the direct survey estimator and regression estimator. One problem that has received attention is the estimation of variance of the area random effects in the …

Automatic Model Identification For Time Series Analysis Using Deep Learning, Paisit Khanarsa

Chulalongkorn University Theses and Dissertations (Chula ETD)

Most time series data can be characterized by a linear process via the autoregressive integrated moving average model requiring a three-component vector which are the autoregressive, differencing, and moving average orders before fitting coefficients. A model identification which determines those orders is analyzed via the partial autocorrelation function to identify the autoregressive order, the autocorrelation function to identify the moving average order and an extended sample autocorrelation function to identify both orders which is a challenging problem for statisticians. Accordingly, the auto-ARIMA model was proposed to automatically vary those orders and estimates their corresponding coefficients. This thesis proposes three architectures …

Bayesian Models For Poverty Mapping In Thailand, Sarasinee Somjettana

Chulalongkorn University Theses and Dissertations (Chula ETD)

Poverty maps are important sources of information for solving social, economic, and environmental problems. Initially, the World Bank used the ELL method to produce poverty maps for used in designing, targeting, prioritizing interventions and allocating the budgets for underdeveloped countries. Even though the ELL method has been shown to have many advantages in poverty mapping, it does not use a survey for the most benefit. Therefore, the Empirical Bayes (EB) method and the hierarchical Bayes (HB) method were proposed in literature. In another aspect, Louis shows that the usual Bayes has a limitation. Therefore, he proposed a new method called …

Self-Balancing Recursive Partitioning Algorithm For Classification Problems, Artit Sagoolmuang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Creating an effective classification model has been played an important role in knowledge discovery in a database methodology for the past several years. However, there is a critical issue that significantly affects the classification performance appearing in many real-world situations, which is called a class imbalanced problem. In this dissertation, a classification model built based on the recursive partitioning algorithm is improved under the concept of modified entropy components for handling a classification problem regardless of the class imbalanced situation. Three methodologies are introduced for achieving different purposes. The first methodology is presented to classify a binary-class imbalanced dataset dealing …

Stochastic Differential Equation With Jumps For Tilapia Population, Kanitin Sukchum

Chulalongkorn University Theses and Dissertations (Chula ETD)

Tilapia population with harvesting in the tilapia farm can be modeled by an ordinary differential equation (ODE). In real life, tilapia population can be affected by many factors. To make the model for tilapia population more realistic, we develop the ODE into the stochastic differential equation (SDE) together with jumps that represent the epidemic occuring for tilapia. Furthermore, we study the effect of some important parameters in the model to the number of tilapia in the tilapia farm via simulation. Both SDEs for tilapia population with and without jumps are simulated by using Euler-Maruyama and jump-adapted Euler methods.

Integer-Valued Time Series Risk Model With Surrender And Investment, Nuntanut Foosarmpok

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this study, we construct the discrete-time risk models based on integer-valued time series models by incorporating the concepts of surrender and investment. The surrender considered in this study is the situation that the policyholder decides to exit the policy before maturity date. In our study, we provide the probabilistic properties of the model. Moreover, we derive approximation of ruin probabilities of the constructed risk model. Finally, we discuss the trends of the ruin probability and the value at risk of the model by numerical simulations.

Text Localization And Extraction From Background With Texture And Noise In Digital Images Using Adaptive Thresholding And Convolutional Neural Network, Pukjira Pattaranuprawat

Chulalongkorn University Theses and Dissertations (Chula ETD)

For the past few years, research topics on finding position of text have received more and more attention from researchers because there are still lots of problems that are needed to be solven. We propose a novel method to find the position of text in an image. The first step of the proposed method is to adjust an image by converting a color image to a gray scale image and then use an average filter to improve an image. An average filter is used to make the background smooth and reduce noise. After that an adaptive thresholding is used to …