Applied Mathematics Commons^™

Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore

CMC Senior Theses

The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude …

Mathematically Modeling The Role Of Triglyceride Production On Leptin Resistance, Yu Zhao, Daniel Burkow, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Diet-induced obesity is becoming more common all over the world, which is increasing the prevalence of obesity-induced chronic diseases such as diabetes, coronary heart disease, cancer, and sleep apnea. Many experimental results show that obesity is often associated with an elevated concentration of plasma leptin and triglycerides. Triglycerides inhibit the passage of leptin across the blood–brain barrier (BBB) to signal the hypothalamus to suppress appetite. However, it is still not clear how triglyceride concentration affects leptin transport across the BBB and energy balance. In this paper, we propose a novel ordinary differential equations model describing the role of leptin in …

Defining Historical Earthquake Rupture Parameters And Proposed Slip Distributions Through Tsunami Modeling In South-Central Chile, Alexander Dolcimascolo

All Master's Theses

Reliable tsunami early warning forecasts rely on accurate initial modeling conditions and interpretations of subduction zone behavior in a multi-century perspective. GPS and seismologic data were introduced this past century to study rupture dynamics in detail, however limited information is known about ruptures that pre-date the 20^th century. I propose a methodology that uses statistics to better understand these pre-20^th century ruptures. This methodology applies the historical and geologic tsunami record as a means to select a suite of tsunami simulations from earthquake source solutions. I chose south-central Chile (46°S to 30°S) to test this new methodology; it …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Rule Extraction And Insertion To Improve The Performance Of A Dynamic Cell Structure Neural Network, Osama Amhamed Elsarrar

Graduate Theses, Dissertations, and Problem Reports (ETD)

Artificial Neural Networks are extremely useful machine learning tools. They are used for many purposes, such as prediction, classification, pattern recognition, etc. Although neural networks have been used for decades, they are still often not completely understood or trusted, especially in safety and mission critical situations. Typically, neural networks are trained on data sets that are representative of what needs to be learned. Sometimes training sets are constructed in order to train the neural network in a certain way, in order to embed appropriate knowledge. The purpose of this research is to determine if there is another method that can …

Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera

Williams Honors College, Honors Research Projects

Coherency strains appear in interacting atomic monolayers due to differing bond lengths, which can arise from different materials or geometries. Examples include extended monolayers interacting with a substrate and the interacting walls of a multi-walled carbon nanotube. These strains can induce various equilibrium configurations, which we will analyze by means of a phenomenological model that incorporates forces from bond stretching and bending within each layer and the weak van der Waals interactions connecting the separate layers. We vary the strengths of each interaction to explore their effects on equilibrium structures, and the specific case of a two-walled carbon nanotube is …

New Reproducing Kernel Hilbert Spaces On Plane Regions, Their Properties, And Applications To Partial Differential Equations, Jabar S. Hassan

Doctoral Dissertations

"We introduce new reproducing kernel Hilbert spaces W₂^(m,n) (D) on unbounded plane regions D. We study linear non-homogeneous hyperbolic partial differential equation problems on D with solutions in various reproducing kernel Hilbert spaces. We establish existence and uniqueness results for such solutions under appropriate hypotheses on the driver. Stability of solutions with respect to the driver is analyzed and local uniform approximation results are obtained which depend on the density of nodes. The local uniform approximation results required a careful determination of the reproducing kernel Hilbert spaces on which the elementary …

Efficient Local Comparison Of Images Using Krawtchouk Descriptors, Julian Deville

Online Theses and Dissertations

It is known that image comparison can prove cumbersome in both computational complexity and runtime, due to factors such as the rotation, scaling, and translation of the object in question. Due to the locality of Krawtchouk polynomials, relatively few descriptors are necessary to describe a given image, and this can be achieved with minimal memory usage. Using this method, not only can images be described efficiently as a whole, but specific regions of images can be described as well without cropping. Due to this property, queries can be found within a single large image, or collection of large images, which …

Description Of Motor Control Using Inverse Models, Anton Sobinov

Graduate Theses, Dissertations, and Problem Reports (ETD)

Humans can perform complicated movements like writing or running without giving them much thought. The scientific understanding of principles guiding the generation of these movements is incomplete. How the nervous system ensures stability or compensates for injury and constraints – are among the unanswered questions today. Furthermore, only through movement can a human impose their will and interact with the world around them. Damage to a part of the motor control system can lower a person’s quality of life. Understanding how the central nervous system (CNS) forms control signals and executes them helps with the construction of devices and rehabilitation …

Associated Primes And Syzygies Of Linked Modules, Olgur Celikbas, Mohammad T. Dibaei, Mohsen Gheibi, Arash Sadeghi, Ryo Takahaski

Department of Mathematics: Faculty Publications

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a Gorenstein ideal c, such that AssR(M)\AssR(N) = ;, then M R N is isomorphic to direct sum of copies of R=a, where a is a Gorenstein ideal of R of grade g + 1. We give a criterion for the depth of a local ring (R;m; k) in terms of the homological dimensions of the modules linked to the syzygies of the residue eld k. As a …

Kings In The Direct Product Of Digraphs, Morgan Norge

Theses and Dissertations

A k-king in a digraph D is a vertex that can reach every other vertex in D by a directed path of length at most k. A king is a vertex that is a k-king for some k. We will look at kings in the direct product of digraphs and characterize a relationship between kings in the product and kings in the factors. This is a continuation of a project in which a similar characterization is found for the cartesian product of digraphs, the strong product of digraphs, and the lexicographic product of digraphs.

Determination Of Optimal Parameter Estimates For Medical Interventions In Human Metabolism And Inflammation, Marcella Torres

Theses and Dissertations

In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases.

We develop …

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

Solutions For Fermi Questions, November 2019: Question 1: Cell Phones Make Me Boil; Question 2: Charging The Phone, Larry Weinstein

Physics Faculty Publications

Answers to the Fermi questions:

How much water can you boil with the energy stored in a cell phone battery?

How much does the electrical energy for a cell phone cost each year?

Complex Varieties As Minima, Richard Koss

Masters Theses

We will explore various numeric methods of finding roots of an analytic function over some open set of the complex plane. We will discuss a method of visually observing the roots, a gradient descent method for finding the roots of an analytic function, a gradient descent method for solving systems of analytic functions, and finally a method of descent that uses osculating circles to find roots of an analytic function. Of particular interest to this thesis are roots of complex polynomials. There will be examples, code snippets, and outputs of programs to illustrate all of these methods.

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, earthquake is considered as one of the disasters that record 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 Inverse Gaussian (a,b) process. Inverse Gaussian (a,b) Ornstein-Uhlenbeck processes offer 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 market by fitting the superposed Inverse Gaussian (a,b) Ornstein-Uhlenbeck model to earthquake and …

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. …

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.

A Detection And Data Acquisition System For Precision Beta Decay Spectroscopy, Aaron P. Jezghani

Theses and Dissertations--Physics and Astronomy

Free neutron and nuclear beta decay spectroscopy serves as a robust laboratory for investigations of the Standard Model of Particle Physics. Observables such as decay product angular correlations and energy spectra overconstrain the Standard Model and serve as a sensitive probe for Beyond the Standard Model physics. Improved measurement of these quantities is necessary to complement the TeV scale physics being conducted at the Large Hadron Collider. The UCNB, ⁴⁵Ca, and Nab experiments aim to improve upon existing measurements of free neutron decay angular correlations and set new limits in the search for exotic couplings in beta decay. To …

The Effect Of Using A Project-Based Learning (Pbl) Approach To Improve Engineering Students' Understanding Of Statistics, Fionnuala Farrell, Michael Carr

Articles

Over the last number of years we have gradually been introducing a project based learning approach to the teaching of engineering mathematics inDublin Institute of Technology. Several projects are now in existence for the teaching of both second-order differential equations and first order differential equations.We intend to incrementally extend this approach acrossmore of the engineering mathematics curriculum. As part of this ongoing process, practical realworld projects in statistics were incorporated into a second year ordinary degree mathematics module. This paper provides an overview of these projects and their implementation. As a means to measure the success of this initiative, we …