Physical Sciences and Mathematics Commons^™

Bayesian Experimental Design For Control And Surveillance In Epidemiology, Bren Case

Graduate College Dissertations and Theses

Effective public health interventions must balance an array of interconnected challenges, and decisions must be made based on scientific evidence from existing information. Building evidence requires extrapolating from limited data using models. But when data are insufficient, it is important to recognize the limitations of model predictions and diagnose how they can be improved. This dissertation shows how principles from Bayesian experimental design can be applied to surveillance and control efforts to allow researchers to get more out of their data and direct limited resources to best effect. We argue a Bayesian perspective on data gathering, where design decisions are …

Studies On The Tempered Fractional Natural Decomposition Method, Nazek Ahmad Obeidat

Graduate College Dissertations and Theses

In Fractional Calculus (FC), the notion of fractional derivatives and integrals arise from convolutions with a power law, which, when multiplied by an exponential factor, one obtains tempered fractional derivatives and integrals.

The purpose of this dissertation is to develop theories and applications of a new technique in FC called the Tempered Fractional Natural Transform Method (TFNTM). This method can be used to solve a myriad of problems in linear and nonlinear ordinary and partial differential equations.

We present convergence analysis, give error estimates, and provide exact solutions, with graphical illustrations, to many well-known problems in tempered fractional differential equation, …

Developing Natural Language Processing Instruments To Study Sociotechnical Systems, Thayer Alshaabi

Graduate College Dissertations and Theses

Identifying temporal linguistic patterns and tracing social amplification across communities has always been vital to understanding modern sociotechnical systems. Now, well into the age of information technology, the growing digitization of text archives powered by machine learning systems has enabled an enormous number of interdisciplinary studies to examine the coevolution of language and culture. However, most research in that domain investigates formal textual records, such as books and newspapers. In this work, I argue that the study of conversational text derived from social media is just as important. I present four case studies to identify and investigate societal developments in …

Three-Phase Hybrid Model Of Bacterial Biofilm Growth, Xing Jin

Graduate College Dissertations and Theses

Bacterial biofilms play a critical role in environmental processes, water treatment, human health, and food processing. They exhibit highly complex dynamics due to the interactions between the bacteria and the extracellular polymeric substance (EPS), water, nutrients, and minerals that make up the biofilm. In the current dissertation, a hybrid computational model was proposed for simulation of biofilm growth processes using a multiphase continuum for the transport of water and EPS, as well as nutrient diffusion, and discrete phase particles for simulation of bacterial cells and their interactions. Mass and momentum conservations of each phase and bacterial motion, rotation, growth, division, …

Some Results On A Set Of Data Driven Stochastic Wildfire Models, Maxfield E. Green

Graduate College Dissertations and Theses

Across the globe, the frequency and size of wildfire events are increasing. Research focused on minimizing wildfire is critically needed to mitigate impending humanitarian and environmental crises. Real-time wildfire response is dependent on timely and accurate prediction of dynamic wildfire fronts. Current models used to inform decisions made by the U.S. Forest Service, such as Farsite, FlamMap and Behave do not incorporate modern remotely sensed wildfire records and are typically deterministic, making uncertainty calculations difficult. In this research, we tested two methods that combine artificial intelligence with remote sensing data. First, a stochastic cellular automata that learns algebraic expressions was …

Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, David Rushing Dewhurst

Graduate College Dissertations and Theses

A sociotechnical system is a collection of humans and algorithms that interact under the partial supervision of a decentralized controller. These systems often display in- tricate dynamics and can be characterized by their unique emergent behavior. In this work, we describe, analyze, and model aspects of three distinct classes of sociotech- nical systems: financial markets, social media platforms, and elections. Though our work is diverse in subject matter content, it is unified though the study of evolution- and adaptation-driven change in social systems and the development of methods used to infer this change.

We first analyze evolutionary financial market microstructure …

Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond

Graduate College Dissertations and Theses

With the rise of social media, researchers have become increasingly interested in understanding how individuals inform, influence, and interact with others in their social network and how the network mediates the flow of information. Previous research on information flow has primarily used models of contagion to study the adoption of a technology, propagation of purchase recommendations, or virality of online activity. Social (or "complex") contagions spread differently than biological ("simple") contagions. A limitation when researchers validate contagion models is that they neglect much of the massive amounts of data now available through online social networks. Here we model a recently …

Measuring Linguistic And Cultural Evolution Using Books And Tweets, Tyler Gray

Graduate College Dissertations and Theses

Written language provides a snapshot of linguistic, cultural, and current events information for a given time period. Aggregating these snapshots by studying many texts over time reveals trends in the evolution of language, culture, and society. The ever-increasing amount of electronic text, both from the digitization of books and other paper documents to the increasing frequency with which electronic text is used as a means of communication, has given us an unprecedented opportunity to study these trends. In this dissertation, we use hundreds of thousands of books spanning two centuries scanned by Google, and over 100 billion messages, or ‘tweets’, …

Mathematical Analysis Of Some Partial Differential Equations With Applications, Kewang Chen

Graduate College Dissertations and Theses

In the first part of this dissertation, we produce and study a generalized mathematical model of solid combustion. Our generalized model encompasses two special cases from the literature: a case of negligible heat diffusion in the product, for example, when the burnt product is a foam-like substance; and another case in which diffusivities in the reactant and product are assumed equal. In addition to that, our model pinpoints the dynamics in a range of settings, in which the diffusivity ratio between the burned and unburned materials varies between 0 and 1. The dynamics of temperature distribution and interfacial front propagation …

Weighted Networks: Applications From Power Grid Construction To Crowd Control, Thomas Charles Mcandrew

Graduate College Dissertations and Theses

Since their discovery in the 1950's by Erdos and Renyi, network theory (the study of objects and their associations) has blossomed into a full-fledged branch of mathematics.

Due to the network's flexibility, diverse scientific problems can be reformulated as networks and studied using a common set of tools.

I define a network G = (V,E) composed of two parts: (i) the set of objects V, called nodes, and (ii) set of relationships (associations) E, called links, that connect objects in V.

We can extend the classic network of nodes and links by describing the intensity of these associations with weights. …

Wronskian And Gram Solutions To Integrable Equations Using Bilinear Methods, Benjamin Wiggins

Graduate College Dissertations and Theses

This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.

Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations.

N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches.

Temporal Feature Selection With Symbolic Regression, Christopher Winter Fusting

Graduate College Dissertations and Theses

Building and discovering useful features when constructing machine learning models is the central task for the machine learning practitioner. Good features are useful not only in increasing the predictive power of a model but also in illuminating the underlying drivers of a target variable. In this research we propose a novel feature learning technique in which Symbolic regression is endowed with a ``Range Terminal'' that allows it to explore functions of the aggregate of variables over time. We test the Range Terminal on a synthetic data set and a real world data in which we predict seasonal greenness using satellite …

Quantifying Cultural Changes Through A Half-Century Of Song Lyrics And Books, Robert Bruce Woodward Iii

Graduate College Dissertations and Theses

Music is an ever-changing cultural reflection. It is deeply integrated into our society, ubiquitous

in movies, television shows, restaurants, sport venues, churches and a plethora of

other places. This thesis proposes that we consider the lyrics in popular music, as determined

by Billboards Hot 100 chart, as a natural medium to analyze the changes in culture

over the past half-century. Using this collection of lyrics, we analyze the change in relative

frequency of individual words over time, and compare to works of literature. Furthermore,

we use the ranking in the Top 100 as a metric with which to explore the …

Mathematical Modeling Of Public Opinion Using Traditional And Social Media, Emily Cody

Graduate College Dissertations and Theses

With the growth of the internet, data from text sources has become increasingly available to researchers in the form of online newspapers, journals, and blogs. This data presents a unique opportunity to analyze human opinions and behaviors without soliciting the public explicitly. In this research, I utilize newspaper articles and the social media service Twitter to infer self-reported public opinions and awareness of climate change. Climate change is one of the most important and heavily debated issues of our time, and analyzing large-scale text surrounding this issue reveals insights surrounding self-reported public opinion. First, I inquire about public discourse on …

Lexical Mechanics: Partitions, Mixtures, And Context, Jake Ryland Williams

Graduate College Dissertations and Theses

Highly structured for efficient communication, natural languages are complex systems. Unlike in their computational cousins, functions and meanings in natural languages are relative, frequently prescribed to symbols through unexpected social processes. Despite grammar and definition, the presence of metaphor can leave unwitting language users "in the dark," so to speak. This is not problematic, but rather an important operational feature of languages, since the lifting of meaning onto higher-order structures allows individuals to compress descriptions of regularly-conveyed information. This compressed terminology, often only appropriate when taken locally (in context), is beneficial in an enormous world of novel experience. However, what …

Using Empirical Mode Decomposition To Study Periodicity And Trends In Extreme Precipitation, Noah Pfister

Graduate College Dissertations and Theses

Classically, we look at annual maximum precipitation series from the perspective of extreme value statistics, which provides a useful statistical distribution, but does not allow much flexibility in the context of climate change. Such distributions are usually assumed to be static, or else require some assumed information about possible trends within the data. For this study, we treat the maximum rainfall series as sums of underlying signals, upon which we perform a decomposition technique, Empirical Mode Decomposition. This not only allows the study of non-linear trends in the data, but could give us some idea of the periodic forces that …

Exploring The Google Books Corpus: An Information-Theoretic Approach To Linguistic Evolution, Eitan Pechenick

Graduate College Dissertations and Theses

The Google Books corpus contains millions of books in a variety of languages. Due to this incredible volume and its free availability, it is a treasure trove that has inspired a plethora of linguistic research.

It is tempting to treat frequency trends from Google Books data sets as indicators for the true popularity of various words and phrases. Doing so allows us to draw novel conclusions about the evolution of public perception of a given topic. However, sampling published works by availability and ease of digitization leads to several important effects, which have typically been overlooked in previous studies. One …

Rogue Wave Solutions To Integrable System By Darboux Transformation, Xin Kou

Graduate College Dissertations and Theses

The Darboux transformation is one of the main techniques for finding solutions of integrable equations. The Darboux transformation is not only powerful in the construction of muilti-soliton solutions, recently, it is found that the Darboux transformation, after some modification, is also effective in generating the rogue wave solutions. In this thesis, we derive the rogue wave solutions for the Davey-Stewartson-II (DS-II) equation in terms of Darboux transformation. By taking the spectral function as the product of plane wave and rational function, we get the fundamental rogue wave solution and multi-rogue wave solutions via the normal Darboux transformation. Last but not …