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Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial

Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study

Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
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Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that

Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
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Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In

Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
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Description

The COVID-19 pandemic has and will continue to radically shift the workplace. An increasing percentage of the workforce desires flexible working options and, as such, firms are likely to require less office space going forward. Additionally, the economic downturn caused by the pandemic provides an opportunity for companies to secure

The COVID-19 pandemic has and will continue to radically shift the workplace. An increasing percentage of the workforce desires flexible working options and, as such, firms are likely to require less office space going forward. Additionally, the economic downturn caused by the pandemic provides an opportunity for companies to secure favorable rent rates on new lease agreements. This project aims to evaluate and measure Company X’s potential cost savings from terminating current leases and downsizing office space in five selected cities. Along with city-specific real estate market research and forecasts, we employ a four-stage model of Company X’s real estate negotiation process to analyze whether existing lease agreements in these cities should be renewed or terminated.

ContributorsSaker, Logan (Co-author) / Ries, Sarah (Co-author) / Hegardt, Brandon (Co-author) / Patterson, Jack (Co-author) / Simonson, Mark (Thesis director) / Hertzel, Michael (Committee member) / Department of Finance (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

Following the Global Financial Crisis of 2007-2008, financial institutions faced regulatory changes due to inherent weaknesses that were exposed by the recession. Within the United States, regulation came via the passing of the Dodd-Frank Wall Street Reform and Consumer Protection Act in 2010, which was heavily influenced by the internationally

Following the Global Financial Crisis of 2007-2008, financial institutions faced regulatory changes due to inherent weaknesses that were exposed by the recession. Within the United States, regulation came via the passing of the Dodd-Frank Wall Street Reform and Consumer Protection Act in 2010, which was heavily influenced by the internationally focused Basel III accord. A key component to both of these sets of regulations focused on raising the capital requirements for financial institutions, as well as creating capital buffers to help protect solvency during economic downturns in the future. The goal of this study is to evaluate the effectiveness of these changes to capital requirements, and to hypothesize as to what would happen if the modern banking system experienced the COVID-19 pandemic recession with the capital and leverage levels of the banking institutions circa 2007. To accomplish this, data from the Federal Reserve describing the capital and leverage ratios of the banking industry will be evaluated during both the Global Financial Crisis of 2007-2008, as well as during the COVID-19 Recession. Specifically, we will look at by how much capital was improved due to Dodd-Frank/Basel III, the resiliency of the capital and leverage ratios during the modern COVID-19 recession, and we will look at the average drop in capital levels caused by the COVID-19 recession and apply these percentage changes to the leverage/capital levels seen in 2007. Given the results, it is clear to see that the change in capital requirements along with the counter-cyclical buffers described in Dodd-Frank and Basel III allowed the banking system to function throughout the COVID recession without approaching insolvency in the slightest, something that ailed many large banks and firms during the Global Financial Crisis. As an answer to our hypothetical, we found that the drop seen affecting the measures of bank capital experienced during the COVID pandemic when applied to values seen at the beginning of the 2007 recession still led to a well-capitalized banking industry as a whole, highlighting the resiliency seen during the COVID recession thanks to the capital buffers put in place, as well as the direct assistance provided by the federal government (via PPP loans and stimulus checks) and the Federal Reserve in keeping the hit on capital to minimal values throughout the pandemic.

ContributorsMiner, Jackson J (Author) / McDaniel, Cara (Thesis director) / Wong, Kelvin (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

This thesis project is part of a larger collaboration documenting the history of the ASU Biodesign Clinical Testing Laboratory (ABCTL). There are many different aspects that need to be considered when transforming to a clinical testing laboratory. This includes the different types of tests performed in the laboratory. In addition

This thesis project is part of a larger collaboration documenting the history of the ASU Biodesign Clinical Testing Laboratory (ABCTL). There are many different aspects that need to be considered when transforming to a clinical testing laboratory. This includes the different types of tests performed in the laboratory. In addition to the diagnostic polymerase chain reaction (PCR) test that is performed detecting the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), antibody testing is also performed in clinical laboratories. Antibody testing is used to detect a previous infection. Antibodies are produced as part of the immune response against SARS-CoV-2. There are many different forms of antibody tests and their sensitives and specificities have been examined and reviewed in the literature. Antibody testing can be used to determine the seroprevalence of the disease which can inform policy decisions regarding public health strategies. The results from antibody testing can also be used for creating new therapeutics like vaccines. The ABCTL recognizes the shifting need of the community to begin testing for previous infections of SARS-CoV-2 and is developing new forms of antibody testing that can meet them.

ContributorsRuan, Ellen (Co-author) / Smetanick, Jennifer (Co-author) / Majhail, Kajol (Co-author) / Anderson, Laura (Co-author) / Breshears, Scott (Co-author) / Compton, Carolyn (Thesis director) / Magee, Mitch (Committee member) / School of Life Sciences (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

In this project, I examined the relationship between lockdowns implemented by COVID-19 and the activity of animals in urban areas. I hypothesized that animals became more active in urban areas during COVID-19 quarantine than they were before and I wanted to see if my hypothesis could be researched through Twitter

In this project, I examined the relationship between lockdowns implemented by COVID-19 and the activity of animals in urban areas. I hypothesized that animals became more active in urban areas during COVID-19 quarantine than they were before and I wanted to see if my hypothesis could be researched through Twitter crowdsourcing. I began by collecting tweets using python code, but upon examining all data output from code-based searches, I concluded that it is quicker and more efficient to use the advanced search on Twitter website. Based on my research, I can neither confirm nor deny if the appearance of wild animals is due to the COVID-19 lockdowns. However, I was able to discover a correlational relationship between these two factors in some research cases. Although my findings are mixed with regard to my original hypothesis, the impact that this phenomenon had on society cannot be denied.

ContributorsHeimlich, Kiana Raye (Author) / Dorn, Ronald (Thesis director) / Martin, Roberta (Committee member) / Donovan, Mary (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

The COVID-19 pandemic has resulted in preventative measures and has led to extensive changes in lifestyle for the vast majority of the American population. As the pandemic progresses, a growing amount of evidence shows that minority groups, such as the Deaf community, are often disproportionately and uniquely affected. Deaf

The COVID-19 pandemic has resulted in preventative measures and has led to extensive changes in lifestyle for the vast majority of the American population. As the pandemic progresses, a growing amount of evidence shows that minority groups, such as the Deaf community, are often disproportionately and uniquely affected. Deaf people are directly affected in their ability to personally socialize and continue with daily routines. More specifically, this can constitute their ability to meet new people, connect with friends/family, and to perform in their work or learning environment. It also may result in further mental health changes and an increased reliance on technology. The impact of COVID-19 on the Deaf community in clinical settings must also be considered. This includes changes in policies for in-person interpreters and a rise in telehealth. Often, these effects can be representative of the pre-existing low health literacy, frequency of miscommunication, poor treatment, and the inconvenience felt by Deaf people when trying to access healthcare. Ultimately, these effects on the Deaf community must be taken into account when attempting to create a full picture of the societal shift caused by COVID-19.

ContributorsDubey, Shreya Shashi (Co-author) / Asuncion, David Leonard (Co-author) / Patterson, Lindsey (Thesis director) / Lee, Lindsay (Committee member) / School of Molecular Sciences (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

Actuaries can analyze healthcare trends to determine if rates are reasonable and if reserves are adequate. In this talk, we will provide a framework of methods to analyze the healthcare trend during the pandemic. COVID-19 may influence future healthcare cost trends in many ways. First, direct COVID-19 costs may increase

Actuaries can analyze healthcare trends to determine if rates are reasonable and if reserves are adequate. In this talk, we will provide a framework of methods to analyze the healthcare trend during the pandemic. COVID-19 may influence future healthcare cost trends in many ways. First, direct COVID-19 costs may increase the amount of total experienced healthcare costs. However, with the implementation of social distancing, the amount of regularly scheduled care may be deferred to a future date. There are also many unknown factors regarding the transmission of the virus. Implementing epidemiology models allows us to predict infections by studying the dynamics of the disease. The correlation between infection amounts and hospitalization occupancies provide a methodology to estimate the amount of deferred and recouped amounts of regularly scheduled healthcare costs. Thus, the combination of the models allows to model the healthcare cost trend impact due to COVID-19.

ContributorsGabric, Lydia Joan (Author) / Zhou, Hongjuan (Thesis director) / Zicarelli, John (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05