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- Creators: School of Mathematical and Statistical Sciences
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Description
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
Previous research discusses students' difficulties in grasping an operational understanding of covariational reasoning. In this study, I interviewed four undergraduate students in calculus and pre-calculus classes to determine their ways of thinking when working on an animated covariation problem. With previous studies in mind and with the use of technology, I devised an interview method, which I structured using multiple phases of pre-planned support. With these interviews, I gathered information about two main aspects about students' thinking: how students think when attempting to reason covariationally and which of the identified ways of thinking are most propitious for the development of an understanding of covariational reasoning. I will discuss how, based on interview data, one of the five identified ways of thinking about covariational reasoning is highly propitious, while the other four are somewhat less propitious.
ContributorsWhitmire, Benjamin James (Author) / Thompson, Patrick (Thesis director) / Musgrave, Stacy (Committee member) / Moore, Kevin C. (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor)
Created2014-05
Description
As we count down the years remaining before a global climate catastrophe, ever increases the importance of teaching environmental history and fostering environmental stewardship from a young age. In the age of globalization, nothing exists in a vacuum, yet our traditional education system often fails to reflect the abundant connections between content areas that are prevalent outside of schools. In fact, many of the flaws of the field of education have been exacerbated by the COVID-19 pandemic and a forced transition to online schooling, with many educators reverting to outdated practices in a desperate attempt to get students through the year. The aim of this project was to design a unit curriculum with these issues in mind. This month-long environmental history unit engages students through the use of hands-on activities and promotes interdisciplinary connections. The unit can be taught in a physical, online, or hybrid American history class, and will hopefully inspire and motivate students to become environmental stewards as they look toward their futures on this planet.
ContributorsColeman, Lauren Jean (Author) / Walters, Molina (Thesis director) / Anthony, Charles (Committee member) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Division of Teacher Preparation (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This study estimates the effect of district wealth on Arizona Empowerment Scholarship Account program participation using data from the Arizona Department of Education. We find that students from poor districts are not more likely to participate as school performance decreases.Conversely, those from wealthy districts do increase participation as school performance decreases. We briefly try to explain the observed heterogeneity through survey results and commenting on the program design.
ContributorsAngel, Joseph Michael (Author) / Kostol, Andreas (Thesis director) / Kuminoff, Nicolai (Committee member) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Schools across the United States have been subject to a rise in violent incidents since 2013. Reading about school shootings, racist acts, and violent demonstrations in schools has unfortunately become commonplace, which is contributing to inequitable outcomes for some student populations. These equity gaps have triggered demands for more equitable solutions in schools, a responsibility that falls on the shoulders of stakeholders like school governing boards, principals, and parents.
Chandler Unified School District (CUSD), a large school system in Arizona that serves 45,000 students from preschool through high school, has been unable to escape similar structural and frictional inequities within its schools. One instance of a racially charged student performance at Santan Middle School motivated CUSD to take a more immediate look at equity in the district. It is during this response that our team of New Venture Group consultants engaged with Matt Strom, Assistant Superintendent of CUSD, in analyzing the important question of “how CUSD can take steps towards closing equity gaps within the district?”
CUSD defines an equity gap as any difference in student opportunity, achievement, discipline, attendance, etc. contributable to a student’s ethnicity, gender, or socioeconomic status. Currently, certain student populations in CUSD perform vastly different academically and receive different opportunities within schools, but as was our problem statement, CUSD is aiming to reduce (and eventually close) these gaps.
Our team approached this problem in three phases: (1) diagnosis, (2) solution creation, and (3) prevention. In phase one, we created a dashboard to help principals easily and visually identify gaps by toggling parameters on the dashboard. Phase two focused on the generation of recommendations for closing gaps. To achieve this goal, a knowledge of successful gap-closing strategies will be paired with the dashboard. In our final phase, the team of consultants created a principal scorecard to ensure equity remains a priority for principals.
Chandler Unified School District (CUSD), a large school system in Arizona that serves 45,000 students from preschool through high school, has been unable to escape similar structural and frictional inequities within its schools. One instance of a racially charged student performance at Santan Middle School motivated CUSD to take a more immediate look at equity in the district. It is during this response that our team of New Venture Group consultants engaged with Matt Strom, Assistant Superintendent of CUSD, in analyzing the important question of “how CUSD can take steps towards closing equity gaps within the district?”
CUSD defines an equity gap as any difference in student opportunity, achievement, discipline, attendance, etc. contributable to a student’s ethnicity, gender, or socioeconomic status. Currently, certain student populations in CUSD perform vastly different academically and receive different opportunities within schools, but as was our problem statement, CUSD is aiming to reduce (and eventually close) these gaps.
Our team approached this problem in three phases: (1) diagnosis, (2) solution creation, and (3) prevention. In phase one, we created a dashboard to help principals easily and visually identify gaps by toggling parameters on the dashboard. Phase two focused on the generation of recommendations for closing gaps. To achieve this goal, a knowledge of successful gap-closing strategies will be paired with the dashboard. In our final phase, the team of consultants created a principal scorecard to ensure equity remains a priority for principals.
ContributorsFerrara, Justin Christopher (Co-author) / Lee, Cynthia (Co-author) / Weston, Joshua (Co-author) / Licon, Wendell (Thesis director) / Strom, Matthew (Committee member) / Department of Economics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Information Systems (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission line data for [Fe II] 12660 Å, Hα 6563 Å, and [S II] 6720 Å to compare with Hubble Space Telescope observations of the HH 901 jets presented in Reiter et al. (2016). We derived the emissivities for these lines from the spectral synthesis code Cloudy by Ferland et al. (2017). In addition, we used WENO simulations of density, temperature, and radiative cooling to model the jet. We found that the computed surface brightness values agreed with most of the observational surface brightness values. Thus, the 3D cylindrically symmetric simulations of surface brightness using the WENO code and Cloudy spectral emission models are accurate for jets like HH 901. After detailing these agreements, we discuss the next steps for the project, like adding an external ambient wind and performing the simulations in full 3D.
ContributorsMohan, Arun (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The field of robotics is rapidly expanding, and with it, the methods of teaching and introducing students must also advance alongside new technologies. There is a challenge in robotics education, especially at high school levels, to expose them to more modern and practical robots. One way to bridge this gap is human-robot interaction for a more hands-on and impactful experience that will leave students more interested in pursuing the field. Our project is a Robotic Head Kit that can be used in an educational setting to teach about its electrical, mechanical, programming, and psychological concepts. We took an existing robot head prototype and further advanced it so it can be easily assembled while still maintaining human complexity. Our research for this project dove into the electronics, mechanics, software, and even psychological barriers present in order to advance the already existing head design. The kit we have developed combines the field of robotics with psychology to create and add more life-like features and functionality to the robot, nicknamed "James Junior." The goal of our Honors Thesis was to initially fix electrical, mechanical, and software problems present. We were then tasked to run tests with high school students to validate our assembly instructions while gathering their observations and feedback about the robot's programmed reactions and emotions. The electrical problems were solved with custom PCBs designed to power and program the existing servo motors on the head. A new set of assembly instructions were written and modifications to the 3D printed parts were made for the kit. In software, existing code was improved to implement a user interface via keypad and joystick to give students control of the robot head they construct themselves. The results of our tests showed that we were not only successful in creating an intuitive robot head kit that could be easily assembled by high school students, but we were also successful in programming human-like expressions that could be emotionally perceived by the students.
ContributorsRathke, Benjamin (Co-author) / Rivera, Gerardo (Co-author) / Sodemann, Angela (Thesis director) / Itagi, Manjunath (Committee member) / Engineering Programs (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
A thorough understanding of the key concepts of logic is critical for student success. Logic is often not explicitly taught as its own subject in modern curriculums, which results in misconceptions among students as to what comprises logical reasoning. In addition, current standardized testing schemes often promote teaching styles which emphasize students' abilities to memorize set problem-solving methods over their capacities to reason abstractly and creatively. These phenomena, in tandem with halting progress in United States education compared to other developed nations, suggest that implementing logic courses into public schools and universities can better prepare students for professional careers and beyond. In particular, logic is essential for mathematics students as they transition from calculation-based courses to theoretical, proof-based classes. Many students find this adjustment difficult, and existing university-level courses which emphasize the technical aspects of symbolic logic do not fully bridge the gap between these two different approaches to mathematics. As a step towards resolving this problem, this project proposes a logic course which integrates historical, technical, and interdisciplinary investigations to present logic as a robust and meaningful subject warranting independent study. This course is designed with mathematics students in mind, with particular stresses on different formulations of deductively valid proof schemes. Additionally, this class can either be taught before existing logic classes in an effort to gradually expose students to logic over an extended period of time, or it can replace current logic courses as a more holistic introduction to the subject. The first section of the course investigates historical developments in studies of argumentation and logic throughout different civilizations; specifically, the works of ancient China, ancient India, ancient Greece, medieval Europe, and modernity are investigated. Along the way, several important themes are highlighted within appropriate historical contexts; these are often presented in an ad hoc way in courses emphasizing technical features of symbolic logic. After the motivations for modern symbolic logic are established, the key technical features of symbolic logic are presented, including: logical connectives, truth tables, logical equivalence, derivations, predicates, and quantifiers. Potential obstacles in students' understandings of these ideas are anticipated, and resolution methods are proposed. Finally, examples of how ideas of symbolic logic are manifested in many modern disciplines are presented. In particular, key concepts in game theory, computer science, biology, grammar, and mathematics are reformulated in the context of symbolic logic. By combining the three perspectives of historical context, technical aspects, and practical applications of symbolic logic, this course will ideally make logic a more meaningful and accessible subject for students.
ContributorsRyba, Austin (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05