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- Creators: School of Mathematical and Statistical Sciences
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Description
In this paper, we study the prime factorizations of numbers slightly larger than the factorial function. While these are closely related to the factorial prime, they have more inherent structure, which allows for explicit results as of yet not established on factorial prime. Case in point, the main result of this paper is that these numbers, which are described in concrete terms below, cannot be prime powers outside of a handful of small cases; this is a generalization of a classical result stating they cannot be primes. Minor explicit results and heuristic analysis are then given to further characterize the set.
ContributorsLawson, Liam John (Author) / Jones, John (Thesis director) / Childress, Nancy (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
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
This paper presents a study done to gain knowledge on the communication of an object’s relative 3-dimensional position in relation to individuals who are visually impaired and blind. The HapBack, a continuation of the HaptWrap V1.0 (Duarte et al., 2018), focused on the perception of objects and their distances in 3-dimensional space using haptic communication. The HapBack is a device that consists of two elastic bands wrapped horizontally secured around the user’s torso and two backpack straps secured along the user’s back. The backpack straps are embedded with 10 vibrotactile motors evenly positioned along the spine. This device is designed to provide a wearable interface for blind and visually impaired individuals in order to understand how the position of objects in 3-dimensional space are perceived through haptic communication. We were able to analyze the accuracy of the HapBack device through three vectors (1) Two different modes of vibration – absolute and relative (2) the location of the vibrotactile motors when in absolute mode (3) and the location of the vibrotactile motors when in relative mode. The results provided support that the HapBack provided vibrotactile patterns that were intuitively mapped to distances represented in the study. We were able to gain a better understanding on how distance can be perceived through haptic communication in individuals who are blind through analyzing the intuitiveness of the vibro-tactile patterns and the accuracy of the user’s responses.
ContributorsLow, Allison Xin Ming (Author) / McDaniel, Troy (Thesis director) / Duarte, Bryan (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
We consider programmable matter as a collection of simple computational elements (or particles) that self-organize to solve system-wide problems of movement, configuration, and coordination. Here, we focus on the compression problem, in which the particle system gathers as tightly together as possible, as in a sphere or its equivalent in the presence of some underlying geometry. Within this model a configuration of particles can be represented as a unique closed self-avoiding walk on the triangular lattice. In this paper we will examine the bias parameter of a Markov chain based algorithm that solves the compression problem under the geometric amoebot model, for particle systems that begin in a connected configuration with no holes. This bias parameter, $\lambda$, determines the behavior of the algorithm. It has been shown that for $\lambda > 2+\sqrt{2}$, with all but exponentially small probability, the algorithm achieves compression. Additionally the same algorithm can be used for expansion for small values of $\lambda$; in particular, for all $0 < \lambda < \sqrt{\tau}$, where $\lim_{n\to\infty} {(p_n)^{1
}}=\tau$. This research will focus on improving approximations on the lower bound of $\tau$. Toward this end we will examine algorithmic enumeration, and series analysis for self-avoiding polygons.
}}=\tau$. This research will focus on improving approximations on the lower bound of $\tau$. Toward this end we will examine algorithmic enumeration, and series analysis for self-avoiding polygons.
ContributorsLough, Kevin James (Author) / Richa, Andrea (Thesis director) / Fishel, Susanna (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
A defense-by-randomization framework is proposed as an effective defense mechanism against different types of adversarial attacks on neural networks. Experiments were conducted by selecting a combination of differently constructed image classification neural networks to observe which combinations applied to this framework were most effective in maximizing classification accuracy. Furthermore, the reasons why particular combinations were more effective than others is explored.
ContributorsMazboudi, Yassine Ahmad (Author) / Yang, Yezhou (Thesis director) / Ren, Yi (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Economics Program in CLAS (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The oxygen sensitivity of hydrogenase is a large barrier in maximizing the efficiency of algal hydrogen production, despite recent efforts aimed at rewiring photosynthesis. This project focuses on the role of photosystem II (PSII) in extended hydrogen production by cells expressing the PSI-HydA1 chimera, with the goal of optimizing continuous production of photobiohydrogen in the green alga, Chlamydomonas reinhardtii. Experiments utilizing an artificial PSII electron
Therefore, it can be concluded that downstream processes are limiting the electron flow to the hydrogenase. It was also shown that the use of a PSII inhibitor, 3-(3,4-dichlorophenyl)-1,1- dimethylurea (DCMU), at sub-saturating concentrations under light exposure during growth temporarily improves the duration of the H2 evolution phase. The maximal hydrogen production rate was found to be approximately 32 nmol h-1 (µg Chl)-1. Although downregulation of PSII activity with DCMU improves the long-term hydrogen production, future experiments must be focused on improving oxygen tolerance of the hydrogenase as a means for higher hydrogen yields.
Therefore, it can be concluded that downstream processes are limiting the electron flow to the hydrogenase. It was also shown that the use of a PSII inhibitor, 3-(3,4-dichlorophenyl)-1,1- dimethylurea (DCMU), at sub-saturating concentrations under light exposure during growth temporarily improves the duration of the H2 evolution phase. The maximal hydrogen production rate was found to be approximately 32 nmol h-1 (µg Chl)-1. Although downregulation of PSII activity with DCMU improves the long-term hydrogen production, future experiments must be focused on improving oxygen tolerance of the hydrogenase as a means for higher hydrogen yields.
ContributorsO'Boyle, Taryn Reilly (Author) / Redding, Kevin (Thesis director) / Ghirlanda, Giovanna (Committee member) / Vermaas, Willem (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This project attempts to create an accurate numerical simulation of the eastern limb of the HH 901 jet in the Mystic Mountain formation located in the Carina Nebula. Using a 3rd order accurate WENO numerical scheme in space, and a 3rd order accurate RK method in time, the temperature, density, radiative cooling, length, and average jet velocity of this astrophysical phenomenon were simulated based on observations made by Hubble Space Telescope and the work of Reiter and Smith (2013) and (2014). The results of this simulation are displayed in three figures, one each for temperature, radiative cooling, and density, which show a jet displaying morphology consistent with that of the HH 901 eastern limb without adjustment for stellar wind. Also discussed are the effects of different jet speeds, initial conditions, and pulse parameters on the shape and behavior of the simulated jets, as well as continuing work to be done on the simulation to enhance its accuracy and usefulness.
ContributorsKreitzer, Kyle (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
In baseball, a starting pitcher has historically been a more durable pitcher capable of lasting long into games without tiring. For the entire history of Major League Baseball, these pitchers have been expected to last 6 innings or more into a game before being replaced. However, with the advances in statistics and sabermetrics and their gradual acceptance by professional coaches, the role of the starting pitcher is beginning to change. Teams are experimenting with having starters being replaced quicker, challenging the traditional role of the starting pitcher. The goal of this study is to determine if there is an exact point at which a team would benefit from replacing a starting or relief pitcher with another pitcher using statistical analyses. We will use logistic stepwise regression to predict the likelihood of a team scoring a run if a substitution is made or not made given the current game situation.
ContributorsBuckley, Nicholas J (Author) / Samara, Marko (Thesis director) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Information Systems (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
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 purpose of this thesis project is to analyze the impact that patient death has on long-term care providers. This study draws upon my own experience working as a licensed nursing assistant in a long-term care facility and also uses a qualitative analysis of six semi-structured interviews with other nursing assistants and hospice volunteers. With patient death being an unavoidable part of working in this area of healthcare, I explore how these care providers cope with losing their patients and the effectiveness of these coping mechanisms. Some strategies found that aided in coping with grief included staying detached from patients, being distracted by other aspects of the job, receiving support from co-workers, family members and/or supervisors, and having a religious outlook on what happens following death. In addition to these, I argue that care providers also utilize the unconscious defense mechanism of repression to avoid their feelings of grief and guilt. Repressing the grief and emotions that come along with patient death can protect the individual from additional pain in order for them to continue to do their difficult jobs. Being distracted by other patients also aids in the repression process by avoiding personal feelings temporarily. I also look into factors that have been found to affect the level of grief including the caregiver’s closeness to the patient, level of preparedness for the death, and first experience of losing a patient. Ultimately, I show that the common feelings accompanied by patient death (sadness, anger and stress) and the occurrence of burnout are harmful symptoms of the repression taking place.
ContributorsMasterson, Kaitlin (Author) / Loebenberg, Abby (Thesis director) / Mack, Robert (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05