2020 Abstracts

Smith, Heather; Chellamuthu, Dr. Vinodh (Dixie State University)
Faculty Advisor: Chellamuthu, Vinodh (Dixie State University, Mathematics)

The Zero Waste movement aims to reduce the amount of waste sent to landfills, incinerators, and recycling through education on more sustainable choices. Individuals are educated on how to avoid single-use items, reduce, reuse, and compost as much as possible, and recycle when necessary. Making more sustainable choices on an individual or family level can be a significant part of the solution to plastic pollution and climate change. We developed an individual-based model that shows the relationship between idea dissemination, individual choices, and waste collection. The model is based on statistical data concerning waste, pollution, and idea dissemination to better understand how education about Zero Waste can efficiently reduce landfill contributions and help the local economy. Our results from this model can help policymakers make decisions about waste management, and influencers educate people on the Zero Waste movement.

Jake, Baldauf; Nolan, Cole; Zabriskie, Brinley (Brigham Young University)
Faculty Advisor: Zabriskie, Brinley (Brigham Young University, Physical and Mathematical Sciences)

Meta-analysis is a statistical procedure that combines data from multiple studies. This is particularly useful in clinical research when multiple studies produce conflicting results or when reaching a definitive conclusion on the effectiveness of a medication. Determining the extent to which these studies differ from one another due to differences in treatment administration and patient populations is key to identifying treatment efficacy. Estimation of the differences the studies demonstrate is known as heterogeneity. Estimating the heterogeneity test statistic tau for meta-analysis is key to ensuring the validity of clinical research. We investigate the ability of available heterogeneity methods for dichotomous data by analyzing data from multiple clinical trials; we have found that specific methods of estimating heterogeneity outperform others while a select few consistently underperform. Understanding which method performs best will allow clinical researchers to better estimate heterogeneity, thereby improving their ability to find new treatments.

Larsen, Aaron; Chow, Sum (Brigham Young University)
Faculty Advisor: Chow, Sum (Brigham Young University, Mathematics)

Many definitions and fractional derivative operators are used in the application of mathematics. This paper analyzes a newly presented definition of the fractional derivative by R. Khali, el al. Numerical methods, specifically the finite difference method using boundary conditions, are applied to the Bagley-Torvik equation. This equation is used to describe the motion of a rigid plate in a Newtonian fluid. This results of using this new definition are then compared to those of the known fractional derivative operators of Riemann-Liouville and Caputo.

Islam, Mohammad; Heiny, Erik; Robles, Francisco; Ram, Trevor (Utah Valley University)
Faculty Advisor: Islam, Mohammad (Utah Valley University, Mathematics); Heiny, Erik (Utah Valley University, Mathematics)

In this project, we investigate two methods to detect trend in the time series data, of which one proposed method what we call it "ADM- Average Difference Method" gives the estimate of trend , and the other method what we call it "AMD-Absolute Max Difference" determines if there is any trend in the time series data. Both methods are applicable to linear and nonlinear time series data. We assess the quality of our proposed methods and compare our methods with nonparametric Mann-kendall test through Monte Carlo simulation by calculating the power of the tests. The power comparisons show that ADM- Average Difference Method performs better than Mann-Kendall test when there is no autocorrelation in the time series observations and non-monotonic autocorrelated series. However, absolute max difference method works well compared to Mann-Kendall test for detecting the trend when data are autocorrelated. Finally, we use our proposed method along with those in use to detect trend in two standard datasets -Alta Snowfall data and Nile river water flow data. ADM was able to detect trend in the Nile water flow data as did MK test, which is supported by the visual identification. On the other hand, AMD method failed to detect the trend in the Nile data. For Alta snowfall data, our proposed methods and MK test didn't find any trend over time as supported by visual inspection result.

Evans, Parker; Han, Jianlong (Southern Utah University)
Faculty Advisor: Han, Jianlong (Southern Utah University, Mathematics)

A Lengyel-Epstein system, describing the reactions of chlorite-iodide and malonic acid(CIMA), is studied through methods of numerical analysis. These reactions, describing certain natural patterns such as the recurring stripes in zebras, are examples of Turing Structures, with a non-diffusion rate application. The stability of the steady state solution of this system is analyzed to modelend-term behavior of such phenomena. We develop some numerical schemes that guarantee positive solutions and realistic applications. These numerical schemes model and verify of the theoretical results for the system.

Taylor, Ammon; Otterson, Jisun; Chellamuthu, Vinodh (Dixie State University)
Faculty Advisor: Chellamuthu, Vinodh (Dixie State University, Mathematics)

Dengue fever is one of the most common mosquito borne infections, and it is commonly spread in tropical climates. It can only be spread from the bite of a female Aedes aegypti mosquito. Wolbachia is a natural bacteria found in around 60% of all mosquito species, but it is not found naturally in the Aedes aegypti mosquito, the mosquito primarily responsible for the spread of Dengue virus. By infecting the Aedes aegypti mosquitoes with Wolbachia, it will slow the growth of any viruses the mosquito may carry, including Dengue. One of the objectives of the proposed project is to develop a temperature-dependent mathematical model in order to predict the spread of the Dengue virus between mosquitoes and humans. Moreover, to make our simulation show the optimal range of temperature as well as what times during the year Wolbachia-infected mosquitoes should be released in order to be as cost-effective as possible. Furthermore, we will design a robust GUI that could be used by mosquito abatement centers in order to determine optimal strategies in order to most efficiently mitigate the disease outbreaks.

Jones, Gerald; Zhao, Jia; Ellis, Dylan; Sims, Ronald (Utah State University)
Faculty Advisor: Zhao, Jia (College of Science, Mathematics and Statistics Department); Sims, Donald (College of Engineering, Biological Engineering Department)

Algal blooms are a worsening issue across the United States. Algal blooms are formed by an overabundance of nutrients in the water such as Nitrogen and Phosphorus. To combat this, Utah State University is collaborating with the Central Valley Water Reclamation Center, the largest water treatment plant in Utah, with innovating ways to reduce Nitrogen and Phosphorus levels in wastewater before being discharged into the local bodies of water.

One process shows promise. The Rotating Algae Biofilm Reactor (RABR) consists of an attached biofilm growth that rotates through a growth substrate. As the biofilm grows, it assimilates the nutrients in the water, thereby transferring them from the water into the biofilm algae.

No referred literature exists on mathematically connecting RABR biofilm productivity with actual data. The purpose of this research is to formulate a model of the mass production of the RABR as a function of sunlight and rate of exposure. This process is done by combining an analytical and data-driven approach to discover the equation. Sparse Identification of Nonlinear Dynamics (SINDy) is a data-driven approach that represents a potential breakthrough in being able to identify and quantify the most important parameters influencing algae biofilm yield and productivity. This study will go through the process of creating an analytical model and then scrutinizing said model with real data and make necessary adjustments.

An analytical model using Bara and Bonneford's work on photoinhibition is provided as a baseline for this study. Some data-driven results will also be presented to address the fundamental characteristics of biofilm growth.

The biofilm harvested from the RABR has significant potential for bioproducts such as biofuel, medicine, bioplastics, and livestock feed. Across different industries, this robust model describing algae biofilm growth will provide a mathematical foundation for future algae-based biofilm technologies.

Esplin, Rylee: Chellamuthu, Vinodh (Dixie State University)
Faculty Advisor: Chellamuthu, Vinodh (Dixie State University, Mathematics)

The Zika Virus (ZIKV) is a mosquito-borne disease that inhabits Aedes Aegypti mosquitoes. This disease can be passed to humans three different ways: first, through the bite of an infected mosquito; second, sexual transmission between humans who are already infected with the disease; and finally, from humans to their unborn children through vertical transmission. Several studies have shown the dynamics of ZIKV and its dependency on temperature. We developed a temperature-dependent mathematical model using systems of first order differential equations to analyze the spread of the ZIKV in an effort to control the mosquito population. Our model explicitly incorporates the temperature dependency of the vital rates of the mosquito population. Furthermore, our model will also take into account the local environmental data to show the effects of seasonality within the transmission of ZIKV. Our simulation results show the importance of temperature and its impact on the mosquito-human interaction.

West, Noelle; Chellamuthu, Vinodh (Dixie State University)
Faculty Advisor: Chellamuthu, Vinodh (Dixie State University, Mathematics)

West Nile Virus (WNV) is a vector-borne illness that has circulated among birds, eventually spreading across the globe. This disease has resulted in thousands of infections and deaths. Several studies suggest that passive immunity in birds and vertical transmission in mosquitoes play a crucial role in the spread of the disease. We have developed a mathematical model to investigate the effects of passive immunity and vertical transmission within the disease dynamics. Our simulation results suggest that passive immunity increases bird resistivity to WNV and that vertical transmission among mosquitoes increases the spread of WNV. Moreover, we expect this model to be used by mosquito abatement centers to estimate the populations of immune birds and to simulate disease outbreaks in the local community.

Froberg, Matthew (University of Utah)
Faculty Advisor: Asparouhove, Elena (University of Utah, David Eccles School of Business (Finance))

This research examines two fundamental topics of economics: accuracy of prices and the effect of market participation on individuals. In particular, it asks how security structure affects price and allocational efficiency through the equilibration process.

Security structure is defined as the payoff correlation structure between tradable assets. Economists agree that the markets they are studying are in equilibrium and also that there are equilibration forces that will drive markets towards equilibrium if they are not already there (see, for example, Arrow and Hahn (1971)). There is much less agreement, however, on what these equilibration forces are. Furthermore, it is very difficult to learn about these driving forces through the analysis of historical data because not enough is known about the fundamentals (wealth, human capital, and preferences of individuals) of past markets. This represents a great opportunity for experimental finance, where markets can be created in a laboratory setting allowing researchers to know, control, and change the fundamentals of the markets they create. This research examines what asset structures yield the most efficient allocations as a result of imposed fundamentals. The trading platform is Continuous Double Auction and is implemented in a software called Flexemarkets (flexemarkets.com). The main hypothesis is that markets consisting of securities that correlate negatively will exhibit the highest allocational efficiency. Data collection with human traders will be collected in the months of November and December. Pilot sessions with humans suggest that negatively correlated assets aid price discovery but more data is needed to address allocational efficiency.

The question regarding asset structure and its effect on financial well-being is especially relevant given the increasing popularity of index funds (see Bogle (2016)), which are typically positively correlated. Results of the experiment could yield substantial policy implications concerning what types of security designs lead to optimal allocational outcomes.

Calzado Real, Tamara; Blair, Ariel; Tenney, Elizabeth (University of Utah)
Faculty Advisor: Blair, Barbara "Ariel" (David Eccles School of Business, Management)

The purpose of this study is to understand how racial dissimilarity affects people of color's voice behavior in a student or class group. In a group where a person's social category is underrepresented, they become more aware of that social identity and their ability to perform at their full potential reduces because they are more focused on monitoring their performance and suppressing negative thoughts and feelings than improving group performance. However, in situations where people are more identified with the group, they are more likely to feel committed to or express themselves in a group. Additionally, in groups where people of color don't perceive themselves as different from all or most of the other group members, subgroups and division among team members is less likely to occur. In order for people of color to contribute in meaningful and innovative ways, having the confidence to speak up and express new ideas is crucial. We will run a survey where participants recall groups that they have been a part of and rank their voice (participation) in the group, their perceived racial dissimilarity of the group, and the importance of race on their personal identity. Afterwards, they will placed in an online student group chat with high or low dissimilarity and will be asked to reflect on their experiences. In line with previous research we expect that the importance of race on their personal identity will be positively related to perceived racial dissimilarity and therefore, we expect peoples' voice behaviors to decrease when they are in a group where racial dissimilarity is high.

Bowden, Lucy; Monroe, Jacquelyn; Bowden, Anton E.; Jensen, Brian D. (Brigham Young University)
Faculty Advisor: Bowden, Anton (Engineering, Mechanical Engineering); Jensen, Brian (Engineering, Mechanical Engineering)

Previously our lab has shown that carbon-infiltrated carbon nanotube (CI-CNT) surfaces enhance osseointegration and resist biofilm formation, making them attractive possibilities as orthopedic implant materials. For these applications, CI-CNTs and their underlying substrate material must be able to withstand aqueous physiologic conditions. Due to microstructural changes that occur during CI-CNT production, we hypothesized that stainless steel substrate materials experience a loss of their protective, passivating layer, subsequently corroding when immersed in a simulated biological environment. The purpose of the study was to compare corrosion resistance of CI-CNT coated stainless steel substrates to bare stainless steel control samples after two days of incubation in different physiological analog media.

CI-CNTs were grown on 316L stainless steel samples which were sonicated for 20 minutes in isopropyl alcohol and given a 2 minute heat treatment in air at 800°C, followed by a 20 minute growth at the same temperature in ethylene and argon. Carbon infiltration was done for 5 minutes in the same gases at 900°C. The samples were autoclaved and placed into different media including deionized water, phosphor buffered saline solution (PBS), and DMEM culture media. The samples were then incubated for 48 hours at 37°C.

Macroscopic observation showed no obvious signs of corrosion (e.g., discoloration of the liquid media, cloudiness, physical changes in sample appearance) for any of the control samples, or for CI-CNT coated samples in deionized water. In contrast, the CI-CNT coated samples immersed in PBS and culture media exhibited significant discoloration and a cloudy appearance. Subsequent SEM images of the CI-CNT coated samples which had been immersed in culture media and PBS showed foreign residue. Energy dispersive x-ray analysis characterized this residue as having markedly higher levels of sodium and phosphorus than a baseline CI-CNT coated stainless steel sample. SEM images of the bare stainless steel samples and the CI-CNT samples cultured in deionized water showed no signs of corrosion or residue.

Our preliminary results illustrate that media containing salts initiated corrosion of CI-CNT coated stainless steel samples, likely due to disruption of the passivating layer in the substrate. Future work will explore methods for re-establishing the passivating layer in stainless steel materials.

Colver, Mitchell; Hagman, Amanda (Utah State University)
Faculty Advisor: Colver, Mitchell; Hagman, Amanda

Making the choice of where to live while in college is frequently acknowledged as one of the most important decisions an undergraduate student makes. Housing decisions influence students' access to campus resources and social integration, elements thought to be key indicators of their progression towards graduation. Interestingly, however, the association between living on-campus and persistence has not been considered thoroughly in the literature. While many studies leverage survey data and retention rates to make direct comparisons between on-campus and off-campus groups, most are unable to account for self-selection bias, i.e. that students who live on-campus may be qualitatively different from students who chose to live off-campus. The present study overcame this challenge by utilizing a matching technique called Prediction-based Propensity Score Matching (PPSM). Using this theoretically-driven and methodologically robust technique, researchers were able to account for self-selection bias and estimate the impact of on-campus living on student persistence. After matching, researchers estimated that students living on-campus experience a 1.19% lift (CI: 0.55% to 1.83%) in persistence. In other words, the model suggests that 46 students (CI: 21 to 71) remain enrolled at the institution simply because they live on-campus. This conclusion indicates that living in university housing is not only important because it provides students with campus proximity and social activities, but ultimately because it helps them persist towards graduation.

Judd, Emma J.; Clark, Sarah K. (Brigham Young University)
Faculty Advisor: Clark, Sarah (Education, Teacher Education)

The study examined the integration of science into literacy instruction for the early grades. The study specifically explored how science-infused literacy instruction influenced the quality of compare and contrast science informational text produced by second graders, compared to literacy instruction alone. Additionally, the motivation of the students to read was examined in connection to the quality of the informational text they produced. The participants were second-graders (N = 72) between the ages of 7 – 9 and were enrolled in the first quarter of the school year at a Title 1 school. Seventy-three percent of these students were White, 22% were Hispanic, 2% were Asian, and 1% were Black, with 63% of the students eligible for free or reduced lunch. The treatment group (N = 35) received science-infused literacy instruction and the control group (N = 37) received their regular literacy instruction. Two instruments for measurement were used: a motivation survey which measured the students’ motivation to read, and a weighted writing rubric with an emphasis on signal words, content-specific vocabulary words, and word count, which was used to score the informational text writing samples produced by the students. The students took the reading motivation survey and answered the same informational text writing prompt before and after the instruction. The instruction for compare and contrast writing took place over the course of a four-week unit, and consisted of three 30-minute lessons weekly. The research was designed as quasi-experimental using a paired samples t-test with follow-up effect size measures. The results demonstrate that students in the treatment group produced significantly higher reading motivation scores but wrote lower-quality text, while students in the control group produced lower motivation scores but wrote higher-quality informational text. Implications from this study will be provided for educators and literacy instructional practices, and for researchers and future studies.

Kaytriauna Flint, Allison Fishler, Mosese Manu, and Justus Te'i (Utah State University)
Faculty Advisor: Soyer, Mehmet (College of Humanities and Social Sciences; Sociology, Social Work and Anthropology Department)

Here at Utah State, there are many resources available for students, staff, faculty, and administration to travel to and from campus in eco-friendly ways. While there are many resources readily available, they are not well known across campus. Our initiative is to bring awareness to these hard-working groups and generous programs while incentivizing those who participate in our social media campaign where they will submit creative photos of their sustainable transportation to and from campus. Not only will it be extremely beneficial for these groups and programs across campus to get well-deserved recognition through this initiative, but it will give Aggies the greater opportunity to Go Green and travel to and from campus in an eco-friendly way!

Joshua Luchs; Angela Kline (Brigham Young University)
Faculty Advisor; Wright, Geoff (Brigham Young University, Technology and Engineering Studies)

Despite the continual efforts of researchers and academic institutions, STEM fields such as Engineering remain male-dominated in representation. This study explores many of the positive and negative influencers affecting women in the determination to invest in engineering as an academic pathway. Whereas previous literature details many of the social barriers women encounter while pursuing male-dominated fields, this study uniquely investigates the technical focuses, academic mapping, and natural interests with potential to counteract said barriers. To achieve this, data was collected by interviews and surveys among both post-parted collegiate female engineers as well as sixth-grade males and females from local public schools. Surveys given among the younger group particularly provided insight into the framework through which developing females prefer to receive STEM instruction. The Standards for Technological Literacy serve as one of these primary frameworks assessed. By comparing the data on female interest within each Technological Literacy Standard, conclusions offered insight into the applications by which females more naturally take interest in STEM studies. These conclusions lead into the important pursuit of properly mapping STEM curriculum to actively engage and support all genders in a balanced pedagogical model.

Evans, Hannah; Peterson, Rebecca (Utah State University)
Faculty Advisor: Shumway, Jessica (Emma Eccles Jones College of Education & Human Services, School of Teacher Education and Leadership); Clarke-Midura, Jody (Emma Eccles Jones College of Education & Human Services, Instructional Teachnology and Learning Sciences Department); Lee, Victor (Emma Eccles Jones College of Education & Human Services, Instruction Technology and Learning Sciences Department); Silvis, Deborah (Emma Eccles Jones College of Education & Human Services, Instruction Technology and Learning Sciences Department)

The push for computer science integration in kindergarten classrooms is a surfacing topic in public education in the United States. One approach to this is to integrate computer science with mathematics. However, there is minimal research on computer science and computational thinking as it relates to mathematics in early childhood education. In order to address this need, we are part of a larger research project that is studying the integration of computer science and mathematics in kindergarten classrooms. Specifically, we are exploring computational thinking (CT) elements that we see students engaging in (e.g., algorithmic thinking, debugging, and decomposition) while at the same time exploring mathematics skills that emerge (e.g., measurement, spatial reasoning, and pattern recognition). We study these skills and elements as we teach formal coding instruction using play-based, screen free coding robots. In this presentation, we will present early results of this integration in local kindergarten classrooms. Our main research question is: What CT and mathematics skills and strategies emerge as a result of this formal coding instruction?

Our sample consists of 16 kindergarten students. Groups of 3-4 students participated in six 30-minute coding lessons, followed by an assessment interview. Our data set is made up of video data from both the coding instruction and the assessment interviews, as well as field notes and assessment score sheets. We will present descriptive statistics regarding these assessments, as well as in-depth case studies of 2 students (one student who scored high on their post-test, and one who scored low). We will present data from the videos of their individual experiences as they engaged in formal instruction, as well as data regarding their assessments, in order to answer our research question and analyze what CT and mathematics skills and strategies emerged as a result of their formal coding instruction.

(Pace, Jenessa; Ence, Elodie; Kunz, Allison; Stevens, Rebecca; Kunz, Amber; Cooper, Izaak; Nelson, Alicia; Asplund, Alyssa; Stock, Julianna) (Brigham Young University)
Faculty Advisor: Williams, Gustavious (Ira A. Fulton College of Engineering and Technology, Civil and Environmental Engineering)

Photogrammetry using Unmanned Aerial Vehicles (UAV) has become more relevant to water resources issues. The models generated can be highly accurate and detailed. The use of ground truth is an integral part of ensuring the accuracy of such models. Ground truth based on GPS-obtained data of visual targets gathered in the field prior to UAV data collection are used to improve post processing accuracy. Proper spacing of ground truth is primarily dependent on the flight path of the UAV during data collection, flight height, and image resolution.
One developing task is creating models of full-pool bathymetric maps for reservoirs - using UAVs for above the waterline and sonar for below. Due to their erratic shapes, capturing the shorelines of reservoirs requires erratic flight paths. Planning ground truth spacing requires special care.
To determine proper ground truth spacing we completed a field survey at Starvation Reservoir, near Duchesne, Utah. We selected a two mile stretch along the north side of the reservoir to test various ground truth spacings. We flew the test stretch with two flights, one taking nadir photos and one with the photos taken at an angle of about 30 degrees, more normal to the shoreline. The primary placement of ground truth points was approximately 0.25 miles apart. After the data was recorded, we created models using Metashape software using different ground truth spacing, using spacings of 0.25, 0.5 and 1 mile. We used Cloud Compare software to determine the error between each model. We assumed that the model generated using 0.25 points/mile was "truth". We used this preliminary information to determine that for bathymetry maps, a ground truth spacing of 1 mile/point was acceptable, we are continuing our research to refine this finding.