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.

Knudson, Adam; Faught, Nolan (Brigham Young University)
Faculty Advisor: Kempton, Mark (Brigham Young University, College of Physical and Mathematical Sciences)

Resistance distance is a form of metric on connected graphs that becomes exponentially difficult to compute as the size of a graph increases. We examine the resistance distance on a class of graphs that may be decomposed into chains of some graph G and derive a generalized formula for the resistance between any two vertices. We apply this formula to a subclass of these graphs, named flower graphs, and proceed to give an explicit formula for Kemeny's constant and the Kirchhoff index of these flower graphs.

Jonah Nicoll; Zach Clement; Hal Svien; Gary Burlingame (Brigham Young University)
Faculty Advisor: Burlingame, Gary (Brigham Young University, Psychology)

Aims: Many practice guidelines place cognitive-behavioral therapy (CBT) as the gold-standard treatment for psychotic disorders. Our previous meta-analysis on group psychotherapy for schizophrenia (Burlingame et al., under review) employed a strict set of inclusion criteria (e.g., RCT, use of 2 measures, comparison groups, etc.) limiting the number of CBT studies applied to patients presenting on the psychosis spectrum. It found no meta-analytic evidence for group CBT (GCBT) ameliorating psychotic symptoms but only included 5 studies. This meta-analysis will be less restrictive to include more interventions under a broader GCBT umbrella to extend our earlier findings.

Methods: A literature search identified nearly 20 more randomized controlled trials that included in our previous analysis that evaluated some form of GCBT in treating psychosis. Three main outcomes will be assessed: schizophrenia-specific measures of psychotic symptoms, treatment-specific measures assessing treatment aims, and general measures assessing broad functioning.

Results: Preliminary results are still being calculated. Subgroup analyses will include Burlingame et al.'s (under review) CBT categorization and include interventions broadly focused on behavior and cognition, including social skills interventions that also emphasize cognition (viz., Granholm et al., 2005, 2007).

Discussion: Results will be framed in relation to Burlingame et al.'s (under review) meta-analysis. It is likely that the stricter classification of CBT resulted in an attenuation of the effects with a psychosis population. Furthermore, there is a general lack of agreement on what interventions should be labeled CBT (nb., Wampold et al., 1997; Wampold & Imel, 2015).

Keywords: group treatment, schizophrenia

Jensen, Samuel J. (Brigham Young University)
Faculty Advisor: Allison, James (Brigham young University, Anthropology)

The development of Portable X-ray Fluorescence (PXRF) technology has allowed researchers to accurately determine the source of obsidian lithic material. The data produced using this method in turn allow researchers to examine the social interactions of prehistoric peoples through analysis of potential spheres of trade or points of contact. Prior researchers have applied PXRF technology to the analysis of obsidian from the Mesa Verde and Northern San Juan regions of the Ancestral Puebloan world respectively. Despite this work, however, there is a conspicuous lack of data from San Juan County, Utah, which lies at the northwestern edge of the Ancestral Puebloan extent and contains a high density of archaeological sites spanning almost the entirety of Ancestral Puebloan occupation in the American Southwest. This paper aims to fill this gap in data so as to make observations about the potential spheres of interaction that existed across time in this region of the Ancestral Puebloan world. Specifically, this research compares obsidian samples from across San Juan County and from sites with different time periods of occupation to reveal potential patterns of obsidian procurement throughout temporal space in San Juan County.

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.

Moore, Sydney; Lech, Kimberly; Richardson, Bianca; Jensen, Amber; Thiel, Rebecca (Weber State University)
Faculty Advisor: Dunn, Charles (Weber State University, College of Nursing); Miles, Leslie (Brigham Young University, College of Nursing)

"The impact of child maltreatment on attachment is established in childhood" (Stronach et al., 2011), "with this effect remaining relatively stable through adulthood" and most often manifested as an anxious or avoidant attachment. (Weinfeld, Sroufe, & Egeland, 2000) (Oshri et al., 2105) Anxious individuals fear abandonment, are obsessive and desire high levels of reciprocity with others whereas avoidant individuals fear intimacy and closeness and avoid committed relationships (Hazan & Shaver, 1987). Can the quality of adult romantic relationships also known as "attachment" be determined by the type and frequency of Adverse Childhood Experiences (ACEs) or trauma those adults experienced growing up? The ACE survey consisting of 10 questions covering abuse, neglect, and household dysfunction, and 17 questions from the Experiences of Close Relationships (ECR) questionnaire rating participants' responses on a Lickert scale of 0-4 were used to compile the data. We propose the following hypothesis, in concordance with existing research, a higher ACE score will be an indicator of lower relationship quality/satisfaction in adulthood. Primarily through social media, the study was conducted among the student population of Weber State University and our circles of influence to explore a possible connection. This study targeted adults aged 18-70 with varying genders, backgrounds, and education levels. 344 people completed the survey. A connection can be seen between the instances of abuse, neglect, and household dysfunction experienced as children and the quality of their romantic relationships as adults. The current study shows a strong negative correlation between ACE and ECR scores supporting our hypothesis. The average ACE score was 2.6 out of 10. The average ECR score 48.1 out of 68. with a significance of .000. This shows a strong negative correlation between ACE and ECR scores supporting our hypothesis.

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.

O'Grady, K.A., PhD; Yirenya-Tawiah, Abena; Stewart, Mason (Brigham Young University)
Faculty Advisor: O'Grady, Kari (Brigham Young University, Nutrition Dietetics and Food Science)

In light of recent high profile cases of sexual assault on university campuses, BYU's Organizational Psychology and Societal Resilience Lab explored aspects of sexual assault at faith-based universities. The unique climate of faith-based universities provides insight into the influence of gender role stereotypes and religious expectations on women's vulnerability to sexual assault within the hook-up culture. The lab conducted a qualitative meta-analysis of 25 articles about sexual assault at university campuses, sexual assault at faith-based universities, hookup culture and the roles dating apps play in encouraging hook up culture. Themes were analyzed for their consistency, intersectionality and cross-variability. Emerging themes indicated that hookup culture reinforces masculine stereotypes and hyper-masculinity. These sterotypes are associated with higher endorsement of rape myth beliefs. The anonymity and prevalence of dating apps on college campuses creates an avenue for sexual assaults to take place. The location aware aspect of dating apps also presents the opportunity for users to find those in close proximity, thus making hook-ups more convenient. These apps give users the opportunity to present themselves in socially desirable ways. There is a stark difference between the way women at faith-based universities tend to utilize dating apps than their male counterparts.

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.

Anderson, Brianna; Williams, Amanda; Collins, Lois; Hoover, Natalie Renee; Martinez, Samantha Coyne; Huang, Hui; Fernandez, Sofia; Rhoden, Michelle-Ann; Rigaud, Joseph; Kirk, Chris; Lewis, Rhonda; Nilsen, Corinne; Colvin, Deltha (University of Utah)
Faculty Advisor; Diener, Marissa (College of Social and Behavioral Science, Undergraduate Studies and Family & Consumer Studies)

Each year, approximately 25,000 youth "age out" of foster care (Courtney, Piliavin, Grogn-Kaylor, & Nesmith, 2001). These foster youth often face barriers to higher education. In Utah, fewer than five percent of foster youth go to earn a college-degree (Hahnal; 2007; Dworsky, Napolitani, & Courtney, 2011). Foster youth who could pursue a bachelor's degree may not be encouraged to do so, as the adults surrounding them may underestimate their potential (Dworsky & Perez, 2010); Vacca, 2008). Despite the challenges youth in foster care face in the pursuit of higher education, many succeed and take advantage of education programs. A study reported that over 70% of foster youth aged 15 to 19 years old reported a desire to go to college, and an additional 19% reported a desire to attend graduate school (Tzawa-Hayden, 2004). The goal of the present study was to develop a better understanding of how to better support youth and address barriers in achieving higher education and to empower foster youth to have a voice in the system. The study interviewed 15 adults who were formerly in foster care, 10 foster parents, and 9 foster care stakeholders. In addition, interviews were audiotaped and transcribed verbatim. Transcripts were coded using qualitative techniques. Themes identified were strengths of foster youth, emotional impact of foster care, and foster care best practices. These data will be used to inform the University of Utah First Star program about areas for improvement in the pathway to higher education they create for their students. This research study will provide insight into the facilitators and barriers to higher education from multiple perspectives and will empower foster youth to advocate for themselves through the use of narratives of adults formerly in foster care, whose voices are often excluded from foster care research.

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.

Geist, Claudia; Collins, Saffron (University of Utah)
Faculty Advisor: Geist, Claudia (Social and Behavioral Sciences, Sociology)

Unplanned pregnancies can have negative effects, especially in poor communities. There is little research about the perceived impact of a hypothetical pregnancy. Understanding individuals' ideas about how unplanned pregnancies might affect their lives will help us understand contraceptive behavior and ideas about family formation.

We explore the perceived impact of a hypothetical pregnancy among individuals who participated in the HER Salt Lake Contraceptive Initiative (Sanders et al., 2018). We coded 800 responses to the question "Please tell us a bit more about how a pregnancy now or in the next few weeks would affect your life." A desire to avoid pregnancy for the next year was an enrollment criterium, so most participants had negative feelings about a hypothetical pregnancy. However, we found that the kind of anticipated impact varied.

The most common response was a worry about financial resources (30.6%), followed by educational goals (20.4%): "It would stop my plans of going to graduate school and hurt my financial situation greatly. It would hurt my current relationships with partners and family and would be very emotionally and physically stressful." "Pregnancy now would rock my world. I am a single mom of 2 toddlers who's going to school part time and working part time. If I were to become pregnant now or in the next few weeks I wouldn't be able to accomplish the goals that I have set for myself." About 16.9% of participants mentioned negative impact without being specific. However, 5.4% of the respondents reported positive thoughts about a hypothetical pregnancy.

Our study may help scholars and medical providers get a better understanding of the precursors of decision-making processes for contraception and family planning. It will also illustrate where individuals faced with an unplanned pregnancy may need support.

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.

Dallon, John; Neubert, Nathaniel; Evans, Emily (Brigham Young University)
Faculty Advisor: Dallon, John (Brigham Young University, Mathematics); Evans, Emily Brigham Young University, Mathematics)

The organization of collagen fibers within the various connective tissues of the body plays an important role in the functionality of the organs they support. While the biochemical composition of collagen lattices is largely understood, it is difficult to study how the microstructural organization of collagen affects the macroscopic tissue properties. In this project we computationally stretch stochastically generated lattices consisting of nodes joined by spring like connections representing the fibers of a collagen lattice to examine how varied nodal connectivity, fiber length and fiber orientation affect the Young's Modulus of the lattice. This information will aid biologists in the production of synthetic lattices by providing a guideline of parameters that are most important to control in the creation of lattices with specific desired properties. This in turn will provide insights into bioengineering, wound care and other medical sciences.