A Latin square is a nxn square that contains n different symbols, often numbers, and are arranged such that each symbol appears exactly once in each row and column. In this project, we look at the probability of a random arrangement of symbols being a Latin square. I start with n number of n symbols, for example a 3x3 square will contain the numbers 1,1,1,2,2,2,3,3,3 in a random assortment. Using counting methods and statistical estimation through Python, we discover the proportion of total squares that are Latin squares.

Geodesics are significant objects and a major topic in differential geometry. They are "straight" curves on surfaces that can locally represent the shortest path between two points. In this research, we employ the genetic algorithm, an optimization method in classical Artificial Intelligence, to construct a geodesic net on closed surfaces. A geodesic net is a network that connects multiple points with the shortest curves while ensuring that each point is ``balanced'' and stretched equally by its neighbors through those curves.

Despite the significant prevalence of food intolerances in children and adolescents (2 to 18-year olds), food intolerance mechanisms and testing is severely misunderstood and under researched. A food intolerance is a non-immunological response that occurs after consuming a specific food particle causing gastrointestinal (GI) issues such as bloating, nausea, diarrhea, and abdominal pain. The lack of understanding of food intolerances is causing too many children to unnecessarily follow unsupervised elimination diets which increases the risk of developing nutrient deficiencies. The objectives of this study were to demonstrate the serious impact to the quality of life (QOL) that food intolerances have towards children and adolescents by analyzing available literature and utilizing a case study participant. Findings suggested that there must be more research done to understand food intolerance to improve the QOL in children and adolescents.

Although there is an effective vaccine for SARS-CoV-2, or COVID-19, the virus is still spreading and affecting millions of people worldwide. SARS-CoV-2, along with many other viruses, is able to form large, multi-nucleated cells, known as syncytia. Syncytia formation, along with syncytia death, may affect the SARS-CoV-2 course of infection. We have been able to compute the death rate of syncytia using data from a study by Vanhulle et al. (2023) that used measurements of electrical impedence to study syncytia formation in cell-cell fusion assays. The death rate of syncytia was found using mathematical modeling. This knowledge can help further our understanding of syncytia and viral disease propagation.

Zinc Oxide (ZnO) nanoparticles are attractive candidates for application as antibacterial agents due to high biocompatibility with effectiveness against antibiotic-resistant strains of both Gram-positive and Gram-negative bacteria. Despite this potential, applications are limited by fundamental gaps in understanding of the underlying antibacterial pathways. ZnO nanoparticles are currently more widely used in antibacterial research compared to ZnO microparticles due to the potential for internalization into bacterial cells. Microparticles are nevertheless of interest as a research platform as the increased scale allows both the nonpolar and polar facets of the ZnO crystals to be distinguished. This in turn provides a useful platform to experiment on and study surface interactions with bacteria. In addition, because of their larger size, ZnO microparticles would not internalize inside typical bacteria, allowing for more targeted investigation of other, potentially more potent, antibacterial mechanisms.

Preliminary studies indicate that hydrothermally grown ZnO microparticles exhibit comparable antibacterial activity to commercial ZnO nanoparticles further adding to their utility. The goal of this research is to validate the nature of these behaviors by investigating differences in surface cleanliness between “home-grown” microparticles which were synthesized in the lab through a bottom-up hydrothermal growth method and commercial nanoparticles. Such differences may influence cytotoxicity, skewing the results of antibacterial studies. To do so, both Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectroscopy were used to probe the quality and cleanliness of the ZnO crystalline free surface of the microparticles and nanoparticles.

In this work we detected similarities in the vibrational modes at the surface stemming from ZnO growth precursors. These are seen to be similar across all samples investigated, however, a weak O-H bending is found in the home-grown microparticles. We demonstrate that these results justifies our low-cost hydrothermally lab-grown specimen as a suitable platform for future surface-specific antibacterial studies.