We show that a discrete two-dimensional logistic predator-prey dynamical system with two parameters undergoes a Neimark-Sacker bifurcation under certain conditions. Our evidence includes numerical computations of orbits and bifurcation diagrams.

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.