This thesis details a Python-based software designed to calculate the Jones polynomial, a vital mathematical tool from Knot Theory used for characterizing the topological and geometrical complexity of curves in 3-space, which is essential in understanding physical systems of filaments, including the behavior of polymers and biopolymers. The Jones polynomial serves as a topological invariant capable of distinguishing between different knot structures. This capability is fundamental to characterizing the architecture of molecular chains, such as proteins and DNA. Traditional computational methods for deriving the Jones polynomial have been limited by closure-schemes and high execu- tion costs, which can be impractical for complex structures like those that appear in real life. This software implements methods that significantly reduce calculation times, allowing for more efficient and practical applications in the study of biological poly- mers. It utilizes a divide-and-conquer approach combined with parallel computing and applies recursive Reidemeister moves to optimize the computation, transitioning from an exponential to a near-linear runtime for specific configurations. This thesis provides an overview of the software’s functions, detailed performance evaluations using protein structures as test cases, and a discussion of the implications for future research and potential algorithmic improvements.

Out of all of the participants in World War I, the most curious, in my opinion, is Great Britain. With the English Channel guaranteeing a navally superior Britain could guarantee its independence indefinitely, joining a world war does not seem like the obvious move to make. Despite this, on August 4th, 1914 Britain was at war with Germany. In my paper, I will argue that the invasion of Belgium provided the catalyst for a great power conflict due to the institutional, material, and personal realities that set the two nations on a collision course.

This thesis will explore the causality and link between Child Crisis Arizona (or “CCA'') and the applicability of the life-course framework. Child Crisis Arizona operates an emergency children’s shelter in Maricopa County, AZ, under the broader Arizona Department of Child Safety (or “DCS”) mission of providing safe and effective interventions for children at risk of being displaced from their homes. Utilizing a framework initially designed under a sociologist’s purview, the life-course perspective has evolved into a multidisciplinary approach to illuminate the complex nature of criminal behaviors, especially early in life in childhood. As such, the first section will detail the current issues regarding Arizona’s child safety system, the background of CCA, and the fundamental principles of the life-course framework to address how CCA provides beneficial results to a child’s life-course. The thesis will then discuss the policy measures provided by CCA that positively intervene in a child’s educational, medical, and other holistic developments. This is followed by examining the applications of CCA and course while incorporating various scholarly literature to link the two. The thesis will conclude with a brief discussion of this paper’s research limitations, future implications, and concluding remarks. Ultimately, this thesis highlights how children who go into Child Crisis Arizona’s emergency children’s shelter present significant potential of utilizing the event as a turning point to lead conventional lives through an early positive life experience.

It is my position that Kendrick Lamar takes a journey over the course of his album “To Pimp a Butterfly” (TPAB) that is similar to the journey taken by the prisoner up and out of the cave described by Socrates in the Republic. Using the structure and ideas of the Republic, I will provide a novel interpretation of the album that highlights Lamar’s transformation and development. The general lesson that I have learned by connecting these two works is that becoming a better person is a difficult and continuous process but also a fulfilling one. First, I will provide some points of context from the Republic and TPAB that are relevant to my argument. Second, I will identify the three stages of the cave prisoner’s ascent out of the cave and Lamar’s escape from Compton together. Third, I will split up the three stages into their own three chapters and show how Lamar’s three-staged journey is similar to the cave prisoner’s. To do this, I will propose shadows, statues, and forms present in TPAB. In each chapter, I will demonstrate using Plato’s tripartite model of the soul how each stage corresponds to one of the three stages of Lamar’s metaphorical metamorphosis on TPAB: caterpillar, cocoon, and butterfly. In the third chapter, I will bring everything together to show how a Platonic understanding of TPAB allows us to better understand the process of Lamar’s self-realization. In my conclusion, I will end with summary of what I have accomplished and the personal thoughts and lessons I have learned from assembling all of this.

Ice hockey is widely recognized as one of the most exciting sports to watch and the NHL boasts very good in-game attendance figures when compared to similar professional sports leagues. In this study, we compare the NHL to the NBA, two leagues that share the same size stadiums and in-game attendance numbers but show huge disparities in national television viewership. The most watched NHL game of 2022/23, game 5 of the Stanley Cup Finals totaled 2.72 million viewers nationally and the most watched NBA game of the 22/23 season was the final game of the NBA Finals totaled 17.88 million viewers nationwide. This is especially startling given the fact that on the local level, in cities with both NHL and NBA teams, the local rating are relatively even and oftentimes favor the NHL team. To investigate why this discrepancy exists, four cities that are home to both an NHL and NBA franchise were chosen as the focus of research. Youth participation and cost of both basketball and ice hockey were examined in each city and it was determined that they account for a large portion of the differences in national TV viewership. Marketing strategies of each league were also investigated, but it was found that these had little impact on the discrepancies in national TV viewership. The study concludes with possible solutions for the NHL to decrease costs and increase accessibility play, resulting in an increase in youth participation, especially in nontraditional hockey markets without NHL teams. In turn, this will bridge the gap in national viewership between themselves and the NBA.