In this paper, a novel model of Hotelling duopoly is introduced that explains horizontal product variety as the result of consumer preferences, expanding on and meshing the works of Hotelling (1929) and Neven (1985). From this model, two opposing forces from consumer preferences are found that impact the variety and price decisions of firms: market share revenues and price revenues. As firms face consumers with highly linear (weak) preferences over variety, the profit incentive is to simply capture the market by offering products that appeal to the middle consumer. However, as firms face consumers with highly quadratic (strong) preferences over variety, the profit incentive is to carve out and exploit a market segment by offering a distinct variety. Thus, observed product variety between minimal and maximal differentiation is emergent from consumer preferences, as firms face a balance of price and market share incentives.

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.

Puberty is a critical stage in the human life course. Specifically, puberty is the physiological transitionary period that marks the beginning of human reproduction capability. These physiological changes are markedly different in boys and girls and accordingly typically occur on different timelines. Furthermore, these timelines are not a set guideline for every child as some may develop earlier and others later. This age of onset is a general range that has been observed and considered to be the normal age of onset. The normal age of onset of puberty is typically between ages 8 and 13 for girls or 9 and 14 for boys (Brito & Latronico, 2015, 93). Any development seen before these ages is typically defined as early onset and development seen after is late development. Professionals have further defined different stages of puberty in both boys and girls. In girls, this involves breast development, body hair growth, changes in height and weight, and menarche (Wheeler, 1991, pg. 2). In boys, pubertal development often involves genital growth, body hair growth, deepening of voice, and growth spurts (6). Puberty onset has been a popular topic of study in the health sciences as the age of onset can indicate the impact of biological and environmental factors. In particular, inequality in research of pubertal onset, the effects of early/delayed onset, and race/ethnicity is of special interest. For instance, there is a lack of existing literature on the role that culture plays on pubertal onset in Latino youth. This analysis intends to investigate the relationship between the integration of Hispanic culture in children’s lives and pubertal onset.

We studied binomial edge ideals, which are at the intersection of graph theory and abstract algebra. Our focus was the multidegrees of these ideals, which contain valuable geometric information. We proved algebraic results that allowed us to write a closed formula for the multidegree of the binomial edge ideal of a graph based on combinatorial properties of the graph. Then we discovered methods to make the process more efficient. We concluded our research by using our results to find the multidegrees of the binomial edge ideals of many families of graphs.

It has been recently claimed that there is a local enhancement of neutrino-antineutrino asymmetry in the Cosmic Neutrino Background (CNB) near the surface of the Earth of order $10^{-4}$ due to the in-matter potential experienced by relic neutrinos. This asymmetry is significantly larger than the expected $10^{-9}$ from the baryon asymmetry and is a promising step towards detecting the CNB. However, this claim makes many simplifying assumptions to reach this outcome, the most significant of which is the geometry used to model the Earth. Here, we approach the problem with a more realistic geometry for the Earth, and we find that the neutrino-antineutrino asymmetry near Earth is $10^{-8}$, which agrees with other recently reported results from other authors}.

The specific and concrete motives to use social media are likely to grow as social media multiplies. Study 1 was conducted to identify the hierarchical structure of motives of using social media that explain a wide range of previously identified motives from Uses and Gratification theory (Katz & Blumler, 1974). College students (N = 948) completed previously established measures of social media motives and a range of social media behaviors. Findings revealed two higher-order factors: (1) “Instrumental” motivation captures motives to achieve a specific aim by using social media (e.g., for information, self-expression, social interaction) and these motives are positively correlated with private self-conscious on social media, and (2) “Experiential” motivation captures motives to escape from reality by using social media (e.g., for entertainment, passing time, convenience) and these motives are positively correlated with social media addiction. Study 2 aimed to determine if the higher order structure, “Instrumental” and “Experiential”, emerge across a wider range of motivations to use social media. College students (N = 216) completed a survey on the 7 social media motivations from study 1 and 16 more social media motivations found in the two pilot studies. Findings from the confirmatory factor analysis revealed the 23-factor model was the better predictor to use social media than the higher order factors. The predictive validity of the higher order factors suggests “Instrumental” motivation is the better predictor of personality and “Experiential” motivation is positively correlated with social media addiction.

Historical trends of artificial intelligence have, as shown by recent quantitative and qualitative studies, shown that the reported threats (as understood by the general public) are vastly different from the tech industry’s most pressing and vital concerns. The modern AI that most people interact with on a daily basis are mostly helpful commercialized products or generative AI, leading to a cultural mindset where AI is an assistant capable of autonomous tasks. Popular fictional depictions of artificial intelligence clearly demonstrate that those perceptions of threats fall closely in line with the sorts of actions portrayed by AI characters, suggesting that pop media has a significant influence over its audience’s understanding of AI technology and its potential ramifications. To mitigate harm that AI tools can inflict upon the general public, there is an immediate need for technology-specific legislation, incentives and deterrents, and oversight so that artificial intelligence can be regulated and controlled.

The field of neuroscience continues to grow in findings and opportunity. Similarly, this Honor’s Thesis aims to increase the diversity within the field. This children's book, Making Sense of Your Senses seeks to foster an early interest in the wonders of the brain by making neuroscience accessible to young readers through comprehensible text and entertaining illustrations.