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Sphere Packings through Persistence Homology of Root Lattices
No full texthttps://rdc.reed.edu/v1/resources/e90b81df-0d28-4741-af86-38f80d4c8928/thumb/128.jpgDespite the simplicity of the shape, the problem of densely packing spheres in space remains open today. Since the time of its introduction by Newton, work on this problem has developed substantially and included a wide range of mathematical techniques. In this thesis we explore these packings via an introduction to some lattice theory and root systems. Traditionally, root systems are core to the study of Lie algebras, however we investigate different applications than the typical use. Additionally, we leverage some algebraic and topological techniques, looking at the structure of persistence homology of simplicial complexes on root systems
(2,ℝ) Version of Oscillation Representation and its relation to Quantum Physics
No full texthttps://rdc.reed.edu/v1/resources/0a371ce6-bb2d-437b-999a-217ea96ae5d4/thumb/128.jpgThis thesis focuses on the construction of representations of (2,ℝ) in polynomial space and in Schwartz space. First, we define the Lie algebra (2,ℝ) and its standard generators , , ℎ along with their Lie bracket relations, verifying their action on polynomial spaces. Then, by constructing lowest weight vectors, we obtain an irreducible representation and prove that second-order weight chains decompose into at most two lowest weight chains, thereby revealing the decomposition of higher-order weight chains and completing the representation in polynomial spaces. Considering the important role of Schwartz space in distribution theory, in order to extend the (2,ℝ) representations from polynomial space to Schwartz space, we apply the Cayley transform to introduce new generators , , on the Schwartz space and construct their lowest representation chains, thus constructing some representation of (2,ℝ) in Schwartz space. Although this thesis does not further verify, some experts using the Fock model have demonstrated the commuting action of (2,ℝ) and the orthogonal group (), proving that this representation exhaust all representations on the Schwartz space. Finally, using the property that (2,ℝ) raises and lowers by two orders at each time, we find that a type of Schwartz equation—the harmonic oscillator general solution—constructed from Hermite polynomials multiplied by Gaussian functions, preserves parity during the raising and lowering process. This proves that (2,ℝ) can decompose the solution space of the harmonic oscillator into non-mixing even and odd subspaces.This property corresponds to the structure in quantum mechanics where parity symmetry divides the state space into even-parity and odd-parity subspaces
“Lights Are Gonna Find Me:” Creating a Reactive Lighting Control Scheme
No full texthttps://rdc.reed.edu/v1/resources/c3ca020c-d720-44e0-b76e-73b23409cbd2/thumb/128.jpgI propose a stereoscopic vision system to track a performer in a theatrical space, and cover the process to creating such a software. Part of that includes an overview of photogrammetry, and the process for calibrating cameras, locating objects in three-dimensional space, and positioning a light in said space. This project is informed by hundreds of years of innovation in lighting control that has culminated in a system that forgoes the need for human operators, and is essentially "perfect." However, this "perfect" system is not a "living" or "live" system, which disconnects it from the performers
Everyday Violence or Tragedy?: Race and the Media Construction of Mass Shootings in Illinois
No full texthttps://rdc.reed.edu/v1/resources/a54556ac-1211-416d-8a41-17b67fd55618/thumb/128.jpgGun violence occurring on the South Side of Chicago has been extensively documented in the news media. However, despite the prevalence of these incidents targeting inner-city minority communities on the South Side, there have been few calls for structural policy change at the state level to address this issue. Conversely, shortly following the mass shooting at the 2022 4th of July Parade in Highland Park, Illinois, which impacted the residents of an affluent, white suburb, the State promptly implemented an assault weapons ban in the aftermath. This thesis emphasizes the racialized ways the news media frames mass shooting incidents in Illinois as a reason behind the disparate public response to such violence. Based on a comparative analysis of the construction of mass shooting incidents in newspaper articles on Chicago’s South Side and the Highland Park incident, I argue that the differences in the framing of mass shooting is a racial project, which socially normalizes gun violence in minority communities and thus justifies the lack of responsive action. The media narratives pathologize minority groups as responsible for gun violence in their communities, while framing non-urban shootings in white communities as tragedies. As a result, the victims of suburban shootings are recognized and remembered in the media. However, the symbolic perversity of racialized reporting of gun violence incidents in Illinois renders the suffering of predominately Black, inner-city victims illegible and habitual. Ultimately, established attitudes and perceptions of the incident as curated by the news media contribute to the disparate public and political responses that shape policy outcomes
ov' è questa giustizia che 'l condanna?": The Paradox of the Virtuous Pagans in Dante's Commedia
No full texthttps://rdc.reed.edu/v1/resources/6fb3278f-6bc5-4e04-aabc-3a5c0b4b442a/thumb/128.jpgVirtuous pagans, as Dante Alighieri portrays them in the Commedia, are pagans who died free of personal sin but are damned because they had no way to know of Christ and therefore lacked faith. Dante’s portrayal of the virtuous pagans creates an urgent ethical paradox, a tension that lies at the heart of the Commedia: how can it be just for God to refuse grace to someone despite their merit and purely for reasons beyond their control? Drawing on the detheologized formalism of Teodolinda Barolini, as well as historically and theologically-located analysis Amilcare Iannucci, Kenelm Foster, and Vittorio Montemaggi, this thesis examines how Dante constructs the paradox as a paradox, how he emotionally invests the reader into the plight of the pagans through Virgil, and how he answers the question—or rather, why he doesn’t. Special attention will be paid to Paradiso XIX, where the Pilgrim is rebuked for asking about the justice of damning the pagans in an episode whose exceptional nature has yet to receive the attention it deserves from critics. The conclusion will argue that the justice of damning the pagans remains invisible because Dante himself could not find it; thus, the Pilgrim and the Reader must make peace with the paradox by placing their faith in God that it does, in fact, have an answer
Some Approaches to Hilbert-Kunz Multiplicity
No full texthttps://rdc.reed.edu/v1/resources/4df3a5c2-b86e-4e42-88e4-1b42285ceaf1/thumb/128.jpgWe investigate some methods in the computation of the Hilbert-Kunz multiplicity, a statistic that detects regularity of rings, analyzing specifically quotients of polynomial rings in positive characteristic. After giving the background necessary for our investigation and defining Hilbert-Kunz multiplicity, we describe results in the study of 'p-fractals' defined in "p-Fractals and power series–I. Some 2 variable results" by Paul Monsky and Pedro Teixeira. We then construct a module that detects an important behavior of the Hilbert-Kunz function of powers of a polynomial, before using conjectural properties of the module to put forward potential behaviors of the Hilbert-Kunz function on some general classes of diagonal hypersurfaces
Becoming a Body of One's Own
No full texthttps://rdc.reed.edu/v1/resources/2f582097-214b-4d34-ae03-ddcb16995972/thumb/128.jpgA hybrid collection
Using Machine Learning to Predict Reading Comprehension Based on Demographic Factors
No full texthttps://rdc.reed.edu/v1/resources/85cf87b5-aa38-40f9-b79f-4f7ac79b5163/thumb/128.jpgThis thesis explores the intricate relationship between demographic features and text readability, employing machine learning (ML) models to predict comprehension levels. Traditional readability metrics often fail to account for reader-specific factors; thus, this research integrates demographic variables such as age, education level, and first language to enhance prediction accuracy. Utilizing crowdsourced data from Prolific, our study analyzes reading comprehension across diverse reader profiles. We present a comprehensive methodology, including experiment design and data collection procedures, to examine the impact of demographic features on readability. By incorporating ML models like Decision Trees, Random Forests, and Deep Neural Networks, our research offers novel insights into the factors influencing text comprehension. We also discuss the challenges in applying ML to readability prediction, emphasizing the importance of data quality and model interpretability. Overall, this research contributes to a more nuanced understanding of readability and paves the way for advancements in educational technology
Rethinking Plant-Based Foods: Obstacles to Broad Adoption of Plant-Based Diets
No full texthttps://rdc.reed.edu/v1/resources/f1322dfb-2ca8-4e82-9ab7-900da87b6bf7/thumb/128.jpgThis thesis examines challenges of broader adoption of plant-based diets and the ways in which plant-based firms are addressing these obstacles. The research is presented in the form of a literature review and case studies on three firms in the plant-based food industry. Data was gathered from both information published online by the firms and one-on-one interview with a representative from the firms. The case study reveals that firms in the plant-based industry have integrated health food stores and are now shifting focus to expanding into other grocery stores in order to make plant-based alternatives. This thesis also provides the perspective of a producer regarding challenges and opportunities for improvement in the industry that is supported by the academic literature for the plant-based food industry. Taste and higher price points for plant-based alternatives appear to be main deterrents for purchasing these products. The obstacle of taste is thought to be addressable through food science and efforts to mimic animal-based products. However, this will require continued funding and time. Making plant-based products more financially feasible by way of setting competitive price points is less straight forward and could be explored in further research of this industry
The New, Womanly Jewish Man: Leopold Bloom’s Public and Private Negotiations of Jewish Identity in James Joyce’s Ulysses
No full texthttps://rdc.reed.edu/v1/resources/ac3ade88-8a4b-4640-bf30-0bcaa57c48ec/thumb/128.jpgThis thesis concerns James Joyce’s modernist novel Ulysses and explores the unsettled Jewish identity of its hero, Leopold Bloom, and highlights the complex connotations about gender and sexuality this identity conjures within the narrative. My first chapter analyzes how Bloom’s Jewishness is defined and questioned externally and internally within the text, and primarily concerns the chapters “Hades” and “Cyclops” which highlight Bloom’s position as a social outcast in Dublin. I ultimately conclude that Bloom’s identification with Jewishness only concerns how others view him. My second chapter analyzes the turn-of-the-nineteenth century association of Jewish masculinity with femininity and homosexuality. I argue that Bloom’s position as a cuckold places him as sexually inferior to his peers, shown in the “Sirens” chapter, and that the “Circe” chapter uses his Jewish identity and cuckoldry to explore the associated connotations of culturally assigned feminine traits such as emotionality, gentleness, and submission