Hilbert Reciprocity over Number Fields

A Hilbert symbol has the value 1 or −1 depending on the existence of solutions to a certain quadratic equation in a local field, R, or C. Hilbert reciprocity states that for a number field F and two nonzero a and b in F, the product of Hilbert symbols associated to a and b at all the places of F is 1. That is, these Hilbert symbols are −1 for a finite, even number of places of F . Hilbert reciprocity when F = Q is equivalent to the classical quadratic reciprocity law, so Hilbert reciprocity in number fields can be considered an extension of quadratic reciprocity to all number fields. This thesis presents a proof of Hilbert reciprocity in all number fields and then uses it to derive a quadratic reciprocity law in three quadratic rings that resembles the quadratic reciprocity law in Z, both in terms of Legendre symbols and Jacobi symbols

On the Exact Helium Wave Function Expansion, II, an exponential modulated form

A 11S wave function’s expansion for 2 electron atoms and ions is proposed employing an appropriate exponential factor and Fock’s logarithmic terms. The leading coefficient’s are presented

Incorporating Avoiding Plagiarism into a Drug Information Course

Background: Maintaining academic integrity is a priority for professional pharmacy programs, but fitting this topic into the curriculum can be a challenge. In the absence of a medical writing course, our institution uses a drug information course to introduce students to the topic of avoiding plagiarism. The professor of this course approached their librarian for ideas on improving the way this topic had historically been presented. The librarian used an existing resource to build a LibWizard tutorial on avoiding plagiarism that is tailored to the PharmD curriculum. Description: The tutorial includes 24 slides that present information and are accompanied by knowledge check questions. The tutorial is completed asynchronously by the students and then discussed in a synchronous class session. Concepts covered include but are not limited to: defining plagiarism, unintentional plagiarism, incorporating common knowledge and opinions, referring to sources in written work, using images, fair use, detecting plagiarism, and consequences of plagiarism. We also point out that common knowledge within the pharmacy field is different versus that of the general population. After the appearance of various AI chatbots in recent years, we felt it was important to add a slide on guidelines for using these tools in an academic setting. The tutorial has been used by three PharmD classes since Fall 2021 (286 submissions). It also has come to serve as a source that any student or professor in the school can use as a refresher when plagiarism issues arise. Conclusion: We will present selected slides from the tutorial and discuss general trends regarding topics that the students understood well and what they appeared to struggle with, including what constitutes plagiarism and incorporating sources via quotation, paraphrase, and summary

Characterization of Developmentally Downregulated Nfe2l3 in Retinal Ganglion Cell Survival and Axon Regeneration

Retinal ganglion cells (RGCs) are central nervous system projection neurons essential for transmitting visual information from the eye to the brain. Damage to RGCs, caused by conditions such as glaucoma and traumatic optic neuropathy (TON), may lead to vision loss or blindness, as adult RGCs lack regenerative capacity. This study focuses on Nfe2l3 (Nrf3), a developmentally downregulated transcription factor known to mediate cellular responses to oxidative stress, a key pathological event following optic nerve injury. We hypothesized that overexpressing Nfe2l3 in RGCs would enhance their survival and promote axon regeneration after optic nerve crush (ONC) injury. To test this, we utilized an AAV2 vector to overexpress Nfe2l3 in RGCs and assessed its effects on RGC survival and axon regeneration in vivo. Results showed a significant increase in RGC survival (approximately 20% compared to controls) and robust axon regeneration, with fibers extending around 3 mm beyond the injury site. These findings indicate Nfe2l3’s potential as a therapeutic target for optic nerve repair and treatment of vision loss due to RGC damage

UConn Baseball Reliever Lane Optimization Tool

The building of a tool to be utilized by UConn’s Division I baseball team that will generate a game plan for when different relievers should be used against different parts of the opponent’s lineup to achieve the lowest total expected value of runs allowed for the remainder of the game based on game situations and matchup probabilities. The tool will also examine and determine situations that may be vital enough to the outcome of the game to bring in a better reliever normally saved for later in the game

Nondelegation and Native Nations

There is no nondelegation doctrine for Native nations, nor should there be one even if the Supreme Court revives the nondelegation doctrine for federal agencies and private parties. The Court has never struck down a statute on the ground that it delegated legislative power to a Native nation. Instead, it has held that Congress may recognize the sovereignty of Native nations and that their independent authority sustains statutes that rely upon Native governments to implement policy goals that they share with the United States. The Court’s deferential approach is consistent with the rational-basis standard of review that applies to Indian affairs statutes. The jural argument against a nondelegation doctrine is that the sovereignty of Native nations distinguishes them from federal agencies and private parties. The functional argument against a nondelegation doctrine is twofold. First, the functionalist justifications for restricting Congress’s authority to rely upon Native nations to implement shared goals are unconvincing on their own terms. Second, a robust nondelegation doctrine would undermine Congress’s capacity to fulfill the federal government’s obligations to support tribal self-government. This is the answer to the most trenchant critique of the Court’s jurisprudence concerning delegation and Native nations

The Mature Minor Doctrine and COVID Vaccination in Connecticut

The mature minor doctrine is an exception to the common law rule of parental informed consent for a child’s medical decisions. The mature minor doctrine is applicable as either doctrine or statute in some states, but not all. Connecticut currently upholds the common law view for a minor child’s medical decision-making authority. Consequently, one prominent topic of discussion in recent years deals with the Covid-19 pandemic and the public policy discussions over nation-wide vaccination efforts. Many minors, children legally under the age of eighteen, are looking to make their own medical decisions when dealing with vaccination for the Coronavirus. By expanding the parameters of the mature minor doctrine, and implementing it into Connecticut statute, mature minors can be given the autonomy to acquire, or resist, vaccination despite their parent’s wishes. Although there has been a history of case law favoring parental authority over children, psychologists and legal scholars have brought to light new studies demonstrating adolescent development and capacity with understanding medical treatment. Furthermore, other northeastern U.S. states have gradually started to recognize mature minors in the context of vaccinations. As with any new introduction of a rule to a particular state, Connecticut legislation and courts must weigh the benefits, as well as the potential drawbacks that the mature minor doctrine may bring to light. Overall, the mature minor doctrine is a complicated doctrine, and it includes many different competing interests. However, if applied correctly, the doctrine can help competent and capable minors to make their own informed medical decisions in the state of Connecticut

Understanding Human Statistical Learning in Language Acquisition: Insights from Neural Networks

This project explores how the cognitive mechanisms associated with human statistical learning in language acquisition align with computational processes in three kinds of neural networks: feedforward networks (FFN), simple recurrent networks (SRN), and long short-term memory (LSTM) recurrent networks. Prior research in infants has provided evidence of statistical learning in discovering word boundaries within continuous spoken speech. Replicating statistical learning tasks using neural networks could allow for a better understanding of the fundamentals of these parallel processes in our brains and neural networks alike. This project tested the ability of FFNs, SRNs, and LSTMs to make syllable-by-syllable predictions from sequential data in order to determine if the network could accurately attune to word-like structures. Preference for words over part-words and non-words was measured to see if the network could understand transitional probabilities in the same way that human infants can. The results showed that all three networks could perform as well or better than infants on the same word segmentation tasks, where the LSTM was able to achieve the highest proportion better values for both non-word and part-word tasks, followed by the SRN, and finally the FFN. These results suggest that neural networks, specifically the LSTM, develop internal structures that could behave analogously to the cognitive mechanisms behind human statistical learning in human language acquisition. Additionally, they may provide a foundation for continuing work where I will investigate the limits of each network using more complex learning paradigms

Understanding the Role of Minor Intron Splicing in Spermatogenesis

The minor spliceosome is composed of the unique small nuclear RNAs (snRNA), U11, U12, U4atac, and U6atac, and is necessary for the splicing of less than 0.5% of introns, termed minor introns. Minor intron containing genes (MIGs) regulate diverse processes, one of which is spermatogenesis. Specifically, 111 testis-specific MIGs have been identified, suggesting that minor splicing is necessary for spermatogenesis. To interrogate the role of minor splicing in spermatogenesis, we conditionally ablated the Rnu11 gene, which encodes for the U11 snRNA, in the developing testes via Stra8-iCre, creating a Rnu11Flx/Flx::Stra8-Cre+ mutant. We found, at postnatal day (p) 42, the mutant testes are smaller than the wildtype (WT). Assay for cell death confirmed that U11 ablation results in cell death in the mutant at 6 weeks of age. Lastly, we found that our mutant resulted in varying spermatogenesis defects, such as an increase of asynchronous meiosis and a decrease in differentiating cells. Despite this, meiotic recombination can still occur in these mutants, concluding that U11 is important but not essential for meiotic recombination. This work is the first study to assess the importance of minor splicing in spermatogenesis which is underscored by the phenotype observed when the minor spliceosome is inhibited. Furthermore, the importance of studying spermatogenesis is highlighted by a decrease in sperm count over the last decades, which contributes to rising rates of male infertility

Practiced Peril: The Flawed Role of Experience in Accidental Death Determinations

Words often carry an intuitive meaning that defies explicit definition. While this vagueness typically poses no issue in our daily lives, it presents distinct challenges within the legal realm where words and their definitions wield the power to influence the course of justice. One abstract concept is notoriously elusive: what is an accident? Despite the apparent simplicity of identifying what is commonly understood implicitly, there are inherent challenges in “giving substance to a concept which is largely intuitive.” The Wickman framework was crafted to navigate these challenges, recognizing that an insured’s background, experience, and skill in a particular activity may shape their perception of risk. However, with this deference comes the potential for imbalance—under Wickman, it’s not the average person’s viewpoint that matters, but rather how the insured, with their unique characteristics, interprets the danger. When applying the framework, a focal point has emerged: the significance of prior successful practice of the ultimately fatal activity. If an insured has previously engaged in the activity and survived, subsequent death from that activity is often deemed accidental because prior survival indicates a subjective belief of continued survival. The existence of prior successful practice weighs heavily on the court’s perspective of the chain of events and, thus, its determination of accidental death. This becomes complicated when analyzing fatal first-time undertakings, i.e. intentional acts not committed by the insured before that which ultimately caused their death, leading to questions about the temporal and experiential aspects of the insured’s actions