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On a Higher-order Method for the Solution of Singular Polynomial Systems: Beyond Classical Newton’s Method
Get PDFPolynomial systems arise in many scientific and engineering applications, but classical Newton’s method can struggle when the system possesses a singular zero, where the Jacobian matrix loses rank. In such cases, Newton’s iterations may stagnate, converge slowly (linearly rather than quadratically), or fail entirely. To address these difficulties, we introduce a single-parameter regularization framework: we deform the original polynomial equations by adding a small positive parameter, thereby removing the immediate singularity. As the parameter decreases to zero, we smoothly transition back to the original system while preserving nonsingularity for most parameter values. This approach both stabilizes the Newton iterations and provides a continuous solution path. Further, we develop higher-order predictor–corrector techniques that exploit additional derivative information, enhancing the local convergence rate near singular solutions. Numerical experiments illustrate that our single-parameter regularization and higher-order techniques can potentially improve convergence reliability and speed, particularly around singular points, compared to the use of Newton’s method alone.Bachelor of Scienc
Effects of fish oil on omega-3 and omega-6 levels across lipid depots in humans
Get PDFBackground
Eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids have anti-inflammatory properties and may improve health outcomes in inflammatory conditions. We previously demonstrated that fish oil supplementation in adults leads to an elevation in anti-inflammatory oxylipins in human adipose tissue. However, the localization of EPA and DHA in differing plasma lipid pools [phosphatidylcholines (PC), triglycerides (TAG), cholesterol ester (CE), and non-esterified (NEFA)] and the downstream generation of inflammatory oxylipins remains unknown.
Objectives
Herein, we extended this research to investigate the localization of EPA and DHA in differing plasma lipid pools [phosphatidylcholines (PC), triglycerides (TAG), cholesterol ester (CE), and non-esterified (NEFA)] and downstream generation of pro- and anti-inflammatory oxylipins.
Methods
We conducted a secondary analysis from our previous double-blind, placebo-controlled trial of 100 participants (aged 18–65), who were randomized to consume 3g fish oil (1.1g EPA + 0.8g DHA) or corn oil for 12 weeks. Here, plasma samples from a subset of the trial (n=21) were analyzed using gas chromatography and mass spectrometry to respectively quantify fatty acids and downstream oxylipin profiles before and after supplementation.
Results
Significant increases in EPA and DHA were identified within the PC and TAG pools. EPA substantially increased in the CE and NEFA pools, whereas DHA remained unchanged. Additionally, fish oil consistently reduced omega-6 PUFA levels across all lipid pools except for TAG. We also observed significant shifts in circulating oxylipin profiles post-supplementation, with increases in anti-inflammatory mono-hydroxylated oxylipins (e.g., 5-HEPE, 15-HEPE, 17(S)-HDHA) and reductions in pro-inflammatory oxylipins (e.g., 12-HHTrE, 12-HETE, TXB2).
Conclusions
Collectively, these findings provide valuable insights into the control of plasma fatty acids and oxylipins by supplemental omega-3 PUFAs, with potential benefit to improving systemic inflammation and health. Further studies are needed to evaluate relationships between these changes in PUFAs and oxylipins, and markers of inflammation and health.Bachelor of Science in Public Healt
Spaced Out: Attention Deficit Hyperactivity Disorder at Home
Get PDFClinical researchers developed attention deficit hyperactivity disorder (ADHD) from observations of impaired self-regulation in school aged children. These conceptual roots influenced the modern cognitive-behavioral understanding of the condition, which appears in all settings and across the lifespan. But the prevalence of medicalized perspectives on ADHD has limited our understanding of the condition. Drawing from neurodiversity and critical disability studies frameworks, this project explores visual and spatial conceptions of ADHD at home through an analysis of comics and a series of interviews with adults who have ADHD. I argue that experiential knowledge and an emphasis on interpersonal and material contexts can provide a better understanding of ADHD-related support needs and compensation strategies in home environments. Bachelor of Art
Khi ta sống, làn thơ thở theo ta - When i live, the poem flows through me
Get PDFin this year-long thesis project, i investigated what it means to be a poet who is the intersection of so many marginalized identities: queer, Vietnamese, Asian-American girl who attends UNC-Chapel Hill.Bachelor of Art
Evaluating Multiple Diagnostic Tests with and without a Gold Standard
Get PDFBackground: Diagnostic tests are central to clinical decision-making, yet their evaluation often relies on a gold standard —an assumed true label—which is usually partially missing, imperfect, or not available. Traditional methods assume full gold-standard data, limiting their applicability in real-world settings where reference data are incomplete, as in large-scale systematic reviews or clinical diagnostics with ethical or logistical constraints. Our main interest lies in applying these methods to study screening in systematic reviews using large language models (LLMs).
Methods: We conducted simulation studies to compare the performance of several statistical methods—including latent class analysis (LCA), logistic principal components analysis (logistic PCA), and standard PCA—in evaluating diagnostic tests without access to gold standard data. Simulations were based on 10 binary diagnostic outcomes across varying sample sizes (400 to 10,000 observations). Performance metrics included sensitivity, specificity, and mean squared differences between true and estimated item-response probabilities. A real-world dataset of systematic review screening data was also analyzed, with pre-processing to handle missingness.
Results: Logistic PCA combined with k-means clustering showed great accuracy. However, it explained only ~52–53% of variability, suggesting limited ability to capture latent diagnostic structures. The difference in performance between PCA and LCA was minimal even though the data generation model was a LCA model.
Conclusions: Existing methods provide partial solutions but are limited by assumptions about the data generation model. Future work should focus on developing approaches capable of handling partially missing gold standards, incorporating flexible missing data mechanisms, and scaling to larger numbers of diagnostic tests, and considering more extensive simulation scenarios (proportion of missingness, data generation model, proportion of gold standard data). Ultimately, our goal is to design a method that not only evaluates multiple diagnostic tools under uncertainty but also combines them into a more accurate composite test.Bachelor of Science in Public Healt
Reconciling Kantian Marriage and Misogyny
Get PDFBecause Kant’s sexism and racism “ramifies throughout his practical philosophy in the ethical, political, and cosmopolitan spheres,” Charles Mills argues that it is impossible to “bracket off the racism” and assimilate those who Kant viewed as sub-human to full status as human beings. I believe that Kant’s sexism and racism do affect his theory but that we can do our due diligence of attending to his prejudicial views and their bearing on his moral theory. If we do so, there is hope of salvaging a framework that is both recognizably Kantian and capable of illuminating the patterns and effects of historical and ongoing oppression. In this light, I will ask how we might develop one such framework for Kantian marriage. Ultimately, I argue for using Jeanine Grenberg’s model of Deontological Eudaemonism to reimagine Kantian marriage and resolve the tension between gender roles and the cultural demand for an egalitarian model of marital relationships.
[1] Mills, 2017, p. 10.Bachelor of Art
Portugal’s (post–)colonial pedagogy: A history of legitimization and “re”–imagination
Get PDFThis thesis works to explicate the positioning of colonial praxis within the Portuguese school over time—beginning with the dictatorship, and then moving through post-revolutionary phases, forward into the 21st century—paying close attention to textbook studies and policy reform in hopes of demystifying the context enabling this perceived inability to move past the fetishization of the colonial figures, as well as to understand what may have prevented a meaningful shift within the educational sector following the revolutionary period of transition after April 25th, 1974. This project gives special focus to the analysis of persisting colonial ideologies within present curricular structures, reform, goals, and documents to make clear how educational materials function as instruments of identity building and the possible implications that arise with a resident ongoing coloniality of power within these tools.Bachelor of Art
A quantification of behavioral patterns in sand tigers Carcharias taurus at four North Carolina shipwrecks
Get PDFSand tiger sharks (Carcharias taurus) aggregate at shipwrecks along the North Carolina coast, yet their behavioral patterns at these artificial reefs remain poorly understood. This study quantifies sand tiger shark movement and activity at four shipwreck sites, comparing daytime and nighttime behavioral observations. A total of 56 sharks were recorded, with 30 observed during the day and 26 at night. Analyses revealed significant differences in behavior based on time of day. During daylight hours, sharks exhibited higher activity levels, as indicated by increased tail beat frequency and movement away from the wrecks into open areas such as the sand and water column. In contrast, nighttime observations showed sharks in closer proximity to the wreck structure, with reduced tail beat frequency, suggesting lower activity levels. Statistical analyses, including chi-square tests and t-tests, confirmed that time of day significantly influenced both spatial distribution and movement patterns. These findings contrast with previous studies suggesting nocturnal activity optimization in poikilothermic predators, highlighting the potential role of artificial reefs in modifying shark behavior. The results emphasize the ecological importance of shipwrecks for sand tiger sharks, potentially serving as shelter sites or influencing social behaviors. Given the species’ critically endangered status and site fidelity to shipwreck habitats, conservation efforts should prioritize the protection of these artificial reefs. Continued monitoring and research, including collaborations with citizen science initiatives, will be essential for informing conservation strategies and understanding the longterm behavioral ecology of sand tiger sharks in North Carolina waters. Bachelor of Scienc
Optimization of Silicon Hybrid Photoelectrodes for Light-Driven CO2 Reduction
Get PDFModern energy demands and the threat of climate change necessitate the development of innovative and sustainable strategies for energy production. Renewable energy sources such as wind, hydro, solar, and geothermal offer promising alternatives to the combustion of fossil fuels, but they present challenges due to their reliance on ideal environmental conditions and the logistical difficulty associated with their energy storage. One novel approach to leveraging solar energy harnesses artificial photosynthesis to generate and store energy in the form of chemical bonds. This process can be accomplished via one or more electrochemical reaction(s) at the interface of a hybrid photoelectrode comprised of a visible light-absorbing semiconductor and a catalyst to reduce carbon dioxide.
In this work, sonochemical hydrosilylation was first leveraged to study the loading behavior of select Re-bipyridine(CO)3Cl catalysts on the surface of low-doped p-type silicon (111) before investigating the impact that the loading behavior of these complexes has on the photoelectrochemical performance of the resulting hybrid photoelectrodes. X-ray photoelectron spectroscopy confirmed covalent attachment of the relevant catalysts. 1H NMR spectroscopy and attenuated total reflectance-Fourier transform infrared spectroscopy supported the maintenance of the catalysts’ molecular integrity after sonication. Through analysis by inductively coupled plasma mass spectrometry, it was determined that a maximum surface coverage of approximately 0.25 nmol/cm2 of Re-bipyridine(CO)3Cl molecules is achieved by sonochemical hydrosilylation after ca. 5 hr. of sonication. Hybrid photoelectrodes featuring maximum surface coverage were then determined to have catalytic layers that are approximately 3 nm thick. Cyclic voltammetry, linear sweep voltammetry, and controlled potential bulk photoelectrolysis were finally used to confirm the catalytic activity of optimized hybrid photoelectrodes, report a photovoltage for such photoelectrodes of 406 mV, and determine a Faradaic efficiency for CO of 34% +/- 5%.
Bachelor of Scienc
X-marks the spot and hidden treasures in Drosophila meiotic recombination patterning: unearthing the role of specialized sites in assuring and patterning crossovers
Get PDFMeiotic recombination patterning is thought to be dependent on the location of a crossover event on a chromosome and distance to other events. Chromosomal aberrations result in disruptions to recombination patterning, with lower recombination rates near translocation breakpoints (Hawley, 1980). This reduction in recombination is not distance dependent, and instead is confined to within the interval between the two nearest "Hawley Sites," with recombination rates returning to wild-type levels beyond these sites.
To investigate the nature of these Hawley Sites, we measured recombination using genetic marker screens in female flies heterozygous for deficiencies spanning the 11A Hawley Site (HS11). We found that flies carrying deficiencies that remove all or part of HS11 exhibit reduced recombination globally, a reduction not attributable to missing genetic material within deficiency boundaries. Flies carrying deficiencies which did not remove HS11 had slightly reduced recombination rates, a reduction attributable to missing genetic material within deficiency boundaries. These provide insight into the factors regulating recombination patterning.Bachelor of Scienc