Physical Sciences and Mathematics Commons^™

Generation And Dimension For Derived Categories, Pat Lank

Theses and Dissertations

This work focuses on problems regarding derived categories arising in algebraic geometry and commutative algebra. There are six chapters regarding generation in the bounded derived category of coherent sheaves over a Noetherian scheme. The targeted topics involve explicitly identifying generators, proving existence results thereof, and producing estimates on Rouquier dimension.

New Deep Learning Approaches To Classical Statistical Problems, Shijie Wang

Theses and Dissertations

The field of deep learning (DL) has received considerable attention in recent years. Thanks to rapid growth in computational power, the ability to collect massive datasets, and improvements in software and algorithms, DL is now routinely applied to areas as diverse as computer vision, natural language processing, and bioinformatics. At the same time, DL is only starting to be explored in the context of classical statistical inference problems such as bootstrapping, quantile regression, and mixture modeling. In this dissertation, we develop new DL methodology for three classical statistical problems: 1) weighted M-estimation, 2) joint quantile regression, and 3) mixing density …

Who Am I As A Learner? The Effects Of A Self-Regulated Learning Intervention On Ninth Graders’ Academic Self-Concepts And Intrinsic Motivation, Kaitlyn Elizabeth Bailey

Theses and Dissertations

The transition from middle school to high school is a notoriously difficult one, and a student’s success in ninth grade is typically a predictor of future success in high school. Unfortunately, many ninth graders struggle to engage in school. Despite their capability to complete the work, these students appear unmotivated and simply disengaged from school. In this action research case study, three students had the opportunity to share their education stories and the experiences that have shaped their academic self-concepts. These students also participated in a self-regulated learning intervention to determine if students’ feelings of autonomy, competence, and relatedness could …

Symmetries Of Del Pezzo Surfaces, Jonathan Smith

Theses and Dissertations

For each del Pezzo surface X of degree d, the action of the automorphism group Aut(X) on the exceptional curves of X induces a map ρ : Aut(X) → W(R_d), where W(R_d) is the Weyl group of a root system R_d dependent on the degree of X. The image of ρ is well defined up to conjugacy in W(R_d), so we say that a group G acts by automorphisms on a del Pezzo surface X of degree d if a representative of the …

Bayesian Joint Modeling Of Longitudinal Data And Interval-Censored Failure Time Data, Yuchen Mao

Theses and Dissertations

Longitudinal data are a collection of repeated observations of the same subjects at different points in time. Interval-censored data arise when the time to the event of interest for each subject is never exactly observed but known to fall between two consecutive points in time. Joint analysis of longitudinal data and interval-censored failure time data can lead to more accurate estimates compared to separate modeling when the correlation among events of interest or intracluster correlation is present. The aim of this dissertation is to develop efficient and reliable joint analyses of longitudinal and interval-censored failure time data using Bayesian methods. …

Building A Framework For Analyzing Non-Linear And Multidimensional Kinetics, Mainak Dhar

Theses and Dissertations

Many materials exhibit multiple rates of molecular relaxation due to structural complexities. Standard linear and one-dimensional kinetic cannot extract all the necessary dynamic information about these systems. This dissertation contributes to an overarching scheme to develop new non-linear and multidimensional kinetic experiments to obtain this information. The studies span computation and experiments, picosecond to second timescales, and both single-molecule and pulsed-laser kinetics

Single-molecule kinetics experiments yield time series that contain information about unique structural and dynamic properties of materials. However, these time series are noisy, and data analysis is challenging. Parametric methods are computationally intensive and require strong, unverifiable assumptions …

On Finite Groups With Essential Dimension 2 Over ℚ, Michael Huggins

Theses and Dissertations

We determine all finite subgroups of Aut(X) which have essential dimension 2 over ℚ, where X is a minimal Del Pezzo surface of degree at least 5. Additionally, finite groups with essential dimension 2 whose order is divisible only by the prime numbers 2 and 3 are classified with the exception of the groups dic ₁₂ , C₁₂, and Dih₂₄, whose essential dimensions remain unknown, but may possibly be equal to 2.

Expanding Tailored Nanomaterials With Precise Spatial And Morphological Control, Mengxue Zhang

Theses and Dissertations

Multicomponent nanocomposites with precise spatial control are important for diverse fields spanning from energy conversion to optoelectronics and catalysis. Traditional methods using hydrophilic interactions alone are limited to random mixtures when multiple nanoparticle (NP) types are combined. To improve capabilities, a new strategy for polymer micelle design combining orthogonal hydrophilic (H) and fluorophobic (F) interactions to independently control two distinct NP populations was developed.

Initial research aimed at understanding F-interaction adjustments, which further enabled the switchability of FNP distribution states (dispersion vs aggregation) within polymer films through immersion annealing. Next, dual-NP assembly was examined using a diblock poly (H-b-F) where …

Generalized Sierpiński Numbers And New Irreducibility Criteria On Legendre Polynomials, Robert Scottfield Groth

Theses and Dissertations

A Sierpiński number is an odd positive integer k such that k·2n +1 is composite for all n ∈ Z+. Similarly, a Riesel number is an odd positive integer k such that k · 2n − 1 is composite for all n ∈ Z+, and a Brier number is a number that is both Sierpiński and Riesel. In this dissertation, we consider a generalization of a Sierpiński number and establish their existence by showing, for every fixed A ≥ 2, there are infinitely many odd positive integers k such that the k · an + 1 is composite for every …

Explorations Of Multi-Carboranyl Thiols And Phosphines, Jared Ross Riffle

Theses and Dissertations

In order to ascribe the impact of substituent groups on the bis-ortho-carborane, closo-{C2B10}-closo-{C2B10} multi-cluster system, the first sulfur-containing biscarborane derivatives were synthesized. Biscarborane dithiol, disulfide, bis(methyl)thioether, as well as multiple dithiolate salts were structurally characterized. The exceedingly long C–C bonds and shortened C–S bonds in biscarborane dithiol and its doubly deprotonated dithiolate salts are indicative of significant delocalization of electron density from the sulfur atoms into the cluster. Additionally, a new concept of ligand ambiphilicity is described where, instead of the involvement of only a single center in a ligand, this amphiphilicity relies on the redox behavior of the indirectly …

Stability Of Space-Time Finite Element Discretizations Of Subdiffusive Time-Fractional Differential Equations, Gabriel Kenneth Staton

Theses and Dissertations

The study of anamolous diffusion, and in particular of subdiffusive time-fractional differential equations, is of great interest for its ability to describe transport of particles through porous media. The time-fractional derivatives in these problems are nonlocal, which notably hinders performance of classical time-stepping methods. As a result, there is significant interest in using simultaneous space-time discretizations for these subdiffusive problems, which have the additional benefit of significantly relaxing the regularity requirements for candidate solutions. These types of Petrov-Galerkin schemes require a careful choice of discretized trial and test spaces in order to guarantee stability; in particular, the usual Galerkin choice …

The Design And Optimization Of Optical Systems For The Detection And Characterization Of Phytoplankton, Caitlyn M. English

Theses and Dissertations

Phytoplankton are among the smallest organisms found in marine and freshwater ecosystems. Despite their small size, phytoplankton play a vital role in sustaining life on Earth as primary producers. Through oxygenic photosynthesis phytoplankton are also responsible for large scale carbon fixation and oxygen production. The distribution of phytoplankton in a given water resource can exhibit a high degree of variability across time and space, and this is in large part due to their varying sensitivities to environmental conditions such as resource availability and grazing by predator organisms. As such, phytoplankton community structure is widely used as an investigative tool for …

Extracting Metamorphic Histories Utilizing U-Pb Laser Ablation Zircon Geochronology From The Southern Appalachians Crystalline Rocks And Detrital Sediment, Meredith Kay Love Gawai

Theses and Dissertations

The southern Appalachian mountain belt is an accretionary orogen that formed in the southeastern United States through several phases of oceanic subduction and continental collision during the Paleozoic Era and culminated in the formation of the supercontinent Pangaea. Although many U-Pb zircon ages have been collected from the igneous, metaigneous and metasedimentary rocks in the crystalline core of the southern Appalachians, there remain opportunities to better reconstruct the metamorphic and magmatic history of the southern Appalachians through the lens of zircon geochronology. Such data are valuable in identifying genetic relationships between candidate terranes of the orogen. Herein, I present laser-ablation …

Changes In The Incidence, Viral Coinfection Pattern And Outcomes Of Pneumococcal Hospitalizations During And After The Covid-19 Pandemic, King-Pui Florence Chan, Ting Fung Ma, Hanshu Fang, Wai-Kai Tsui, James Chung-Man Ho, Mary Sau-Man Ip, Pak-Leung Ho

Faculty Publications

Background

The incidence of pneumococcal pneumonia in the context of the Coronavirus Disease 2019 (COVID-19) pandemic, along with the real-world data on the ratio of non-invasive to invasive pneumococcal pneumonia, is an area that has not been thoroughly studied. The outcomes associated with coinfection of influenza and COVID-19 remain unknown. This study examined the incidence, demographics, coinfection with influenza and/or COVID-19, and clinical outcomes of pneumococcal hospitalizations in Hong Kong during the baseline, pandemic, and post-pandemic periods.

Methods

Hospitalization records of individuals aged 18 years and above with pneumococcal disease from January 2015 to August 2024 were extracted from the …

Sexually Transmitted Infection (Sti) Incidence And Risk Factors Among People With Hiv (Pwh): Insights From A 13-Year Cohort Study In South Carolina, Salome-Joelle Gass, Shujie Chen, Jiajia Zhang Ph.D., Bankole Olatosi

Faculty Publications

The Ending the HIV Epidemic (EHE) initiative aims to reduce new HIV infections by 90% by 2030 in the United States (US). However, rising sexually transmitted infection (STI) rates exacerbate the bidirectional infection risk between HIV and STIs. Most research on STIs among people with HIV (PWH) has focused on high-risk groups, resulting in limited data on broader populations. This study addresses that gap by examining the incidence and risk factors for gonorrhea, chlamydia, and syphilis in a statewide cohort of PWH in South Carolina. Data from South Carolina’s HIV and STI surveillance systems were linked, and all PWH aged …

Environmental Risk And Alpha-Gal Syndrome (Ags) In The Mid-Atlantic United States, Brandon D. Hollingsworth Ph.D., Margaret Wiener, Dana A. Giandimenico, Scott P. Commins, Ross M. Boyce

Faculty Publications

Alpha-gal syndrome (AGS), commonly referred to as the tick bite red meat allergy, has been reported worldwide with the number of suspected cases in the United States increasing from 24 in 2009 to over 34,000 in 2019. Within the US, AGS is associated with the bite of two tick species, Amblyomma americanum and Ixodes scapularis, and has particularly high incidence rates in the mid-Atlantic region. Because AGS is associated with tick bites, the risk of developing AGS is affected by the environment individuals visit. Despite this, as well as the numerous studies associating the environment with Am. americanum, …

Human Capital And Lifetime Income Gains Of Scaling-Up Small-Quantity Lipid Nutrient Supplements Among Children Under 2 Years: A Modelling Analysis, Nandita Perumal Phd, Goodrarz Danaei, Günther Fink, Mark Lambiris, Christopher R. Sudfeld

Faculty Publications

Undernutrition in early childhood is associated with adverse health and developmental outcomes later in life and remains a persistent global public health problem. Providing small-quantity lipid nutrient supplements (SQ-LNS) to children aged 6-24 months improves child growth and neurodevelopmental outcomes, but the potential long-term benefits to human capital have not been previously estimated. We estimated the potential returns to schooling and lifetime income attributable to increasing coverage of SQ-LNS for children < 2 years of age from 0% to 50% or 90% per five-year birth cohort in five countries (Bangladesh, Burkina Faso, Ethiopia, Pakistan, and Uganda) with a high burden of undernutrition. Random-effects meta-analyses were used to estimate the effect of SQ-LNS on child development using evidence from randomized controlled trials, and to estimate the returns to lifetime income as a function of change in development based on a de novo meta-analysis of observational economic studies. Gains in school years attributable to scaling-up SQ-LNS to 90% coverage ranged from 0.14 million school years (95% uncertainty interval [UI]: 0.064, …

Repositioning The Game: Traditional Positions Vs Tracking-Based Archetypes In Nba Performance Models, Jacob Floyd

Senior Theses

Driven by the rise of advanced analytics and player tracking technologies, the NBA has transitioned away from traditional positional roles and toward more fluid player archetypes. This investigation uses principal component analysis and k-means clustering to group players based on season-long tracking data, creating new pseudo-positions that more accurately reflect modern playing styles. Predictive models were then built using both the classic position system and the newly generated clusters to forecast player scoring performance. Across every model comparison, both in terms of fit and predictive accuracy, the cluster-based system significantly outperformed the traditional position-based model. These results reinforce the idea …

Kinetic Control And Trapping In The Supramolecular Polymerization Of M-Terphenyl Bis-Urea Macrocycles, Sophya V. Garashchuk, Gamage Isuri P. Wijesekera, Isabella G. Rushton, Vaibhavi A. Samant, Fahidat A. Gbadamosi, Dr. Md Faizul Islam, Sophya V. Garashchuk, Prof. Dr. Linda S. Shimizu

Faculty Publications

Herein, we examine pathway complexity in the supramolecular polymerization of a novel m-terphenyl bis-urea macrocycle. Designed to induce kinetically metastable states, the macrocycle‘s concentration-dependent aggregation was studied via 1H NMR and IR spectroscopy in THF and CHCl₃. Temperature-dependent UV-Vis spectroscopy in water/THF revealed a cooperative nucleation-growth mechanism, indicated by a shift in λmax to longer wavelengths upon cooling. Morphological studies using DLS, AFM, and SEM demonstrated fibrous aggregate formation. Thermal hysteresis observed in assembly-disassembly cycles indicated kinetically trapped species, with cooling governed by kinetic control and heating by thermodynamic processes. Deviations in ΔH values during cooling, compared to van′t …

Tritium As A Model Tracer For Predicting Per- And Polyfluoroalkyl Exposure And Potential Ecosystem And Human Health Impacts, Erika Craig

Theses and Dissertations

For this thesis, historical tritium and per-and polyfluoroalkyl substances (PFAS) concentrations measured in surface waters of South Carolina at or near the Savannah River Site (SRS) were compared. Statistical linear regression analysis was used to assess the ability of tritium as a model tracer for predicting PFAS concentrations, specifically perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) distributions. Nine years of tritium monitoring data, (2014 – 2022), were analyzed and used in linear regressions to assess their association with PFAS levels of PFOA and PFOS measured during 2023, in and around the SRS and the adjoining Savannah River. Initially, a normality …

Neural Network-Based Low-Level 3d Point Cloud Processing, Pingping Cai

Theses and Dissertations

3D computer vision is a promising research field with the potential to revolutionize future lifestyles. Among various 3D representation formats, point clouds stand out for their efficiency in depicting 3D objects using a set of coordinates, enabling advancements in fields such as autonomous driving, virtual reality, and robotics. Due to the limitations of sensor fields of view and scanning trajectories, the collected point clouds are usually sparse, noisy, and incomplete, impeding the performance of many downstream applications. Thus, the tasks of low-level point cloud processing are proposed to refine and generate dense, clean, and complete point clouds. To accomplish these …

Augmenting Deep Learning For Efficient Nextg Wireless Communication And Sensing Systems, Hem Kanta Regmi

Theses and Dissertations

Wireless networks have become an integral aspect of our daily lives. Over the years, earlier generations of wireless networks have enabled some innovative applications, such as wireless gaming, fast internet browsing, and home automation, which were previously unattainable. However, to support emerging technologies like autonomous driving, virtual reality, telemedicine, and intelligent manufacturing, which require high data throughput and low latency, there is a need for advanced wireless networks. Legacy networks like WiFi/LTE, which operate below 6 GHz, have limited bandwidth and are insufficient to fulfill the high data throughput demands of several applications. Millimeter-wave (mmWave) networks, operating between 30 GHz …

Building Trustable Methods For Group Recommendations: Advancing Fairness And Robustness Across Domains, Siva Likitha Valluru

Theses and Dissertations

On the internet, where the number of available choices for information is exponentially growing, there is a need to prioritize and deliver relevant results to users efficiently, on demand. Recommendation systems (RSs) address that need by searching through and filtering large amounts of dynamically generated information and providing users with recommendations tailored to them. These systems have primarily focused on (1) single-user models, where recommendations are tailored towards a specific individual, or (2) single-item models, where items are recommended based on a broader appeal to users and similarities in item metadata, in the past. In many real-world scenarios, however, recommendation …

Hallucinations In Large Foundation Models: Characterization, Quantification, Detection, Avoidance, And Mitigation, Vipula Rawte

Theses and Dissertations

Deception is an inherent aspect of social interactions, with research indicating that most people engage in deceptive behavior at least once or twice daily . In parallel, advances in artificial intelligence have led to machines exhibiting deceptive tendencies. These deceptions can be categorized into two types: unintended and intentional. Unintended deceptions - often referred to as hallucinations - occur when generative AI systems produce plausible and convincing narratives yet are factually inaccurate. This phenomenon primarily results from the systems' architectural design, extensive parametric memory, and reliance on statistical assumptions. In this thesis, we provide a comprehensive discussion on the characterization, …

Racial And Ethnic Inequalities In Actual Vs Nearest Delivery Hospitals, Nansi S. Boghossian, Lucy T. Greenberg, Jeffrey S. Buzas, Joshua Radack, Molly Passarella, Jeannette Rogowski, George R. Saade, Ciaran S. Phibbs, Scott A. Lorch

Faculty Publications

IMPORTANCE Minoritized racial and ethnic groups, such as American Indian and Black individuals, often receive lower quality health care compared with White individuals. There is limited understanding of how these disparities extend to obstetric care, particularly when comparing the quality of care at the actual delivery hospital vs the nearest obstetric hospital based on the birthing individual’s residence. OBJECTIVE To examine inequality in care based on the actual delivery hospital and the closest delivery hospital to the birthing individual’s residential zip code centroid. DESIGN, SETTING, AND PARTICIPANTS This population-based retrospective cohort study used data from 5 states (2008 to 2020 …

Special Delivery Of Proteinaceous Matter To Deep-Sea Microbes, Yuan Shen, Ronald Benner, Taylor A.B. Broek, Brett D. Walker, Matthew D. Mccarthy

Faculty Publications

Earth’s deep ocean holds a vast reservoir of dissolved organic carbon, traditionally considered old and resistant to microbial degradation. Radiocarbon analyses indicate the hidden occurrence of younger dissolved organic carbon components, assumed to be accessible to deep-sea microorganisms but not yet demonstrated. Using compound-class radiocarbon analysis, molecular characterization, and bioassay experiments, we provide direct evidence for rapid microbial utilization of young, labile, high–molecular weight proteinaceous material in bathypelagic waters. The abundance of labile proteinaceous material diminishes from epipelagic to mesopelagic waters but notably increases in bathypelagic waters, where it exhibits a short turnover time (days) and resembles surface plankton in …

Synthesis Of A Series Of Rare-Earth-Based Multi-Anion Chalcogenide Iodides Re3Si2SeXS8-XI (Re = La, Ce, Pr, And Nd) Using The Flux-Assisted Boron-Chalcogen Mixture Method, Gopabandhu Panigrahi, Habiba Binte Kashem, Gregory Morrison, Hans Conrad Zur Loye

Faculty Publications

Single crystals and polycrystalline powders of rare earth mixed chalcogenide iodides La3Si2Se1.21S6.79I, Ce3Si2Se1.39S6.61I, Pr3Si2Se1.22S6.78I, and Nd3Si2Se1.18S6.82I were prepared using the reactive flux-assisted boron-chalcogen mixture (BCM) method at 850 °C. All compounds crystallized in the monoclinic crystal system, space group C2/c (space group number 15). The series adopts the La3Si2O8Cl structure type, containing isolated SiQ4 tetrahedra connected by REQ8 (RE = La, Ce, Pr and Nd) polyhedra; this arrangement creates tunnels that are filled by I atoms. The partial substitution of S by Se was carried out to modulate the optical properties. Phase pure samples and uniform solid solutions were obtained …

Time-Dependent Shear Flows And Their Applications In Parabolic–Parabolic Patlak–Keller–Segel Systems*, Siming He

Faculty Publications

In this study, we investigate the behavior of three-dimensional parabolic–parabolic Patlak–Keller–Segel systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection.

Pre-Exposure Prophylaxis Uptake Among Black/African American Men Who Have Sex With Other Men In Midwestern, United States: A Systematic Review, Oluwafemi Adeagbo, Oluwaseun Abdulganiyu Badru, Prince Addo, Amber Hawkins, Monique J. Brown Ph.D., Mph, Xiaoming Li, Rima Afifi

Faculty Publications

Introduction: Black/African American men who have sex with other men (BMSM) are disproportionately affected by HIV, experience significant disparities in HIV incidence, and face significant barriers to accessing HIV treatment and care services, including pre-exposure prophylaxis (PrEP). Despite evidence of individual and structural barriers to PrEP use in the Midwest, no review has synthesized this finding to have a holistic view of PrEP uptake and barriers. This review examines patterns of, barriers to, and facilitators of PrEP uptake among BMSM in the Midwest, United States (US).

Methods: Five databases (CINAHL Plus, PUBMED, PsycINFO, SCOPUS, and Web of Science) were searched …

Nanostructure Retention To 1100 °C In Soft-Templated Niobium Tungstates Using Dual-Carbon Strategy, Sean C. Wechsler, Alexander Gregg, Coby S. Collins, Santosh Kiran Balijepalli, Morgan Stefik

Faculty Publications

Mesoporous metal oxides (MMOs) have diverse applications including energy storage, catalysis, and separation membranes. Block polymer structure directing agents enable the control of morphology and pore size, however preservation of the nanostructure is often limited to a narrow range of heat treatment temperatures which constrains the tailoring of defect chemistries. High temperature treatments typically lead to collapse of the porous structure as surface area is reduced during crystal growth. Here, using a mesoporous niobium tungstate it is shown that neither in situ carbon generation nor ex situ carbon infiltration alone enable preservation of the ordered mesostructure at temperatures high enough …