In this dissertation, we explore two applications of discrete tempered stable (DTS) distributions, a flexible class of distributions well-suited for modeling heavy-tailed and overdispersed data. DTS distributions are derived by tempering the tail of discrete stable distributions.
The first application addresses challenges in simulating positive tempered stable (PTS) distributions. Except for a few cases, there is no known simulation method for these distributions. We propose a novel simulation method using DTS distributions to approximate PTS simulations and establish a convergence rate for our estimation.
The second application focuses on modeling high-frequency financial data, or tick data, characterized by discrete price changes dictated by tick size. We compare the performance of DTS distributions against standard discrete models, specifically Poisson and negative binomial distributions, in modeling price changes. Additionally, we employ Monte Carlo methods to approximate the future distribution of portfolio values, utilizing these insights for risk assessment.
Students with disabilities face challenges navigating the educational system in the United States.
In rural school settings their obstacles are compounded. In the 21st century,
most students with disabilities are educated for most of their school day in the general classroom
setting. Guiding the support for their learning growth and success in the general education
learning environment is their Individual Education Plan (IEP).
Despite inclusion and an IEP, the graduation rate for students with disabilities is lower than all
other demographics.
To understand the perceptions and experiences of rural elementary general
education teachers this qualitative study is set in two rural districts in North Carolina. The
researcher gained insight into the experiences of 6 experienced elementary teachers. Findings
showed that while there is a basic knowledge of the IEP process, it is gained through participation in
IEP meetings and collaboration with the school EC teacher. Teachers are left with feelings of
inadequacy and frustration due to the high needs of students and the limited access to resources
to support them. Collaboration between the general education teacher and the EC teacher is
essential in rural schools where professional development opportunities for general education
teachers on the topic of special education are limited.
This study examined horizontal fiscal equity in North Carolina’s public school funding system from 2012 to 2022, expanding on previous research by Rolle et al. (2008) for the 1996–2006 decade. The research assessed whether the state’s school funding mechanism aligns with its constitutional obligation to provide a "sound basic education" for all students, as established in Leandro v. State (1997). Using statistical measures of horizontal fiscal equity, this study evaluates per-pupil expenditures at the local, state, and federal levels, providing a longitudinal comparison of funding disparities over time.
Findings indicated persistent and, in some cases, worsening inequities in school funding across North Carolina districts. Local per-pupil expenditures exhibited stagnation and decline in real-dollar terms, particularly during the COVID-19 pandemic, contributing to increasing disparities. While state per-pupil expenditures grew moderately, measures such as the range, standard deviation, and coefficient of variation suggest that funding inequities persisted and, in some cases, expanded. The analysis of combined local and state per-pupil expenditures revealed continued funding increases, yet disparities remained evident, particularly in lower-wealth districts. Total per-pupil expenditures, including federal funding, showed modest increases, yet gaps between high- and low-poverty districts persisted, reinforcing concerns regarding the adequacy and fairness of North Carolina’s school finance system.
Despite legal mandates and increased investment, North Carolina’s school finance system continues to exhibit inequities, particularly for districts with high concentrations of economically disadvantaged students. While some progress has been made in funding distribution, challenges in ensuring equitable access to resources remain. The findings underscored the need for policy reforms aimed at revising the state’s funding model, increasing targeted investments in high-needs student populations, and improving the overall efficiency of resource allocation. Future research should explore broader fiscal capacity, revenue equalization, and policy impact assessments to further understand and address systemic inequities in school funding.
ABSTRACT
HOLLY R. ROGERS: Decreasing patient falls in a medical unit by increasing fall risk assessment tool compliance: A quality improvement project. (Under the direction of DR. KATHERINE SHUE-MCGUFFIN)
Falls have a significant impact on patients physical, emotional, and financial well-being. Many healthcare facilities depend on fall risk prediction tools to help guide prevention efforts. These predictions tools are used to calculate a fall risk score for patients and identify interventions for fall prevention. The prediction tool used at this project site is the Hester Davis Fall Risk Assessment tool.
This project was guided by the PICO question: In a population of nurses on a medical-surgical unit, (P) does improving knowledge of the Hester Davis Fall Risk Assessment tool using in-person education (I), compared to standard education (C), affect the accuracy of fall risk scores, and fall prevention interventions (O) over a period of 12 weeks (T)? An in-person education intervention was conducted, and a pre- and post- self-efficacy survey was administered to the 43 nurse participants. Results using a paired sample t-test showed overall statical improvement in nurse confidence (t = -6.129, p = <.001) and statistically significant improvements for each question. Run charts identified a positive trend in compliance with fall risk scoring and fall prevention intervention implementation. For this quality improvement project in-person education on the Hester Davis Fall Risk Assessment tool was effective and produced an increase in nursing confidence in conducting fall risk assessments, which clinically increased fall risk scoring and prevention intervention compliance.
This project educated nurses on trauma-informed care (TIC) principles to build their perceived confidence and ability to apply TIC practices in clinical settings. The goal was to increase knowledge, affective commitment, beliefs, and self-efficacy with TIC through an educational intervention. Trauma significantly impacts well-being, leading to chronic health issues, substance abuse, and mental health problems. Nurses can also experience trauma, such as vicarious or secondary trauma. TIC focuses on identifying the impact of trauma and preventing re-traumatization within the healthcare setting. The project was conducted to enhance TIC behaviors in nurses using an interactive educational intervention. The project used a pre-post survey design with validated assessment tools to measure knowledge, affective commitment, self-efficacy, and beliefs about trauma. An interactive session included a didactic presentation, case studies, and open discussion. Data analysis used paired t-tests and descriptive statistics. Participants (N=44) achieved a 100% post-survey response rate. Although improvements in knowledge scores were not statistically significant (p < .077), affective commitment, self-efficacy, and beliefs showed significant improvements (p < 0.001). Evaluation surveys revealed that 91% indicated they gained knowledge, and 89% would apply their knowledge to practice. The project is replicable and scalable, promoting enhanced safety and wellness for patients and nurses.
Inadvertent perioperative hypothermia is a significant concern in surgical settings, leading to post-operative complications such as prolonged hospital stays, infection, and increased mortality. This quality improvement project aimed to educate operating room staff on evidence-based strategies to prevent perioperative hypothermia, thereby improving patient outcomes. The intervention included a structured educational module on maintaining normothermia, emphasizing pre-warming techniques, fluid warming devices, and standardized temperature monitoring. A quasi-experimental pre-post study design assessed changes in staff knowledge and patient normothermia rates before and after the intervention. Data analysis demonstrated a statistically significant improvement in staff knowledge scores (p = 0.015) and an increase in normothermia rates from 93.43% to 98.3%. The findings suggest that targeted education enhances adherence to best practices, reducing the incidence of hypothermia-related complications. Sustaining this intervention through continued education and policy reinforcement is recommended to ensure long-term improvements in perioperative patient care.
Preconception care is designed to ensure that women begin pregnancy at optimal health by having received proper chronic and sexual transmitted infection screenings, provider counseling about necessary health improvements, and treatment for conditions or illnesses that may impact the likelihood of a healthy pregnancy or childbirth. This type of care is especially important for Black women who continue to face disproportionate risk of pregnancy-related death in the United States. Due to the higher maternal mortality rates among Black women, a more targeted investigation and implementation of consistent care prior to pregnancy is needed.
My dissertation thematically examines the trends, knowledge, and experiences of preconception care among Black women who reside in the United States. I investigated the offer, reception, and administration of preconception care services using a mixed methodology approach. First, I analyzed preconception care reception among Black women using 2016-2021 PRAMS (Pregnancy Risk Assessment Monitoring System) data. This secondary analysis concluded that hypertensive Black women had 21% decreased odds of receiving preconception care, compared to their non-hypertensive counterparts despite their diagnosis of hypertension. Second, I developed and preliminarily validated the Preconception Care Health Knowledge Scale, which was designed to assess a woman’s knowledge level of the preconception care services needed for a healthy pregnancy. By community validation, psychometric validation, and content validation, I established that the instrument, once revised, will be suitable for assessing the knowledge of preconception care among Black women in the US. Third, I conducted a qualitative study that analyzed the healthcare experiences of Black women who began pregnancy with hypertension. Through semi-structured interviews, the participants identified Health Literacy and Knowledge, Provider Counseling, Provider Interaction, and Provider Race/Ethnicity as the most impactful themes related to their overall healthcare. The participants were knowledgeable about their hypertensive condition and expected their healthcare providers to inform them about the risks associated with beginning pregnancy with hypertension. However, several participants reported not being properly diagnosed with hypertension prior to pregnancy, which resulted in delayed treatment and increased the potential for adverse outcomes stemming from pregnancy-related hypertensive disorders.
My findings address critical gaps in the literature on the use of preconception care as a method to prevent maternal morbidity and mortality among Black women. I found Black women’s preconception care treatment to be inconsistent, especially among women who were hypertensive. These findings inform the development of frameworks, interventions, and policy to reduce the disproportionate and unnecessary maternal morbidity and mortality among Black women in the United States.
Social-emotional learning (SEL) programs have gained attention in K-12 education for their role in supporting students’ social development, emotional well-being, behavioral development, and academic success. While SEL programs have been widely studied in elementary schools, there is a gap in research regarding their implementation and effectiveness in middle schools. This descriptive qualitative multiple-case study explored middle school teachers’ perceptions of implementing the CharacterStrong SEL program. It focused on the program’s perceived benefits, challenges, and impact on middle school students’ academic, behavioral, and social-emotional outcomes. Guided by the CASEL framework for SEL and Self-Determination Theory, data were collected through four focus groups and 12 middle school teachers from a rural district in North Carolina who have implemented the CharacterStrong program for at least three years.
Findings indicated that SEL is valuable for fostering students’ emotional regulation, resilience, and interpersonal skills. Participants reported improvements in student behavior and classroom climate and identified challenges related to teacher training and time constraints. Teachers also emphasized the importance of aligning SEL instruction with content curriculum and the need for ongoing professional development to enhance program fidelity. This study offers valuable insight for school leaders, policymakers, educators, curriculum developers, school counselors, and mental health professionals by providing strategies for improving SEL implementation, enhancing professional development, and shaping future studies on social-emotional learning in middle schools.
This dissertation explores elementary educators' perceptions of trauma-informed practices (TIPs) in schools. It examines how teachers develop knowledge of childhood trauma, its classroom manifestations, and implementation of TIPs. The study investigates challenges in identifying trauma-related behaviors and educators' preparedness, aiming to improve teacher training and school-wide TIP implementation.
With the modernization of power grids, high penetration of distributed energy resources (DERs), and modern state-of-the-art loads are increasing to the grid, optimal power flow (OPF) analysis is one of the essential tools for reliable power system planning, operation, and control. This research proposes novel OPF power distribution and transmission network models using non-linear programming (NLP). The advantages of NLP-based OPF models are that they are accurate and give optimal global solutions for both transmission and distribution networks. To confirm solution accuracy, the necessary conditions for the formulations of power flow models are addressed in this research work for the proposed OPF models. In this dissertation, a centralized and distributed model based on NLP is proposed for OPF analysis in power distribution networks, solved with the Sequential Quadratic Programming (SQP) algorithm. This work proposes the method and illustrates the necessary conditions for the global optimality of the solution. The main advantages of the methods are obtaining global optimal solutions in less than a minute (for more than 2000 nodes with high penetration of DERs) without approximations and relaxations in power flow equations and improving scalability by reducing the number of iterations significantly for both centralized and distributed OPF. This research also proposes an SQP-based centralized and distributed optimal power flow (D-OPF) method for bulk power transmission grids with a modified equal network approximation framework (MENA). Moreover, a method is proposed for integrated transmission-distribution (T&D) OPF, and the efficiency of the integrated (T&D) is shown. This article also proposed a novel volt-var-optimization (VVO)-based centralized closed-loop voltage management co-simulation methodology that uses an NLP-based optimization (OPF) model and a real-time Opal-RT simulator. This research developed a real-time model of an integrated T\&D network with fully detailed and dynamic models of energy sources such as synchronous generators and inverter-based resources (IBRs) to fully understand the voltage profile of both the transmission and distribution system, with penetration of IBRs on both sides, and a volt/var optimization framework is developed to control the distribution side voltage. The models are validated using different IEEE test cases consisting of both transmission and distribution networks. The simulated results prove the accuracy and efficiency of the models.