Dissertation Defense Announcements

Policies and procedures in modern society have unintentionally perpetuated inequities for marginalized students, particularly African Americans, exacerbating math anxiety. Despite efforts to improve mathematics education, African American students continue to experience disproportionately high rates of math anxiety, negatively impacting academic performance, mathematical identity, and future opportunities. While there is extensive research on math anxiety among African American girls, there is a notable lack of studies focusing on African American, elementary aged, boys. Through a qualitative, case study design, the research utilizes a questionnaire, classroom observations, and student interviews to gain insights into the emotional and psychological challenges African American 3rd grade boys face in mathematics. The study investigates the role of race, gender, and socio-economic status in shaping African American 3rd grade boys' experiences with math, as well as the impact of instructional practices and teacher-student relationships on mitigating or exacerbating math anxiety. Findings from this research contribute to the broader conversation about inequities in mathematics education, highlighting the need for culturally responsive teaching strategies and support systems to foster confidence and resilience in students from marginalized communities. This dissertation aims to provide actionable recommendations for educators to recognize, address, and reduce math anxiety in young learners, with a particular focus on African American boys, to promote positive mathematical identity and long-term academic success.

Partly interval-censored failure time data are common in clinical and epidemiological studies, where the failure time of interest is either exactly observed or known to lie within a specific interval. Additionally, two-phase sampling designs are often employed to measure covariates for a subset of participants, reducing study costs. This paper addresses regression analysis of partly interval-censored failure time data under stratified semiparametric transformation models, incorporating time-dependent covariates subject to: (i) missingness due to two-phase sampling and (ii) measurement errors during observation. We propose a maximum weighted likelihood estimation method and develop an EM algorithm for implementation. A weighted bootstrap approach is introduced for variance estimation, and the asymptotic properties of the proposed estimator are established. Extensive simulation studies demonstrate the method’s satisfactory finite-sample performance, and its practical utility is illustrated through an application to data from the HIV prevention trials HVTN-703/HVTN-704.

Hydrodynamic simulations are computational models used to study the behavior of fluids. The data generated by these simulations contains critical information about fluid dynamics, and researchers utilize data analysis techniques to extract meaningful insights, which are essential for optimizing designs and making informed decisions across diverse research fields. Traditionally, data analysis has been performed through post-analysis. For post-analysis, the data is saved during the simulation, and the analysis is performed afterward using the previously saved data. This approach involves extensive data storage and transfer, which becomes increasingly challenging as simulation data grows in volume and complexity. Another approach named in-situ analysis has emerged as an alternative, where data is analyzed directly within the system or environment where it is generated during the simulation. This approach eliminates the need for storing and transferring large amounts of data, making it more scalable and efficient for analyzing hydrodynamic simulations.

However, existing in-situ analysis methods and tools have three challenges: First, human intervention is frequently required in in-situ analysis to ensure high-quality data analysis, but it often interrupts the simulation. In this way, the simulation needs to be paused to wait for human interpretation. The requirement for expert knowledge further hinders the efficiency of in-situ analysis, as non-expert users may struggle to make appropriate decisions during runtime. Second, in-situ analysis struggle to balancing data analysis with requirement for minimal computational cost. As simulation data grows in volume, the complexity of data analysis algorithms also increases for extracting more information from the simulation to enhance the quality of data analysis. They often come at the expense of increased computational overhead, potentially disrupting simulation efficiency. Third, implementing in-situ analysis is not straightforward. While existing frameworks typically support in-situ data collection or visualization, extracting meaningful insights from the collected simulation data still requires additional manual effort.

To address these challenges, this dissertation proposes an automated in-situ analysis approach for hydrodynamic simulation. While prior in-situ analysis efforts have focused on data collection and visualization, we approach the problem from a new perspective by formulating in-situ analysis as a feature extraction task. This shift enables more targeted and automated insight generation within the simulation process. First, based on domain discretization and the iterative nature of hydrodynamic simulations, our method aligns tasks to simulation steps and spatial decomposition. This allows data collection and analysis to be triggered automatically. Users define analysis goals and conditions before the simulation; once running, the system triggers analysis when conditions are met, continuing until objectives are achieved. Second, to balance analysis quality and computational performance, we employ lightweight, simulation-agnostic algorithms such as tuning, variable tracking, and surrogate modeling. These algorithms efficiently extract meaningful insights with minimal overhead, ensuring simulations remain uninterrupted. Third, to simplify implementation, we provide a flexible framework with a user-friendly interface. Users only need to specify key variables, models, and triggering conditions, reducing programming effort and making high-quality in-situ analysis accessible to non-experts. We evaluate the effectiveness of our approach across a range of hydrodynamic simulation applications, including proxy simulations such as LULESH, Laghos, and Kripke, as well as large-scale simulations like Castro and ImpactX. Our findings demonstrate that this automated in-situ approach provides an efficient, scalable solution for hydrodynamic simulation analysis, bridging the gap between usability, accuracy, and computational efficiency.

Supercell thunderstorms occur most frequently in the Great Plains region of the central United States, and are often responsible for extreme severe weather, including the majority of violent tornadoes and large hail. Given the societal implications, this study bridges the long-term climate scale and shorter-term storm-scale through exploration of how a future warmer, moister climate influences supercell behavior, characteristics, and potential severe weather production. The future near-supercell environment shifted towards more favorable severe weather conditions with a net increase in magnitude and vertical nature of convective available potential energy and convective inhibition, along with surprising changes in near-storm kinematics and wind fields. Using fine-scale idealized simulations, future supercells were found to be slightly shorter lived and stronger in intensity but also “less efficient” at converting their environment into notable strengthening. These fine scale simulations showed that while increases in favorable supercell environments are expected, the storm scale impact does not necessarily translate to proportional changes in supercell behavior or characteristics.