Kira Adaricheva

Improving undergraduate success in STEM requires identifying actionable factors that impact student outcomes, allowing institutions to prioritize key leverage points for change. Based on Astin’s Input–Environment–Output model, we examined academic, demographic, and institutional factors that might be associated with graduation rates of STEM majors at two private four-year colleges in the northeastern United States using a novel association algorithm called D-basis to rank attributes associated with graduation. Importantly, the data included outcomes of students who left their original institutions. Key attributes associated with graduation included performance in introductory STEM courses, the choice of first mathematics class, and flexibility in major selection. Specifically, high grades in introductory biology, general chemistry, and mathematics courses were strongly associated with graduation. Students who changed majors—especially from STEM to non-STEM—also had higher overall graduation rates. Financial need and demographic factors, although less predictive overall, revealed disparities in time to graduation. The findings highlight the importance of early academic support to enhance student success in STEM gateway courses and the implementation of institutional policies that provide flexibility in major selection. This study offers data-driven insights to guide strategies to increase bachelor’s degree completion.

We present a new implementation of the $D$-basis algorithm called the Small Space which considerably reduces the algorithm's memory usage for data analysis applications. The previous implementation delivers the complete set of implications that hold on the set of attributes of an input binary table. In the new version, the only output is the frequencies of attributes that appear in the antecedents of implications from the $D$-basis, with a fixed consequent attribute. Such frequencies, rather than the implications themselves, became the primary focus in analysis of datasets where the $D$-basis has been applied over the last decade. The $D$-basis employs a hypergraph dualization algorithm, and a dualization implementation known as Reverse Search allows for the gradual computation of frequencies without the need for storing all discovered implications. We demonstrate the effectiveness of the Small Space implementation by comparing the runtimes and maximum memory usage of this new version with the current implementation.

Improving undergraduate success in STEM requires identifying actionable factors that impact student outcomes, allowing institutions to prioritize key leverage points for change. We examined academic, demographic, and institutional factors that might be associated with graduation rates at two four-year colleges in the northeastern United States using a novel association algorithm called D-basis to rank attributes associated with graduation. Importantly, the data analyzed included tracking data from the National Student Clearinghouse on students who left their original institutions to determine outcomes following transfer. Key predictors of successful graduation include performance in introductory STEM courses, the choice of first mathematics class, and flexibility in major selection. High grades in introductory biology, general chemistry, and mathematics courses were strongly correlated with graduation. At the same time, students who switched majors - especially from STEM to non-STEM - had higher overall graduation rates. Additionally, Pell eligibility and demographic factors, though less predictive overall, revealed disparities in time to graduation and retention rates. The findings highlight the importance of early academic support in STEM gateway courses and the implementation of institutional policies that provide flexibility in major selection. Enhancing student success in introductory mathematics, biology, and chemistry courses could greatly influence graduation rates. Furthermore, customized mathematics pathways and focused support for STEM courses may assist institutions in optimizing student outcomes. This study offers data-driven insights to guide strategies to increase STEM degree completion.

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math 342(N3):726–746, 2019) and the Polymath REU 2020 team (Convex geometries representable by at most 5 circles on the plane. arXiv:2008.13077), continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors.

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of K. Adaricheva and M. Bolat (2016) and the Polymath REU 2020 team, continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors.