GILP: An Interactive Tool for Visualizing the Simplex Algorithm

The Simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the Simplex algorithm relies on intuitive geometric ideas, the computationally-involved mechanics of the algorithm can obfuscate a geometric understanding. In this paper, we present gilp, an easy-to-use Simplex algorithm visualization tool designed to explicitly connect the mechanical steps of the algorithm with their geometric interpretation. We provide an extensive library with example visualizations, and our tool allows an instructor to quickly produce custom interactive HTML files for students to experiment with the algorithm (without requiring students to install anything!). The tool can also be used for interactive assignments in Jupyter notebooks, and has been incorporated into a forthcoming Data Science and Decision Making interactive textbook. In this paper, we first describe how the tool fits into the existing literature on algorithm visualizations: how it was designed to facilitate student engagement and instructor adoption, and how it substantially extends existing algorithm visualization tools for Simplex. We then describe the development and usage of the tool, and report feedback from its use in a course with roughly 100 students. Student feedback was overwhelmingly positive, with students finding the tool easy to use: it effectively helped them link the algebraic and geometrical views of the Simplex algorithm and understand its nuances. Finally, gilp is open-source, includes an extension to visualizing linear programming-based branch and bound, and is readily amenable to further extensions.Comment: ACM SIGCSE 2023 Manuscript, 13 pages, 5 figure

Phospho-Ablated Id2 Is Growth Suppressive and Pro-Apoptotic in Proliferating Myoblasts

Inhibitor of differentiation protein-2 (Id2) is a dominant negative helix-loop-helix (HLH) protein, and a positive regulator of proliferation, in various cells. The N-terminal region of Id2 contains a consensus cdk2 phosphorylation sequence SPVR, which may be involved with the induction of apoptosis, at least in myeloid 32d.3 cells. However, the role of Id2 phosphorylation at serine 5 in skeletal muscle cells is unknown. The objective of this study was to determine if the phosphorylation of Id2 at serine 5 alters its cellular localization and its role in apoptosis in C2C12 myoblasts. Overexpression of wild type Id2 decreased MyoD protein expression, which corresponded to the increased binding of Id2 to basic HLH proteins E47 and E12. Bromodeoxyuridine incorporation was significantly decreased by the overexpression of phospho-ablated Id2 (S5A); conversely, overexpression of wild type Id2 increased cellular proliferation. The subcellular localization of Id2 and phospho-mimicking Id2 (S5D) were predominantly nuclear compared to S5A. The decreased nuclear localization of S5A corresponded to a decrease in cellular proliferation, and an increase in apoptosis. These data suggest that unphosphorylated Id2 is primarily localized in the cytosol, where it is growth suppressive and potentially pro-apoptotic. These results imply that reducing unphosphorylated Id2 may improve the pool of myoblasts available for differentiation by increasing proliferation and inhibiting apoptosis

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

The ability of future engineering professionals to solve complex real‐world problems depends on their design education and training. Because engineers engage with open‐ended problems in which there are unknown parameters and multiple competing objectives, they engage in fuzzy decision‐making, a method of making decisions that takes into account inherent imprecisions and uncertainties in the real world. In the design‐based decision‐making field, few studies have applied fuzzy decision‐making models to actual decision‐making process data. Thus, in this study, we use datasets on student decision‐making processes to validate approximate fuzzy models of student decision‐making, which we call data‐enabled cognitive modeling. The results of this study (1) show that simulated design problems provide rich datasets that enable analysis of student design decision‐making and (2) validate models of student design cognition that can inform future design curricula and help educators understand how students think about design problems

Teaching and Assessing Engineering Design Thinking with Virtual Internships and Epistemic Network Analysis

An engineering workforce of sufficient size and quality is essential for addressing significant global challenges such as climate change, world hunger, and energy demand. Future generations of engineers will need to identify challenging issues and design innovative solutions. To prepare young people to solve big and increasingly global problems, researchers and educators need to understand how we can best educate young people to use engineering design thinking. In this paper, we explore virtual internships, online simulations of 21st-century engineering design practice, as one method for teaching engineering design thinking. To assess the engineering design thinking, we use epistemic network analysis (ENA), a tool for measuring complex thinking as it develops over time based on discourse analysis. The combination of virtual internships and ENA provides opportunities for students to engage in authentic engineering design, potentially receive concurrent feedback on their engineering design thinking, and develop the identity, values, and ways of thinking of professional engineers