Tootfinder

Pivot probabilities and norm effects in Gaussian elimination for $\beta$-ensembles
Kenji Gunawan, John Peca-Medlin
https://arxiv.org/abs/2506.20470 https:/…

Pivot probabilities and norm effects in Gaussian elimination for $β$-ensembles
We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical observations by deriving the exact pivot probability under standard LAPACK-style implementations. We further show that Dumitriu-Edelman tridiagonal $β$-ensembles agree with the earlier theoretical expectations. Finally, we propose an open question on pivot behavi…

WIP: Large Language Model-Enhanced Smart Tutor for Undergraduate Circuit Analysis
Liangliang Chen, Huiru Xie, Jacqueline Rohde, Ying Zhang
https://arxiv.org/abs/2506.08962

WIP: Large Language Model-Enhanced Smart Tutor for Undergraduate Circuit Analysis
This research-to-practice work-in-progress (WIP) paper presents an AI-enabled smart tutor designed to provide homework assessment and feedback for students in an undergraduate circuit analysis course. We detail the tutor's design philosophy and core components, including open-ended question answering and homework feedback generation. The prompts are carefully crafted to optimize responses across different problems. The smart tutor was deployed on the Microsoft Azure platform and is currently in…