Tootfinder

Second-order prestress stability and third-order rigidity of polyhedral surfaces
Zeyuan He
https://arxiv.org/abs/2506.22019 https://a…

Second-order prestress stability and third-order rigidity of polyhedral surfaces
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to polyhedral surfaces, we derive new criterion for testing second-order prestress stability. Additionally, we discuss the limitations of testing third-order rigidity, except in the special case where the null space of the rigidity matrix is one-dimensional. Altho…

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Paul N. Patrone, Anthony J. Kearsley
https://arxiv.org/abs/2508.01065 h…

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We begin by adopting a set-theoretic perspective to show how two main tasks in diagnostics -- classification and prevalence estimation -- can be recast in terms of a variation on the confusion (or error) matrix ${\boldsymbol {\rm P}}$ typically considered in super…