Tootfinder

GPU-based complete search for nonlinear minimization subject to bounds
Guanglu Zhang, Qihang Shan, Jonathan Cagan
https://arxiv.org/abs/2507.01770 https://…

GPU-based complete search for nonlinear minimization subject to bounds
This paper introduces a GPU-based complete search method to enclose the global minimum of a nonlinear function subject to simple bounds on the variables. Using interval analysis, coupled with the computational power and architecture of GPU, the method iteratively rules out the regions in the search domain where the global minimum cannot exist and leaves a finite set of regions where the global minimum must exist. For effectiveness, because of the rigor of interval analysis, the method is guaran…

Stability with minuscule structure for chromatic thresholds
Jaehoon Kim, Hong Liu, Chong Shangguan, Guanghui Wang, Zhuo Wu, Yisai Xue
https://arxiv.org/abs/2506.14748

Stability with minuscule structure for chromatic thresholds
The chromatic threshold $δ_χ(H)$ of a graph $H$ is the infimum of $d>0$ such that the chromatic number of every $n$-vertex $H$-free graph with minimum degree at least $d n$ is bounded by a constant depending only on $H$ and $d$. Allen, B{ö}ttcher, Griffiths, Kohayakawa, and Morris determined the chromatic threshold for every $H$; in particular, they showed that if $χ(H)=r\ge 3$, then $δ_χ(H) \in\{\frac{r-3}{r-2},~\frac{2 r-5}{2 r-3},~\frac{r-2}{r-1}\}$. While the chromatic thresholds have…