Tootfinder

Divide and Conquer: A Large-Scale Dataset and Model for Left-Right Breast MRI Segmentation
Maximilian Rokuss, Benjamin Hamm, Yannick Kirchhoff, Klaus Maier-Hein
https://arxiv.org/abs/2507.13830

Divide and Conquer: A Large-Scale Dataset and Model for Left-Right Breast MRI Segmentation
We introduce the first publicly available breast MRI dataset with explicit left and right breast segmentation labels, encompassing more than 13,000 annotated cases. Alongside this dataset, we provide a robust deep-learning model trained for left-right breast segmentation. This work addresses a critical gap in breast MRI analysis and offers a valuable resource for the development of advanced tools in women's health. The dataset and trained model are publicly available at: www.github.com/MIC-DKFZ…

Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
Nic Fellini, M. Ram Murty
https://arxiv.org/abs/2508.08472 https://

Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
For a prime $p\equiv 1 \,(\bmod{4})$, let \[ \varepsilon = \frac{1}{2}\left( t + u\sqrt{p}\right) \] be the fundamental unit of the real quadratic field $\mathbb{Q}(\sqrt{p})$. In 1951, N. Ankeny, E. Artin, and S. Chowla asked whether $p$ can divide $u$. They suggested that this can never happen and this has since been called the Ankeny--Artin--Chowla (AAC) conjecture. We show that if $\mathfrak{p}$ is the prime above $p$ in $\mathbb{Q}(\sqrt{p})$, then the AAC conjecture is false if and only…