Tootfinder

Dihedral sign patterns in $\mathcal{M}_{0,n}$
Veronica Calvo Cortes, Hannah Tillmann-Morris
https://arxiv.org/abs/2508.14714 https://arxiv.org/pdf/2508.147…

Dihedral sign patterns in $\mathcal{M}_{0,n}$
The connected components of $\mathcal{M}_{0,n}(\mathbb{R})$ are in bijection with the $(n-1)!/2$ dihedral orderings of $[n]$. They are all isomorphic. We construct monomial maps between them, and use these maps to prove a conjecture of Arkani-Hamed, He, and Lam in the case of $\mathcal{M}_{0,n}$. Namely, we provide a bijection between connected components and sign patterns that are consistent with the extended $u$-relations for the dihedral embedding.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space
Michal Jablonowski
https://arxiv.org/abs/2507.20360 https://arxiv.or…

Biquandle cocycle condition for invariants of immersed surface-links in the four-space
We consider a biquandle-cohomological framework for invariants of oriented immersed surface-links in the four-space. After reviewing projections and Roseman moves for immersed surfaces, we prove that the move types (a,b,c,e,f,g,h) form a minimal generating set, showing in particular that the singular move (h) is independent of the embedded-case set (a,b,c,e,f,g). We extend biquandle colorings to broken surface diagrams with singular points and establish that coloring sets are in bijection for d…

Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory
Yueqi Zhao, Michael M. Fogler, Yi-Zhuang You
https://arxiv.org/abs/2510.06508 …

Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory
We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the…

The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
Yue Yu, Moulinath Banerjee, Ya'acov Ritov
https://arxiv.org/abs/2508.17591 https://

The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
We introduce Sequential Probability Ratio Bisection (SPRB), a novel stochastic approximation algorithm that adapts to the local behavior of the (regression) function of interest around its root. We establish theoretical guarantees for SPRB's asymptotic performance, showing that it achieves the optimal convergence rate and minimal asymptotic variance even when the target function's derivative at the root is small (at most half the step size), a regime where the classical Robbins-Monro procedure …