Tootfinder

Invariant sets for the wind-tree model
Yuriy Tumarkin
https://arxiv.org/abs/2510.10760 https://arxiv.org/pdf/2510.10760

Invariant sets for the wind-tree model
We consider the wind-tree model, a $\mathbb{Z}^2$ - periodic billiard. In the case when the underlying compact translation surface lies on a periodic orbit of the Teichmüller geodesic flow, and at least one of the two homology classes defining the $\mathbb{Z}^2$ - cover is unstable for the Kontsevich-Zorich cocycle, we prove that every orbit closure of the billiard has Hausdorff dimension strictly smaller than 2. The proof relies on a construction of explicit invariant functions, which along t…

Large Language Model-Empowered Channel Prediction and Predictive Beamforming for LEO Satellite Communications
Zhixiong Chen, Hyundong Shin, Arumugam Nallanathan, Jonathon Chambers
https://arxiv.org/abs/2510.10561

Large Language Model-Empowered Channel Prediction and Predictive Beamforming for LEO Satellite Communications
Accurate channel prediction and effective beamforming are essential for low Earth orbit (LEO) satellite communications to enhance system capacity and enable high-speed connectivity. Most existing channel prediction and predictive beamforming methods are limited by model generalization capabilities and struggle to adapt to time-varying wireless propagation environments. Inspired by the remarkable generalization and reasoning capabilities of large language models (LLMs), this work proposes an LLM…