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Structural and rigidity properties of Lie skew braces
Marco Damele, Andrea Loi
https://arxiv.org/abs/2507.06214 https://arxiv.org/pdf…

Structural and rigidity properties of Lie skew braces
We investigate structural and rigidity properties of \emph{Lie skew braces} (LSBs), objects essentially known in the literature as \emph{post--Lie groups}, obtained by endowing a manifold with two compatible group laws that share the same identity element. LSBs extend skew left braces, which are central to the study of non-involutive set-theoretic solutions of the Yang--Baxter equation, to the smooth category. Our first main result shows that, for every connected LSB $(G,\cdot,\circ)$, linearit…

This https://arxiv.org/abs/2504.07884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

CatCMA with Margin: Stochastic Optimization for Continuous, Integer, and Categorical Variables
This study focuses on mixed-variable black-box optimization (MV-BBO), addressing continuous, integer, and categorical variables. Many real-world MV-BBO problems involve dependencies among these different types of variables, requiring efficient methods to optimize them simultaneously. Recently, stochastic optimization methods leveraging the mechanism of the covariance matrix adaptation evolution strategy have shown promising results in mixed-integer or mixed-category optimization. However, such …