The set of morphisms mapping any Sturmian sequence to a forms together with composition the so-called monoid Sturm. For this monoid, we defne faithful representation by $(3\times 3)$-matrices integer entries. We find three convex cones in $\mathbb{R}^3$ and show that matrix $R \in Sl(\mathbb{Z},3)$ is representing morphism if are invariant under multiplication $R$ or $R^{-1}$. This property off...

Federated learning enables machine algorithms to be trained over decentralized edge devices without requiring the exchange of local datasets. Successfully deploying federated requires ensuring that agents (e.g., mobile devices) faithfully execute intended algorithm, which has been largely overlooked in literature. In this study, we first use risk bounds analyze how key feature learning, unbalan...