Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order for gravity with cosmological constant as independent scalar field, and supplemented Euler Pontryagin densities multiplied $1/\Lambda$. We identify canonical structure of these which turn out to represent example irregular systems. find five degrees freedom on generic backgrounds values ...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...