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In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For expansive systems remarkable properties are observed. Known examples are revisited and new examples are presented.
We provide a simple characterization of simplicial complexes on few vertices that embed into the $d$-sphere. Namely, a simplicial complex on $d+3$ vertices embeds into the $d$-sphere if and only if its non-faces do not form an intersecting family. As
Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: kno
We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost surely contains infinitely many copies of every compact
The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical tr
We estimate the upper bound for the $ell^{infty}$-norm of the volume form on $mathbb{H}^2timesmathbb{H}^2timesmathbb{H}^2$ seen as a class in $H_{c}^{6}(mathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R};mathbb{R})$. T