Quantifying networks complexity from information geometry viewpoint

Computational Geometry from the Viewpoint of Affine Differential Geometry

Sub-riemannian geometry from intrinsic viewpoint

Gromov proposed to extract the (differential) geometric content of a sub-riemannian space exclusively from its Carnot-Carathéodory distance. One of the most striking features of a regular sub-riemannian space is that it has at any point a metric tangent space with the algebraic structure of a Carnot group, hence a homogeneous Lie group. Siebert characterizes homogeneous Lie groups as locally co...

Affine Integral Geometry from a Differentiable Viewpoint

The notion of a homogeneous contour integral is introduced and used to construct affine integral invariants of convex bodies. Earlier descriptions of this construction rely on a Euclidean structure on the ambient vector space, so the behavior under linear transformations is established after the fact. The description presented here relies only on the linear structure and a Lebesgue measure on t...

Information Geometry on Complexity and Stochastic Interaction

Interdependencies of stochastically interacting units are usually quantified by the Kullback-Leibler divergence of a stationary joint probability distribution on the set of all configurations from the corresponding factorized distribution. This is a spatial approach which does not describe the intrinsically temporal aspects of interaction. In the present paper, the setting is extended to a dyna...

Information geometry on complexity and stochastic interaction