Application of universal multipoint invariants in Euclidean and pseudo-Euclidean spaces

Phone classification in pseudo-euclidean vector spaces

Recently we have proposed a structural framework for modelling speech, which is based on patterns of phonological distinctive features, a linguistically well-motivated alternative to standard vector-space acoustic models like HMMs. This framework gives considerable representational freedom by working with features that have explicit linguistic interpretation, but at the expense of the ability t...

Euclidean Invariants of Linear Scale-Spaces

The similarity jet of a linear scale-space is described in its most concise set of local and multi-local Euclidean invariants. The stability and (partial) equivalence of topologies on these invariants regardless additive uniform Gaussian noise is demonstrated.

Spaces of pseudo - Riemannian geodesics and pseudo - Euclidean billiards Boris

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...

Spaces of pseudo-Riemannian geodesics and pseudo-Euclidean billiards

Many classical facts in Riemannian geometry have their pseudoRiemannian analogs. For instance, the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce an...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains