The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by Gray category data. These can be viewed as a generalisation of ribbon diagrams. The Gray categories present two types of duals, which are extended to functor...

Abstract. According to Thurston’s classification, the set of homotopy classes orientation-preserving homeomorphisms orientable surfaces is split into four disjoint subsets. A class from each subset characterized by existence a homeomorphism called canonical form, namely: periodic homeomorphism, reducible nonperiodic algebraically finite order, that not an and pseudo-Anosov homeomorphism. forms ...

We present a relation between the rotation of chain transitive sets and the rotation shadowing for annulus homeomorphisms isotopic to identity.

This paper extends, in a multi-dimensional framework, pattern recognition techniques for generation or recognition of digital lines. More precisely, we show how the connection between chain codes of digital lines and continued fractions can be generalized by a connection between tilings and multi-dimensional continued fractions. This leads to a new approach for generating and recognizing digita...

1Marvell Hong Kong Ltd., Hong Kong 2CSIRO Information Communication Technologies Center, Australia 3Telecommunications Research Center Vienna (ftw.), Donau-City-StraBe 1, 1220 Vienna, Austria 4Division of Signal Processing, Luleå University of Technology, and Upzide Labs, Luleå, Sweden 5Aktino Inc., Irvine, California, USA 6Electrical and Computer Engineering Department, University of Toronto, ...