The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A single parameter of control allows to describe, in a common framework, different types of decorations, by liquid triangles or 3-sided bubbles, and other non-conv...

In this work, we describe a set of coordinates on the PU(2,1)-representation variety of the fundamental group of an oriented punctured surface Σ with negative Euler characteristic. The main technical tool we use is a set of geometric invariants of a triple of flags in the complex hyperpolic plane H C . We establish a bijection between a set of decorations of an ideal triangulation of Σ and a su...

The Decoration Conjecture describes the structure of the set of braid types of Smale’s horseshoe map ordered by forcing, providing information about the order in which periodic orbits can appear when a horseshoe is created. A proof of this conjecture is given for the class of so-called lone decorations, and it is explained how to calculate associated braid conjugacy invariants which provide add...

the relative eye size, types of visual cell and mosaic, and the existence of retinal tapetum in the eyes of the spotted barb puntius binotatus were determined to gain baseline information on its visual capability. the p. binotatus acquired relatively larger eye size than the other similar sized freshwater fish species with its retina being contained both cone and rod visual cells (cone ellipsoi...

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as a coloring of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.

decorations of parse forests usingdynamic programming and algebraicpower series. Theoretical Computer Science.To appear.Tendeau, Frédéric. 1997b. An Earleyalgorithm for generic attribute augmentedgrammars and applications. In Proceedingsof the International Workshop on ParsingTechnologies 1997, pages 199–209.Viterbi, Andrew J. 1967. Error bounds forconvol...

This paper proposes a novel method of applying feedback control for legged robots, by directly modifying parameters of a robot’s gait pattern. Gaits are a popular means of producing stable locomotion for legged robots, through the use of cyclic feedforward motion patterns, while requiring little to no sensory information. We are interested in incorporating feedback with these systems, and make ...