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...

This paper presents evidence for a conjecture concerning the structure of the set of braid types of periodic orbits of Smale’s horseshoe map, partially ordered by Boyland’s forcing order. The braid types are partitioned into totally ordered subsets, which are defined by parsing the symbolic code of a periodic orbit into two segments, the prefix and the decoration: the set of braid types of orbi...

In this talk, I will discuss results from our group in the area of computational modeling using density functional theory for reversible hydrogen storage materials. The reversible hydrogen storage is an important area in the context of renewable energy and the reversibility places important challenge. We have studied doped magnesium hydrides as well as decorated metal organic frameworks (MOF). ...

Decoration with atomic motifs in high dimension space is considered in simple cases, and related to the theory of curved spaces in non-periodic structures.

The presence, forms and techniques used in artificial cranial deformation and dental decoration were studied in 1,515 skeletons found in 94 mostly pre-Hispanic archeological sites (in Mexico, Guatemala and Honduras) dating from the Preclassical, Classic and Postclassic periods. Biographical and associated archeological information was analyzed, based on a theoretical model of biocultural intera...