Recently, Dal Lago and Gaboardi have proposed a type system, named d`PCF as a framework for implicit computational complexity. d`PCF is a non-standard type system for PCF programs which is relatively complete with respect to complexity properties thanks to the use of linear types inspired by Bounded linear logic and dependent types à la Dependent ML. In this work, we adapt the framework of quan...

The local structure of a tiling is described in terms of a multiplicative structure on its pattern classes. The groupoid associated to the tiling is derived from this structure and its integer group of coinvariants is defined. This group furnishes part of the K0-group of the groupoid C ∗-algebra for tilings which reduce to decorations of Z Z . The group itself as well as the image of its state ...

We present a technique for automating the construction of Celtic knotwork and decorations similar to those in illuminated manuscripts such as the Lindisfarne Gospels. Our method eliminates restrictions imposed by previous methods which limited the class of knots that could be produced correctly by introducing new methods for smoothing and orienting threads. Additionally, we present techniques f...

2014 We study dense packings of particles with interactions favouring pentagonal symmetry. Such structures can be obtained by decorations of Penrose tilings or directly with a cut-and-projection method. We prove that they form the degenerated ground-state in the case of pair potentials limited to first neighbours and for interaction strength parameters lying in broad ranges of values. Cooling r...

mohammad-karim pirnia, one of the most prominent scholars of the history of iranian architecture, has recorded two major achievements: the principles of iranian architecture and the stylistics of iranian architecture. in this article we will discuss his suggested principles for iranian architecture. for this purpose, we will first show how his five principles have evolved and completed through ...