Enemy observers, such as cameras and guards, are common elements that provide challenge to many stealth and combat games. Defining the exact placement and movement of such entities, however, is a non-trivial process, requiring a designer balance level-difficulty, coverage, and representation of realistic behaviours. In this work we explore systems for procedurally generating both camera and gua...

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.

This paper shows how to translate the problem of deciding trace refinement between two data independent (DI) CSP processes to an unreachability problem in a DI Unity program. We cover here the straightforward but practically useful case when the specification satisfies a normality condition, Norm, meaning that we do not have to worry about hidden or unrecorded data variables. This allows us to ...

We present some techniques to obtain smooth derivations of concurrent programs that address both safety and progress in a formal manner. Our techniques form an extension to the calculational method of Feijen and van Gasteren using a UNITY style progress logic. We stress the role of stable guards, and we illustrate the derivation techniques on some examples in which progress plays an essential r...

We must mention that the assumption that we are dealing with a Cartan matrix of finite type and a root of unity appears only at the very end (see Chapter 4). We need these assumptions in order to compare our representations with the conventional definition of the category C. All previous results are valid in more general assumptions. In particular a Cartan matrix could be arbitrary and a deform...

A novel idea to construct flat-top partition of unity functions in a closed form on a general (structured or unstructured) finite element mesh is presented. An efficient and practical construction method of a flat-top partition of unity function is important in the generalized finite element method (GFEM). Details on how to construct flat-top partition of unity functions on a provided mesh are ...

pantheism (unity of entity) and unity of intuition are famous concepts in mysticism which have been discussed variously and philosophers and mystics have been presented various opinions and definitions about them. some of them believe pantheism is a spiritual authority which is superior from unity of intuition, and some are opposite to this belief and others believe these two concepts are the s...

Let p ≡ 1 (mod 4) be a prime number and let ζ = e be a primitive root of unity. Then there exists a unique biquadratic extension eld Q(y)/Q that is a sub eld of Q(ζ). The aim of this work is to construct an algorithm for nding such y explicitly. Finally we state a general conjecture about the y we found.