We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a ...

As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent ...

Wigner's particle classification provides for "continuous spin" representations of the Poincaré group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by ...

On the other hand, Virtual Element Methods (VEM) [1, 12, 13] allow to handle general polygonal elements. In the case of triangular elements, VEM reduces to the usual FEM. Thus, VEM is a natural choice for constructing space ...

This chapter discusses a simple mathematical model of drinking lapse. Problem drinking is modeled as an acquired state - the result of frequent or intense interactions among individuals in three drinking states within a ...

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal ...

An ant colony optimization approach for partitioning a set of objects is proposed. In order to minimize the intra-variance, or within sum-of-squares, of the partitioned classes, we construct ant-like solutions by a ...