We study the geometry of tessellation defined by the walls in the Moussong complex MW of a Coxeter group W . It is proved that geodesics in MW can be approximated by geodesic galleries of the tessellation. A formula for the translation length of an element of W is given. We prove that the restriction of the word metric on the W to any free abelian subgroup A is Hausdorff equivalent to a regular...

A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods f...

It is proved that the shape of the typical cell of a stationary Poisson-Voronoi tessellation in Euclidean space, under the condition that the volume of the typical cell is large, must be close to spherical shape, with high probability. The same holds if the volume is replaced by the surface area or other suitable functionals. Similar results hold for the zero cell of a stationary and isotropic ...

A homogeneous Poisson-Voronoi tessellation of intensity γ is observed in a convex body W . We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and included in the cell, and the circumscribed radius, i.e. the radius of the smallest ball centered at the nucleus and containing the cell. We investigate the...

A vector quantizer maps N -dimensional vectors in the domain Ω ⊂ R into a finite set of vectors {zi}i=1 . Each vector zi is called a code vector or a codeword, and the set of all the codewords is called a codebook. A special, yet popular, quantization scheme is given by the Voronoi tessellation associated with some codewords {zi} , also called generators. A Voronoi tessellation for the given ge...

This paper is about the role of the operating system (OS) within computer nodes of network audio systems. While many efforts in the network-audio community focus on low-latency network protocols, here we highlight the importance of the OS for network audio applications. We present Tessellation, an experimental OS tailored to multicore processors. We show how specific OS features, such as guaran...

Quantum walks have received a great deal of attention recently because they can be used to develop new quantum algorithms and to simulate interesting quantum systems. In this work, we focus on a model called staggered quantum walk, which employs advanced ideas of graph theory and has the advantage of including the most important instances of other discrete-time models. The evolution operator of...

In this paper we define the chromatic number of a lattice: It is least colors one needs to color interiors cells Voronoi tessellation lattice so that no two sharing facet are same color. We compute root lattices, their duals, and Leech lattice, consider lattices Voronoi's first kind, investigate asymptotic behaviour when dimension tends infinity. introduce spectral lower bound for in spirit Hof...

We study a probabilistic algorithm for the computation of the centroidal Voronoi tessellation which is a Voronoi tessellation of a given set such that the associated generating points are centroids (centers of mass) of the corresponding Voronoi regions. We discuss various issues related to the implementation of the algorithm and provide numerical results. Some measures to improve the performanc...