Related papers: Logarithmic Voronoi cells

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…

In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in…

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…

For a two dimensional vector $\bar v=(\alpha,\beta)$, where $\alpha>0, \beta>0$ are irrational numbers independent over $\mathbb{Q}$, we consider the set $D_n=\{(i\alpha\,{\rm mod}\,1,i\beta\,{\rm mod}\,1),i=1,\ldots,n\}$ in a two…

This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…

Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples…

We apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\QQ $-algebra. This may be used to show in small cases that non-conjugate…

This article proves the Voronoi conjecture on parallelotopes in the special case of 3-irreducible tilings. Parallelotopes are convex polytopes which tile the Euclidean space by their translated copies, like in the honeycomb arrangement of…

By a new Monte Carlo algorithm we evaluate the sidedness probability p_n of a planar Poisson-Voronoi cell in the range 3 \leq n \leq 1600. The algorithm is developed on the basis of earlier theoretical work; it exploits, in particular, the…

The relative algebraic monodromy of abelian logarithms (defined as the kernel of a map between algebraic monodromy groups attached to an abelian scheme with and without a section) was computed in \cite{A1}: under natural assumptions, this…

Consider a Voronoi tiling of the Euclidean space based on a realization of a inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles. In this paper we provide tail bounds for the number of…

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…

We study the differential structure of the set of real logarithms of a non-singular real matrix, under the assumption that the matrix is either semi-simple or orthogonal.

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…

Volume polynomials form a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties. I will survey realization problems related to them, review fundamental inequalities they satisfy, and discuss…

In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is…

In this paper, we are interested in the behavior of the typical Poisson-Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to infinity. We prove a law of large numbers for…

We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in…

For a Borel set $A$ and a homogeneous Poisson point process $\eta$ in $\R^d$ of intensity $\lambda >0$, define the Poisson--Voronoi approximation $ A_\eta$ of $A$ as a union of all Voronoi cells with nuclei from $\eta$ lying in $A$. If $A$…