Related papers: A note on generating Voronoi cells with a given si…
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…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…
The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that…
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…
In this paper, we construct a new family of random series defined on $\R^D$, indexed by one scaling parameter and two Hurst-like exponents. The model is close to Takagi-Knopp functions, save for the fact that the underlying partitions of…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
We study percolation in the following random environment: let $Z$ be a Poisson process of constant intensity in the plane, and form the Voronoi tessellation of the plane with respect to $Z$. Colour each Voronoi cell black with probability…
The intersections of beta-Voronoi, beta-prime-Voronoi and Gaussian-Voronoi tessellations in $\mathbb{R}^d$ with $\ell$-dimensional affine subspaces, $1\leq \ell\leq d-1$, are shown to be random tessellations of the same type but with…
The distributions that regulate the spatial domains of the Poissonian Voronoi Diagrams are discussed adopting the sum of gamma variate of argument two. The distributions that arise from the product and quotient of two gamma variates of…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
We review the model of the Voronoi Diagrams which allows to reproduce the large-scale structures of our universe as given by the astronomical catalogs. The observed number of galaxies in a given solid angle with a chosen flux/magnitude…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…
We review the concepts of the Voronoi binning technique (Cappellari & Copin 2003), which optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum…
In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…
Position $n$ points uniformly at random in the unit square $S$, and consider the Voronoi tessellation of $S$ corresponding to the set $\eta$ of points. Toss a fair coin for each cell in the tessellation to determine whether to colour the…
We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which…