Related papers: Voronoi Cell Patterns: theoretical model and appli…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ~40% and a skewed parent size distribution. We introduce a novel…
Given a set $\mathsf{P}$ of $n$ points in $\mathbb{R}^d$, we show how to insert a set $\mathsf{X}$ of $O( n^{1-1/d} )$ additional points, such that $\mathsf{P}$ can be broken into two sets $\mathsf{P}_1$ and $\mathsf{P}_2$, of roughly equal…
The pair correlation function (PCF) has proven an effective tool for analyzing many physical systems due to its simplicity and its applicability to simulated and experimental data. However, as an averaged quantity, the PCF can fail to…
Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the origin. When the intensity goes to infinity, we show that…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving…
We extend the theory of logarithmic Voronoi cells to Gaussian statistical models. In general, a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log-normal spectrahedron. We show that for models of ML…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
We investigate the local- and long-range structure of four different space-filling cellular patterns: bubbles in a quasi-2d foam plus Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton…
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$.…
A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…
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…
Multicellular rosettes are observed in different situations such as morphogenesis, wound healing, and cancer progression. While some molecular insights have been gained to explain the presence of these assemblies of five or more cells…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…