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Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for…
We describe two new -- stochastic-geometrical -- methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods,…
Identifying Blaschke-Santal\'o diagrams is an important topic that essentially consists in determining the image $Y=F(X)$ of a map $F:X\to{\mathbb{R}}^d$, where the dimension of the source space $X$ is much larger than the one of the target…
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…
Computed tomography (CT) can capture volumes large enough to measure a statistically meaningful number of micron-sized particles with a sufficiently good resolution to allow for the analysis of individual particles. However, the development…
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
Design of photonic crystals having large bandgaps above a prescribed band is a well-known physical problem with many applications. A connection to an interesting mathematical construction was pointed out some time ago: it had been…
We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…
Machine learning techniques have been used to quantify the relationship between local structural features and variations in local dynamical activity in disordered glass-forming materials. To date these methods have been applied to an array…
Swarm robotics, or very large-scale robotics (VLSR), has many meaningful applications for complicated tasks. However, the complexity of motion control and energy costs stack up quickly as the number of robots increases. In addressing this…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
We present a simple wavefront-like approach for computing multiplicatively weighted Voronoi diagrams of points and straight-line segments in the Euclidean plane. If the input sites may be assumed to be randomly weighted points then the use…
Image recognition tasks that involve identifying parts of an object or the contents of a vessel can be viewed as a hierarchical problem, which can be solved by initial recognition of the main object, followed by recognition of its parts or…
The typical cell of a Voronoi tessellation generated by $n+1$ uniformly distributed random points on the $d$-dimensional unit sphere $\mathbb S^d$ is studied. Its $f$-vector is identified in distribution with the $f$-vector of a beta'…
This work describes and demonstrates the operation of a virtual X-ray algorithm operating on finite-element post-processing results which allows for higher polynomial orders in geometry representation as well as density distribution. A…
A new approach to the generation of random sequences and two dimensional random patterns is proposed in this paper in which random sequences are generated by making use of either Delaunay triangulation or Voronoi diagrams drawn from random…
This paper presents a new technique for the virtual reality (VR) visu-alization of complex volume images obtained from computer tomography (CT) and Magnetic Resonance Imaging (MRI) by combining three-dimensional (3D) mesh processing and…
A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric…
Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using…