Related papers: A new method for accurate velocity statistics esti…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
The survey volume of a proper motion-limited sample is typically much smaller than a magnitude-limited sample. This is because of the noisy astrometric measurements from detectors that are not dedicated for astrometric missions. In order to…
The motion of pedestrians is subject to a wide range of influences and exhibits a rich phenomenology. To enable precise measurement of the density and velocity we use an alternative definition using Voronoi diagrams which exhibits smaller…
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…
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…
The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because…
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…
We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…
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 $\theta$.…
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms…
We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the…
Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on…
We systematically develop beneficial and practical velocity measures for accurate and efficient statistical simulations of the Langevin equation with direct applications to computational statistical mechanics and molecular dynamics…
In this paper two new classes of stationary random simplicial tessellations, the so-called $\beta$- and $\beta'$-Delaunay tessellations, are introduced. Their construction is based on a space-time paraboloid hull process and generalizes…
In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…