Related papers: A new method for accurate velocity statistics esti…
We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic…
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…
The reconstruction of density and velocity fields is of central importance to the interpretation of $N$-body simulations. We propose a phase-space extension of the Delaunay tessellation field estimator (DTFE) that tracks the dark matter…
In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular…
We propose a new velocity reconstruction method based on the displacement estimation by recently developed methods. The velocity is first reconstructed by transfer functions in Lagrangian space and then mapped into Eulerian space. High…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
Mobile network operator (MNO) data are a rich data source for official statistics, such as present population, mobility, migration, and tourism. Estimating the geographic location of mobile devices is an essential step for statistical…
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…
Characterizing the spacing of primary dendrite arms in directionally-solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing…
The Voronoi Entropy (VE) and the continuous measure of symmetry (CSM) characterize the orderliness of a set of points on a 2D plane. The Voronoi entropy is the Shannon entropy of the Voronoi tessellation of the plane into polygons,…
Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically non-trivial fluctuations of the velocity field, over a wide range of length- and time-scales, and it can be quantitatively described…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
In a crowd, individuals make different motion choices such as "moving to destination", "following another pedestrian", and "making a detour". For the sake of convenience, the three direction choices are respectively called destination…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
$n$ independent random points drawn from a density $f$ in $R^d$ define a random Voronoi partition. We study the measure of a typical cell of the partition. We prove that the asymptotic distribution of the probability measure of the cell…
Analyzing the microscopic dynamics of pushing behavior within crowds can offer valuable insights into crowd patterns and interactions. By identifying instances of pushing in crowd videos, a deeper understanding of when, where, and why such…
Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely…
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…
Quantization of a probability distribution is the process of estimating a given probability by a discrete probability that assumes only a finite number of levels in its support. Centroidal Voronoi tessellations (CVT) are Voronoi…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…