Related papers: Strongly mixing smooth planar vector field without…
We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…
We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…
In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with…
We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on…
This paper is concerned with an algorithm for finding a singularity of the nonsmooth vector fields. Firstly, we discuss the main results of the Newton method presented in [1] for solving the aforementioned problem. Combining this method…
We propose and demonstrate a novel method for generating propagation-invariant spatially-stationary fields in a controllable manner. Our method relies on producing incoherent mixtures of plane waves using planar primary sources that are…
Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…
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 $\theta$.…
This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational…
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…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…
We construct a polynomial planar vector field of degree two with one invariant algebraic curves of large degree. We exhibit an explicit quadratic vector fields which invariant curves of degree nine, twelve, fifteen and eighteen degree.
The following observation must surely be "well-known", but it seems worth giving a simple and quite explicit proof. Take any finite subset X of Rn, n>1. Then, there is a polynomial function P:Rn -> R which has local minima on the set X, and…
I present a concise review of advances realized over the past three years on planar Poisson-Voronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data.
Mixing-via-shearing is a powerful and versatile method for establishing mixing properties of smooth parabolic flows. In its quantitative form, it provides upper bounds on the decay of correlations for sufficiently smooth observables.…
We are developing a new method for the analysis of queuing systems with heterogeneous in time and space compound (marked) Poisson input flow. The state space of the input flow is embedded in a higher-dimensional space with a homogeneous…
The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors,…
The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated…