Related papers: Voronoi and Voids Statistics for Super-homogeneous…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…
Uniform laws of large numbers form a cornerstone of Vapnik--Chervonenkis theory, where they are characterized by the finiteness of the VC dimension. In this work, we study uniform convergence phenomena in cartesian product spaces, under…
We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit…
The full statistical distribution of the superfluid fraction characterizing one-dimensional Bose gases in random potentials is discussed. Rare configurations with extreme fluctuations of the disorder potential can fragment the condensate…
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 suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. However, its existence and significance in jammed solids is still a matter of debate. We explore the presence of this hidden order in a…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
The information about the current-carrying ability of a type-II superconductor can be obtained by studying the flux relaxation and vortex penetration phenomena in the superconductor. In early studies, the infinite series models of the flux…
Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result…
We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in…
In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…
Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…
We investigate the statistical properties of two dimensional random cellular systems (froths) in term of their shell structure. The froth is analyzed as a system of concentric layers of cells around a given central cell. We derive exact…
It is well known that the similar universal behavior of infinite-size (bulk) systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range) of the…
We study logarithmic Voronoi cells for linear statistical models and partial linear models. The logarithmic Voronoi cells at points on such model are polytopes. To any $d$-dimensional linear model inside the probability simplex…
Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyse the effect of thermal fluctuations on several signatures of the transition. We show that…
Point processes have broad applications in science and engineering. In physics, their use ranges from quantum chaos to statistical mechanics of many-particle systems. We introduce a spatial form factor (SFF) for the characterization of…
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…