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The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$.…
This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped).…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
With the use of {\em ab initio} based molecular dynamics simulations we study the structural, dynamical and electronic properties of glassy g-GeS$_2$ at room temperature. From the radial distribution function we find nearest neighbor…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…
Let $\mathbb{F}_q$ be a finite field of order $q$ and $E$ be a set in $\mathbb{F}_q^d$. The distance set of $E$ is defined by $\Delta(E):=\{\lVert x-y \rVert :x,y\in E\}$, where $\lVert \alpha \rVert=\alpha_1^2+\dots+\alpha_d^2$. Iosevich,…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
We demonstrate the scale-invariant behavior of electromagnetic wave-driven radio-frequency plasmas across different dimensional scales. Using two-dimensional electromagnetic particle-in-cell simulations, we show that plasma uniformity…
We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite…
We present systematic calculations on the spectroscopy and transition properties of even-even Te isotopes by using the large-scale configuration interaction shell model approach with a realistic interaction. These nuclei are of particular…
From a three-dimensional boundary value problem for the time harmonic classical Maxwell equations, we derive the dispersion relation for a surface wave, the edge plasmon-polariton (EP), that is localized near and propagates along the…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
We analyze polarization phenomena for elastic lepton-nucleon scattering, parametrizing the $2\gamma$-exchange contribution, as the product of lepton and nucleon axial vector currents, that correspond to $C=+1$ exchange in the annihilation…
This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical…
Let $\mathfrak{m}$ be a random tessellation in $\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point $z(C)$…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…