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The maximum achievable rate or mutual informa- tion of multidimensional rotationally invariant distributions in the presence of additive white Gaussian noise is analyzed. A simple expression for the special case of multisphere distributions…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way ensuring that the morphology of the reconstructed…
We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions…
We derive the stellar and circumstellar parameters of the Galactic compact planetary nebula Hen 2-90 with two models: the classical constant density nebula model where the emission (especially of the forbiden lines) is formed in a sphere or…
The relaxed motion of stars and gas in galactic discs is well approximated by a rotational velocity that is a function of radial position only, implying that individual components have lost any information about their prior states.…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
We use spin-density-functional theory to study the spacing between conductance peaks and the ground-state spin of 2D model quantum dots with up to 200 electrons. Distributions for different ranges of electron number are obtained in both…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We propose two novel algorithms for distributed and location-free boundary recognition in wireless sensor networks. Both approaches enable a node to decide autonomously whether it is a boundary node, based solely on connectivity information…
We analyze formation of grand-design two-arm spiral structure in the nuclear regions of disk galaxies. Such morphology has been recently detected in a number of objects using high-resolution near-infrared observations. Motivated by the…
In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…
The distributions of the random distances associated with hexagons, rhombuses and triangles have been derived and verified in the existing work. All of these geometric shapes are related to each other and have various applications in…
We investigate the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard sphere systems using a theoretical framework based on the equilibrium model of crowding. We derive a closed-form solution for $\phi_\textrm{RCP}$ in…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
The minimum orbital separation of planets in long-stable planetary systems is often modeled as a step function, parameterized with a single value $\Delta_{min}$ (measured in mutual Hill radius of the two neighboring planets). Systems with…