相关论文: A numerical study on the dimension of an extremely…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
We consider a toy metric in four dimensional space-time defined in terms of a recursive hierarchical prescription. The matter distribution turns out to be extremely inhomogeneous. Surprisingly, for very large samples the average mass…
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the `most difficult location and scale' at which to cover the set and its…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…
We present a geometrical model of the distribution of luminous matter in the universe, derived from a very simple reaction-diffusion model of turbulent phenomena. The apparent dimension of luminous matter, $D(l)$, depends linearly on the…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
We study the irregularities of distribution on two-point homogeneous spaces. Our main result is the following: let $d$ be the real dimension of a two point homogeneous space $\mathcal{M}$, let $\left( \{ a_{j}\} _{j=1}^{N},\{ x_{j}\}…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
We investigate structure formation in a one dimensional model of a matter-dominated universe using a quasi-newtonian formulation. In addition to dark matter, luminous matter is introduced to examine the potential bias in the distributions.…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
Dark matter (DM) clustering at the present epoch is investigated from a fractal viewpoint in order to determine the scale where the self-similar scaling property of the DM halo distribution transits to homogeneity. Methods based on…