Related papers: Fractal dimension analysis for automatic morpholog…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
We examine a general framework for visualizing datasets of high (> 2) dimensionality, and demonstrate it using the morphology of galaxies at moderate redshifts. The distributions of various populations of such galaxies are examined in a…
The results of morphological galaxy classifications performed by humans and by automated methods are compared. In particular, a comparison is made between the eyeball classifications of 454 galaxies in the Sloan Digital Sky Survey (SDSS)…
In this paper, we prove the identity $\dim_{\textrm H}(F)=d\cdot \dim_{\textrm H}(\alpha^{-1}(F))$, where $\dim_{\textrm H}$ denotes Hausdorff dimension, $F\subseteq \mathbb{R}^d$, and $\alpha:[0,1]\to [0,1]^d$ is a function whose…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
We present a star/galaxy classification for the Southern Photometric Local Universe Survey (S-PLUS), based on a Machine Learning approach: the Random Forest algorithm. We train the algorithm using the S-PLUS optical photometry up to $r$=21,…
Morphology is the starting point for understanding galaxies. Elmegreen et al. classified spiral galaxies into flocculent, multiple-arm, and grand-design galaxies based on the regularity of their spiral arm structure. With the release of a…
Traditionally globular clusters and dwarf spheroidal galaxies have been distinguished by using one or more of the following criteria: (1) mass, (2) luminosity, (3) size, (4) mass-to-light ratio and (5) spread in metallicity. However, a few…
We study the possibility of detecting the transition to homogeneity using photometric redshift catalogs. Our method is based on measuring the fractality of the projected galaxy distribution, using angular distances, and relies only on…
Galaxy morphology encodes key information about formation and evolution. Large imaging surveys require automated, reproducible methods beyond visual inspection. Non--parametric indices provide an useful framework, but their performance must…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
The study of the morphology of galaxies is important in order to understand the formation and evolution of galaxies and their sub-components as a function of luminosity, environment, and star-formation and galaxy assembly over cosmic time.…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
We explore the fractal nature of particle showers using Monte-Carlo simulation. We define the fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
In this work we quantify the degree to which star-forming events are clumped. We apply a precise and accurate technique to calculate the correlation dimension Dc of the distribution of HII regions in a sample of disk galaxies. Our reliable…
We study the distribution of stars, HII regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal…