Related papers: Fractal dimension analysis for automatic morpholog…
Encoded within the morphological structure of galaxies are clues related to their formation and evolutionary history. Recent advances pertaining to the statistics of galaxy morphology include sophisticated measures of concentration (C),…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
The two-step galaxy morphology classification framework {\tt USmorph} successfully combines unsupervised machine learning (UML) with supervised machine learning (SML) methods. To enhance the UML step, we employed a dual-encoder architecture…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
The Interstellar Medium seems to have an underlying fractal structure, which can be characterized through its fractal dimension (Df). However, several factors may affect the determination of Df, such as distortions due to projection, low…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
We discuss the problem of galaxy correlations by considering the various methods by which this information can be obtained. We focus in particular on the volume limited three dimensional samples and discuss a new way to increase the scale…
Accurate measurement of galaxy structures is a prerequisite for quantitative investigation of galaxy properties or evolution. Yet, the impact of galaxy inclination and dust on commonly used metrics of galaxy structure is poorly quantified.…
In this work we introduce the curvature of a galaxy brightness profile to identify its structural subcomponents in a non-parametrically fashion. Bulges, bars, disks, lens, rings and spiral arms are key to understand the formation and…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…
The classification of galaxy morphology is a hot issue in astronomical research. Although significant progress has been made in the last decade in classifying galaxy morphology using deep learning technology, there are still some…
The incredible variety of galaxy shapes cannot be summarized by human defined discrete classes of shapes without causing a possibly large loss of information. Dictionary learning and sparse coding allow us to reduce the high dimensional…
We present a simple method for evaluating the nonlinear biasing function of galaxies from a redshift survey. The nonlinear biasing is characterized by the conditional mean of the galaxy density fluctuation given the underlying mass density…
In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
We created a catalog of photometric redshift of ~3,000,000 SDSS galaxies annotated by their broad morphology. The photometric redshift was optimized by testing and comparing several pattern recognition algorithms and variable selection…