Related papers: Complexity hierarchies in Euclidean stars
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…
Massive stars are linked with diverse astronomical processes and objects including star formation, supernovae and their remnants, cosmic rays, interstellar media, and galaxy evolution. Understanding their properties is of primary importance…
Masking the horizontal branch and giant stars allows unambiguous measurements of mean age and metallicity in simple old stellar populations from metal and hydrogen line strengths. Billion year resolution is possible in the luminous halos of…
The large amount of data on galaxies, up to higher and higher redshifts, asks for sophisticated statistical approaches to build adequate classifications. Multivariate cluster analyses, that compare objects for their global similarities, are…
We investigate the Ulrich complexity of certain examples of Brauer--Severi varieties, twisted flags and involution varieties and establish lower and upper bounds. Furthermore, we relate Ulrich complexity to the categorical representability…
The aim of Galactic archaeology is to recover the history of our Galaxy through the information encoded in stars. An unprobed assumption of this field is that the chemical composition of a star is an immutable marker of the gas from which…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
Some factors connecting the evolutionary histories of galaxies with the characteristics of their cluster systems are reviewed. Unanswered questions include: How is one to understand the observation that some globular cluster systems have…
We analyze the properties of stars whose interior is described by the stiffest equation of state consistent with causality. We note the remarkable fact that the entropy of such stars scales like the area.
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
A brief overview of the properties of massive star clusters in early-type galaxies is given. All ellipticals (with only one known exception) host massive star clusters in the form of globular clusters, suggesting that their formation is…
We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely…
In this work, we construct stellar models ba-\break sed on the complexity factor as a supplementary condition which allows to close the system of differential equations arising from the Gravitational Decoupling. The assumed complexity is a…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
A dense-enough gas-accumulation evolves, over a few Myr of intensifying star formation, to an embedded cluster. If it contains a sufficient amount of mass, O stars form and explosively expel the remaining gas, whereas poorer clusters reduce…
The Hubble tuning fork diagram, based on morphology and established in the 1930s, has always been the preferred scheme for classification of galaxies. However, the current large amount of data up to higher and higher redshifts asks for more…
Nuclear star clusters are among the densest stellar systems known and are common in both early- and late-type galaxies. They exhibit scaling relations with their host galaxy which may be related to those of supermassive black holes. These…