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• W4200465235 abstract "In this report we discuss topological studies of large scale structure of the Universe (LSS) from XMM-Newton, Sloan Digital Sky Survey and simulated data of galaxy distribution. Early works in this mentioned field were based on genus statistics, which is averaged curvature of isosurface of smoothed density field. Later, significant number of other methods was developed. This comprise Euler characteristics, Minkowski functionals, Voronoi clustering, alpha shapes, Delanuay tesselation, Morse theory, Hessian matrix and Soneira-Peebles models. In practice, modern topology methods are reducedto calculation of the three Betti numbers which shall be interpreted as a number of galaxy clusters, filaments and voids. Such an approach was applied by different authors both for simulated and observed LSS data. Topology methods are generally verified using LSS simulations. Observational data normally includes SDSS, CFHTLS and other surveys. These data have many systematical and statistical errors and gaps. Furthermore, there is also a problem of underlying dark matter distribution. The situation is not better in relation to calculations of the power spectrum and its power law index which does not provide a clear picture as well. In this work we propose some tools to solve above problems. First, we performed topology description of simple LSS models such as cubic, graphite-like and random Gaussian distribution of matter. Our next idea is to set a task for LSS topology assessment using X-ray observations of the galaxies. Although, here could be a major complication due to current lack of detected high energy emitting galaxies. Nevertheless, we are expecting to get sufficient results in the future encouraging comprehensive X-ray data. Here we present analysis of statistical moments for four galaxy samples and compare them with the behavior of Betti numbers. Finally, we consider the options of applying artificial neural networks to observed galaxies and fill the data deficiency. This shall enable to define topology at least for superimposed superclusters and other LSS elements." @default.
• W4200465235 created "2021-12-31" @default.
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• W4200465235 date "2021-12-03" @default.
• W4200465235 modified "2023-09-27" @default.
• W4200465235 title "DETERMINATION OF GALAXY DISTRIBUTION WITH STATISTICAL MOMENTS" @default.
• W4200465235 doi "https://doi.org/10.18524/1810-4215.2021.34.244253" @default.
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