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Cosmic web environments : identification, characterisation, and quantification of cosmological information
Abstract
The late-time matter distribution depicts a complex pattern commonly called the cosmic web. In this picture, the spatial arrangement of matter is that of dense anchors, the nodes, linked together by elongated bridges of matter, the filaments, found at the intersection of thin mildly-dense walls, themselves surrounding large empty voids. This distribution, shaped by gravitational forces since billions of years, carries crucial information on the underlying cosmological model and on the evolution of the large-scale structures. Detecting and studying elements of cosmic web, playing also a key role in the formation and evolution of galaxies, are challenging tasks requiring the elaboration of optimised methods to handle the intrinsic complexity of the pattern made of multi-scale structures of various shapes and densities.With the aim of identifying and characterising the cosmic web environments, we propose several approaches to analyse spatially structured point-cloud datasets, not restricted to cosmological ones, by means of unsupervised machine learning methods based on mixture models. In particular, we use principles emanating from statistical physics to get a better understanding of the learning dynamics of a clustering algorithm and expose how statistical physics can be used to explore the data distribution and obtain key insights on its structure.In order to identify the filamentary part of the pattern, its most prominent feature, we propose a regularisation of the clustering procedure to iteratively learn a non-linear representation of structured datasets, assuming it was generated by an underlying one-dimensional manifold. The method models this latent structure as a graph embedded as a prior in the Bayesian formulation of the problem to estimate a principal graph passing in the ridges of the matter distribution as traced by galaxies or halos.We show that this formulation is especially well-suited for the description of the filaments since it allows the description of their geometrical properties (lengths, widths, etc.) and associates to each tracer a probability of residing in a given filament. The resulting algorithm is successfully used to detect filaments in state-of-the-art numerical simulations. It also allows us to study the relation between the connectivity of galaxy clusters to the cosmic web and their dynamical and morphological properties. Finally, based on a large suite of N-body simulations, we perform a comprehensive analysis of the cosmological information content based on the two-point statistics derived in the cosmic web environments (nodes, filaments, walls and voids). We show that they can break some degeneracies among key parameters of the model making them a suitable alternative probe to significantly improve the constraints on cosmological parameters obtained by standard analyses.
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The primary goal of pattern recognition is supervised or
unsupervised classification. Among the various frameworks in which
pattern recognition has been traditionally formulated, the statistical
approach has been most intensively studied and used in practice. More
recently, neural network techniques and methods imported from
statistical learning theory have been receiving increasing attention.
The design of a recognition system requires careful attention to the
following issues: definition of pattern classes, sensing environment,
pattern representation, feature extraction and selection, cluster
analysis, classifier design and learning, selection of training and test
samples, and performance evaluation. In spite of almost 50 years of
research and development in this field, the general problem of
recognizing complex patterns with arbitrary orientation, location, and
scale remains unsolved. New and emerging applications, such as data
mining, web searching, retrieval of multimedia data, face recognition,
and cursive handwriting recognition, require robust and efficient
pattern recognition techniques. The objective of this review paper is to
summarize and compare some of the well-known methods used in various
stages of a pattern recognition system and identify research topics and
applications which are at the forefront of this exciting and challenging
field
The 3D 2-point correlation function xi(R) for a sample of 70 Abell
clusters in the richness class 2 or greater and redshifts of z between
0.06 and 0.24 in the southern galactic hemisphere (southern semi-cone)
is calculated. Redshifts for 30 clusters from the sample were measured
directly; for other clusters, the Leir-van den Bergh estimates were
used. The validity of the method used was tested on a previously used
sample from the northern cone region. The correlation function has a
peak of xi = 0.6 at R = 250(50/H) Mpc, as in the case of the Northern
cone sample. The peak disappears when a larger sample including less
rich Abell clusters of the same region is used. A list of 23 new values
of z for Abell clusters in the southern galactic hemisphere, measured
with a 6-m telescope, is also presented.
Because of mass assignment onto grid points in the measurement of the power spectrum using a fast Fourier transform (FFT), the raw power spectrum |δf(k)|2 estimated with the FFT is not the same as the true power spectrum P(k). In this paper we derive a formula that relates |δf(k)|2 to P(k). For a sample of N discrete objects, the formula reads |δf(k)|2 = [|W( + 2kN)|2P( + 2kN) + 1/N|W( + 2kN)|2], where W(k) is the Fourier transform of the mass assignment function W(r), kN is the Nyquist wavenumber, and n is an integer vector. The formula is different from that in some previous works in which the summation over n is neglected. For the nearest grid point, cloud-in-cell, and triangular-shaped cloud assignment functions, we show that the shot-noise term |W( + 2kN)|2 can be expressed by simple analytical functions. To reconstruct P(k) from the alias sum |W( + 2kN)|2P( + 2kN), we propose an iterative method. We test the method by applying it to an N-body simulation sample and show that the method can successfully recover P(k). The discussion is further generalized to samples with observational selection effects.
Data for 24 galaxies shows a correlation between distance and radial velocity.