Related papers: Minkowski Functionals of Abell/ACO Clusters
Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously…
We apply Shapefinders, statistical measures of `shape' constructed from two dimensional partial Minkowski functionals, to study the degree of filamentarity in the Las Campanas Redshift Survey (LCRS). In two dimensions, three Minkowski…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL,…
We study the dimensional Brunn-Minkowski inequality for even log-concave probability measures $\mu$ on $\mathbb{R}^n$ via an analytic approach based on diffusion operators and gradient estimates. Our main result asserts that for every pair…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
A novel definition of holographic correlation functions on the celestial sphere of Minkowski space was recently introduced in arXiv:2301.01810 as the extrapolation of bulk time-ordered correlation functions to the celestial sphere. In this…
We study the possible rotation of cluster galaxies, developing, testing and applying a novel algorithm which identifies rotation, if such does exist, as well as its rotational centre, its axis orientation, rotational velocity amplitude and,…
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was…
We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-Hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By…
The $k$-Nearest Neighbour Cumulative Distribution Functions are measures of clustering for discrete datasets that are fast and efficient to compute. They are significantly more informative than the 2-point correlation function. Their…
We present new estimates of the spatial two-point correlation function of rich clusters of galaxies selected from the APM Galaxy Survey. We have measured redshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. The…
We use high resolution dissipationless N-body simulations to examine the spatial distribution of galaxy clusters on large scales. The Standard CDM model and two of its main competitors, Low density CDM and Mixed Dark Matter are compared.The…
The recent progress in obtaining larger and deeper galaxy catalogues is of fundamental importance for cosmological studies, especially to robustly measure the large scale density fluctuations in the Universe. The present work uses the…
The detection of primordial $B$-mode polarisation of the Cosmic Microwave Background (CMB) is a major observational goal in modern Cosmology, offering a potential window into inflationary physics through the measurement of the…
We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble Volume N-body simulations. The correlation function of clusters shows no enhancement along the line of sight, due to the lack of…
We report the {\em first} systematic study of the supercluster-void network in the $\Lambda$CDM concordance cosmology treating voids and superclusters on an equal footing. We study the dark matter density field in real space smoothed with…
Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators for point clouds, e.g., representing voxelized data, however, are unavoidably biased…
We have made a comparative study of morphological evolution in simulated DM halos and X-ray brightness distribution, and in optical clusters. Samples of simulated clusters include star formation with supernovae feedback, radiative cooling,…
We recover the luminosity distributions over a wide range of absolute magnitude (-24.5 < M_{R} < -16.5) for a sample of seven rich southern galaxy clusters. We find a large variation in the ratio of dwarf to giant galaxies, DGR: 0.8\le $…