Related papers: Weak Separation, Pure Domains and Cluster Distance

Clusters of galaxies, the most massive virialized systems known, provide a powerful tool for studying the structure, the mass density, and the cosmology of our universe. Clusters furnish one of the best estimates of the dynamical mass…

Weak lensing applied to deep optical images of clusters of galaxies provides a powerful tool to reconstruct the distribution of the gravitating mass associated to these structures. We use the shear signal extracted by an analysis of deep…

We investigate the problem of exact cluster recovery using oracle queries. Previous results show that clusters in Euclidean spaces that are convex and separated with a margin can be reconstructed exactly using only $O(\log n)$ same-cluster…

We present two weak lensing reconstructions of the nearby ($z_{cl}=0.055$) merging cluster Abell 3667, based on observations taken $\sim 1$ year apart under different seeing conditions. This is the lowest redshift cluster with a weak…

The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be…

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…

Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…

In the kernel clustering problem we are given a large $n\times n$ positive semi-definite matrix $A=(a_{ij})$ with $\sum_{i,j=1}^na_{ij}=0$ and a small $k\times k$ positive semi-definite matrix $B=(b_{ij})$. The goal is to find a partition…

Stars in open clusters are powerful probes of the intervening Galactic magnetic field, via background starlight polarimetry, because they provide constraints on the magnetic field distances. We use 2MASS photometric data for a sample of 31…

An irreducible algebraic decomposition $\cup_{i=0}^{d}X_i=\cup_{i=0}^{d} (\cup_{j=1}^{d_i}X_{ij})$ of an affine algebraic variety X can be represented as an union of finite disjoint sets $\cup_{i=0}^{d}W_i=\cup_{i=0}…

Let $X$ be a Banach space and $\mu$ a probability measure. A set $K \subseteq L^1(\mu,X)$ is said to be a $\delta\mathcal{S}$-set if it is uniformly integrable and for every $\delta>0$ there is a weakly compact set $W \subseteq X$ such that…

The early evolution of massive cluster progenitors is poorly understood. We investigate the fragmentation properties from 0.3 pc to 0.06 pc scales of a homogenous sample of infrared-quiet massive clumps within 4.5 kpc selected from the…

The galaxy cluster 1E0657-56 (z = 0.296) is remarkably well-suited for addressing outstanding issues in both galaxy evolution and fundamental physics. We present a reconstruction of the mass distribution from both strong and weak…

We propose counting peaks in weak lensing (WL) maps, as a function of their height, to probe models of dark energy and to constrain cosmological parameters. Because peaks can be identified in two-dimensional WL maps directly, they can…

In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…

Galaxy clusters provide a unique probe of the late-time cosmic structure and serve as a powerful independent test of the $\Lambda$CDM model. This work presents the first set of cosmological constraints derived with ~16,000 optically…

Galaxy clusters are the most massive gravitationally bound systems consisting of dark matter, hot baryonic gas and stars. They play an important role in observational cosmology and galaxy evolution studies. We develop a deep learning model…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

Aims: We present a wide-field multi-color survey of a homogeneous sample of eleven clusters of galaxies for which we measure total masses and mass distributions from weak lensing. Methods: The eleven clusters in our sample are all X-ray…