Related papers: Weak Separation, Pure Domains and Cluster Distance

We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…

We test the precision with which weak lensing data can provide characteristic cluster mass profiles within Cold Dark Matter scenarios. Using a parallel treecode to simulate volumes as large as 500h-1 Mpc with good resolution, we generate…

Let $X$ be a finite collection of sets (or "clusters"). We consider the problem of counting the number of ways a cluster $A \in X$ can be partitioned into two disjoint clusters $A_1, A_2 \in X$, thus $A = A_1 \uplus A_2$ is the disjoint…

Weak gravitational lensing provides a direct way to study the mass distribution of clusters of galaxies at large radii. Unfortunately, large scale structure along the line of sight also contributes to the lensing signal, and consequently…

Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…

Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…

This is the third of a series of papers of low X-ray luminosity galaxy clusters. In this work we present the weak lensing analysis of eight clusters, based on observations obtained with the Gemini Multi-Object Spectrograph in the $g'$, $r'$…

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…

The reliability of cluster lens reconstruction techniques based on weak lensing is studied in terms of the accuracy of their reproduction of the total cluster mass as a function of distance from the cluster center. To do so, a variety of…

The sensitivity and wide area reached by ongoing and future wide-field optical surveys allows for the detection of an increasing number of galaxy clusters uniquely through their weak lensing (WL) signal. This motivates the development of…

We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight $w(x)=\operatorname{dist}(x,E)^{-\alpha}$ belongs to the Muckenhoupt class $A_1$, for some $\alpha>0$, if and only if…

Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster…

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…

We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…

We use the galaxy cluster X-ray temperature distribution function to constrain the amplitude of the power spectrum of density inhomogeneities on the scale corresponding to clusters. We carry out the analysis for critical density universes,…

We derive cosmological constraints using a galaxy cluster sample selected from the 2500~deg$^2$ SPT-SZ survey. The sample spans the redshift range $0.25< z<1.75$ and contains 343 clusters with SZ detection significance $\xi>5$. The sample…

Galaxy clusters are important targets for peculiar velocity studies as a direct comparison of the various distance indicators can be made. The potential problem of an environmental effect biasing the distances to clusters of different…

We report on the XMM-Newton (XMM) observation of RXJ1053.7+5735, one of the most distant X-ray selected clusters of galaxies, which also shows an unusual double-lobed X-ray morphology, indicative of a possible equal-mass cluster merger. The…

The statistical properties of galaxy clusters can only be used for cosmological purposes if observational effects related to cluster detection are accurately characterized. These effects include the selection function associated to cluster…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…