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We study the redshift space correlation function of galaxy clusters for observational samples constructed in different surveys. We explore correlation amplitudes, pairwise velocity distributions and bias factors. Systematics in cluster…
The Northern Sky Optical Cluster Survey is a project to create an objective catalog of galaxy clusters over the entire high-galactic-latitude Northern sky, with well understood selection criteria. We use the object catalogs generated from…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
Measuring the evolution in the clustering of galaxies over a large redshift range is a challenging problem. For a two-dimensional galaxy catalog, however, we can measure the galaxy-galaxy angular correlation function which provides…
The upcoming XMM Large Scale Structure Survey (XMM-LSS) will ultimately provide a unique mapping of the distribution of X-ray sources in a contiguous 64 sq. deg. region. In particular, it will provide the 3-dimensional location of about 900…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
An important aspect of the shape of a distribution is the level of asymmetry. Strong asymmetries play a role in many ecosystems and are found in the size and reproductive success of individuals. But the standard third moment coefficient of…
In the near future a new generation of CCD based galaxy surveys will enable high precision determination of the N-point correlation functions. The resulting information will help to resolve the ambiguities associated with two-point…
We present models for the three-point correlation function (3PCF) of both dark matter and galaxies. We show that models based on the halo model can reasonably match the dark matter 3PCF obtained from high-resolution $N$-body simulations. On…
In the classical transformer attention scheme, we are given three $n \times d$ size matrices $Q, K, V$ (the query, key, and value tokens), and the goal is to compute a new $n \times d$ size matrix $D^{-1} \exp(QK^\top) V$ where $D =…
We exploit the VST ATLAS quasar/QSO catalogue to perform three measurements of the quasar halo mass profile. First, we make a new estimate of the angular auto-correlation function of $\approx230,000$ ATLAS quasars with $z_{photo}\lesssim…
The growing availability of three-dimensional point process data asks for a development of suitable analysis techniques. In this paper, we focus on two recently developed summary statistics, the conical and the cylindrical $K$-function,…
We discuss statistical techniques for detecting and quantifying bimodality in astronomical datasets. We concentrate on the KMM algorithm, which estimates the statistical significance of bimodality in such datasets and objectively partitions…
In many applications of X-ray computed tomography, an unsupervised segmentation of the reconstructed 3D volumes forms an important step in the image processing chain for further investigation of the digitized object. Therefore, the goal is…
Scaling relations of galaxy clusters are a powerful probe of cosmic isotropy in the late Universe. Owing to their strong cosmological dependence, galaxy cluster scaling relations can obtain tight constraints on the spatial variation of…
Previous work on three-point statistics of cosmic shear has mainly concentrated on the convergence, or on aperture measures of the shear. However, as has become clear recently for the two-point statistics of cosmic shear, the basic quantity…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method. In this paper, we extend our…
High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing such correlation functions is computationally expensive. We aim to circumvent these challenges by designing…
One emerging application of machine learning methods is the inference of galaxy cluster masses. In this note, machine learning is used to directly combine five simulated multiwavelength measurements in order to find cluster masses. This is…