Related papers: Computing 3 point correlation function randoms cou…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
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…
Though Fourier Transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle…
The three-point correlation function (3PCF) of a weak lensing shear field contains information that is complementary to that in the two-point correlation function (2PCF), which can help improve the cosmological parameters and calibrate…
Starting from first principles, we derive the fundamental equations that relate the $n$-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full…
The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF,…
In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…
We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point…
In the advent of new large galaxy surveys, which will produce enormous datasets with hundreds of millions of objects, new computational techniques are necessary in order to extract from them any two-point statistic, the computational time…
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…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
We present new predictions for the galaxy three-point correlation function (3PCF) using high-resolution dissipationless cosmological simulations of a flat LCDM Universe which resolve galaxy-size halos and subhalos. We create realistic mock…
With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo…
An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces…
The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any}…
Cosmological measurements require the calculation of nontrivial quantities over large datasets. The next generation of survey telescopes (such as DES, PanSTARRS, and LSST) will yield measurements of billions of galaxies. The scale of these…
Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of $n$ points is specified by $n^3$ triplets, making collecting…
This paper presents a novel perspective on correlation functions in the clustering analysis of the large-scale structure of the universe. We first recognise that pair counting in bins of radial separation is equivalent to evaluating…
We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions…
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation…