Related papers: Generalised Cumulant Correlators and Hierarchical …
This work presents a set of new statistics, the cumulant correlators, aimed at high precision analysis of the galaxy distribution. They form a symmetric matrix, $Q_{NM}$, related to moment correlators the same way as cumulants are related…
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…
The highly nonlinear regime of gravitational clustering is characterized by the presence of scale-invariant form of many-body correlation functions. Useful insights can be obtained by investigating the consequences of a generic scaling {\em…
We apply a new statistics, the factorial moment correlators, to density maps obtained from the APM survey. The resulting correlators are all proportional to the two point correlation function, substantially amplified, with an amplification…
We develop a diagrammatic technique to represent the multi-point cumulative probability density function (CPDF) of mass fluctuations in terms of the statistical properties of individual collapsed objects and relate this to other statistical…
The calculation of the characteristic function of the signal fluctuations due to clustered astrophysical sources is performed in this paper. For the typical case of power-law differential number counts and two-point angular correlation…
We present the generalization of recently introduced observables for the studies of correlated fluctuations of different anisotropic flow amplitudes, dubbed Symmetric Cumulants. We introduce a new set of higher order observables and outline…
We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier…
We present a comparison of the predictions of perturbation theory for the hierarchical J-order correlation amplitudes $S_J=\xibar_J/\xibar_2^{J-1}$, $J=3-10$, with the results of large numerical simulations of gravitational clustering. We…
We introduce methods which allow observed galaxy clustering to be used together with observed luminosity or stellar mass functions to constrain the physics of galaxy formation. We show how the projected two-point correlation function of…
We present results of searching for the possible typical scales in the spatial distribution of QSOs. Our method is based on the second derivative of the two-point correlation function. This statistic is sensitive to the scale of the maximum…
We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…
Second-order measures, such as the two-point correlation function, are geometrical quantities describing the clustering properties of a point distribution. In this article well-known estimators for the correlation integral are reviewed and…
In two previous papers a semi-analytical model was presented for the hierarchical clustering of halos via gravitational instability from peaks in a random Gaussian field of density fluctuations. This model is better founded than the…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
We use the two-degree field Galaxy Redshift Survey (2dFGRS) to test the hierarchical scaling hypothesis: namely, that the $p$-point galaxy correlation functions can be written in terms of the two point correlation function or variance. This…
The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate…
Clustered data are common in practice. Clustering arises when subjects are measured repeatedly, or subjects are nested in groups (e.g., households, schools). It is often of interest to evaluate the correlation between two variables with…
Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…