The Cascade-Correlation architecture which is designed for classification tasks has been studied to see if it can be modified to perform function evaluation and interpolation tasks.

We study the evolution of the cluster correlation function and its richnessdependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ωm = 0.3 and, for comparison, a tilted Ωm = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation st...

We calculate the expected angular correlation function of Sunyaev–Zel’dovich (SZ)–detected galaxy clusters and discuss its use as a cosmological probe. As a projection of the real–space cluster correlation function, the angular function samples the underlying SZ cluster redshift distribution. The method proposes a way to increase the immediate scientific return from an SZ survey by studying cos...

This paper studies the problem of default correlation. We first introduce a random variable called “timeuntil-default” to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the jo...

We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long-distance behavior of radial distribution functions is determined by requiring that the corresponding ...

We consider variational (density functional) models of fluids confined in parallelplate geometries (with walls situated in the planes z = 0 and z = L respectively) and focus on the structure of the pair correlation function G(r1, r2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(zμ, zν ; q) and the zeroth momen...

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a uni...

We give a path integral prescription for the pair correlation function of Wilson loop observables on the worldvolume of a Dbrane in the bosonic string theory in flat spacetime. We determine the coefficient of the 1/R term in the static heavy quark potential from the static pair correlation function of Wilson lines at small spatial separation in the critical string theory. We verify that the pai...

The recent COSY-11 collaboration measurement of the two-proton correlation function in the pp → ppη reaction, reported at this meeting [1], arouse some interest in a simple theoretical description of the correlation function. In these notes we present a pedagogical introduction to the practical methods that can be used for calculating the correlation function.

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 properties that cannot be extracted from the two-point correlation function. We use the halo clustering model to analytically calculate the three-point correlati...