Nonparametric integral statistics ωkn = nk2 ∫∞−∞ [Sn(x) − F(x)]k dF(x): Main properties and applications

AbstractThe main characteristics of nonparametric statistics, ωkn, which can be represented as integrals of the kth degree of the empirical process, are considered. An algebraic form of these statistics, convenient for practical usage, is derived. Tables of percentage points for k = 1,2, …, 5 and small empirical sample sizes n = 1,2, …, 10 are obtained. Goodness-of-fit criteria based on ωkn statistics are constructed, and their main properties are studied. A method for classifying multidimensional data based on these criteria, which was successfully applied in several experiments, is described

Multivariate data analysis based on the ωkn-criteria and multilayer perceptron

AbstractA comparative study of multidimensional classifiers based on the goodness-of-fit criteria ωkn and multilayer perceptrons (MLP) has been carried out. It is shown that MLP exhibits the “instantaneous” learning effect and improves the quality of recognition in the case of input data represented in the form of variational series. The reasons are analyzed that underlie these effects. Recommendations for joint usage of the ωkn criteria and of MLPs are given

Determination of ππ\pi\pi scattering lengths from measurement of π+π−\pi^+\pi^- atom lifetime

The DIRAC experiment at CERN has achieved a sizeable production of $\pi^+\pi^-$ atoms and has significantly improved the precision on its lifetime determination. From a sample of 21227 atomic pairs, a 4% measurement of the S-wave $\pi\pi$ scattering length difference $|a_0-a_2| = (.0.2533^{+0.0080}_{-0.0078}|_\mathrm{stat}.{}^{+0.0078}_{-0.0073}|_\mathrm{syst})M_{\pi^+}^{-1}$ has been attained, providing an important test of Chiral Perturbation Theory.Comment: 6 pages, 6 figure