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Normalized mutual information is widely used as a similarity measure for evaluating the performance of clustering and classification algorithms. In this paper, we argue that results returned by the normalized mutual information are biased…
Bose-Einstein correlations of pairs of identical charged pions produced in hadronic Z decays are analyzed for both two- and three-jet events. A parametrization suggested by the tau-model is used to investigate the dependence of the…
We analyze the influence of classical Gaussian noise on Landau-Zener transitions during a two-level crossing in a time-dependent regular external field. Transition probabilities and coherence factors become random due to the noise. We…
Relations between Wigner functions and the source functions used in models of Bose-Einstein correlations in multiple particle production are derived and discussed. These relations are model dependent. In particular it is important whether…
For non-equilibrium systems of interacting particles and for interacting diffusions in d dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
A simple new algorithm for the calculation of two-particle Bose-Einstein correlations from classical event generators is derived and discussed.
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and…
Model-independent considerations are presented for the calculation of Bose-Einstein correlation functions and momentum distributions which describe boson-emitting systems containing a central part surrounded by a large halo. If the…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the…
To estimate the strength of the Bose-Einstein correlations and the radius of the hadronization region in multiparticle production, the two-particle correlation functions $R$ for identical pairs is adjusted to a parametric function…
q-deformed oscillators and the q-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept ("strength") $\lambda^{(2)}\equiv C^{(2)}(K,K)-1$ of two-particle correlation function $C^{(2)}(p_1,p_2)$…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…