Nonparametric correlation estimators as the Kendall and Spearman correlation are widely used in the applied sciences. They are often said to be robust, in the sense of being resistant to outlying observations. In this paper we formally study their robustness by means of their influence functions and gross-error sensitivities. Since robustness of an estimator often comes at the price of an incre...

We study the rate-distortion relationship in the set of permutations endowed with the Kendall τ-metric and the Chebyshev metric. Our study is motivated by the application of permutation rate-distortion to the average-case and worst-case analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall τ-metric we provide bounds for small, medium,...

The SUSY signals in the dominant stau-neutralino coannihilation region at a 500(800) GeV linear collider are investigated. The region is consistent with the WMAP measurement of the cold dark matter relic density as well as all other current experimental bounds within the mSUGRA framework. The signals are characterized by an existence of very low-energy tau leptons in the final state due to smal...

The discovery of the tau lepton and the third generation of fermions came from the convergence of three physics streams in the late 1960’s and early 1970’s. These streams were: the failed attempts by myself and others to understand the connection between the electron and the muon, the development of electron-positron storage rings, and the development of the theory of sequential leptons. In thi...

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic r...

cortex leading to the discovery of cortisone (Mason, Myers and Kendall, 1936; Wintersteiner and Pfiffner, 1936 ; Reichstein, 1936). The beneficial effect of pregnancy on rheumatoid arthritis was first observed by Hench in 1938 but the antirheumatic arthritic action of cortisone was established as late as 1949 by Hench, Kendall and their collaborators. Since then beneficial effect of cortisone h...

This paper bears on the comparison of two well-known metrics between linear orders called the Kendall and Spearman metrics or/and of their normalized versions respectively known as the Kendall tau and the Spearman rho. Using a combinatorial approach based on the partial order intersection of the two compared linear orders, we first prove a relation between these two metrics and a semi-metric, e...