An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.

Levels of dioxin-like PCBs in low-volume serum samples of male patients attending fertility clinics

An accurate and easy method for the extraction, cleanup, and HRGC-HRMS analysis of dioxin-like PCBs (DL-PCBs) in low-volume serum samples (1 mL) was developed. Serum samples were extracted several times using n-hexane and purified by acid washing. Recovery rates of labeled congeners ranged from 70 to 110 % and the limits of detection were below 1 pg/g on lipid basis. Although human studies are limited and contradictory, several studies have shown that DL-PCBs can have adverse effects on the male reproductive system. In this way, the present method was applied to 21 serum samples of male patients attending fertility clinics. The total levels obtained for the patients ranged from 6.90 to 84.1 pg WHO-TEQ/g lipid, with a mean value of 20.3 pg WHO-TEQ/g lipid. The predominant PCBs (the sum of PCB 118, 156, and 105) contributed 67 % to the mean concentration of total DL-PCBs in the samples analyzed.