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.

The influence of the sample introduction system on signals of different tin compounds in inductively coupled plasma-based techniques

The influence of the sample introduction system on the signals obtained with different tin compounds in inductively coupled plasma (ICP) based techniques, i.e., ICP atomic emission spectrometry (ICP–AES) and ICP mass spectrometry (ICP–MS) has been studied. Signals for test solutions prepared from four different tin compounds (i.e., tin tetrachloride, monobutyltin, dibutyltin and di-tert-butyltin) in different solvents (methanol 0.8% (w/w), i-propanol 0.8% (w/w) and various acid matrices) have been measured by ICP–AES and ICP–MS. The results demonstrate a noticeable influence of the volatility of the tin compounds on their signals measured with both techniques. Thus, in agreement with the compound volatility, the highest signals are obtained for tin tetrachloride followed by di-tert-butyltin/monobutyltin and dibutyltin. The sample introduction system exerts an important effect on the amount of solution loading the plasma and, hence, on the relative signals afforded by the tin compounds in ICP–based techniques. Thus, when working with a pneumatic concentric nebulizer, the use of spray chambers affording high solvent transport efficiency to the plasma (such as cyclonic and single pass) or high spray chamber temperatures is recommended to minimize the influence of the tin chemical compound. Nevertheless, even when using the conventional pneumatic nebulizer coupled to the best spray chamber design (i.e., a single pass spray chamber), signals obtained for di-tert-butyltin/monobutyltin and dibutyltin are still around 10% and 30% lower than the corresponding signal for tin tetrachloride, respectively. When operating with a pneumatic microconcentric nebulizer coupled to a 50 °C-thermostated cinnabar spray chamber, all studied organotin compounds provided similar emission signals although about 60% lower than those obtained for tin tetrachloride. The use of an ultrasonic nebulizer coupled to a desolvation device provides the largest differences in the emission signals, among all tested systems.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.