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Ten techniques used for selection of useful predictors in multivariate calibration and in other cases of multivariate regression are described and discussed in terms of their performance (ability to detect useless predictors, predictive power, number of retained predictors) with real and artificial data. The techniques studied include classical stepwise ordinary least-squares (SOLS), techniques based on the genetic algorithms, and a family of methods based on partial least-squares (PLS) regression and on the optimization of the predictive ability. A short introduction presents the evaluation strategies, a description of the quantities used to evaluate the regression model, and the criteria used to define the complexity of PLS models. The selection techniques can be divided into conservative techniques that try to retain all the informative, useful predictors, and parsimonious techniques, whose objective is to select a minimum but sufficient number of useful predictors. Some combined techniques, in which a conservative technique is used to perform a preliminary selection before the use of parsimonious techniques, are also presented. Among the conservative techniques, the Westad-Martens uncertainty test (MUT) used in Unscrambler, and uninformative variables elimination (UVE), developed by Massart et al., seem the most efficient techniques. The old SOLS can be improved to become the most efficient parsimonious technique, by means of the use of plots of the F-statistics value of the entered predictors and comparison with parallel results obtained with a data matrix with random data. This procedure indicates correctly how many predictors can be accepted and substantially reduces the possibility of overfitting. A possible alternative to SOLS is iterative predictors weighting (IPW) that automatically selects a minimum set of informative predictors. The use of an external evaluation set, with objects never used in the elimination of predictors, or of "complete validation" is suggested to avoid overestimate of the prediction ability.

SUMMARYA new method for the elimination of useless predictors in multivariate regression problems is proposed. The method is based on the cyclic repetition of PLS regression. In each cycle the predictor importance (product of the absolute value of the regression coefficient and the standard deviation of the predictor) is computed, and in the next cycle the predictors are multiplied by their importance. The algorithm converges after 10-20 cycles. A reduced number of relevant predictors is retained in the final model, whose predictive ability is acceptable, frequently better than that of the model built with all the predictors. Results obtained on many real and simulated data are presented, and compared with those obtained from other techniques.

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Context. The diffusion of volatile species on amorphous solid water ice affects the chemistry on dust grains in the interstellar medium as well as the trapping of gases enriching planetary atmospheres or present in cometary material. Aims. The aim of the work is to provide diffusion coefficients of CH 4 on amorphous solid water (ASW) and to understand how they are affected by the ASW structure. Methods. Ice mixtures of H 2 O and CH 4 were grown in different conditions and the sublimation of CH 4 was monitored via infrared spectroscopy or via the mass loss of a cryogenic quartz crystal microbalance. Diffusion coefficients were obtained from the experimental data assuming the systems obey Fick's law of diffusion. Monte Carlo simulations were used to model the different amorphous solid water ice structures investigated and were used to reproduce and interpret the experimental results. Results. Diffusion coefficients of methane on amorphous solid water have been measured to be between 10 −12 and 10 −13 cm 2 s −1 for temperatures ranging between 42 K and 60 K. We show that diffusion can differ by one order of magnitude depending on the morphology of amorphous solid water. The porosity within water ice and the network created by pore coalescence enhance the diffusion of species within the pores. The diffusion rates derived experimentally cannot be used in our Monte Carlo simulations to reproduce the measurements. Conclusions. We conclude that Fick's law can be used to describe diffusion at the macroscopic scale, while Monte Carlo simulations describe the microscopic scale where trapping of species in the ices (and their movement) is considered.

ElsevierLuna Molina, R.; Millán Verdú, C.; Domingo Beltran, M.; Santonja Moltó, MDC.; Satorre, MÁ. (2015). Experimental study of the frequency factor in the Polanyi-Wigner equation: the case of C2H6. Vacuum. 122:154-160. doi:10.1016Vacuum. 122:154-160. doi:10. /j.vacuum.2015 AbstractFor the first time, an experimental procedure to calculate the frequency factor of the Polanyi-Wigner equation and to study how temperature influences on it is presented. This parameter is necessary to calculate desorption rates for environments where this process occurs. The method presented is based on the analysis of a quartz crystal microbalance signal. In the literature the frequency factor is not experimentally obtained but it is rather assumed as k B ·T/h, proposed by the activated state theory for first order desorption processes, or it is estimated by other methods.Additionally, its variation with temperature is not experimentally explored so far.Two different kind of desorption experiments of zeroth order desorption have been carried out to perform this study. The first experiment, carried out at a constant rate of warming up, is devoted to obtain the desorption energy, which is comparedwith previous values reported in the literature. The second group of desorption Preprint submitted to Elsevier 15 May 2015experiments is performed at constant temperature and is used to calculate and study the frequency factor. Several temperatures have been specifically selected, allowing us to derive the influence of the temperature on this parameter. For ethane, we have calculated an increase of around a 50% for the frequency factor corresponding to an increase in temperature of only 6 K. This result must be taken into account when the Polany-Wigner equation is used for calculation purposes.

8We report the density and refractive index, at 633 nm, of ethane and ethylene ices at temperatures from 13 to 65 K, measured by double laser interferometry and a cryogenic quartz crystal microbalance in a high vacuum chamber. Both quantities rise with the temperature of deposition from 13 K up to a plateau, 40 K for ethane and 22 K for ethylene. An amorphous structure is suggested for temperatures below 40 K for ethane and below 20 K for ethylene. Above these temperatures, 40 K for ethane and 20 K for ethylene, a crystalline structure is proposed. Ethylene results deviate from linear growth between 25 and 35 K, where a metastable structure is reported in the literature. Density values increase from about 0.40 to 0.60 g cm −3 for ethane and from about 0.45 to almost 0.65 g cm −3for ethylene. The real part of the refractive index changes from about 1.27 to 1.45 for ethane and from about 1.30 to almost 1.48 for ethylene. Results are relevant especially to the outer Solar System, where the presence of these molecules is reported, and for experiments involving them.

We present a spectroscopic study of methane-ethane ice mixtures. We have grown CH 4 :C 2 H 6 mixtures with ratios 3:1, 1:1, and 1:3 at 18 and 30 K, plus pure methane and ethane ices, and have studied them in the near-infrared (NIR) and mid-infrared (MIR) ranges. We have determined densities of all species mentioned above. For amorphous ethane grown at 18 and 30 K we have obtained a density of 0.41 and 0.54 g cm −3 , respectively, lower than a previous measurement of the density of the crystalline species, 0.719 g cm −3. As far as we know this is the first determination of the density of amorphous ethane ice. We have measured band shifts of the main NIR methane and ethane features in the mixtures with respect to the corresponding values in the pure ices. We have estimated band strengths of these bands in the NIR and MIR ranges. In general, intensity decay in methane modes was detected in the mixtures, whereas for ethane no clear tendency was observed. Optical constants of the mixtures at 30 and 18 K have also been evaluated. These values can be used to trace the presence of these species in the surface of trans-Neptunian objects. Furthermore, we have carried out a theoretical calculation of these ice mixtures. Simulation cells for the amorphous solids have been constructed using a Metropolis Monte Carlo procedure. Relaxation of the cells and prediction of infrared spectra have been carried out at density functional theory level.