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The analysis of temperature-dependent EXAFS spectra based on the cumulant expansion is critically reviewed, seeking for accurate relations between EXAFS parameters and physical properties of crystals. The treatment is based on the distinction between the real and effective distribution of distances, and is divided into three logical steps. (a) The connection between lattice dynamics and cumulants C(n)* of the real distribution is studied and the extent of the usual approximations are numerically evaluated. Atomic vibrations perpendicular to the bond direction make the EXAFS thermal expansion larger than the crystallographic one; the difference is connected to a shift of the effective pair potential rather than to its asymmetry. Peculiar information on lattice dynamics of crystals can be obtained from accurate EXAFS measurements and their cumulant analysis. (b) The differences between cumulants of the real and effective distribution (C(n)* and C(n), respectively) are calculated for various physically realistic distributions. The largest discrepancy concerns the first cumulant: C(1)* measures the thermal expansion of the interatomic bond, while C(1) is a better estimate of the crystallographic thermal expansion. (c) The convergence properties of the cumulant series are discussed and some phenomenological procedures are suggested to monitor and possibly work out the connected failures of the cumulant method. Benefits and risks of the use of an effective pair potential are at last debated.

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The discrimination and classification of allergy-relevant pollen was studied for the first time by mid-infrared Fourier transform infrared (FT-IR) microspectroscopy together with unsupervised and supervised multivariate statistical methods. Pollen samples of 11 different taxa were collected, whose outdoor air concentration during the flowering time is typically measured by aerobiological monitoring networks. Unsupervised hierarchical cluster analysis provided valuable information about the reproducibility of FT-IR spectra of the same taxon acquired either from one pollen grain in a 25 x 25 microm2 area or from a group of grains inside a 100 x 100 microm2 area. As regards the supervised learning method, best results were achieved using a K nearest neighbors classifier and the leave-one-out cross-validation procedure on the dataset composed of single pollen grain spectra (overall accuracy 84%). FT-IR microspectroscopy is therefore a reliable method for discrimination and classification of allergenic pollen. The limits of its practical application to the monitoring performed in the aerobiological stations were also discussed.

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