A progressive global increase in the burden of allergic diseases has affected the industrialized world over the last half century and has been reported in the literature. The clinical evidence reveals a general increase in both incidence and prevalence of respiratory diseases, such as allergic rhinitis (common hay fever) and asthma. Such phenomena may be related not only to air pollution and changes in lifestyle, but also to an actual increase in airborne quantities of allergenic pollen. Experimental enhancements of carbon dioxide (CO) have demonstrated changes in pollen amount and allergenicity, but this has rarely been shown in the wider environment. The present analysis of a continental-scale pollen data set reveals an increasing trend in the yearly amount of airborne pollen for many taxa in Europe, which is more pronounced in urban than semi-rural/rural areas. Climate change may contribute to these changes, however increased temperatures do not appear to be a major influencing factor. Instead, we suggest the anthropogenic rise of atmospheric CO levels may be influential.

Lyapunov characteristic exponents measure the rate of exponential divergence between neighboring trajectories in the phase space. For a given autonomous dynamical system, the maximum Lyapunov characteristic exponent (hereafter LCE) is computed from the solution of the variational equations of the system. There are many dynamical systems in which the formulation and solution of the variational equations is a cumbersome task. In those cases an alternative procedure, Ðrst introduced by Benettin et al., is to replace the variational solution by computing two neighbor trajectories (the test particle and its shadow) and calculating the mutual distance. In this paper, we deal with a comparison between these two di †erent techniques for the calculation of LCE : the variational method and the two-particle method. We point out a problem that can appear when the two-particle method is used, which can lead to a false estimation of a positive LCE. The explanation of this phenomenon can be analyzed in two di †erent situations : (1) for relatively large initial separations the two-particle method is not a good approximation to the solution of the variational equations, and (2) for small initial separations the two-particle method have problems related to the machine precision, even when the separation can be many order of magnitudes larger than the machine precision. We show some examples of false estimates of the LCE that have already appeared in the literature using the two-particle method, and Ðnally we present some suggestions to be taken into account when this method has to be used.

Abbreviations: ALEH, Asociación Latinoamericana para el Estudio del Hígado; DILI, drug-induced liver injury; INH, isoniazid; LATINDILIN, Latin American DILI Network; NSAID, nonsteroidal anti-inflammatory drug; PIZ, pyrazinamide; RIP, rifampicin.From the

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