Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

The determinants of inward foreign direct investment in business services across European regions

The determinants of inward foreign direct investment in business services across European regions, Regional Studies. The role of forward linkages with manufacturing sectors and other service sectors as attractors of business services foreign direct investment (FDI) is studied at the regional level. Using data on 146 NUTS-2 regions, it is found that regions specialized in those (manufacturing) sectors that are high potential users of business services attract more FDI in the business services than other regions. Results are robust to the inclusion of the traditional determinants of foreign investments at the regional level as well as to controls for spatial dependence. The results suggest that regional policies aimed at attracting foreign investors in the business service industry might prove ineffective in the absence of a pre-existing local intermediate demand