Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

Foreign MNEs and domestic innovative capabilities: are there conditions for reverse spillovers in the spanish industry?

We analyse, over 2004-2008, a sample of approximately 700 foreign subsidiaries and 4,500 domestic firms located in Spain in order to understand the relationship between local R&D cooperation and innovativeness of the firm. Our ultimate objective is to understand whether foreign subsidiaries are likely to make a contribution to local innovative capabilities or if, conversely, they may eventually benefit from conditions for reverse spillovers. Using a variety of specifications for the innovation-related activities of the firm, we find that foreign subsidiaries are more cooperative than the average firm located in Spain, but not necessarily more than affiliated domestic firms (entrepreneurial groups). However, foreign subsidiaries are more cooperative than affiliated domestic firms in sectors considered highly dynamic by international technological standards, whether Spain has a technical advantage in these specific sectors or not. When we focus on companies which are more innovative than the two-digit industries in which they operate, we find that foreign subsidiaries tend to be more cooperative than domestic firms in sectors where Spain displays technological advantage. These sectors comprise traditional industries displaying little innovation dynamism from an international point of view. This finding suggests that there may be conditions for reverse spillovers in these specific Spanish sectors (though measuring them is beyond the objectives of this paper).