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.

On the forecast accuracy and consistency of exchange rate expectations: The Spanish PwC Survey.

We examine the predictive ability and consistency properties of exchange rate expectations for the dollar/euro using a survey conducted in Spain by PwC among a panel of experts and entrepreneurs. Our results suggest that the PwC panel have some forecasting ability for time horizons from 3 to 9 months, although only for the 3-month ahead expectations we obtain marginal evidence of unbiasedness and efficiency in the forecasts. As for the consistency properties of the exchange rate expectations formation process, we find that survey participants form stabilising expectations in the short-run and destabilising expectations in the long- run and that the expectation formation process is closer to fundamentalists than chartists.

Rational choice, social identity, and beliefs about oneself

Social identity poses one of the most important challenges to rational choice theory, but rational choice theorists do not hold a common position regarding identity. On one hand, externalist rational choice ignores the concept of identity or reduces it to revealed preferences. On the other hand, internalist rational choice considers identity as a key concept in explaining social action because it permits expressive motivations to be included in the models. However, internalist theorists tend to reduce identity to desire—the desire of a person to express his or her social being. From an internalist point of view, that is, from a viewpoint in which not only desires but also beliefs play a key role in social explanations as mental entities, this article rejects externalist reductionism and proposes a redefinition of social identity as a net of beliefs about oneself, beliefs that are indexical, robust, and socially shaped.