Pinpointing gravitational waves via astrometric gravitational wave antennas.

The direct detection of gravitational waves by ground-based optical interferometers has opened a new window in astronomy. Besides, the sensitivity of these linear detectors to the direction of arrival of an incoming gravitational wave is limited compared to current prospects of high-precision, space-based, astrometry. Indeed, advanced methods of differential relativistic astrometry offer a unique opportunity to overcome that situation.

OCReP: An Optimally Conditioned Regularization for pseudoinversion based neural training.

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability.

Fizeau interferometer for global astrometry in space.

We discuss the design and the performance of a Fizeau interferometer with a long focal length and a large field of view that is well suited for a global astrometry space mission. Our work focuses on the geometric optimization and minimization of aberration of such an astrometric interferometer, which is able to observe astronomical targets down to the visual magnitude (mag) mv = 20 mag, with an accuracy in the measurements of 10 micro-arcseconds at mv = 15 mag. We assume a mission profile similar to that of the Global Astrometric Interferometer for Astrophysics mission of the European Space Agency.