The abundance distribution (number of stars vs. [Fe/H]) in the solar neighborhood is more peaked than the one predicted by closed models. This is known as the G dwarf problem (first observed in the sixties by van den Bergh 1962). I proposed, for the first time, the idea that the Initial Mass Function (IMF) can be time dependent.
By assuming a closed model for the solar neighborhood, I obtained the analytic expression that relates the time behavior of the IMF to the G Dwarf abundance distribution. Here you can find all the results. I want to emphasize that, the most critical step in this research, was the derivation of an analytic expression of the G Dwarf abundance distribution without introducing any physical a priori assumption. To achieve this, I applied basic results on learning in conjunction with the regularization theory of Tikhonov. Specifically, by using the regularization theory, I approximated the G Dwarf abundance distribution by a linear superposition of multivariate Gaussian basis functions. Then, to fix the number of Gaussian functions and to fix their parameters, I used basic learning methods. Specifically, I based my approach on the theory of Vapnik-Chervonenkis and, in practice, thanks to the results found by Amari et al. at the end of 90's, I applied a simple form of cross-validation.