Ring graphs and complete intersection toric ideals

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Groebner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Groebner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation.Comment: Discrete Math., to appea

Design of an Artificial Neural Network for the Analysis of Stellar Spectra

We have developed an artificial neural network, whose purpose is to automatically find in a database of synthetic stellar spectra the one which best reproduces an observed spectrum. Using the equivalent widths of selected spectral lines, the network fits a set of lines related to the physical parameters in the stellar atmosphere (i.e., temperature, gravity and mass loss rate). The main advantage of this approach is its scalability