  Studying evolutionary correlations in alignments of homologous sequences by
means of an inverse Potts model has proven useful to obtain residue-residue
contact energies and to predict contacts in proteins. The quality of the
results depend much on several choices of the detailed model and on the
algorithms used. We built, in a very controlled way, synthetic alignments with
statistical properties similar to those of real proteins, and used them to
assess the performance of different inversion algorithms and of their variants.
Realistic synthetic alignments display typical features of low--temperature
phases of disordered systems, a feature that affects the inversion algorithms.
We showed that a Boltzmann--learning algorithm is computationally feasible and
performs well in predicting the energy of native contacts. However, all
algorithms suffer of false positives quite equally, making the quality of the
prediction of native contacts with the different algorithm much
system--dependent.
