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We numerically study the interplay between heterogeneous dynamics andproperties of negatively curved regions of the potential energy surface in amodel glassy system. We find that the unstable modes of saddles andquasi-saddles undergo a localization transition close to the Mode-Couplingcritical temperature. We also find evidence of a positive spatial correlationbetween clusters of particles having large displacements in the unstable modesand dynamical heterogeneities.Comment: 7 pages, 3 figures, submitted to Europhys. Let

Are there localized saddles behind the heterogeneous dynamics of supercooled liquids?