  By means of molecular dynamics simulations and the Voronoi tessellation, we
study the influence of the history on the low temperature characteristics of
soft sphere and silica glasses. The quench from the liquid is interrupted at an
intermediate temperature $T_i$ for a given relaxation time, and then the
cooling process is continued down to 0K. The local structure at 0K depends on
the temperature $T_i$ and the effect is larger for $T_i$ close to the glass
transition temperature $T_g$. This dependence, coherent with recent results, is
expected in the strong glass former where the characteristics of a particular
state depend on its history. In the soft-sphere case, because of
crystallization effects, the dependence of the local structure of the glassy
samples on their history can only be detected in the supercooled liquid region.
