  The 2003 seminal paper entitled "Is the Fragility of a Liquid Embedded in the
Properties of Its Glass?" by Tullio Scopigno, Giancarlo Ruocco, Francesco
Sette, and Giulio Monaco, reported that the properties of the structural
$\alpha$-relaxation of glass-formers are already present in the faster caged
dynamics. Their important discovery has far-reaching implication of the
processes faster than the structural $\alpha$-relaxation that cannot be ignored
in solving the glass transition problem. Since then, experiments and
simulations performed on many glass-formers with diverse chemical and physical
structures have found strong connections of the $\alpha$-relaxation with not
only the caged dynamics but also with the secondary relaxation of the special
kind, called the JGX $\beta$-relaxation. The general results indicate that
these fast processes are inseparable from the $\alpha$-relaxation, and any
attempt to solve the glass transition problem should take account of this fact.
Examples of the connections are given in this paper to elucidate the
developments and advances made since the inspiring publication of Scopigno et
al.
