  Vacuum and medium modified fragmentation functions are used to study the
properties of hadrons produced in hard interactions, in $p$-$p$ and $A$-$A$
collisions, respectively. We study the modification of reconstructed jets and
high transverse momentum (high-$p_\mathrm{T}$) hadrons as they propagate
through a dense medium. Jets and jet modification are studied within the
framework of a factorized jet function. The vacuum jet function is found
consistent with PYTHIA simulations. Both the modification of the fragmentation
function and the jet function are carried out within the identical higher-twist
energy loss formalism. This approach is then extended to di-hadron production
within a jet. Its further extension to a "di-prong" function and its
application to the soft-drop measurements are discussed. The methodology of
extending these semi-analytical calculations to full Monte-Carlo simulations is
outlined. All calculations are carried out within a (2+1)-D viscous
hydrodynamic simulation and compared to experimental data from a variety of
collision energies.
