  Charm and bottom quarks are formed predominantly by gluon fusion in the
initial hard scatterings at RHIC, making them good probes of the full medium
evolution. Previous measurements at RHIC have shown large suppression and
azimuthal anisotropy of open heavy-flavor hadrons in Au+Au collisions at
$\sqrt{s_{NN}}=200~{\rm GeV}$. Explaining the simultaneously large suppression
and flow of heavy quarks has been challenging. To further understand the
heavy-flavor transport in the hot and dense medium, it is imperative to also
measure cold nuclear matter effects which affect the initial distribution of
heavy quarks as well as the system size dependence of the final state
suppression. In this talk, new measurements by the PHENIX collaboration of
electrons from heavy-flavor decays in $p$+$p$, $d$+Au, and Cu+Cu collisions at
$\sqrt{s_{NN}}=200~{\rm GeV}$ are presented. In particular, a surprising
enhancement of intermediate transverse momentum heavy-flavor decay leptons in
$d$+Au at mid and backward rapidity are also seen in mid-central Cu+Cu
collisions. This enhancement is much larger than the expectation from
anti-shadowing of the parton distributions and is theoretically unexplained.
