  Using a novel approach, we study the quenching and bursting of galaxies as a
function of stellar mass ($M_{*}$), local environment ($\Sigma$), and specific
star-formation rate (sSFR) using a large spectroscopic sample of $\sim$ 123,000
$GALEX$/SDSS and $\sim$ 420 $GALEX$/COSMOS/LEGA-C galaxies to $z$ $\sim$ 1. We
show that out to $z$ $\sim$ 1 and at fixed sSFR and local density, on average,
less massive galaxies are quenching, whereas more massive systems are bursting,
with a quenching/bursting transition at log($M_{*}$/$M_{\odot}$) $\sim$ 10.5-11
and likely a short quenching/bursting timescale ($\lesssim$ 300 Myr). We find
that much of the bursting of star-formation happens in massive
(log($M_{*}$/$M_{\odot}$) $\gtrsim$ 11), high sSFR galaxies
(log(sSFR/Gyr$^{-1}$) $\gtrsim$ -2), particularly those in the field
(log($\Sigma$/Mpc$^{-2}$) $\lesssim$ 0; and among group galaxies, satellites
more than centrals). Most of the quenching of star-formation happens in
low-mass (log($M_{*}$/$M_{\odot}$) $\lesssim$ 9), low sSFR galaxies
(log(sSFR/Gyr$^{-1}$) $\lesssim$ -2), in particular those located in dense
environments (log($\Sigma$/Mpc$^{-2}$) $\gtrsim$ 1), indicating the combined
effects of $M_{*}$ and $\Sigma$ in quenching/bursting of galaxies since $z$
$\sim$ 1. However, we find that stellar mass has stronger effects than
environment on recent quenching/bursting of galaxies to $z$ $\sim$ 1. At any
given $M_{*}$, sSFR, and environment, centrals are quenchier (quenching faster)
than satellites in an average sense. We also find evidence for the strength of
mass and environmental quenching being stronger at higher redshift. Our
preliminary results have potential implications for the physics of
quenching/bursting in galaxies across cosmic time.
