Upper limits on the rates of binary neutron star and
  neutron-star--black-hole mergers from Advanced LIGO's first observing run
  We report here the non-detection of gravitational waves from the merger of
binary neutron star systems and neutron-star--black-hole systems during the
first observing run of Advanced LIGO. In particular we searched for
gravitational wave signals from binary neutron star systems with component
masses $\in [1,3] M_{\odot}$ and component dimensionless spins $< 0.05$. We
also searched for neutron-star--black-hole systems with the same neutron star
parameters, black hole mass $\in [2,99] M_{\odot}$ and no restriction on the
black hole spin magnitude. We assess the sensitivity of the two LIGO detectors
to these systems, and find that they could have detected the merger of binary
neutron star systems with component mass distributions of $1.35\pm0.13
M_{\odot}$ at a volume-weighted average distance of $\sim$ 70Mpc, and for
neutron-star--black-hole systems with neutron star masses of $1.4M_\odot$ and
black hole masses of at least $5M_\odot$, a volume-weighted average distance of
at least $\sim$ 110Mpc. From this we constrain with 90% confidence the merger
rate to be less than 12,600 Gpc$^{-3}$yr$^{-1}$ for binary-neutron star systems
and less than 3,600 Gpc$^{-3}$yr$^{-1}$ for neutron-star--black-hole systems.
We find that if no detection of neutron-star binary mergers is made in the next
two Advanced LIGO and Advanced Virgo observing runs we would place significant
constraints on the merger rates. Finally, assuming a rate of
$10^{+20}_{-7}$Gpc$^{-3}$yr$^{-1}$ short gamma ray bursts beamed towards the
Earth and assuming that all short gamma-ray bursts have binary-neutron-star
(neutron-star--black-hole) progenitors we can use our 90% confidence rate upper
limits to constrain the beaming angle of the gamma-ray burst to be greater than
${2.3^{+1.7}_{-1.1}}^{\circ}$ (${4.3^{+3.1}_{-1.9}}^{\circ}$).
