  We report on results of an all-sky search for high-energy neutrino events
interacting within the IceCube neutrino detector conducted between May 2010 and
May 2012. The search follows up on the previous detection of two PeV neutrino
events, with improved sensitivity and extended energy coverage down to
approximately 30 TeV. Twenty-six additional events were observed, substantially
more than expected from atmospheric backgrounds. Combined, both searches reject
a purely atmospheric origin for the twenty-eight events at the $4\sigma$ level.
These twenty-eight events, which include the highest energy neutrinos ever
observed, have flavors, directions, and energies inconsistent with those
expected from the atmospheric muon and neutrino backgrounds. These properties
are, however, consistent with generic predictions for an additional component
of extraterrestrial origin.
