  Observations of atmospheric neutrinos by the SuperKamiokande collaboration
have demonstrated large mixing of the muon-neutrino. However the present
atmospheric neutrino data does not significantly constrain the associated
mixing of the electron-neutrino, or the sign of the mass-squared difference.
Here we identify the diagnostics for these quantities and they also test the
theory of how matter affects neutrino oscillations. These diagnostics are a dip
in the sub-GeV muon flux at a zenith angle of 110 degrees, a bump in the
electron up-down asymmetry at multi-GeV energies and a bump in the
muon-antimuon upward asymmetry.
