  The L/E-flatness of the e-like events observed in the recent
atmospheric-neutrino data from Super-Kamiokande (SuperK) is interpreted to
reflect a new symmetry of the neutrino-oscillation mixing matrix. From that we
obtain an analytical set of constraints yielding a class of mixing matrices of
the property to simultaneously fit both the SuperK and the LSND data. The
resulting mass squared difference relevant for the LSND experiment is found as
0.3 eV^2. The discussed symmetry, e.g., carries the nature that expectation
values of masses for \nu_\mu and \nu_\tau are identical. These considerations
are purely data dictated. A different framework is then applied to the solar
neutrino problem. It is argued that a single sterile neutrino is an unlikely
candidate to accommodate the data from the four solar neutrino experiments. A
scenario is discussed which violates CPT symmetry, and favors the \nu_e -
\bar\nu_e system to belong to the `self'-`anti-self' charge conjugate construct
in the (1/2,0)+(0,1/2) representation space, where the needed helicity flipping
amplitudes are preferred, rather than the usual Dirac, or Majorana, constructs.
In the presented framework the emerging SuperK data on solar neutrino flux is
reconciled with the Homestake, GALLEX, and SAGE experiments. This happens
because the former detects not only the solar \nu_e but also, at a lower cross
section, the oscillated solar \bar\nu_e; while the latter are sensitive only to
the oscillation-diminished solar \nu_e flux. A direct observation of solar
\bar\nu_e by SNO will confirm our scenario. Finally, we consider the
possibility for flavor-dependent gravitational couplings of neutrinos as
emerging out of the noncommutativity of the quantum operators associated with
the measurements of energy and flavor.
