  We show that the space-time foam model from string/D-brane theory predicts a
scenario in which neutrinos can possess linearly energy dependent speed
variation, together with an asymmetry between neutrinos and antineutrinos,
indicating the possibility of Lorentz and CPT symmetry violation for neutrinos.
Such scenario is supported by a phenomenological conjecture from the possible
associations of IceCube ultrahigh-energy neutrino events with the gamma-ray
bursts. It is also consistent with the constraints set by the energy-losing
decay channels~(e.g., $e^{+}e^{-}$ pair emission, or neutrino splitting) upon
superluminal neutrino velocities. We argue that the plausible violations of
energy-momentum conservation during decay may be responsible for the stable
propagation of these neutrinos, and hence for the evasion of relevant
constraints.
