angles, a feature absent in the conventional massive model. At low energies, the mass term dominates and the mixing takes the tribimaximal form, a widely used matrix postulated to describe neutrino mixing. This mixing added to the 1/E dependence of the mass term guarantees agreement with solar and KamLAND data. At high energies, Lorentz-violating contributions take over making the contribution of neutrino masses negligible. A seesaw mechanism is triggered, similar to that in the bicycle model, making one of the eigenvalues proportional to 1/E, which usually come with neutrino masses. This feature lets the model mimic the effects of a mass term at high energies despite the fact that there are only non-negative powers of the energy. The energy dependence of the Lorentz-violating terms produce maximal mixing, which makes the model consistent with atmospheric and accelerator data. The oscillation signal in MiniBooNE appears because the oscillation phase responsible for the oscillation channel grows rapidly with energy and the oscillation amplitude is large only for energies below 500 MeV. The combination of these two effects produces an oscillation signal in MiniBooNE at low energies, in agreement with the data. Additionally, since the model includes a term associated to a CPT-odd Lorentz-violating operator, different probabilities appear for neutrinos and antineutrinos. Moreover, since the amplitude for decreases for energies above 500 MeV, long-baseline experiments searching for nonzero should measure different values depending on the energy; more precisely, the MINOS experiment should measure a value smaller than the T2K experiment according to the puma model, which agrees with current measurements. Isotropic bicycle model In 2011, Barger, Liao, Marfatia, and Whisnant studied general bicycle-type models (without neutrino masses) that can be constructed using the minimal SME that are isotropic (direction independent). Results show that long-baseline accelerator and atmospheric data can be described by these models in virtue of the Lorentz-violating seesaw mechanism; nevertheless, there is a tension between solar and KamLAND data. Given this incompatibility, the authors concluded that renormalizable models with massless neutrinos are excluded by the data. Mathematical theory From a general model-independent point of view, neutrinos oscillate because the effective hamiltonian describing their propagation is not diagonal in flavor space and has a non-degenerate spectrum, in other words, the eigenstates of the hamiltonian are linear superpositions of the flavor eigenstates of the weak interaction and there are at least two different eigenvalues. If we find a transformation that puts the effective hamiltonian