model is an extended version of the bicycle presented in 2006 by Katori, Kostelecky, and Tayloe. It is a hybrid model that includes Lorentz violation and also mass terms for a subset of neutrino flavors. It attempts to construct a realistic model by applying a number of desirable criteria. In particular, acceptable models for neutrino violation should: be based on quantum field theory, involve only renormalizable terms, offer an acceptable description of the basic features of neutrino-oscillation data, have a mass scale for seesaw compatibility, involve fewer parameters than the four used in the standard picture, have coefficients for Lorentz violation consistent with a Planck-scale suppression , and accommodate the LSND signal. All these criteria are satisfied by the tandem model, which looks like a simple extension of the bicycle. Nevertheless, it involves isotropic coefficients only, which means that there is no direction dependence. The extra term is a massive term that reproduces the L/E phase at low energies observed by KamLAND. It turns out that the tandem model is consistent with atmospheric, solar, reactor, and short-baseline data, including LSND. Besides the consistency with all experimental data, the most remarkable feature of this model is the prediction of a low-energy excess in MiniBooNE. When the tandem is applied to short-baseline accelerator experiments, it is consistent with the KARMEN null result, due to the very short baseline. For MiniBooNE, the tandem model predicted an oscillation signal at low energy that drops off very quickly. The MiniBooNE results, released a year after the tandem model was published, did indeed show an unexplained excess at low energies. This excess cannot be understood within the standard massive-neutrino model, and the tandem remains one of the best candidates for its explanation. Puma model The puma model was proposed by Diaz and Kostelecky in 2010 as a three-parameter model that exhibits consistency with all the established neutrino data (accelerator, atmospheric, reactor, and solar) and naturally describes the anomalous low-energy excess observed in MiniBooNE that is inconsistent with the conventional massive model. This is a hybrid model that includes Lorentz violation and neutrino masses. One of the main differences between this model and the bicycle and tandem models described above is the incorporation of nonrenormalizable terms in the theory, which lead to powers of the energy greater than one. Nonetheless, all these models share the characteristic of having a mixed energy dependence that leads to energy-dependent mixing