First, charged pion and proton production is measured at the HARP experiment for two experimental configurations relevant to two contemporary accelerator-based neutrino beams. Double-differential cross-sections for π + , π − and proton production are presented for proton+beryllium collisions at 8.9 GeV/c and proton+aluminum collisions at 12.9 GeV/c. These data have been used in the predictions of neutrino fluxes by the K2K experiment in Japan and the MiniBooNE and SciBooNE experiments at Fermilab.Second, a search for evidence of muon neutrino to electron neutrino oscillations at MiniBooNE is presented. MiniBooNE was designed to search for evidence of ν µ → ν e oscillations consistent with a mass-squared splitting near 1 eV 2 . Evidence of such an oscillation was reported by the LSND collaboration in the 1990s but has not been confirmed by other experiments. A method which combines the electron neutrino candidate sample with the high statistics muon neutrino candidate sample to define a single χ 2 statistic is developed. A complete description of experimental uncertainties is contained within a correlated error matrix which includes correlations between the two samples. This correlation reduces the uncertainty on the prediction of the smaller statistics electron sample and improves MiniBooNE's sensitivity to oscillations. Analysis of the MiniBooNE electron candidate data reveals no evidence of direct ν µ → ν e oscillations consistent with this interpretation of the LSND data.