Uncertainty of the atmospheric neutrino fluxes
  The uncertainty in the calculation of atmospheric neutrino fluxes is studied. The absolute value of atmospheric neutrino fluxes is sensitive to variation of the primary cosmic ray flux model and/or the interaction model. However, the ratios between different kind of neutrinos stay almost unchanged with these variations. It is unlikely that the anomalous ratio $(\nu_{\mu}/\nu_e)_{obs}/(\nu_{\mu}/\nu_e)_{MC}$ reported by Kamiokande and Super Kamiokande is caused by the uncertainty of predicted atmospheric neutrino fluxes. 
M.Honda