  We revisit the model proposed earlier to account for the observed increase in
the positron fraction in cosmic rays with increasing energy, in the light of
new data from the Alpha Magnetic Spectrometer (AMS-02) experiment. The model
accounts for the production and acceleration of secondary electrons and
positrons in nearby supernova remnants which results in an additional, harder
component that becomes dominant at high energies. By fitting this to AMS-02
data we can calculate the expected concomitant rise of the boron-to-carbon
ratio, as well as of the fraction of antiprotons. If these predictions are
confirmed by the forthcoming AMS-02 data it would conclusively rule out all
other proposed explanations, in particular dark matter annihilations or decays.
