Percolation and high energy cosmic rays above $10^{17}$ eV
  In this work we argue that, in the interpretation of the energy dependence of the depth of the shower maximum and of the muon content in high energy cosmic ray showers ($E > 10^{17}$ eV), other variables besides the composition may play an important role, in particular those characterising the first (high energy) hadronic collisions. The role of the inelasticity, of the nature of the leading particle, and of the particle multiplicity are discussed. A consistent interpretation of existing data within a string percolation model implemented in a hybrid, one dimensional simulation method is given. 
J. Alvarez-Muniz, P. Brogueira, R. Conceicao, J. Dias de Deus, M.C.   Espirito Santo, M. Pimenta