On differential uniformity and nonlinearity of functions

We present results related to vectorial plateaued functions and mappings whose derivatives are 2^s-to-1 functions. The results in this note generalize facts about almost perfect nonlinear and almost bent functions. We investigate the connection between plateaued and 2^s-to-1 functions. We show that functions which are both plateaued and differentially uniform give rise to partial difference sets.