Before revision:  Empirical performance evaluations, with both synthetic and real-world datasets, establish the  advantage of the tensor CUR approximations over other state-of-the-art low multilinear rank tensor approximations.
After revision:  Empirical performance evaluations, with both synthetic and real-world datasets, establish the speed advantage of the tensor CUR approximations over other state-of-the-art low multilinear rank tensor approximations.