Before revision:  Here we extend this analysisto any translation-invariant directed transition structure ( displacement and diffusion), showing that a single set of eigenvectors supports prediction via displacement-specific eigenvalues.
After revision:  Here we extend the eigenbasis prediction model, utilising tools from Fourier analysis, to prediction over arbitrary translation-invariant directed transition structure ( displacement and diffusion), showing that a single set of eigenvectors supports prediction via displacement-specific eigenvalues.