Nonnegative Markov Chains with Applications -- Phase Changes with Time and Multi-Scale Homogenizations of a Class of Anomalous Diffusions -- Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes -- Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures -- Enstrophy and Ergodicity Of Gravity Currents -- Stochastic Heat and Burgers …