We study the biased random walk where at each step of a "controller" can, with certain small probability, move to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work time dependent setting and consider cover times this walk. obtain new bounds on hitting times. conjectured that controller can increase stationary probability vertex from $p$ $p^{1-\ep...

This review of scaling theories magnetohydrodynamic (MHD) turbulence aims to put the developments last few years in context canonical time line (from Kolmogorov Iroshnikov–Kraichnan Goldreich–Sridhar Boldyrev). It is argued that Beresnyak's (valid) objection Boldyrev's alignment theory, at least its original form, violates Reduced-MHD rescaling symmetry can be reconciled with if latter understo...