We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for velocity average of solutions kinetic equations. This requires only elementary techniques in Fourier analysis and shows new range assumptions that are sufficient be $L^2([0,T],H^{1/2}_x).$ result not an interesting connection between lemmas local smoothing property dispersive equations, but ...

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. paper, we study one-step iterative weighted parameter averaging in linear models under data parallelism. We do regression on each machine, send results to a ...