I will continue the exposition of different derandmization techniques for probabilistic logspace algorithms.
Since the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this history, and then describe our recent results that provide such a generalization and unify much of the previous work. One key new aspect in the theory is a systematic study of hypergraph eigenvalues.
I will survey some of the basic approaches to derandomizing Probabilistic Logspace computations, including the "classical" Nisan, Impagliazzo-Nisan-Widgerson and Reingold-Raz generators, the Saks-Zhou algorithm and some more recent approaches. We'll see why each falls short of complete derandomization, BPL=L, hopefully motivating further work on this basic problem.
Fundamental questions in basic and applied ecology alike involve complex adaptive systems, in which localized interactions among individual agents give rise to emergent patterns that feed back to affect individual behavior.
Polar codes have recently emerged as a new class of low-complexity codes achieving Shannon capacity. This talk introduces polar codes with emphasis on the probabilistic phenomenon underlying the code construction. New results and connections to randomness extraction for structured sources are discussed.