2017 AWM Lecture Sampler

2017 Lecture 4 : October 9 , 2017

We consider a set of random variables in a particular relationship and its consequences for mutual information. An ordered tuple of random variables (X, Y, Z) is said to form a Markov chain, written as X → Y → Z, if X and Z are independent conditioned on Y. Here, we can think of Y as being sampled given the knowledge of X, and Z being sampled given the knowledge of Y (but not using the “history...

2017 SNMMI Highlights Lecture: Neuroscience.

Lecture 6 — April 14 , 2017

A zero sum game is a simultaneous move game between 2 players. Such a game is represented by a matrix A ∈ Rm×n. The strategies of the “row” (resp. “column”) player are the rows (resp. columns) of A. If the row player plays strategy i ∈ [m] and the column player plays j ∈ [n] then the outcome is Aij . 1 Interpret this as that the row player pays Aij amount of money to the column player, therefor...

Lecture 2 : September 27 , 2017

Lecture 12 : April 13 , 2017

Last Time During the last lecture we completed an argument for a 2 1 d−1 ) lower bound for depth-d circuits for parity (PAR) using Hastad’s Switching Lemma [H̊as87], which stated that, for f : {0, 1} → {−1, 1}, if CNFwidth(f) = t, Pρ←Rp(DNFwidth(f ρ) = s) ≥ (7ps) We proved the Weak Switching Lemma, asserting a (40ps2) lower bound for this probability as opposed to the tighter bound given by the ...