Rudolph Albert Peters, 13 April 1889 - 29 January 1982

Lecture 22 — April 29

Up until now, we have mainly studied how to decrease the query time, and the preprocessing time of our data structures. In this lecture, we will focus on maintaining the data as compactly as possible. Our goal will be to get as close the information theoretic optimum as possible. We will refer to this optimum as OPT. Note that most ”linear space” data structures we have seen are still far from ...

Measles — California, January 1–April 18, 2014

Measles is a highly contagious, acute viral illness that can lead to severe complications and death. Even patients who experience uncomplicated acute measles have a small risk for developing a devastating neurologic illness, subacute sclerosing panencephalitis, years after their infection. Measles was documented as eliminated (defined as interruption of continuous transmission lasting ≥12 month...

of April 13 , 2017 . This

of April 13 , 2017 . This

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 ...