Let $f$ be a nonnegative function on $\{0,1\}^n$. We upper bound the entropy of the image of $f$ under the noise operator with noise parameter $\epsilon$ by the average entropy of conditional expectations of $f$, given sets of roughly $(1-2\epsilon)^2 \cdot n$ variables.

As an application, we show that for ... more >>>

We study the problem of \emph{reconstructing a low-rank matrix}, where the input is an $n\times m$ matrix $M$ over a field $\mathbb{F}$ and the goal is to reconstruct a (near-optimal) matrix $M'$ that is low-rank and close to $M$ under some distance function $\Delta$.
Furthermore, the reconstruction must be local, ... more >>>

We prove a general lower bound on the size of branching programs over any semiring of zero characteristic, including the (min,+) semiring. Using it, we show that the classical dynamic programming algorithm of Bellman, Ford and Moore for the shortest s-t path problem is optimal, if only Min and Sum ... more >>>