We apply recent results on extracting randomness from independent
sources to ``extract'' Kolmogorov complexity. For any $\alpha,
\epsilon > 0$, given a string $x$ with $K(x) > \alpha|x|$, we show
how to use a constant number of advice bits to efficiently
compute another string $y$, $|y|=\Omega(|x|)$, with $K(y) >
(1-\epsilon)|y|$. ... more >>>

Ben-Sasson and Sudan in~\cite{BS04} asked if the following test
is robust for the tensor product of a code with another code--
pick a row (or column) at random and check if the received word restricted to the picked row (or column) belongs to the corresponding code. Valiant showed that ... more >>>

Consider a homogeneous polynomial $p(z_1,...,z_n)$ of degree $n$ in $n$ complex variables .
Assume that this polynomial satisfies the property : \\

$|p(z_1,...,z_n)| \geq \prod_{1 \leq i \leq n} Re(z_i)$ on the domain $\{(z_1,...,z_n) : Re(z_i) \geq 0 , 1 \leq i \leq n \}$ . \\

We prove that ... more >>>