In this note we revisit the construction of high noise, almost
optimal rate list decodable code of Guruswami ("Better extractors for better codes?")
Guruswami showed that based on optimal extractors one can build a
$(1-\epsilon,O({1 \over \epsilon}))$ list decodable codes of rate
$\Omega({\epsilon \over {log{1 \over \epsilon}}})$ and alphabet
size ... more >>>

In general property testing, we are given oracle access to a function $f$, and we wish to randomly test if the function satisfies a given property $P$, or it is $\epsilon$-far from having that property. In a more general setting, the domain on which the function is defined is equipped ... more >>>

We present an algorithm for learning a mixture of distributions.
The algorithm is based on spectral projection and
is efficient when the components of the mixture are logconcave
distributions.

more >>>