We consider the problem of low-rank rectangular matrix completion in the regime where the
matrix $ M $ of size $ n\times m $ is “long", ie, the aspect ratio $ m/n $ diverges to infinity …

We develop a unified approach to bounding the largest and smallest singular values of an
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …

We present a new explicit construction of onesided bipartite lossless expanders of constant
degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our …

We study the problem of constructing explicit sparse graphs that exhibit strong vertex
expansion. Our main result is the first two-sided construction of imbalanced unique-neighbor …

A matrix $ A $ is said to have the $\ell_p $-Restricted Isometry Property ($\ell_p $-RIP) if for
all vectors $ x $ of up to some sparsity $ k $, $\|{Ax}\| _p $ is roughly proportional to $\|{x}\| _p …