A subspace of matrices in F m×n qe can be naturally embedded as a xmlns:xlink="http://www.w3.org/1999/xlink">em×en xmlns:xlink="http://www.w3.org/1999/xlink">q with the property...

Research has shown that rank statistics derived from contextdependent state likelihood can provide robust speech recognition. In previous work, empirical distributions were used to characterize the rank statistics. We present parametric models of the state rank and the rank likelihood, and then based on them, present a new objective function, Maximal Rank Likelihood (MRL), for estimating parame...

We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of [LT10] and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the “non-Abelian” catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially sy...

We consider the conjecture stating that a matrix with rank o(n) and ones on the main diagonal must contain nonzero entries on a 2 2 submatrix with one entry on the main diagonal. We show that a slightly stronger conjecture implies that an explicit linear transformation cannot be computed by linear size and logarithmic depth circuits. We prove some partial results supporting the conjecture.