In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a
generalization of MDS codes. An order-ℓ MDS code, denoted by MDS (ℓ), has the property …

This paper initiates a systematic development of a theory of non-commutative optimization, a
setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and …

We propose a new second-order method for geodesically convex optimization on the natural
hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling …

Symbolic matrices in non-commuting variables, andthe related structural and algorithmic
questions, have a remarkablenumber of diverse origins and motivations. They …

In this paper, we present a deterministic polynomial time algorithm for testing whether a
symbolic matrix in non-commuting variables over QQ is invertible or not. The analogous …

The celebrated Brascamp-Lieb (BL) inequalities [BL76, Lie90], and their reverse form of
Barthe [Bar98], are an important mathematical tool, unifying and generalizing numerous in …

We uncover connections between maximum likelihood estimation in statistics and norm
minimization over a group orbit in invariant theory. We focus on Gaussian transformation …

We study the log-likelihood function and maximum likelihood estimate (MLE) for the matrix
normal model for both real and complex models. We describe the exact number of samples …

Starting from the one-way group action framework of Brassard and Yung (Crypto'90), we
revisit building cryptography based on group actions. Several previous candidates for one …

Alternating minimization heuristics seek to solve a (difficult) global optimization task through
iteratively solving a sequence of (much easier) local optimization tasks on different parts (or …