Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

Purpose A new acquisition and reconstruction method called T2 Shuffling is presented for
volumetric fast spin‐echo (three‐dimensional [3D] FSE) imaging. T2 Shuffling reduces …

Tensor-network techniques have recently proven useful in machine learning, both as a tool
for the formulation of new learning algorithms and for enhancing the mathematical …

It is well-known that any sum of squares (SOS) program can be cast as a semidefinite
program (SDP) of a particular structure and that therein lies the computational bottleneck for …

We solve a 20-year old problem posed by Yannakakis and prove that there exists no
polynomial-size linear program (LP) whose associated polytope projects to the traveling …

Modern massive datasets create a fundamental problem at the intersection of the
computational and statistical sciences: how to provide guarantees on the quality of statistical …

We introduce a method for proving lower bounds on the efficacy of semidefinite
programming (SDP) relaxations for combinatorial problems. In particular, we show that the …

We solve a 20-year old problem posed by Yannakakis and prove that no polynomial-size
linear program (LP) exists whose associated polytope projects to the traveling salesman …

Abstract Let M ∈ R^ p * q M∈ R p× q be a nonnegative matrix. The positive semidefinite
rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite …

In this expository article, we study optimization problems specified via linear and relative
entropy inequalities. Such relative entropy programs (REPs) are convex optimization …