Solar cells based on kesterite absorbers consistently show lower voltages than those based on chalcopyrites with the same bandgap. We use three different experimental methods and associated data analysis to determine minority-carrier lifetime in a 9.4%-efficient Cu 2 ZnSnSe 4 device. The methods are cross-sectional electron-beam induced current, quantum efficiency, and time-resolved photoluminescence. These methods independently indicate minority-carrier lifetimes of a few nanoseconds. A comparison of current-voltage measurements and device modeling suggests that these short minority-carrier lifetimes cause a significant limitation on the voltage produced by the device. The comparison also implies that low minority-carrier lifetime alone does not account for all voltage loss in these devices. V C 2013 AIP Publishing LLC. [http://dx.

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the tensor. We show that this approach can be substantially suboptimal: reliably recovering a K-way tensor of length n and Tucker rank r from Gaussian measurements requires Ω(rn K−1 ) observations. In contrast, a certain (intractable) nonconvex formulation needs only O(r K +nrK) observations. We introduce a very simple, new convex relaxation, which partially bridges this gap. Our new formulation succeeds with O(r K/2 n K/2 ) observations. While these results pertain to Gaussian measurements, simulations strongly suggest that the new norm also outperforms the sum of nuclear norms for tensor completion from a random subset of entries.Our lower bound for the sum-of-nuclear-norms model follows from a new result on recovering signals with multiple sparse structures (e.g. sparse, low rank), which perhaps surprisingly demonstrates the significant suboptimality of the commonly used recovery approach via minimizing the sum of individual sparsity inducing norms (e.g. l1, nuclear norm). Our new formulation for low-rank tensor recovery however opens the possibility in reducing the sample complexity by exploiting several structures jointly.

Abstract. In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB) algorithm is equivalent to a gradient descent method applied to a certain dual formulation. We show that the LB method requires O(1/ǫ) iterations to obtain an ǫ-optimal solution and the ALB algorithm reduces this iteration complexity to O(1/ √ ǫ)while requiring almost the same computational effort on each iteration. Numerical results on compressed sensing and matrix completion problems are presented that demonstrate that the ALB method can be significantly faster than the LB method.

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