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In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.

Developing a convenient and effective method to prepare single-atom catalysts at mild synthetic conditions remains a challenging task. Herein, a voltage-gauged electrofiltration method was demonstrated to synthesize single-atom site catalysts at room temperature. Under regulation of the graphene oxide membrane, a bulk Fe plate was directly converted into Fe single atoms, and the diffusion rate of Fe ions was greatly reduced, resulting in an ultralow concentration of Fe2+ around the working electrode, which successfully prevented the growing of nuclei and aggregating of metal atoms. Monatomic Fe atoms are homogeneously anchored on the as-prepared nitrogen-doped carbon. Owing to the fast photoelectron injection from photosensitizers to atomically dispersed Fe sites through the highly conductive supported N-C, the Fe-SAs/N-C exhibits an outstanding photocatalytic activity toward CO2 aqueous reduction into syngas with a tunable CO/H2 ratio under visible light irradiation. The gas evolution rates for CO and H2 are 4500 and 4950 μmol g–1 h–1, respectively, and the tunable CO/H2 ratio is from 0.3 to 8.8. This article presents an efficient strategy to develop the single-atom site catalysts and bridges the gap between heterogeneous and homogeneous catalysts toward photocatalytic CO2 aqueous reduction into syngas.

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