In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the 1 norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the 1 and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics and machine learning, including compressive sensing (CS), sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git.

Employing seawater splitting systems to generate hydrogen can be economically advantageous but still remains challenging, particularly for designing efficient and high Cl−‐corrosion resistant trifunctional catalysts toward the oxygen reduction reaction (ORR), oxygen evolution reaction (OER), and hydrogen evolution reaction (HER). Herein, single CoNC catalysts with well‐defined symmetric CoN4 sites are selected as atomic platforms for electronic structure tailoring. Density function theory reveals that P‐doping into CoNC can lead to the formation of asymmetric CoN3P1 sites with symmetry‐breaking electronic structures, enabling the affinity of strong oxygen‐containing intermediates, moderate H adsorption, and weak Cl− adsorption. Thus, ORR/OER/HER activities and stability are optimized simultaneously with high Cl−‐corrosion resistance. The asymmetric CoN3P1 structure based catalyst with boosted ORR/OER/HER performance endows seawater‐based Zn–air batteries (S‐ZABs) with superior long‐term stability over 750 h and allows seawater splitting to operate continuously for 1000 h. A self‐driven seawater splitting powered by S‐ZABs gives ultrahigh H2 production rates of 497 μmol h−1. This work is the first to advance the scientific understanding of the competitive adsorption mechanism between Cl− and reaction intermediates from the perspective of electronic structure, paving the way for synthesis of efficient trifunctional catalysts with high Cl−‐corrosion resistance.

This article presents a new method to optimally partition a geometric domain with capacity constraints on the partitioned regions. It is an important problem in many fields, ranging from engineering to economics. It is known that a capacity-constrained partition can be obtained as a power diagram with the squared L2 metric. We present a method with super-linear convergence for computing optimal partition with capacity constraints that outperforms the state-of-the-art in an order of magnitude. We demonstrate the efficiency of our method in the context of three different applications in computer graphics and geometric processing: displacement interpolation of function distribution, blue-noise point sampling, and optimal convex decomposition of 2D domains. Furthermore, the proposed method is extended to capacity-constrained optimal partition with respect to general cost functions beyond the squared Euclidean distance.

Future power grids are fundamentally different from current ones, both in size and in complexity; this trend imposes challenges for situation awareness (SA) based on classical indicators, which are usually model-based and deterministic. As an alternative, this paper proposes a statistical indicator system based on linear eigenvalue statistics (LESs) of large random matrices: 1) from a data modeling viewpoint, we build, starting from power flows equations, the random matrix models (RMMs) only using the real-time data flow in a statistical manner; 2) for a data analysis that is fully driven from RMMs, we put forward the high-dimensional indicators, called LESs that have some unique statistical features such as Gaussian properties; and 3) we develop a three-dimensional (3D) power-map to visualize the system, respectively, from a high-dimensional viewpoint and a low-dimensional one. Therefore, a statistical methodology of SA is employed; it conducts SA with a model-free and data-driven procedure, requiring no knowledge of system topologies, units operation/control models, causal relationship, etc. This methodology has numerous advantages, such as sensitivity, universality, speed, and flexibility. In particular, its robustness against bad data is highlighted, with potential advantages in cyber security. The theory of big data based stability for on-line operations may prove feasible along with this line of work, although this critical development will be reported elsewhere.

Data-driven approaches, when tasked with situation awareness, are suitable for complex grids with massive datasets. It is a challenge, however, to efficiently turn these massive datasets into useful big data analytics. To address such a challenge, this paper, based on random matrix theory (RMT), proposes a datadriven approach. The approach models massive datasets as large random matrices; it is model-free and requiring no knowledge about physical model parameters. In particular, the large data dimension N and the large time span T , from the spatial aspect and the temporal aspect respectively, lead to favorable results. The beautiful thing lies in that these linear eigenvalue statistics (LESs) built from data matrices follow Gaussian distributions for very general conditions, due to the latest breakthroughs in probability on the central limit theorems of those LESs. Numerous case studies, with both simulated data and field data, are given to validate the proposed new algorithms.

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Invisible units mainly refer to small-scale units that are not monitored by, and thus are not visible to utilities. Integration of these invisible units into power systems does significantly affect the way in which a distribution grid is planned and operated. This paper, based on random matrix theory (RMT), proposes a statistical, data-driven framework to handle the massive grid data, in contrast to its deterministic, model-based counterpart. Combining the RMT-based data-mining framework with conventional techniques, some heuristics are derived as the solution to the invisible units detection and estimation task: linear eigenvalue statistic indicators (LESs) are suggested as the main ingredients of the solution; according to the statistical properties of LESs, the hypothesis testing is formulated to conduct change point detection in the high-dimensional space. The proposed method is promising for anomaly detection and pertinent to current distribution networks-it is capable of detecting invisible power usage and fraudulent behavior while even being able to locate the suspect's location. Case studies, using both simulated data and actual data, validate the proposed method.Index Terms-invisible unit, data-mining framework, statistical property, random matrix theory, linear eigenvalue statistic.