We study minimization of the difference of ℓ 1 and ℓ 2 norms as a non-convex and Lipschitz continuous metric for solving constrained and unconstrained compressed sensing problems. We establish exact (stable) sparse recovery results under a restricted isometry property (RIP) condition for the constrained problem, and a full-rank theorem of the sensing matrix restricted to the support of the sparse solution. We present an iterative method for ℓ 1−2 minimization based on the difference of convex functions algorithm (DCA), and prove that it converges to a stationary point satisfying first order optimality condition. We propose a sparsity oriented simulated annealing (SA) procedure with non-Gaussian random perturbation and prove the almost sure convergence of the combined algorithm (DCASA) to a global minimum. Computation examples on success rates of sparse solution recovery show that if the sensing matrix is ill-conditioned (non RIP satisfying), then our method is better than existing non-convex compressed sensing solvers in the literature. Likewise in the magnetic resonance imaging (MRI) phantom image recovery problem, ℓ 1−2 succeeds with 8 projections. Irrespective of the conditioning of the sensing matrix, ℓ 1−2 is better than ℓ 1 in both the sparse signal and the MRI phantom image recovery problems.To appear in SIAM J. Sci. Comput. Introduction.Compressed sensing (CS) has been a rapidly growing field of research in signal processing and mathematics stimulated by the foundational papers [8,6,22,23] and related Bregman iteration methods [57,33]. A fundamental issue in CS is to recover an ndimensional vectorx from m ≪ n measurements (the projection ofx onto m n-dimensional vectors), or in matrix form given b = Ax, where A is the so-called m × n sensing (measurements) matrix. One can also viewx as coefficients of a sparse linear representation of data b in terms of redundant columns of matrix A known as dictionary elements.The conditioning of A is related to its restricted isometry property (RIP) as well as the coherence (maximum of pairwise mutual angles) of the column vectors of A. Breakthrough results in CS have established when A is drawn from a Gaussian matrix ensemble or random row sampling without replacement from an orthogonal matrix (Fourier matrix), then A is wellconditioned in the sense that ifx is s-sparse (s is much less than n), m = O(s log n) measurements suffice to recoverx (the sparsest solution) with an overwhelming probability by ℓ 1 minimization or the basis pursuit (BP) problem [6, 15]:(1.1) minx ∥x∥ 1 subject to Ax = b.In the above formulation, ℓ 1 norm works as the convex relaxation of ℓ 0 that counts the nonzeros. Such a matrix A has incoherent column vectors. On the other hand, if columns of A are coherent enough, such as those arising in discretization of continuum imaging problems (radar and medical imaging) when the grid spacing is below the Rayleigh threshold [25], ℓ 1 minimization may not give the sparsest solution [25,55].

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The bulky m-terphenyl phenol Ar*OH 1 (Ar* = C6H3-2,6-Mes2, Mes = 2,4,6-trimethylphenyl) was synthesized via the treatment of Ar*Li with nitrobenzene. The phenol 1 is prepared in modest to good yield using this method. Attempts were also made to prepare 1 through oxidation of the bulky boronic acid Ar*B(OH)2 with Oxone®, but this reaction was not suitable for preparative-scale reactions. Side products of the reaction between Ar*Li and nitrobenzene were identified as Ar*[N(O)Ph] and [C6H5N(O)]2 and were characterized by X-ray crystallography and EPR spectroscopy. A variety of main-group and transition-metal complexes of Ar*OH were prepared, namely Sn(OAr*)2, Ge(OAr*)2, [N(SiMe3)2]Ge(OAr*), [Me2Al(OAr*)]2, and Ti(NMe2)(OAr*)2. All compounds were characterized spectroscopically and most were studied by single-crystal X-ray diffraction as well.Key words: m-terphenyl, main-group compounds, X-ray crystallography, multinuclear NMR spectroscopy, EPR spectroscopy.

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Massive connectivity is a key requirement for the Internet of Things (IoT). In practice, the network should be capable of accessing thousands of devices and meeting their traffic demands. In this paper, we consider the access phase for IoT in a mixed-analog-to-digital converter distributed massive multipleinput multiple-output system, in which users are classified into light-load users and heavy-load users depending on their traffic load requirements. To meet the low-latency and low-cost demands in IoT, the access scheme for both types of users are designed in a grant-free fashion. For users with light-load traffic demands, by formulating the user activity detection (UAD) and channel estimation (CE) into a compressed sensing problem, we provide a low-complexity algorithm solver which requires no prior information. The simulation results verify that the proposed algorithm can effectively detect user activity and estimate channel state information (CSI) between users and access points (APs). To satisfy the throughput requirements of heavy-load users, after UAD and CE, a two-step dynamic clustering is proposed for coordinated multi-point transmission using the large scale fading (LSF) information. The impact of quantization noise on LSF estimation is investigated, as well as, a corresponding compensation method and accuracy bound. By detecting the clustering behavior among users in the first step, the complexity of the joint user and AP clustering is substantially reduced. Numerical results reveal that the proposed algorithm can offer significant performance gains in various scenarios with fast convergence.

Abstract:In China, environmental pollution generated via industrialization as well as profound changes in the social structure and the gradual maturation of the social hierarchy have jointly contributed to the Chinese people's increased environmental consciousness and appeals for environmental justice (EJ). Because of the absence of an EJ theory and a lack of empirical research focused on China, this paper proposes a "Pyramid Model" for EJ research in China that includes the following three factors: basic demographic and socioeconomic characteristics, U.S.-based EJ principles, and Chinese characteristics. A nationwide pilot analysis of environmental inequality at the prefecture level is conducted by empirically examining the association between the demographic variables and socioeconomic status with sources of industrial pollution in China. The prefecture-based results are shown to be robust, and they indicate that areas inhabited by ethnic minorities and western regions of China carry disproportionate environmental burdens. However, a different picture for migrants is presented, revealing that Chinese migrants are not currently exposed to greater levels of industrial pollution. Relevant interpretations of these findings are provided. The results also show that environmental inequality associated with income level, which is observed in the U.S., does not occur in China.