The sparsity-based approaches have demonstrated promising performance in image processing. In this paper, for better preservation of the salient edge structures of images, we propose an l_0 + l_2-norm based analysis model, which requires solving a challenging non-separable l0-norm related minimiza- tion problem, and we also propose an inexact augmented Lagrangian method with proven convergence to a local minimum. Extensive experiments in image smoothing, including texture removal and context smoothing, show that our method achieves better visual results over various sparsity-based models and the CNN method. Also, experiments on sparse view CT reconstruction further validate the advantage of the proposed method.

We present a conjecture on the complete spectrum of single-trace operators in the infinite N limit of W_N minimal model and evidence for the conjecture. We further propose that the holographic dual of W_N minimal model in the ’t Hooft limit is an unusual “semilocal” higher spin gauge theory on AdS_3×S^1. At each point on the S^1 lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS_3. The Vasiliev theories at different points on the S^1 are correlated only through the AdS_3 boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions.

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This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence and convergence of the trajectory of the neural network. Moreover, we show some stability properties for the considered neural network, such as the Lyapunov stability, asymptotic stability, and exponential stability. The examples in this paper provide a further demonstration of the effectiveness of the proposed neural network. This paper can be viewed as a follow-up version of [20], [26] because more stability results are obtained.

Let G be a connected semi-simple algebraic group of adjoint type over an algebraically closed field and let ar G be the wonderful compactification of G. For a fixed pair (B,B  ) of opposite Borel subgroups of G, we look at intersections of Lusztigs G-stable pieces and the B  B-orbits in ar G , as well as intersections of BB-orbits and B  B  -orbits in ar G . We give explicit conditions for such intersections to be nonempty, and in each case, we show that every nonempty intersection is smooth and irreducible, that the closure of the intersection is equal to the intersection of the closures, and that the nonempty intersections form a strongly admissible partition of .