A human does not have to see all elephants to recognize an animal as an elephant. On contrast, current state-of-the-art deep learning approaches heavily depend on the variety of training samples and the capacity of the network. In practice, the size of network is always limited and it is impossible to access all the data samples. Under this circumstance, deep learning models are extremely fragile to human-imperceivable adversarial examples, which impose threats to all safety critical systems. Inspired by the association and attention mechanisms of the human brain, we propose reverse adversarial examples method that can greatly improve models' robustness on unseen data. Experiments show that our reverse adversarial method can improve accuracy on average 19.02% on ResNet18, MobileNet, and VGG16 on unseen data transformation. Besides, the proposed method is also applicable to compressed models and shows potential to compensate the robustness drop brought by model quantization - an absolute 30.78% accuracy improvement.

The subject of the paper is Schrdinger operators on tree graphs which are radial, having the branching number bn at all the vertices at the distance tn from the root. We consider a family of coupling conditions at the vertices characterized by (bn1)2+4 real parameters. We prove that if the graph is sparse so that there is a subsequence of {tn+1tn} growing to infinity, in the absence of the potential the absolutely continuous spectrum is empty for a large subset of these vertex couplings, but on the the other hand, there are cases when the spectrum of such a Schrdinger operator can be purely absolutely continuous.

In this paper, we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic-Einstein metric on this line bundle, which generalize the classical stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We introduce a Donaldson type functional and show that this functional attains its absolute minimum at geodesic-Einstein metrics, and we also discuss the relations between the existence of geodesic-Einstein metrics and the nonlinear stabilities of the line bundle. As an application, we will prove that a holomorphic vector bundle admits a Finsler-Einstein metric if and only if it admits a Hermitian-Einstein metric, which answers a problem posed by S. Kobayashi.

We present a framework for solving the large-scale \ell_1-regularized convex minimization problem:<div class="gsh_dspfr">\ell_1

Some electromagnetic materials exhibit, in a given frequency range, effective dielectric permittivity and/or magnetic permeability which are negative. In the literature, they are called negative index materials, left-handed materials or meta-materials. We propose in this paper a numerical method to solve a wave transmission between a classical dielectric material and a meta-material. The method we investigate can be considered as an alternative method compared to the method presented by the second author and co-workers. In particular, we shall use the abstract framework they developed to prove well-posedness of the exact problem. We recast this problem to fit later discretization by the staggered discontinuous Galerkin method developed by the first author and co-worker, a method which relies on introducing an auxiliary unknown. Convergence of the numerical method is proven, with the help of explicit infsup