In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasi-primary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.

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.

Computing stationary states is an important topic for phase field crystal (PFC) models. Great efforts have been made for energy dissipation of the numerical schemes when using gradient flows. However, it is always time-consuming due to the requirement of small effective time steps. In this paper, we propose an adaptive accelerated proximal gradient method for finding the stationary states of PFC models. The energy dissipation is guaranteed and the convergence property is established for the discretized energy functional. Moreover, the connections between generalized proximal operator with classical (semi-)implicit and explicit schemes for gradient flow are given. Extensive numerical experiments, including two three dimensional periodic crystals in Landau-Brazovskii (LB) model and a two dimensional quasicrystal in Lifshitz-Petrich (LP) model, demonstrate that our approach has adaptive time steps which lead to significant acceleration over semi-implicit methods for computing complex structures. Furthermore, our result reveals a deep physical mechanism of the simple LB model via which the sigma phase is first discovered.

Recently sparse representation has been applied to visual tracker by modeling the target appearance using a sparse approximation over a template set, which leads to the so-called L_1 trackers as it needs to solve an ℓ_1 norm related minimization problem for many times. While these L_1 trackers showed impressive tracking accuracies, they are very computationally demanding and the speed bottleneck is the solver to ℓ_1 norm minimizations. This paper aims at developing an L_1 tracker that not only runs in real time but also enjoys better robustness than other L_1 trackers. In our proposed L_1 tracker, a new ℓ_1 norm related minimization model is proposed to improve the tracking accuracy by adding an ℓ_1 norm regularization on the coefficients associated with the trivial templates. Moreover, based on the accelerated proximal gradient approach, a very fast numerical solver is developed to solve the resulting ℓ_1 norm related minimization problem with guaranteed quadratic convergence. The great running time efficiency and tracking accuracy of the proposed tracker is validated with a comprehensive evaluation involving eight challenging sequences and five alternative state-of-the-art trackers.

In recent years, how to learn a dictionary from input images for sparse modelling has been one very active topic in image processing and recognition. Most existing dictionary learning methods consider an over-complete dictionary, e.g. the K-SVD method. Often they require solving some minimization problem that is very challenging in terms of computational feasibility and efficiency. However, if the correlations among dictionary atoms are not well constrained, the redundancy of the dictionary does not necessarily improve the performance of sparse coding. This paper proposed a fast orthogonal dictionary learning method for sparse image representation. With comparable performance on several image restoration tasks, the proposed method is much more computationally efficient than the over-complete dictionary based learning methods.