Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.Comment: 5+9 pages, 3 figures, updated references, fixed typos and refinements, added proof for equivalence to Lagrangian subgroups in Abelian case

Background Subtraction via Generalized Fused Lasso Foreground Modeling

Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts

Experiential Teaching is more Conducive to Student Learning than Traditional Teaching

Some drawbacks of traditional teacher-centred teaching have gradually become apparent and have led to a growing interest in experiential teaching. Students and teachers are prominent participants in the teaching process, and their behavioural performance largely determines the learning outcomes. Likewise, a harmonious teacher-student relationship is essential to students’ learning experience. In this paper, we have analysed the impact of experiential teaching on three aspects: student engagement, teacher-teaching innovation and teacher-student collaboration, to show that experiential has clear advantages for student learning. However, some argue that the design and practice of experiential teaching are challenging for teachers and that the student-centred approach is not conducive to managing classroom order. This, therefore, suggests new elements for teacher education and schoolteacher training to avoid the gap between instructional design and practice. And further research is needed by educational researchers on how to manage classroom order in experiential teaching and to make students learn effectively

Higher Education in China should Increase the Proportion of Practical Teaching

With the evolution of society, the demands on human resources have also changed significantly. In the face of such changes, the field of education also needs to adapt. Current higher education in China, influenced by Confucianism, places more emphasis on theory than practice, leading to a lack of applied, innovative, and complex talents in the market, so the proportion of practical teaching should be increased. By discussing the benefits of practice for knowledge, talent development, and employment, this paper illustrates the important role of increasing the proportion of practical teaching in Chinese higher education today, guiding students to become applied, innovative and complex talents with solid theory and good quality and suggesting improvements in response to the problems currently faced by practical teaching

Refinements of Aczél-Type Inequality and Their Applications

We present some new sharpened versions of Aczél-type inequality. Moreover, as applications, some refinements of integral type of Aczél-type inequality are given

A Regularized Opponent Model with Maximum Entropy Objective

In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve the performance of training agents theoretically and empirically in cooperative games. To optimize ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of convergence. We extend the exact algorithm to complex environments by proposing an approximate version, ROMMEO-AC. We evaluate these two algorithms on the challenging iterated matrix game and differential game respectively and show that they can outperform strong MARL baselines.Comment: Accepted to International Joint Conference on Artificial Intelligence (IJCA2019

Enhanced CNN for image denoising

Owing to flexible architectures of deep convolutional neural networks (CNNs), CNNs are successfully used for image denoising. However, they suffer from the following drawbacks: (i) deep network architecture is very difficult to train. (ii) Deeper networks face the challenge of performance saturation. In this study, the authors propose a novel method called enhanced convolutional neural denoising network (ECNDNet). Specifically, they use residual learning and batch normalisation techniques to address the problem of training difficulties and accelerate the convergence of the network. In addition, dilated convolutions are used in the proposed network to enlarge the context information and reduce the computational cost. Extensive experiments demonstrate that the ECNDNet outperforms the state-of-the-art methods for image denoising.Comment: CAAI Transactions on Intelligence Technology[J], 201