Hierarchical neural networks have been shown to be effective in learning representative image features and recognizing object classes. However, most existing networks combine the low/middle level cues for classification without accounting for any spatial structures. For applications such as understanding a scene, how the visual cues are spatially distributed in an image becomes essential for successful analysis. This paper extends the framework of deep neural networks by accounting for the structural cues in the visual signals. In particular, two kinds of neural networks have been proposed. First, we develop a multitask deep convolutional network, which simultaneously detects the presence of the target and the geometric attributes (location and orientation) of the target with respect to the region of interest. Second, a recurrent neuron layer is adopted for structured visual detection. The recurrent neurons can deal with the spatial distribution of visible cues belonging to an object whose shape or structure is difficult to explicitly define. Both the networks are demonstrated by the practical task of detecting lane boundaries in traffic scenes. The multitask convolutional neural network provides auxiliary geometric information to help the subsequent modeling of the given lane structures. The recurrent neural network automatically detects lane boundaries, including those areas containing no marks, without any explicit prior knowledge or secondary modeling.

By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the time and space derivative in the same way. Based on this understanding, a uniform framework to derive globally hyperbolic moment systems from kinetic equations using an operator projection method is proposed. The framework is so concise and clear that it can be treated as an algorithm with four inputs to derive hyperbolic moment system by routine calculations. Almost all existing globally hyperbolic moment system can be included in the framework, as well as some new moment system including globally hyperbolic regularized versions of Grad ordered moment system and a multidimensional extension of the quadrature-based moment system.Comment: 32 pages, 2 figure

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