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This paper is purported to investigate a cross-diffusion system arising in a predator-prey population model including Holling type-II functional response in a bounded domain with Dirichlet boundary condition. The asymptotical stabilities are investigated to this system by using the method of eigenvalue. Moreover, the existence of positive steady states are considered by using fixed points index theory, bifurcation theory, energy estimates and the differential method of implicit function. [ABSTRACT FROM AUTHOR]

Model quantization is essential to deploy deep convolutional neural networks (DCNNs) on resource-constrained devices. In this article, we propose a general bitwidth assignment algorithm based on theoretical analysis for efficient layerwise weight and activation quantization of DCNNs. The proposed algorithm develops a prediction model to explicitly estimate the loss of classification accuracy led by weight quantization with a geometrical approach. Consequently, dynamic programming is adopted to achieve optimal bitwidth assignment on weights based on the estimated error. Furthermore, we optimize bitwidth assignment for activations by considering the signal-to-quantization-noise ratio (SQNR) between weight and activation quantization. The proposed algorithm is general to reveal the tradeoff between classification accuracy and model size for various network architectures. Extensive experiments demonstrate the efficacy of the proposed bitwidth assignment algorithm and the error rate prediction model. Furthermore, the proposed algorithm is shown to be well extended to object detection. [ABSTRACT FROM AUTHOR]

With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspective. The majority of these works, however, focus on adapting the convolution operator to graph representation. At the same time, the pooling operator also plays an important role in distilling multiscale and hierarchical representations, but it has been mostly overlooked so far. In this article, we propose a parameter-free pooling operator, called iPool, that permits to retain the most informative features in arbitrary graphs. With the argument that informative nodes dominantly characterize graph signals, we propose a criterion to evaluate the amount of information of each node given its neighbors and theoretically demonstrate its relationship to neighborhood conditional entropy. This new criterion determines how nodes are selected and coarsened graphs are constructed in the pooling layer. The resulting hierarchical structure yields an effective isomorphism-invariant representation of networked data on arbitrary topologies. The proposed strategy achieves superior or competitive performance in graph classification on a collection of public graph benchmark data sets and superpixel-induced image graph data sets. [ABSTRACT FROM AUTHOR]