Multi-fractal analysis of weighted networks

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal dimension to study complex networks. In this case, multifractal analysis of complex networks are concerned. However, multifractal dimension of weighted networks are less involved. In this paper, multifractal dimension of weighted networks is proposed based on box-covering algorithm for fractal dimension of weighted networks (BCANw). The proposed method is applied to calculate the fractal dimensions of some real networks. Our numerical results indicate that the proposed method is efficient for analysis fractal property of weighted networks

Output regulation of nonlinear singularly perturbed systems

AbstractIn this paper, the state feedback regulator problem of nonlinear singularly perturbed systems is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once this equation is solvable, a feedback law which solves the problem can easily be constructed. The developed control law is applied to a nonlinear chemical process

Part-guided Relational Transformers for Fine-grained Visual Recognition

Fine-grained visual recognition is to classify objects with visually similar appearances into subcategories, which has made great progress with the development of deep CNNs. However, handling subtle differences between different subcategories still remains a challenge. In this paper, we propose to solve this issue in one unified framework from two aspects, i.e., constructing feature-level interrelationships, and capturing part-level discriminative features. This framework, namely PArt-guided Relational Transformers (PART), is proposed to learn the discriminative part features with an automatic part discovery module, and to explore the intrinsic correlations with a feature transformation module by adapting the Transformer models from the field of natural language processing. The part discovery module efficiently discovers the discriminative regions which are highly-corresponded to the gradient descent procedure. Then the second feature transformation module builds correlations within the global embedding and multiple part embedding, enhancing spatial interactions among semantic pixels. Moreover, our proposed approach does not rely on additional part branches in the inference time and reaches state-of-the-art performance on 3 widely-used fine-grained object recognition benchmarks. Experimental results and explainable visualizations demonstrate the effectiveness of our proposed approach. The code can be found at https://github.com/iCVTEAM/PART.Comment: Published in IEEE TIP 202