Entropy has been widely measured the complexity of complex networks. At present, many measures about entropies were defined based on the directed connection of nodes. The similarity of nodes can better represent the relationship among all nodes in complex networks. In the definition of similarity of nodes, the importance of a node in the network depends not only on the degree of the node itself, but also on the extent of dependence of neighboring nodes on the node. In this paper, we proposed a new structure entropy based on nonextensive statistical mechanics and similarity of nodes. In the proposed method, the similarity of nodes and the betweenness of nodes are both quantified. The proposed method considers the extent of dependence between neighbouring nodes. For some complex networks, the proposed structure entropy can distinguish complexity of that while other entropies can not be. Meanwhile, we construct five ER random networks and small-world networks and some real-world complex networks such as the US Air Lines networks, the GD'01-GD Proceedings Self-Citing networks, the Science Theory networks, the Centrality Literature networks and the Yeast networks are measured by the proposed method. The results illustrated our method for quantifying the complexity of complex networks is effective.
Citation: Bing Wang, Fu Tan, Jia Zhu, Daijun Wei. A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3718-3732. doi: 10.3934/mbe.2021187
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Entropy has been widely measured the complexity of complex networks. At present, many measures about entropies were defined based on the directed connection of nodes. The similarity of nodes can better represent the relationship among all nodes in complex networks. In the definition of similarity of nodes, the importance of a node in the network depends not only on the degree of the node itself, but also on the extent of dependence of neighboring nodes on the node. In this paper, we proposed a new structure entropy based on nonextensive statistical mechanics and similarity of nodes. In the proposed method, the similarity of nodes and the betweenness of nodes are both quantified. The proposed method considers the extent of dependence between neighbouring nodes. For some complex networks, the proposed structure entropy can distinguish complexity of that while other entropies can not be. Meanwhile, we construct five ER random networks and small-world networks and some real-world complex networks such as the US Air Lines networks, the GD'01-GD Proceedings Self-Citing networks, the Science Theory networks, the Centrality Literature networks and the Yeast networks are measured by the proposed method. The results illustrated our method for quantifying the complexity of complex networks is effective.
Creating this inaugural special issue on Engineering Applications of Artificial Intelligence (AI) is important due to the rapid technology advancement and the aim to reduce the manpower by incorporating Artificial Intelligence in various Industry 4.0 applications. As my research reflects the multi-disciplinarily of systems (consisting of mechanical, electrical, electronics, acoustical and marine engineering) from initial concepts to the modelling and AI simulation, creating graphical-user interface and their actual implementations and testing on sites. The special issue provides a good platform to share applied research results from different researchers around the world.
For example, the phase partition-based ensemble learning framework upon least squares supports vector regression (LSSVR) was used for soft sensor modeling to improve the prediction accuracy in chemical and biological processes. As a result, the robotic grasping based on improved Gaussian mixture model was also proposed using the virtual robot experimentation platform. The face image recognition algorithm based on two-dimensional (2D) Gabor wavelet transform and Local Binary Pattern (LBP) was presented. It provides a better classification performance in different scales and directions affected by illumination, gesture, expression, and other factor's variation. With more consciousness in cyber-security, the paper that used the Kalman filter-based attack detection model was proposed. The block withholding delay attack and the countermeasure were also proposed in a similar occasion. The well-known convolutional neural network (CNN) based approach was applied to detect the obstacle for the unmanned surface vehicle. Subsequently, an effective classifier based on the CNN and regularized extreme learning machine (ELM) was adopted to reduce the classification time in the training and testing.
In summary, this issue concluded with different engineering applications of AI. It is imperative that we continue to progress in our search for better engineering systems design and simulation using AI. The progress reported in this special issue suggests that achieving these aims is an attainable one. I hope that we can stay in contact and make this world a better place for a "deep" collaborative research.
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Bing Wang, Fu Tan, Jia Zhu, Daijun Wei. A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3718-3732. doi: 10.3934/mbe.2021187
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