Network structure has a great impact both on hazard spread and network immunization. The vulnerability of the network node is associated with each other, assortative or disassortative. Firstly, an algorithm for vulnerability relevance clustering is proposed to show that the vulnerability community phenomenon is obviously existent in complex networks. On this basis, next, a new indicator called network “hyper-betweenness” is given for evaluating the vulnerability of network node. Network hyper-betweenness can reflect the importance of network node in hazard spread better. Finally, the dynamic stochastic process of hazard spread is simulated based on Monte-Carlo sampling method and a two-player, non-cooperative, constant-sum game model is designed to obtain an equilibrated network immunization strategy.

An improved genetic algorithm is employed to optimize the structure of (C60)N (N≤25) fullerene clusters with the lowest energy. First, crossover with variable precision, realized by introducing the hamming distance, is developed to provide a faster search mechanism. Second, the bit string mutation and feedback mutation are incorporated to maintain the diversity in the population. The interaction between C60 molecules is described by the Pacheco and Ramalho potential derived from first-principles calculations. We compare the performance of the Improved GA (IGA) with that of the Standard GA (SGA). The numerical and graphical results verify that the proposed approach is faster and more robust than the SGA. The second finite differential of the total energy shows that the (C60)N clusters with N=7, 13, 22 are particularly stable. Performance with the lowest energy is achieved in this work.

For many fields in real life, time series forecasting is essential. Recent studies have shown that Transformer has certain advantages when dealing with such problems, especially when dealing with long sequence time input and long sequence time forecasting problems. In order to improve the efficiency and local stability of Transformer, these studies combine Transformer and CNN with different structures. However, previous time series forecasting network models based on Transformer cannot make full use of CNN, and they have not been used in a better combination of both. In response to this problem in time series forecasting, we propose the time series forecasting algorithm based on convolution Transformer. (1) ES attention mechanism: Combine external attention with traditional self-attention mechanism through the two-branch network, the computational cost of self-attention mechanism is reduced, and the higher forecasting accuracy is obtained. (2) Frequency enhanced block: A Frequency Enhanced Block is added in front of the ESAttention module, which can capture important structures in time series through frequency domain mapping. (3) Causal dilated convolution: The self-attention mechanism module is connected by replacing the traditional standard convolution layer with a causal dilated convolution layer, so that it obtains the receptive field of exponentially growth without increasing the calculation consumption. (4) Multi-layer feature fusion: The outputs of different self-attention mechanism modules are extracted, and the convolutional layers are used to adjust the size of the feature map for the fusion. The more fine-grained feature information is obtained at negligible computational cost. Experiments on real world datasets show that the time series network forecasting model structure proposed in this paper can greatly improve the real-time forecasting performance of the current state-of-the-art Transformer model, and the calculation and memory costs are significantly lower. Compared with previous algorithms, the proposed algorithm has achieved a greater performance improvement in both effectiveness and forecasting accuracy.

The application of time-series prediction is very extensive, and it is an important problem across many fields, such as stock prediction, sales prediction, and loan prediction and so on, which play a great value in production and life. It requires that the model can effectively capture the long-term feature dependence between the output and input. Recent studies show that Transformer can improve the prediction ability of time-series. However, Transformer has some problems that make it unable to be directly applied to time-series prediction, such as: (1) Local agnosticism: Self-attention in Transformer is not sensitive to short-term feature dependence, which leads to model anomalies in time-series; (2) Memory bottleneck: The spatial complexity of regular transformation increases twice with the sequence length, making direct modeling of long time-series infeasible. In order to solve these problems, this paper designs an efficient model for long time-series prediction. It is a double pyramid bidirectional feature fusion mechanism network with parallel Temporal Convolution Network (TCN) and FastFormer. This network structure can combine the time series fine-grained information captured by the Temporal Convolution Network with the global interactive information captured by FastFormer, it can well handle the time series prediction problem.