No abstract

The study of interdependent networks has become a new research focus in recent years. We focus on one fundamental property of interdependent networks: vulnerability. Previous studies mainly focused on the impact of topological properties upon interdependent networks under random attacks, the effect of degree heterogeneity on structural vulnerability of interdependent networks under intentional attacks, however, is still unexplored. In order to deeply understand the role of degree distribution and in particular degree heterogeneity, we construct an interdependent system model which consists of two networks whose extent of degree heterogeneity can be controlled simultaneously by a tuning parameter. Meanwhile, a new quantity, which can better measure the performance of interdependent networks after attack, is proposed. Numerical simulation results demonstrate that degree heterogeneity can significantly increase the vulnerability of both single and interdependent networks. Moreover, it is found that interdependent links between two networks make the entire system much more fragile to attacks. Enhancing coupling strength between networks can greatly increase the fragility of both networks against targeted attacks, which is most evident under the case of max-max assortative coupling. Current results can help to deepen the understanding of structural complexity of complex real-world systems.

Portfolio optimization is a hot research topic, which has attracted many researchers in recent decades. Better portfolio optimization model can help investors earn more stable profits. This paper uses three deep neural networks (DNNs), i.e., deep multilayer perceptron (DMLP), long short memory (LSTM) neural network and convolutional neural network (CNN) to build prediction-based portfolio optimization models which own the advantages of both deep learning technology and modern portfolio theory. These models first use DNNs to predict each stock's future return. Then, predictive errors of DNNs are applied to measure the risk of each stock. Next, the portfolio optimization models are built by integrating the predictive returns and semi-absolute deviation of predictive errors. These models are compared with three equal weighted portfolios, where their stocks are selected by DMLP, LSTM neural network and CNN respectively. Also, two prediction-based portfolio models built with support vector regression are used as benchmarks. This paper applies component stocks of China securities 100 index in Chinese stock market as experimental data. Experimental results present that the prediction-based portfolio model based on DMLP performs the best among these models under different desired portfolio returns, and high desired portfolio return can further improve the performance of this model. This paper presents the promising performance of DNNs in building prediction-based portfolio models. INDEX TERMS Deep neural network, Prediction-based portfolio, Semi-absolute deviation.