标度指数不大于2的无标度网络的若干性质

将标度指数不大于2的无标度网络称为亚标度网络.通过引入度秩函数研究了亚标度网络的最大度、平均度以及拓扑结构的非均匀性,通过与标度指数大于2的无标度网络对比,揭示了亚标度网络若干特殊性质.     

成品油调合优化模型及其应用研究

为了提高炼油厂制定成品油调合方案的科学性。研究建立成品油调合优化问题的非线性规划模型。首先从不同的层次，分析提出炼油厂成品油调舍工作的三类优化问题；其次，研究给出三类成品油调合优化问题的非线性规划模型形式；再次，针对成品油调合优化模型形式的特点，提出相应的求解技术；最后，通过在某炼油厂的一个应用实例验证上述成品油调合优化模型的有效性。     

Natural Connectivity of Complex Networks

The concept of natural connectivity is reported as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It is shown that the natural connectivity can be derived mathematically from the graph spectrum as an average eigenvalue and that it changes strictly monotonically with the addition or deletion of edges. By comparing the natural connectivity with other typical robustness measures within a scenario of edge elimination, it is demonstrated that the naturM connectivity has an acute discrimination which agrees with our intuition.     

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.     

Normalized entropy of rank distribution： a novel measure of heterogeneity of complex networks

Many unique properties of complex networks result from heterogeneity. The measure and analysis of heterogeneity are important and desirable to the research of the properties and functions of complex networks. In this paper, the rank distribution is proposed as a new statistic feature of complex networks. Based on the rank distribution, a novel measure of the heterogeneity called a normalized entropy of rank distribution (NERD) is proposed. The NERD accords with the normal meaning of heterogeneity within the context of complex networks compared with conventional measures. The heterogeneity of scale-free networks is studied using the NERD. It is shown that scale-free networks become more heterogeneous as the scaling exponent decreases and the NERD of scale-free networks is independent of the number of vertices, which indicates that the NERD is a suitable and effective measure of heterogeneity for networks with different sizes.