Evolution of Spiral Waves in Excitable Systems

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.

一种基于话题演化的意见领袖发现方法

微博中的意见领袖不仅在社交网络的信息传播中发挥着举足轻重的作用,而且在网络舆情演化中也表现出显著的意见代表性。针对已有的意见领袖挖掘方法仅从复杂网络或者基本图模型来建模发现意见领袖,忽略了意见领袖在具体的话题演化中的意见代表性的问题,提出了基于话题演化的意见领袖发现的方法。该方法首先根据用户之间的交互构建图模型,然后利用寻找中心节点的图论算法挖掘潜在意见领袖,再利用话题演化模型判断潜在意见领袖的演化中心度,最后发现在整体舆情上的具有意见代表性的真实意见领袖。在新浪微博的话题数据集上的试验结果表明,该算法较仅考虑网络模型的意见领袖发现方法更优。