论文标题
解剖网络动态过程的本地化现象
Dissecting localization phenomena of dynamical processes on networks
论文作者
论文摘要
本地化现象渗透到许多物理分支中,在异质网络上演变的动态过程中起着基本作用。这些定位分析经常是基础的,例如,在邻接的特征向量或非折线矩阵上,这些矩阵在动态过程的理论中出现在接近活动性转变的动态过程理论中。我们在这个问题中促进了衡量节点活动的问题,以量化网络上动态过程中的定位,无论它们是否接近过渡。该方法是通用的,适用于理论,随机模拟和真实数据。我们在分析和数值上研究了广泛网络上的扩散过程,表明节点活动可以根据网络结构呈现复杂的模式。使用退火网络,我们表明,在过渡时期的局部状态及其上方的地方性阶段不是扩展过程的不兼容特征。我们还报告说,即使对反相反比率的分析表明局部活动,即使过渡近来的流行率也取决于网络的离域组成部分。同样,具有不同关键指数的动态过程可以通过相同的本地化模式来描述。根据激活的类型和学位指数的范围,转向淬灭的网络,这是一个更复杂的图片。我们的工作铺平了研究在网络上扩散和其他过程中局部活动的重要途径。
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or non-backtracking matrices which emerge in theories of dynamic processes near to an active to inactive transition. We advance in this problem gauging nodal activity to quantify the localization in dynamical processes on networks whether they are near to a transition or not. The method is generic and applicable to theory, stochastic simulations, and real data. We investigate spreading processes on a wide spectrum of networks, both analytically and numerically, showing that nodal activity can present complex patterns depending on the network structure. Using annealed networks we show that a localized state at the transition and an endemic phase just above it are not incompatible features of a spreading process. We also report that epidemic prevalence near to the transition is determined by the delocalized component of the network even when the analysis of the inverse participation ratio indicates a localized activity. Also, dynamical processes with distinct critical exponents can be described by the same localization pattern. Turning to quenched networks, a more complex picture, depending on the type of activation and on the range of degree exponent, is observed and discussed. Our work paves an important path for investigation of localized activity in spreading and other processes on networks.