论文标题
多重和相互依赖系统的扩散几何形状
Diffusion geometry of multiplex and interdependent systems
论文作者
论文摘要
复杂的网络的特征是由其拓扑或顶部的动力学引起的潜在几何形状。在后一种情况下，不同的网络驱动过程会引起不同的几何特征，这些特征可以通过足够的指标捕获。最近在[Phys中使用了随机步行，是从简单传染到亚稳定的同步和共识的广泛过程的代理。莱特牧师。 118，168301（2017）]从真正的几何学角度来定义扩散几何类别的类别，并指出复杂网络的功能性中尺度组织。在这里，我们首先将这堂课扩展到多层网络上的独特随机步行动态（包括本地和非本地信息）的家庭，这是一种生物学，神经，社会，社会，运输，生物学和金融系统的范式 - 克服了局限性的局限性，例如存在隔离的节点和脱节组件，以及现实世界中典型的现实世界网络的典型组件。其次，我们表征了合成和经验系统的多层扩散几何形状，突出了不同随机搜索动力学在塑造相应扩散歧管的几何特征中所起的作用。
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used in [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometry and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here, we firstly extend this class to families of distinct random walk dynamics -- including local and nonlocal information -- on multilayer networks -- a paradigm for biological, neural, social, transportation, biological and financial systems -- overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. Secondly, we characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.
