Benigni Barbara, Gallotti Riccardo, De Domenico Manlio
Department of Information Engineering and Computer Science, University of Trento, Via Sommarive, 9, 38123 Povo, Trento, Italy and CoMuNe Lab, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo, Trento, Italy.
CoMuNe Lab, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo, Trento, Italy.
Phys Rev E. 2021 Aug;104(2-1):024120. doi: 10.1103/PhysRevE.104.024120.
Interconnected systems have to route information to function properly: At the lowest scale neural cells exchange electrochemical signals to communicate, while at larger scales animals and humans move between distinct spatial patches and machines exchange information via the Internet through communication protocols. Nontrivial patterns emerge from the analysis of information flows, which are not captured either by broadcasting, such as in random walks, or by geodesic routing, such as shortest paths. In fact, alternative models between those extreme protocols are still eluding us. Here we propose a class of stochastic processes, based on biased random walks, where agents are driven by a physical potential pervading the underlying network topology. By considering a generalized Coulomb dependence on the distance on destination(s), we show that it is possible to interpolate between random walk and geodesic routing in a simple and effective way. We demonstrate that it is not possible to find a one-size-fit-all solution to efficient navigation and that network heterogeneity or modularity has measurable effects. We illustrate how our framework can describe the movements of animals and humans, capturing with a stylized model some measurable features of the latter. From a methodological perspective, our potential-driven random walks open the doors to a broad spectrum of analytical tools, ranging from random-walk centralities to geometry induced by potential-driven network processes.
在最小尺度上，神经细胞通过交换电化学信号进行通信，而在较大尺度上，动物和人类在不同的空间区域之间移动，机器则通过通信协议经由互联网交换信息。对信息流的分析揭示了一些非平凡的模式，这些模式既不是通过诸如随机游走中的广播方式，也不是通过诸如最短路径中的测地线路由方式所能捕捉到的。事实上，介于这些极端协议之间的替代模型仍然难以捉摸。在此，我们基于有偏随机游走提出了一类随机过程，其中主体由遍布基础网络拓扑结构的物理势驱动。通过考虑对目的地距离的广义库仑依赖性，我们表明可以以一种简单有效的方式在随机游走和测地线路由之间进行插值。我们证明，对于高效导航，不可能找到一种适用于所有情况的解决方案，并且网络的异质性或模块化具有可测量的影响。我们说明了我们的框架如何能够描述动物和人类的运动，并用一个程式化模型捕捉到后者的一些可测量特征。从方法论的角度来看，我们的势驱动随机游走为一系列广泛的分析工具打开了大门，从随机游走中心性到由势驱动网络过程诱导的几何结构。
