Allard Antoine, Hébert-Dufresne Laurent, Young Jean-Gabriel, Dubé Louis J
Département de physique, de génie physique et d'optique, Université Laval, Québec (Québec), Canada G1V 0A6.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Feb;89(2):022801. doi: 10.1103/PhysRevE.89.022801. Epub 2014 Feb 6.
In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolationlike emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-L percolation--where the state of nodes up to a distance L of monitored nodes is known--can be mapped onto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a nontrivial coexistence of an observable and of a nonobservable extensive component. This coexistence suggests that monitoring a macroscopic portion of a graph does not prevent a macroscopic event to occur unbeknown to the observer. We also show that real complex systems behave quite differently with regard to observability depending on whether they are geographically constrained or not.
在最近的一篇快报中，杨等人[《物理评论快报》109, 258701 (2012)]引入了可观测性转变的概念：在对一部分节点及其一阶邻域的状态进行监测的图中，宏观可观测分量类似渗流的出现。我们展示了他们的深度-L渗流概念（其中直到被监测节点距离L处的节点状态是已知的）如何能映射到多类型随机图上，并利用这种映射精确求解任意L的可观测性问题。然后我们证明了一个可观测的和一个不可观测的广延分量的非平凡共存。这种共存表明，监测图的宏观部分并不能防止观察者未知的宏观事件发生。我们还表明，真实的复杂系统在可观测性方面的表现根据它们是否受地理约束而有很大不同。
