论文标题
复杂系统中可预测性与可重建性之间的二元性
Duality between predictability and reconstructability in complex systems
论文作者
论文摘要
使用其相互作用结构来预测大型单元系统的演变是复杂系统理论中的一个基本问题。从时间观察中重建相互作用的结构的问题也是如此。在这里，我们发现使用信息理论观点之间的可预测性与可预测性之间存在复杂的关系。我们使用随机图和随机图上演变的随机过程之间的共同信息来量化它们的相互依赖性。然后，我们展示了与该互信息密切相关的不确定性系数如何量化我们从观察到的时间序列中重建图的能力，以及我们从其相互作用的结构中预测过程演变的能力。有趣的是，我们发现即使通过相互信息紧密相关的可预测性和可重建性，即使是双重方式也可能会有所不同。我们证明，在更改过程中的步骤数时，这种二元性如何普遍出现，并提供了在多种不同类型的结构上演变的多个不同过程的关键时期发生的其他双重性的数值证据。
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process, and provide numerical evidence of other dualities occurring near the criticality of multiple different processes evolving on different types of structures.
