How do constraints affect the behaviour of a complex system?

在一个由简单主体组成的系统中，约束如何影响涌现的宏观行为？在自然界中，复杂系统中有许多紧急行为的例子，例如，地震的古登堡-里希特定律，价格波动的幂定律行为，社会网络的连通性等。然而，这些复杂系统的大小是有限的。这些系统的有限性如何扰乱人们在无限系统中观察到的固有(理想)行为？人们能否从有限系统中提取出扰动的标度行为，从而最终可以推算到无限系统？关键系统中的有限大小标度的概念就是这样一个例子，但范围是有限的。另一个相关的问题是，由于这些限制，较小的系统是否天生更具可预测性。如果是，人们能否利用这种提高的可预测性来推断更大系统的可预测性？这些研究首先在简化的复杂系统中进行。研究领域：复杂性科学研究领域：复杂性科学战略领域：数学科学和物理科学

In a system consisting of simple agents, how do constraints affect the emergent macroscopic behaviours? In nature, there are many examples of emergent behaviour in complex systems, for example, the Gutenberg-Richter law of earthquakes, the power-law behaviour of price fluctuations, the connectivity of social networks etc. However, these complex systems are finite in size. How does the finiteness of these systems perturb the inherent (ideal) behaviour that one would observe in an infinite system? Can one extract the scaling behaviour of the perturbation from finite systems that would eventually allow one to extrapolate to the infinite system? The notion of finite-size scaling in critical systems is one such example, but in a limited domain. Another related question is whether smaller systems are inherently more predictable due to the constraints. If yes, can one exploit this increased predictability to extrapolate the predictability of larger systems? These investigations are first pursued in simplified complex systems. TheResearch Area: Complexity ScienceResearch Area: Complexity ScienceStrategic Area: Mathematical Sciences & Physical Sciences