Quantifying Agency in time evolving complex systems.

在这个大数据时代，我们不断监测驱动我们世界的复杂系统，这为我们提供了一个独特的机会，将这些系统理解为简单的模型，可以很容易地与公众沟通。这种将知识提炼成简单故事的努力只能在粗粒度的宏观层面上取得成果，这样各行各业的人都可以很容易地理解。近年来，有人认为这种将复杂系统有效地粗粒度化为相互作用的子系统提供了对复杂系统工作的更深入的了解，而不仅仅是使它们更易于理解。例如，现在人们了解到，某些层次结构具有功能和生物优势，如最佳自我预测和控制（Hoel和Levin， 2020）。因此，可以认为分层复杂系统自组织成被称为“信息”个体的子系统。这些人具有最佳自我预测等特征。在这些个体的尺度上理解系统的动态提供了一种自然的方法，可以对系统进行粗粒度分析，同时捕获感兴趣的突发现象。在这一提议中，我们希望探索这些最佳自我预测集群的存在及其在两种不同设置下的复杂系统中的相关性：1)在生态进化的数学模型中，agent作为个体物种、群落和生态系统共同进化。这些系统中涌现的层次结构将使我们能够探索这些结构中的自组织是否提供了最佳的预测或控制。2)在一项精心设计的实验中，两位古典音乐家一起即兴演奏，当他们转换为领导者和追随者时，他们的大脑活动同时被无线脑电图扫描仪记录下来。这个实验提供了一个机会，将数据中观察到的最佳自预测结构与复杂系统中的代理轨迹联系起来。因此，除了开发跟踪信息个体的方法外，我们还旨在将它们与复杂系统中的代理度量联系起来。

This age of big data, where we are continuously monitoring the complex systems that drive our world, provides us with a unique opportunity to understand these systems as simple models that can be easily communicated to the general public. This effort of distilling the knowledge into simple stories can only come to fruition at a coarse-grained macro level which can be easily understood by people from all walks of life.In recent years, it has been argued that this effective coarse-graining of the complex systems into interacting subsystems offers a deeper insight into the workings of complex systems than just making them more comprehensible. For example, it is now understood that there are functional and biological advantages like optimal self-prediction and control enabled by certain levels of hierarchy (Hoel and Levin, 2020). Therefore, it can be argued that hierarchical complex systems self organizes into sub-systems that are known as "informational" individuals. These individuals possess characteristics like optimal self-prediction. Understanding the dynamics of the system at the scale of these individuals offers a natural way of coarse-graining the system, yet capturing the emergent phenomenon of interest. In this proposal, we wish to explore the existence of these optimally self predicting clusters and their relevance in complex systems in two different settings, 1) In a mathematical model of ecological evolution, where agents co-evolve as individual species, as communities and as ecosystems. These emergent hierarchies in the system will enable us to probe is the self-organisation into these structures offers optimal prediction or control. 2) In a carefully designed experiment with two classical musicians improvising together, as they switch as leaders and followers, while their brain activity is simultaneously recorded using wireless EEG scanners. This experiment offers an opportunity to relate the observed optimally self-predicting structures in the data to the locus of agency in the complex system. Therefore, in addition to developing methods to track informational individuals, we also aim to relate them to a measure of agency in complex systems.