Quantifying Agency in time evolving complex systems.

在这个大数据时代，我们不断地监控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，可以将这些系统理解为简单的模型，可以轻松地与普通公众交流。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，这很容易被各行各业的人理解。近年来，有人认为，将复杂系统有效地粗粒度化成相互作用的子系统，不仅使它们更容易理解，还提供了对复杂系统工作原理的更深层次的洞察。例如，现在人们了解到有功能和生物学上的优势，如由某些等级实现的最佳自我预测和控制(Hoel和Levin，2020)。因此，可以说，层次化的复杂系统自组织成被称为“信息”个体的子系统。这些个体具有最佳自我预测等特征。在这些个体的规模上理解系统的动态提供了一种自然的方式来粗粒化系统，同时捕获感兴趣的新兴现象。在这个建议中，我们希望在两个不同的环境中探索这些最优自预测集群的存在及其在复杂系统中的相关性：1)在生态进化的数学模型中，代理人作为单个物种、作为群落和作为生态系统共同进化。系统中的这些新出现的层次结构将使我们能够探索这些结构的自组织是否提供了最优的预测或控制。2)在一个精心设计的实验中，两位古典音乐家一起即兴演奏，当他们切换为领导者和追随者时，同时使用无线脑电扫描仪记录他们的大脑活动。这项实验提供了一个机会，将数据中观察到的最佳自我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人的方法外，我们还旨在将他们与复杂系统中的代理措施联系起来。

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.