The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess higher-order interactions involving three or more elements directly. In this work, we present a method for capturing higher-order dependencies in discrete data based on partial entropy decomposition (PED). Our approach decomposes the joint entropy of the whole system into a set of strictly non-negative partial entropy atoms that describe the redundant, unique, and synergistic interactions that compose the system's structure. We begin by showing how the PED can provide insights into the mathematical structure of both the FC network itself, as well as established measures of higher-order dependency such as the O-information. When applied to resting state fMRI data, we find robust evidence of higher-order synergies that are largely invisible to standard functional connectivity analyses. This synergistic structure distinct from structural features based on redundancy that have previously dominated FC analyses. Our approach can also be localized in time, allowing a frame-by-frame analysis of how the distributions of redundancies and synergies change over the course of a recording. We find that different ensembles of regions can transiently change from being redundancy-dominated to synergy-dominated, and that the temporal pattern is structured in time. These results provide strong evidence that there exists a large space of unexplored structures in human brain data that have been largely missed by a focus on bivariate network connectivity models. This synergistic "shadow structures" is dynamic in time and, likely will illuminate new and interesting links between brain and behavior.
翻译:将人类大脑建模为复杂系统的标准方法是一个网络, 其基本互动单位是两个大脑区域之间的对称联系。 虽然这个方法很强大, 但因无法直接评估涉及三个或更多元素的更高层次互动关系而受到限制。 在这项工作中, 我们提出了一个方法, 用来捕捉基于部分元素分解( PED) 的离散数据中较高层次依赖性。 我们的方法将整个系统的联合连接点分解成一套严格非负向性的部分通缩原子, 以描述构成系统结构的冗余、 独特和协同互动关系。 虽然这个方法很强大, 但由于无法直接评估涉及三个或更多元素的更高层次互动关系。 在这项工作中, 我们提出一个方法, 获取较高层次依赖性依赖性数据的方法, 如 O- 信息。 当应用到修复状态的 FMRI 数据时, 我们发现一个强有力的证据, 高层次协同性合力的合力, 与以前主导FC分析的冗余性结构不同。 我们的方法也可以在时间上定位, 使得结构结构结构结构结构的 变异变 。