标题： 分形几何预测结构和功能连接组的动态差异 显示英文标题

标题： Fractal geometry predicts dynamic differences in structural and functional connectomes

摘要： 理解大脑网络的复杂结构及其与脑功能的联系对于揭示认知和疾病的基本原理至关重要。虽然传统的图论测量方法已被广泛用于表征这些网络，但它们往往无法充分捕捉大规模神经动力学的涌现特性。在这里，我们介绍了一种替代的方法来量化大脑网络，这种方法基于复杂动力学、分形几何和渐近分析。我们将这些概念应用于大脑连接组，并展示了二次迭代和类似曼德尔布罗集的几何属性如何提供有关结构和功能网络动态的新见解。我们的研究结果揭示了结构（正）连接组和功能（有符号）连接组之间的基本区别，如尖点方向的偏移和等M集几何形状的变化。值得注意的是，结构连接组表现出更稳健、可预测的特征，而功能连接组在非平凡任务中显示出更大的变异性。我们进一步证明，当传统图论测量方法分别应用于功能连接组的正子网络和负子网络时，无法完全捕捉它们的动态复杂性。相反，基于大小和形状的等M集不变量有效地区分了休息状态和情感任务状态，这突显了它们作为涌现网络动力学优越标记的潜力。这些结果表明，将基于分形的方法纳入网络神经科学，为理解信息在自然系统中的流动提供了强有力的工具，同时保持了其简单性，而不是仅仅依赖静态连接性度量。 显示英文摘要

摘要： Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely used to characterize these networks, they often fail to fully capture the emergent properties of large-scale neural dynamics. Here, we introduce an alternative approach to quantify brain networks that is rooted in complex dynamics, fractal geometry, and asymptotic analysis. We apply these concepts to brain connectomes and demonstrate how quadratic iterations and geometric properties of Mandelbrot-like sets can provide novel insights into structural and functional network dynamics. Our findings reveal fundamental distinctions between structural (positive) and functional (signed) connectomes, such as the shift of cusp orientation and the variability in equi-M set geometry. Notably, structural connectomes exhibit more robust, predictable features, while functional connectomes show increased variability for non-trivial tasks. We further demonstrate that traditional graph-theoretical measures, when applied separately to the positive and negative sub-networks of functional connectomes, fail to fully capture their dynamic complexity. Instead, size and shape-based invariants of the equi-M set effectively differentiate between rest and emotional task states, which highlights their potential as superior markers of emergent network dynamics. These results suggest that incorporating fractal-based methods into network neuroscience provides a powerful tool for understanding how information flows in natural systems beyond static connectivity measures, while maintaining their simplicity.