The brain shows a topographical hierarchy along the lines of lower- and higher-order networks. The exact temporal dynamics characterization of this lower-higher-order topography at rest and its impact on task states remains unclear, though. Using 2 functional magnetic resonance imaging data sets, we investigate lower- and higher-order networks in terms of the signal compressibility, operationalized by Lempel-Ziv complexity (LZC). As we assume that this degree of complexity is related to the slow-fast frequency balance, we also compute the median frequency (MF), an estimation of frequency distribution. We demonstrate (i) topographical differences at rest between higher- and lower-order networks, showing lower LZC and MF in the former; (ii) task-related and task-specific changes in LZC and MF in both lower- and higher-order networks; (iii) hierarchical relationship between LZC and MF, as MF at rest correlates with LZC rest-task change along the lines of lower- and higher-order networks; and (iv) causal and nonlinear relation between LZC at rest and LZC during task, with MF at rest acting as mediator. Together, results show that the topographical hierarchy of lower- and higher-order networks converges with their temporal hierarchy, with these neural dynamics at rest shaping their range of complexity during task states in a nonlinear way.
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