Fig. 2: Global and local higher-order topological indicators for fMRI task differentiability.
a We report the distribution of the global hyper-coherence for the concatenated fMRI data at rest and the seven HCP tasks, namely: emotion, gambling, language, motor, relational, social, and working memory (WM). Distributions are obtained when considering the global scores for the 100 unrelated subjects. b Two-dimensional histogram of the global hyper-complexity contributions associated with 1D cycles in the landscape of coherent and decoherent co-fluctuations for rest and task fMRI data. Here, the position of each point in the triangle is determined by the three different contributions associated with the 1D cycles, namely, full coherence (FC), coherence transition (CT), and full decoherence (FD) contributions. Remarkably, the two global measures are not able to decode between the different tasks. c–f We then compare local observables by comparing the temporal recurrence plots (i.e., time-time correlation matrices) for the four methods, from the lower-order methods (BOLD and edge signals) to higher-order ones (triangle and scaffold time signals). We set a common threshold at the 95th percentile to binarize the data when analyzing an fMRI temporal signal obtained by concatenating resting-state and seven HCP tasks. Colored boxes within the plots denote the ground truth of rest and task segments. When comparing the communities identified with the Louvain algorithm62 against the ground truth partition, we observed that higher-order methods are able to temporally discriminate the different task blocks better than lower-order ones, as reflected by the higher values of the element-centric similarity (ECS) measure. Results are averaged over the 100 subjects, considering the mean between LR and RL phase encoding. For (a), a symmetric kernel density estimate has been used for the distributions. Box plots display the median (central line) and interquartile range (IQR). Whiskers extend 1.5 times the IQR, and individual data points, including outliers, are shown with strip plots.
