Figure 1.
Top panel: Setup of a single trial sequence in the attention-demanding task. Here, the target stimulus is a horizontal rectangle on either side of the center cross. In each trial sequence, the cross is presented, followed by a cue (arrow) giving probabilistic information about whether and where the target stimulus wil appear, and finally by the stimuli, displayed for approximately 50 ms. The target will either appear as cued, appear in the uncued location, or not appear at all; subjects are required to choose which of these possibilities occurred. Bottom panel: Setup of the memory-demanding tasks (same format for word and face memory). In the study session, subjects are presented with a sequence of stimuli. During the test session, another sequence of stimuli is presented; subjects are required to distinguish whether each test stimulus is novel or identical to a stimulus from the study session. Colors of lexical stimuli and colored borders of face stimuli (not pictured) indicate the probability that the test stimulus has been seen before.
Table 1.
Brain regions.
Figure 2.
A schematic illustration of the method used to identify hyperedges. We begin with a set of node-node edges (A) and their time series (B), of which three [green, pink and orange traces, (B)] exhibit strong pairwise temporal correlations. These edges are cross-linked (C) by temporal covariance in edge weight time series, and thereby form a hyperedge (D) of size three on six nodes. The final [blue] edge forms a singleton, an edge which is not significantly correlated with any other edges.
Figure 3.
Schematic construction of the hyperedge co-evolution network.
In (A), we analyze edge time series and group edges exhibiting similar temporal profiles into a hyperedge (as in Fig. 1). Here, node colors are used to indicate individual nodes and the edge color indicates distinct edges. We construct hypergraphs for each subject and find the matrix of probabilities that two nodes are in the same hyperedge over all subjects and hyperedges. In (B), this matrix is used to create a co-evolution network, where the weight for an edge connecting nodes
and
corresponds to the entry
.
Figure 4.
In the cumulative frequency distribution of hyperedge sizes, the small hyperedges appear to roughly follow a power law with an exponent of approximately , while the large group is concentrated near the maximum size. In the null overall model, there are no non-singleton hyperedges. Results for the null within-task model, where the data is shuffled within each task, are in green.
Figure 5.
Hyperedge node degree and co-evolution network.
In (A), we show hyperedge node degree on a natural log scale. The cumulative number of hyperedges at each node over all individuals is plotted on the brain, where higher values at a node correspond to more hyperedges that include the node. (B) depicts a sagittal view of the co-evolution network. The edge strength represents the probability that the edge will be in a hyperedge over all individuals. Edge color corresponds to threshold percentage value, where only the top 1% of co-evolution probabilities are shown. Within this 1%, brown connections correspond to the highest 0.2% of probabilities, red connections correspond to 0.2% to 0.4%, orange connections correspond to 0.4% to 0.6%, gold connections correspond to 0.6% to 0.8%, and yellow connections correspond to 0.8% to 1%.
Figure 6.
Left: Average hyperedge correlation in each task for three hyperedges (where hyperedges with small sizes are chosen for illustrative purposes). Right: Correlation (absolute value) time series for the same three hyperedges. The colored lines represent each edge, while the black line is the average edge time series. Each time point represents the static network over 60 seconds, and the attention task is broken into two sections because two separate iterations of the same task were combined in this analysis. These results display the task-specificity of hyperedges, where significant correlations in the hyperedge are restricted to one task. For example, the first hyperedge is word-specific because there is a much stronger average correlation in the word task than in any other task.
Figure 7.
Task-specific hyperedge size distributions.
Cumulative frequency distribution as a function of hyperedge size for all task-specific groups. The results are compared to the overall distribution of hyperedges (dark blue), previously illustrated in Fig. 4. There are fewer large hyperedges attributed to attention and rest tasks, while the memory tasks have a greater number of large task-specific hyperedges.
Figure 8.
Task-specific co-evolution networks and hyperedge node degrees.
(A): Distribution of task-specific hyperedge node degree on the brain. Here, the log of the total number of hyperedges containing each node is represented on the brain. The color scale represents the log of hyperedge node degree as in 5A, although here the range of values is from 0 to 4.8. (B): Co-evolution networks for each task. Edge strength corresponds to the probability that a hyperedge will contain the edge over all individual hypergraphs. Color represents a threshold in percentage value, with the scale given in Fig. 5B, and the top 1% of co-evolution probabilities are shown. Once again, the top 2% of probabilities are brown, red indicates the top 0.2% to 0.4% of connections, orange indicates the top 0.4% to 0.6% of probabilities, gold indicates the top 0.6% to 0.8% of probabilities, and yellow indicates the top 0.8% to 1% of probabilities.
Figure 9.
Task-specific network statistics.
Values for the position-strength metric (blue) and the length-strength metric (red) for the four tasks are depicted in (A). (B) shows -values for the pairwise statistical permutation test between tasks, where black denotes a significant value after a Bonferroni correction for multiple comparisons. Values are obtained for length-strength and position-strength metric. For example, on the
position plot in (B), attention-word is significant. Referring back to (A), we see that this implies the difference in the
position-strength correlation between the attention and word tasks is statistically significant.