Correction for Mitra et al., Lag threads organize the brain’s intrinsic activity

NEUROSCIENCE Correction for “Lag threads organize the brain’s intrinsic activity,” by Anish Mitra, Abraham Z. Snyder, Tyler Blazey, and Marcus E. Raichle, which appeared in issue 17, April 28, 2015, of Proc Natl Acad Sci USA (112:E2235–E2244; first published March 30, 2015; 10.1073/pnas.1503960112).

The authors note that Fig. 1 and its corresponding legend appeared incorrectly. The corrected figure and its corrected legend appear below.

Fig. 1.

Illustration of lag threads. A shows three patterns of propagation (lag threads) through six nodes. The objective is to demonstrate the mapping between lag structure and PCA. The illustration is not intended as a model of propagation in neural tissue. Each lag thread is also shown as a multidimensional time series with spectral content duplicated from real BOLD rs-fMRI data. B shows the superposition of the three lag threads. C shows the time-delay matrix (TD) recovered by analysis of the superposed time series in B, using the technique illustrated in SI Appendix, Fig. S1 (27). The bottom row of C shows the latency projection of TD computed as the average over each column. D illustrates the latency projection as a node diagram. This projection represents nodes that are, on average, early or late. Critically, the projection fails to capture the full lag structure. E illustrates eigendecomposition of the covariance structure of TD_z, derived from TD by removing the mean of each column (see SI Appendix, Eqs. S4–S8). There are three significant eigenvalues (33), indicating the presence of three lag threads. In an ideal case, eigenvalues 4–6 would be zero; in this example, imperfect superposition leads to a small fourth nonzero eigenvalue. The eigenvectors corresponding to the first three eigenvalues are the thread topographies (shown above the eigenvalues). The lag thread sequences defined in A were accurately recovered purely by eigen-analysis of TD_z. It should be noted that the lag threads in this illustration were a priori constructed to be mutually orthogonal (see SI Appendix, Eq. S7). Hence, they were neatly recovered intact by eigendecomposition of TD_z. Also, although the nodes in this illustration are represented as foci, the algebra applies equally well to voxels, ROIs, or extended, possibly disjoint, topographies.