(a) Task design in both simulation and real MEG data. Assuming there is one sequence, A->B->C->D, indicated by the four objects at the top. During the task, participants are shown the objects and asked to figure out a correct sequence for these objects while undergoing MEG scanning. A snapshot of MEG data is shown below. It is a matrix with dimensions of sensors by time. (b) The transitions of interest are shown, with the red and blue entries indicating transitions in the forward and backward direction, respectively. (c) The first step of TDLM is to construct decoding models of states from task data, and (d) then transform the data (e.g. resting-state) from sensor space to the state space. TDLM works on the decoded state space throughout. (e) The second step of TDLM is to quantify the temporal structure of the decoded states using multiple linear regressions. The first-level general linear modelling (GLM) results in a state*state regression coefficient matrix (empirical transition matrix), , at each time lag. (f) In the second-level GLM, this coefficient matrix is projected onto the hypothesized transition matrix (black entries) to give a single measure of sequenceness. Repeating this process for the number of time lags of interest generates sequenceness over time lags (right panel). (g) The statistical significance of sequenceness is tested using a non-parametric state permutation test by randomly shuffling the transition matrix of interest (in grey). To control for multiple comparisons, the permutation threshold is defined as the 95th percentile of all shuffles on the maximum value over all tested time lags. (h) The second-level regressors , , , and , as well as two examples of the permuted transitions of interest, (for constructing permutation test), are shown.