(c) Phase synchronicity and cross-frequency coupling

We assess phase synchronicity within and between three frequency bands: delta (1–4 Hz), theta (4–8 Hz) and gamma (30–50 Hz).

Within-band phase synchronicity is assessed using inter-trial phase clustering (ITPC a.k.a. phase-locking value or phase coherence). This value quantifies the uniformity of phases across trials. This value is higher when different epochs show similar phases, as is the case, for example, if the phase is reset at each word. If phase synchronicity plays a role in syntactic composition, we expect increased ITPC when words are completing larger numbers of phrases. This follows if phase synchronization mediates the processing of additional compositional structure, as predicted by the perceptual inference account of Martin [2]. ITPC is calculated for a given electrode and time-point following Cohen [37, p. 244]:

where eiϕ fr provides the polar representation of phase angle ϕ at frequency f for epoch r.

We assess CFC using two commonly applied measures: power–power correlation (P-P) and phase-amplitude coupling (PAC). P-P is simply the Pearson's correlation between power at two frequency bands. We compute this pairwise measure for each combination of frequency bins in our analysis: delta–theta, delta–gamma and theta–gamma. PAC quantifies the degree to which the phase of a lower-frequency oscillation affects the amplitude of a higher-frequency oscillation. We calculate this following Cohen [37, p. 413]:

where a_r is the power at word onset for epoch r at the higher of two frequency bands, and eiϕr is the polar representation of phase for the lower of two frequency bands. Similar to ITPC, if increased composition is mediated by CFC, for example, between delta and gamma bands (cf. [2]), we expect to find higher P-P and/or PAC values at words that complete a larger number of phrases.

These two measures of CFC have been linked with distinct neurobiological mechanisms [25,38,39]. P-P coupling is more likely to be detectable if there is a direct relationship between activation in one cell assembly with another, for example, if power in a network tracking the speech envelope is amplified by power in a network involved in structural inference as the sentence unfolds. PAC, on the other hand, requires that the phase of one network is affected by the power of the other. This latter might hold, for example, when a lower-frequency signal is used to synchronize (perhaps by resetting) a higher-frequency cell assembly.

Several of these measures, especially ITPC and PAC, are sensitive to the number of epochs entered into the calculation. As this value varies across different phrase bins for our naturalistic stimulus (table 1), we normalize each measure to allow for comparison. To do this, we compute a ‘null’ variant of each measure by shifting the phrase bin assigned to each word by 100 epochs. This removes any potential relationship between phrase count and any of the phase measures. We then recompute the target measure within each phrase bin. These offer an estimate of what we would expect of each measure under the null hypothesis, taking into account the different numbers of epochs per phrase bin and word category. Finally, we compute a z-score by subtracting the mean null value from the target values and dividing the result by the standard deviation of the null variant.

We carry out two additional analyses to complement these assessments of phase. First, we quantify power across phrase bins by simply averaging the single-trial power estimates within each frequency band. Second, test the relationship between phrase completion and the evoked signal using single-trial regression in the following way (e.g. [33,40–42]). Starting with the same artefact-cleaned epochs, described above, the data are low-pass filtered at 40 Hz and then subject to a linear regression, by participant, testing the scalp voltage at each electrode and time-point (0–1 s after word onset) as a function of the number of completed phrases as well as a set of control variables: sound power at word onset, epoch order and word at the target word, the previous word, and following word frequency (HAL corpus, log transformed). A control regression is also carried out per participant in which the rows of the design matrix are randomly permuted. Single-subject regression coefficients are pooled at the group level using the cluster-based permutation test of Maris & Oostenveld [43]. This test returns clusters of electrodes and time-points where the test coefficient for phrase completions is reliably different than the matched term from the control regression. Following Pallier et al. [8], we conduct this analysis on the count of phrase completions and also the log₁₀ transformation of that count.