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Importantly, our results were robust against changes of model order in the range between 3 and 20. The selected model order of 12 corresponds to a time lag of 48 ms, similar to previous studies (Brovelli et al, 2004 Bollimunta et al, 2008), as a compromise between sufficient spectral resolution and the need to avoid overparameterization.
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To this end, we down-sampled the data to 250 Hz and used a model order of 12 to compute time-dependent sets of multivariate autoregressive coefficients in overlapping windows of 500 ms length (moving forward in 4 ms steps).
To account for potential nonstationarity and to comprehend variations of GC in time, we applied GC to short data segments, which have been suggested to approximate stationarity (Ding et al, 2000 Barrett et al, 2021). We defined the directionality of interactions between DMPFC and DLPFC by calculation of time- and frequency-resolved Granger causality (GC) using fieldtrip and the BSMART toolbox (Cui et al, 2008). In general, brain oscillations may support neural communication by synchronously opening and closing the time windows for neural firing (Varela et al, 2001 Fries, 2005, Fell and Axmacher, 2021 Siegel et al, 2021). Similar results were obtained in 2 patients with laminar microelectrodes recorded from within the anterior cingulate cortex (Wang et al, 2005). Furthermore, previous EEG studies associated increases in DMPFC θ (4–8 Hz) power and DMPFC-DLPFC θ phase synchronization with conflict detection, response monitoring, and cognitive control (Trujillo and Allen, 2007 Cohen et al, 2008 Hanslmayr et al, 2008 Cavanagh et al, 2009, 2021 Womelsdorf et al, 2021). Several fMRI studies revealed that brain regions within dorsomedial prefrontal cortex (DMPFC) and dorsolateral prefrontal cortex (DLPFC) play a crucial role in conflict processing (MacDonald et al, 2000 Botvinick et al, 2001, 2004 Kerns et al, 2004 Ridderinkhof et al, 2004 van Veen and Carter, 2005).
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