Cognitive control allows behavior to be guided according to environmental contexts and internal goals. During cognitive control tasks, fMRI analyses typically reveal increased activation in frontal and parietal networks, and EEG analyses reveal increased amplitude of neural oscillations in the delta/theta band (2–3, 4–7 Hz) in frontal electrodes. Previous studies proposed that theta-band activity reflects the maintenance of rules associating stimuli to appropriate actions (i.e., the rule set), whereas delta synchrony is specifically associated with the control over the context for when to apply a set of rules (i.e., the rule abstraction). We tested these predictions using EEG and fMRI data collected during the performance of a hierarchical cognitive control task that manipulated the level of abstraction of task rules and their set-size. Our results show a clear separation of delta and theta oscillations in the control of rule abstraction and of stimulus–action associations, respectively, in distinct frontoparietal association networks. These findings support a model by which frontoparietal networks operate through dynamic, multiplexed neural processes.

Beta and gamma frequency neuronal oscillations have been implicated in top–down and bottom–up attention. In this study, we used rhythmic TMS to modulate ongoing beta and gamma frequency neuronal oscillations in frontal and parietal cortex while human participants performed a visual search task that manipulates bottom–up and top–down attention (single feature and conjunction search). Both task conditions will engage bottom–up attention processes, although the conjunction search condition will require more top–down attention. Gamma frequency TMS to superior precentral sulcus (sPCS) slowed saccadic RTs during both task conditions and induced a response bias to the contralateral visual field. In contrary, beta frequency TMS to sPCS and intraparietal sulcus decreased search accuracy only during the conjunction search condition that engaged more top–down attention. Furthermore, beta frequency TMS increased trial errors specifically when the target was in the ipsilateral visual field for the conjunction search condition. These results indicate that beta frequency TMS to sPCS and intraparietal sulcus disrupted top–down attention, whereas gamma frequency TMS to sPCS disrupted bottom–up, stimulus-driven attention processes. These findings provide causal evidence suggesting that beta and gamma oscillations have distinct functional roles for cognition.