Cognitive control can be adaptive along several dimensions, including intensity (how intensely do control signals influence bottom–up processing) and selectivity (what information is selected for further processing). Furthermore, control can be exerted along slow or fast time scales. Whereas control on a slow time scale is used to proactively prepare for upcoming challenges, control can also be used on a faster time scale to react to unexpected events that require control. Importantly, a systematic comparison of these dimensions and time scales remains lacking. Moreover, most current models of adaptive control allow predictions only at a behavioral, not neurophysiological, level, thus seriously reducing the range of available empirical restrictions for informing model formulation. The current article addresses this issue by implementing a control loop in an earlier model of neural synchrony. The resulting model is tested on a Stroop task. We observe that only the model that exerts cognitive control on intensity and selectivity dimensions, as well as on two time scales, can account for relevant behavioral and neurophysiological data. Our findings hold important implications for both cognitive control and how computational models can be empirically constrained.

A neural synchrony model of cognitive control is proposed. It construes cognitive control as a higher-level action to synchronize lower-level brain areas. Here, a controller prefrontal area (medial frontal cortex) can synchronize two cortical processing areas. The synchrony is achieved by a random theta frequency-locked neural burst sent to both areas. The choice of areas that receive this burst is determined by lateral frontal cortex. As a result of this synchrony, communication between the two areas becomes more efficient. The model is tested on the classical Stroop cognitive control task, and its operation is explored in several simulations. Both reactive and proactive controls are implemented via theta power modulation. Increasing theta power improves behavioral performance; furthermore, via theta–gamma phase–amplitude coupling, theta also increases gamma frequency power and synchrony in posterior processing areas. Thus, the model solves a central computational problem for cognitive control (how to allow rapid communication between arbitrary brain areas), while making rich contact with behavioral and neurophysiological data.

A task that has been intensively studied at the neural level is f lutter discrimination. I argue that f lutter discrimination entails a combination of a temporal assignment problem and a quantity comparison problem, and propose a neural network model of how these problems are solved. The network combines unsupervised and one-layer supervised training. The unsupervised part clusters input features (stimulus + time window) and the supervised part categorizes the resulting clusters. After training, the model shows a good fit with both neural and behavioral properties. New predictions are outlined and links with other cognitive domains are pointed out.

This article addresses the representation of numerical information conveyed by nonsymbolic and symbolic stimuli. In a first simulation study, we show how number-selective neurons develop when an initially uncommitted neural network is given nonsymbolic stimuli as input (e.g., collections of dots) under unsupervised learning. The resultant network is able to account for the distance and size effects, two ubiquitous effects in numerical cognition. Furthermore, the properties of the network units conform in detail to the characteristics of recently discovered number-selective neurons. In a second study, we simulate symbol learning by presenting symbolic and nonsymbolic input simultaneously. The same number-selective neurons learn to represent the numerical meaning of symbols. In doing so, they show properties reminiscent of the originally available number-selective neurons, but at the same time, the representational efficiency of the neurons is increased when presented with symbolic input. This finding presents a concrete proposal on the linkage between higher order numerical cognition and more primitive numerical abilities and generates specific predictions on the neural substrate of number processing.