This bottom-up activation (Stimulus Drive) is depicted along the two stimulus properties, with each pixel representing a single neuron and brightness representing the strength of activation. Paying attention to a certain spatial location (corresponding to the red circle in the left panel) creates an Attention Field that is selective for the RF center dimension, but not for the orientation preference dimension. Multiplying the Attention Field point-by-point with the Stimulus Drive yields an Excitatory Drive, which is then convolved with a Suppressive Field (a Gaussian representing the lateral inhibition) to produce the Suppressive Drive, or surround-inhibition. Finally, dividing the Excitatory Drive by the Suppressive Drive yields a normalized Population Response, with the attended stimulus having a larger output than the unattended stimulus. Figure adapted from Reynolds and Heeger (2009).
When the attention field is large compared to the stimulus size, the modulation is predominantly a contrast-gain enhancement. If, however, the attention field is small compared to the stimulus size, the effect seems to be predominantly response gain. These specific predictions have recently been confirmed with a paradigm that used the spatial certainty of visual stimuli to modulate the size of the attention field (Herrmann et al., 2010).
The concept of an attention field is reminiscent of previously proposed theoretical constructs like a saliency map (Itti and Koch, 2001) or a priority map (Bisley and Goldberg, 2010) and their neurophysiological representations in parietal and prefrontal cortex (Gottlieb et al., 1998; Bisley and Goldberg, 2010; Bisley, 2011). A saliency map represents the relative strength of bottom-up stimulus features that are used to guide attention (Koch and Ullman, 1985; Itti and Koch, 2001). A priority map, on the other hand, combines the bottom-up saliency map with top-down endogenous factors for the selection of objects for eye movements or attention (Serences and Yantis, 2006; Bisley and Goldberg, 2010). The abstract concept of an attention field in the normalization model can perhaps best be seen as the collection of these top-down influences in the priority map. As such it more or less constitutes a top-down counterpart to the bottom-up saliency map. Since their initial reception, the concepts of saliency and priority maps have become common practice in guided visual search models (Itti and Koch, 2001; Bisley and Goldberg, 2010; Bisley, 2011). Enhanced salience of certain objects prioritizes these objects in serial search tasks so that the object that is most likely to be the target will be attended first. In a similar way, an attention field can enhance the firing rate of neurons corresponding to certain object features (orientation) and cause an early bias in neuronal activation in favor of stimuli that correspond to the template represented in the attention field.
Strong correlations have been found between attention and enhanced gamma-band synchronization (Fell et al., 2003; Bichot et al., 2005; Womelsdorf and Fries, 2007). Gamma-band synchronizations are also known to be modulated by oscillations in other frequency ranges, such as the theta-cycle oscillations that are implicated in the shifting of attention (Fries, 2009), and delta-wave oscillations (Lakatos et al., 2008).
--
Consequently, the extent of an excitatory neuron’s depolarizing drive is converted into the moment of spiking relative to the phase of the cycle period. This means that as the excitatory drive of a neuron increases, so does its ability to overcome inhibition earlier in the cycle (Fries et al., 2007).
Moreover, the gamma cycle might provide a way in which pyramidal cells engage in winner-take-all processes (Olufsen et al., 2003; Börgers et al., 2005). Whenever a pyramidal cell fires, it activates local interneurons that send inhibitory signals back to the whole population of excitatory neurons. Because of this process, when the first few pyramidal cells have started firing action potentials, inhibition of all excitatory cells will start to increase. This makes it harder for pyramidal cells that have not yet fired to produce any spikes at all.
Consequently, the phase position of spikes relative to their cycle period is an important indication of the amount of information they carry. In fact, it has been shown that the first 1–5% of the spikes that encode a stimulus contain most information and that the other 95% provide relatively little additional information
In this framework, attention could then control the extent with which rate-codes are transformed into time codes. Since the gamma cycle can convert a neuron’s depolarizing drive into the moment of spiking relative to the phase of the cycle period, an increase of the amplitude of oscillations (as is observed during directed attention) could increase the extent to which rate-coded information is transformed to temporally coded information.
Another possible function of neural oscillations is formulated in the communication-through-coherence (CTC) hypothesis (Fries, 2005). This hypothesis states that neuronal communication between populations is only efficient if these populations are oscillating in synchrony and prevented if their oscillatory cycles are asynchronous. This hypothesis is based on two observations. First, as we have seen in the preceding paragraph neuronal populations have the intrinsic property to produce oscillatory activity (Kopell et al., 2000; Tiesinga et al., 2001). Second, as a neuronal population goes through an oscillatory cycle, its excitability changes drastically. While small excitatory inputs might be enough to activate a neuron when its corresponding interneurons are silent, the same neuron may require an extremely large amount of excitatory input when it is receiving large hyperpolarizing currents from the interneuron population. Accordingly, every oscillation period has a limited temporal window for effective communication that opens and closes with the phases of the oscillatory cycle. This means that only phase-locked neuronal populations are able to influence each other’s firing patterns effectively; a hypothesis that has been verified with neural network modeling (Kremkow et al., 2010).
Furthermore, the modulation strength of a TMS pulse has been shown to depend on the beta oscillation phase of the stimulated neural tissue, which suggests that beta band synchronization (and possibly also gamma-band synchronization) entails a rhythmic gain modulation of neuronal input (Van Elswijk et al., 2010). Such a process could very well be the underlying mechanism of winner-takes-all mechanisms that have recently been found in posterior

This illustration shows three neuronal populations (red, green, and blue). There are two populations (red and green) that each connect to the third (blue), but only one (red) is synchronized to it via neuronal oscillations (middle right), while the other (green) is out-of-phase. Spikes from the synchronized population (red) arrive at their target population (blue) within the peak of excitability, while signals from the out-of-phase population (green) have no effect. Such phase-locking process could explain why higher cortical areas show larger attention effects. When two stimuli are simultaneously presented, the corresponding retinotopic regions in lower level visual cortex (e.g., V1) will overlap less than in higher level visual cortex (e.g., V4). Neurons in subsequent cortical areas that can in principle respond to either stimulus can only be phase-locked to input from one of the stimuli, leading to competitive interactions in the region of overla