## Abstract

Frontal beta oscillations are associated with top-down control mechanisms but also change over time during a task. It is unclear whether change over time represents another control function or a neural instantiation of vigilance decrements over time, the time-on-task effect. We investigated how frontal beta oscillations are modulated by cognitive control and time. We used frontal chronic electrocorticography in monkeys performing a trial-and-error task, comprising search and repetition phases. Specific beta oscillations in the delay period of each trial were modulated by task phase and adaptation to feedback. Beta oscillations in this same period showed a significant within-session change. These separate modulations of beta oscillations did not interact. Crucially, and in contrast to previous investigations, we examined modulations of beta around spontaneous pauses in work. After pauses, the beta power modulation was reset and the cognitive control effect was maintained. Cognitive performance was also maintained whereas behavioral signs of fatigue continued to increase. We propose that these beta oscillations reflect multiple factors contributing to the regulation of cognitive control. Due to the effect of pauses, the time-sensitive factor cannot be a neural correlate of time-on-task but may reflect attentional effort.

## Introduction

Flexibility and efficiency of behavior involves monitoring performance and changing levels of cognitive control in order to properly adapt to the current context (Miller and Cohen 2001). Cognitive control refers to a set of computational mechanisms in prefrontal cortex (PFC), proposed from and supported by computational modeling findings, implementing “active maintenance of task-relevant context and top-down biasing of local competitive interactions that occur during processing” (Braver et al. 2002). Proponents of cognitive control hold that these computational-level mechanisms provide variable mediation of more familiar cognitive-level functions of working memory, inhibition, and attention, such that the latter are applied appropriately to a given task context. Tasks that require flexible and active maintenance of goals and the means to achieve them will demand cognitive control, and neurophysiological processes that support this cognitive control can be inferred from task phases requiring varying levels of control (Miller and Cohen 2001; Procyk and Goldman-Rakic 2006).

Much work on cognitive control has been in the domain of stimulus-response tasks, where cognitive control is used, for example, to overcome response conflict, due to ambiguous stimulus features, that degrades performance (Botvinick et al. 2001; Kerns et al. 2004). But, the mechanism can be applied to a broader class of task, in which strategy rather than stimulus features guide performance, and therefore in which feedback will continually drive the level of cognitive control required (Quilodran et al. 2008). The current study seeks to understand neural mechanisms of cognitive control in such a context.

Neurophysiological markers of cognitive control have been recorded in frontal cortex (Siegel et al. 2012; Phillips et al. 2014). Amongst these, oscillations in local field potentials (LFPs) in the beta band (20–30 Hz) have been linked to top-down control of behavior (Buschman and Miller 2007; Siegel et al. 2012; Bastos et al. 2014), and to the formation of neural ensembles representing rules (Buschman et al. 2012). A potential role of these oscillations is in the interaction of frontal cortex with other related regions, as shown by enhanced frontoparietal beta-band coherence during free decisions compared with instructed decisions (Pesaran et al. 2008).

Control processes in PFC are necessary to provide flexibility, application of strategy, and maintenance of performance despite fatigue. A proposed mechanism for adjusting control in the face of fatigue is the process of attentional effort (Sarter et al. 2006). Attentional effort is a cognitive incentive that integrates explicit and implicit motivational forces (Sarter et al. 2006). Thus, a subject will increase attentional effort in order to maintain good performance, especially when highly motivated. This is a control function, and it might well be considered to result from the computational mechanisms of cognitive control. The way in which such ideas of effort and motivation integrate into cognitive control models is the subject of current experimental and theoretical work (Shenhav et al. 2013; Kool and Botvinick 2014). The current study seeks to understand this relationship in the context of the modulation of beta oscillations by cognitive control.

Attentional effort might contribute to the compensation for the well-established effect of vigilance decrement over time, known as the time-on-task effect. This effect is variously described as leading to impairments in simple performance measures, such as increases in execution errors (Boksem et al. 2006) or response time, but also as causing reduced behavioral flexibility (Lorist et al. 2009) or reduction in cognitive control. Again, the oscillatory dynamic of large-scale networks at lower frequencies is implicated. Frontal and parietal oscillatory signals across a range of low frequencies (theta and alpha) increase in power with time-on-task (Boksem et al. 2005; Borghini et al. 2014). Notably, increasing power in beta frequencies has also been reported (Boksem et al. 2005).

The time-on-task effect is widespread and pervasive in cognitive tasks (Kahneman 1973). Attentional effort can be seen when subjects are motivated to work for a goal (Sarter et al. 2006). Time-on-task effects will lead to continual degradation of performance measures over time whereas attentional effort should maintain goal-directed performance measures and cognitive control when it is applied (Sarter et al. 2006; Boksem and Tops 2008). Hence, these 2 effects may be thought to act in opposition, and in this case, they will both change over time. Changes in neurophysiological markers over time, such as beta oscillations, might therefore seem to correlate with both effects, and separating them out to understand the role of the marker requires careful analysis.

In this study, we examine the relationship between beta oscillations and varying levels of cognitive control, attentional effort, and behavioral changes occurring during time-on-task decrements. We seek to resolve whether each of these factors can be related to changes in beta oscillations. We use chronic ECoG surface recordings in macaque monkeys carrying out a test of cognitive control in conditions that allow us to simultaneously measure time-on-task decrements. The behavioral task requires regular changes in levels of cognitive control (Procyk and Goldman-Rakic 2006), whilst within-session changes in recordings allow us to observe time-on-task decrement or attentional effort effects. Using this approach and mixed-effects statistical modeling, we show the first clear observations of the neurophysiological impact of prolonged within-session work in monkeys with a trial-by-trial resolution.

By contrasting execution with cognitive errors and, uniquely to our knowledge, by looking at the effect of spontaneous pauses in work, we demonstrate that high beta oscillations in the preparatory period at the start of trials are separately modulated by multiple factors acting within-session and in relation to behavioral control. Crucially, pauses in work temporarily reset within-session effects, while cognitive performance is maintained and cognitive control continually represented in the beta oscillations. We propose that such pauses may provide a break in the attentional effort required or applied, yet time-on-task continues to increase despite the pause. These data hence suggest how modulations of the same beta oscillations can reflect more than one single process.

## Materials and Methods

### Subjects and Materials

Two rhesus monkeys (Macaca mulatta), 1 female and 1 male, weighing 7 and 8.5 kg (monkeys R and S, respectively) were used in this study. Ethical permission was provided by the local ethical committee “Comité d’Éthique Lyonnais pour les Neurosciences Expérimentales,” CELYNE, C2EA #42, under reference C2EA42-11-11-0402-004. Animal care was in accordance with European Community Council Directive (2010) (Ministère de l'Agriculture et de la Forêt), and all procedures were designed with reference to the recommendations of the Weatherall report, “The use of non-human primates in research.” Laboratory authorization was provided by the “Préfet de la Région Rhône-Alpes” and the “Directeur départemental de la protection des populations” under Permit Number: #A690290402.

Monkeys were trained to perform a problem-solving task (PST). Animals were seated in a primate chair (Crist Instrument Co.) in front of a tangent touch-screen monitor (Microtouch System). An open-window in front of the chair allowed them to use their preferred hand to interact with the screen (monkey R, left-handed; monkey S, right-handed). The position and accuracy of each touch was recorded on a computer, which also controlled the presentation of visual stimuli via the monitor (CORTEX software, NIMH Laboratory of Neuropsychology). During the behavioral task, eye movements were monitored using an Iscan infrared system (Iscan, Inc.). Electrophysiological data were recorded using an Alpha-Omega multichannel system (AlphaOmega engineering).

#### Principles of Cognitive Control Tasks

The task employed here, in common with much of the cognitive control literature, contains 2 phases, which vary in their cognitive control demands. The aim of the experiment is to make comparable recordings from comparable trials in which the only variation is the level of cognitive control currently being employed. One phase (“Search”) demands higher cognitive control, in that a greater level of mediation of goals, memory, attention, and rules is required. The other phase (“Repetition”) makes simpler demands. The contrast of these 2 phases provides the means to detect cognitive control processes in the neurophysiological data.

#### Problem-Solving Task with 4 Targets (PST4)

Monkeys sought by trial and error the correct target from a choice of four, the search phase. Having found the rewarded target, they were allowed to repeat the discovered rewarded choice 3 times the repetition phase, before being instructed to search again.

Each trial, whether in the search or repetition phase, followed an identical format. Monkeys initiated the trial by touching and holding a lever, represented by a central gray triangle. A fixation point appeared and animals had to fixate it with their gaze. After a delay period of 1400 ms, 4 gray target circles were displayed at different locations, on the upper side of a circular axis (Fig. 1A). At the onset of targets (ON signal), monkeys had to make a saccade toward a selected target and fixate it during a random delay between 400 and 800 ms (steps of 200 ms). At this point, all targets turned from gray to white, providing the GO signal following which monkeys were permitted to touch the target already chosen by fixation. After a random delay interval of 600–1200 ms (steps of 200 ms), a visual feedback stimulus was shown to the monkey for 800 ms. Feedback consisted of horizontal (correct) or vertical (incorrect) rectangles, in the same location and of the same color and luminosity as the circular targets. If the choice was incorrect (negative visual feedback and no reward), the monkey could select another target in the following trial and so on until the solution was discovered (search phase). After discovering the correct target, the animal was allowed to repeat the correct choice 3 times (repetition phase) (Fig. 1A and B). Correct responses were rewarded after the feedback with a 1- or 1.8-mL pulse of fruit juice. Successful discovery of a rewarded stimulus and repetition of that response 3 times is hereafter termed a problem. After the completion of a given problem, a signal-to-change was displayed on screen, consisting of the negative feedback stimulus flashed 3 times. A new correct target was pseudo-randomly selected and the monkey reentered the search phase. The trial after the signal-to-change is referred to as a switch trial.

Figure 1.

Problem-solving task and electrode location. (A) The events of an individual trial of the PST4. The task consists in seeking by trial and error which target was rewarded from a choice of 4 and then in repeating this correct choice 3 times. Frames represent the successive events for each trial during a problem. (B) A sample of successive problems during the PST4, extracted from a testing session. In the first problem, after making an incorrect selection (INC), the monkey discovered the correct target (COR), ending the search phase. After repeating this choice 3 times (repetition phase), a signal (SC) was presented to the animal, which indicated that a new target was going to be rewarded. After the monkey completed a fixed number of problems, a large salient green circle was presented on the screen and a final large bonus reward was delivered. (C) Positions of transcranial electrodes for each monkey. Electrodes (gray/white dots) are reported on stereotaxic coordinates in millimeters and displayed over a standard reconstructed brain surface. Black dots represent the location of reference electrodes in both monkeys. Dark gray dots represent the grid used in the present study. Larger dashed gray dots correspond to the position of the 2 electrodes used for mixed-model selection.

Figure 1.

Problem-solving task and electrode location. (A) The events of an individual trial of the PST4. The task consists in seeking by trial and error which target was rewarded from a choice of 4 and then in repeating this correct choice 3 times. Frames represent the successive events for each trial during a problem. (B) A sample of successive problems during the PST4, extracted from a testing session. In the first problem, after making an incorrect selection (INC), the monkey discovered the correct target (COR), ending the search phase. After repeating this choice 3 times (repetition phase), a signal (SC) was presented to the animal, which indicated that a new target was going to be rewarded. After the monkey completed a fixed number of problems, a large salient green circle was presented on the screen and a final large bonus reward was delivered. (C) Positions of transcranial electrodes for each monkey. Electrodes (gray/white dots) are reported on stereotaxic coordinates in millimeters and displayed over a standard reconstructed brain surface. Black dots represent the location of reference electrodes in both monkeys. Dark gray dots represent the grid used in the present study. Larger dashed gray dots correspond to the position of the 2 electrodes used for mixed-model selection.

#### Problem-Solving Task with 2 Targets (PST2)

PST2 task was identical to the PST4 task, with the sole exception that there were only 2 stimuli presented throughout, randomly selected from the 4 possible stimuli used in PST4. The feedback and signal to change stimuli likewise had only 2 stimuli, those corresponding to the 2 targets used.

The simple effect was that the search phase was easier for the monkeys, as the rewarded target could be found among fewer possibilities. The repetition phase was unchanged, requiring 3 correct responses. All other delays and procedures were identical. PST2 and PST4 problems were presented in the same sessions, in a pseudorandom manner.

#### Final Reward

In order to motivate and maintain performance at a stable level throughout each daily session, animals were asked to complete a fixed number of problems each day (n = 120 and 60 problems for monkey R and S, respectively). Upon successfully completing this number of problems (average session duration ± sd, 132.5 ± 18.1 and 89.46 ± 29.2 min for monkey R and S, respectively), a salient green signal was displayed on the screen and monkeys received a large reward bonus (20–30 mL of fruit juice, calculated on the effectiveness in motivating the monkey). In addition, monkeys who had completed their session to this bonus received a reward of fruit immediately upon returning to the home-cage. Data in this study are derived only from sessions when the monkeys successfully completed the requested number of trials and received this juice bonus (86.4% and 59.8% of sessions for monkeys R and S, respectively).

### Surgical Procedures

Surgical procedures were performed under aseptic conditions. The monkey was sedated on the morning of surgery with both ketamine (10 mg/kg) and xylazine (0.5 mg/kg) following pre-anesthetic treatment with glycopyrrolate (0.006 mg/kg). Once sedated, the monkey was given antibiotic (amoxicillin, 8.75 mg/kg) for prophylaxis of infection, and a nonsteroidal anti-inflammatory (ketoprofen, 2 mg/kg) agent for analgesia. The head was shaved and an intravenous cannula put in place for intraoperative delivery of fluids (sterile saline drip, 5 mL/h/kg). The monkey was intubated, placed on isoflurane anesthesia (0.5–2.75%, to effect, in an O2 and NO2 mix), and then mechanically ventilated. Heating blankets allowed maintenance of normal body temperature during surgery. Heart rate, oxygen saturation of hemoglobin, expired CO2, body temperature, and respiration rate were monitored continuously throughout surgery.

Each animal was implanted with a head-holder (Crist Instrument Co.) and intracranial electrodes. Both the placement of the electrodes and their depth were determined from separately acquired structural MRI images of each monkey. Using stereotaxic guidance, holes were drilled through the skull and then stainless steel surgical screws (Synthes) were fixed into the holes, with the aim at each site of advancing the screw through the thickness of the bone to rest on the dura mater. Each electrode was connected to a standard connector constructed in-house. The ensemble was then anchored with dental acrylic to the head-holder. For monkey R, a grid of 14 electrodes spaced by 5 mm was implanted throughout the frontal cortex, and 8 electrodes were fixed over sensorimotor cortex near the central sulcus in a later surgery (Fig. 1C, left panel). Monkey S was implanted in a single procedure, and a larger grid of 31 electrodes, spaced by 7 mm, covered the frontal and sensorimotor cortex (Fig. 1C, right panel). For both monkeys, the last electrode serving as reference was screwed into the bone of the thick brow of the monkey on the midline anterior to the frontal grid. The present investigation concerns the grid of electrodes placed over the PFC for both monkeys (electrodes in gray in Fig. 1C).

### Behavioral Analysis

When discussing performance on the tasks, we distinguish between “execution performance” and “cognitive performance.” Cognitive performance measures the optimality of the choices made on the task itself. This therefore assesses the success of the monkey in completing problems and advancing toward the important final reward and fruit reward. Execution performance measures the successful completion of the trial itself, regardless of outcome, and so is measured by testing accurate touching of the screen, correct fixation of the stimuli, and reaction times (RT).

Cognitive performance was measured by 2 independent measures of nonoptimal choice. It is important to note that nonoptimal choice has a different definition in the 2 phases. When the monkey is searching, it is optimal to make some errors up to once per stimulus (this is a trial-and-error task), but nonoptimal to repeat those incorrect responses. Hence, in the search phase, the nonoptimal choice measure was the proportion of trials on which the monkey repeated an incorrect choice already made during that search (i.e., this is a measure of perseverative errors). In contrast, during the repetition phase, the monkey has found the correct response, and optimal performance means no errors. Hence, the nonoptimal measure is simply the proportion of incorrect choices during the repetition. A further measure of behavior tested whether monkeys re-initialized their search at the start of a new problem by using the signal-to-change. A monkey that successfully uses the signal-to-change should immediately change chosen target, because each new problem has a new pseudo-randomly assigned correct target. The measure is simply the percentage of cases where the choice is different before and after the signal-to-change.

Execution errors, which are preemptive touch responses or breaks of fixation, were also computed throughout the session. Motivational parameters, such as the number of trials not initiated by the animal over the total number of trials presented (i.e., “no start” trials), and the number and length of pauses in work during each session, were recorded.

RT (i.e., time between the appearance of white targets and the release of the lever) and movement times (MT, i.e., time of arm movements from lever to target) were computed on each trial.

We qualitatively investigated changes in behavioral parameters as a function of session progress by dividing each recording session into 3 groups of an equal number of trials. These 3 bins were made without taking into account any missed trials in which the animals did not initiate within a given start time, nor did it consider trials following pauses in work (see below for details on pause definition and analysis). PST2 and PST4 trials were pooled together for execution but not cognitive measures.

### Electrophysiological Data Processing

All electrodes were referenced to the most frontal reference electrode (Fig. 1C). The signal from each electrode was amplified and filtered (1–250 Hz) and digitized at 781.25 Hz. Data analysis was performed off-line with FieldTrip toolbox (Oostenveld et al. 2011) and homemade Matlab scripts (Matlab, The MathWork, Inc.). Movement artifacts were removed by decomposing ECoG recordings with an independent component analysis, using the logistic infomax algorithm (Bell and Sejnowski 1995). Data were analyzed in the time-frequency (TF) domain by convolution with complex Gaussian Morlet's wavelets with a ratio f/δf of 12. Single-trial TF analysis was aligned to the target onset (ON signal) for analysis of the delay period, and on the touch of the selected target for analysis of the post-touch period. The continuous ECoG data were epoched from −2500 to 2000 ms (by steps of 10 ms), and the power of each frequency ranging from 5 to 40 in 0.5-Hz steps was computed. Inspection of power spectrum density representations revealed different oscillatory activities, used to define frequencies of interest. Oscillations in the beta range (beta 1: 15–18 Hz and beta 2: 20–24 Hz for monkey R; beta 1: 10–18 Hz and beta 2: 24–32 Hz for monkey S) were analyzed and averaged over the delay period (−1200 to −200 ms before the ON signal) and the post-touch period (0–600 ms after the target touch). This procedure led to a mean beta power for each trial during the 2 periods of interest. We focused on the delay period in this task in particular, because this is the period where the monkey is integrating feedback information from the previous trial with preparation for the upcoming trial, and therefore likely to be employing cognitive control (Procyk and Goldman-Rakic 2006). It should be noted that we consider the delay period for all trials in these analyses. This includes the first trial in each problem, even though the monkey is yet to receive feedback within that problem. This is because the signal-to-change acts as a feedback to initiate the search period, and so this initial delay is part of the search. Previous work from our laboratory on the same task has confirmed that monkeys show behavioral and neural evidence of entering into search immediately after the signal-to-change (Quilodran et al. 2008; Khamassi et al. 2015). Indeed, the response to the signal-to-change along with other forms of feedback is explicitly considered in the “response to feedback” analysis.

Data were acquired in 36 and 33 sessions (days) in monkey S and R, respectively. We rejected from our analysis 2 sessions (one for each monkey) for which data observation revealed abnormal distributions of single-trial beta powers. Moreover, the 2 most posterior electrodes in monkey S were rejected due to high signal variance. Trials with execution errors (38.60 ± 6.02% and 22.50 ± 3.48% for monkeys R and S, respectively) were included in our analysis if they occurred after the target onset, except for statistics including RT as covariate (see mixed-effects models below).

### Measuring Cognitive Control Processes

As laid out in Introduction, cognitive control is a computational process rather than a psychological function, and so there is no direct behavioral measure of cognitive control. Rather, we induce variable use of cognitive control and then show how neurophysiological processes, in our case beta oscillations, are modulated with cognitive control demands. The current task is well established in this regard (Procyk and Goldman-Rakic 2006; Quilodran et al. 2008; Rothé et al. 2011; Khamassi et al. 2015; Procyk et al. 2016). The search period, during which the monkey is maintaining the goal, information on prior trials, and its progress, requires high levels of cognitive control. The repetition period, during which a single response must be maintained, requires minimal cognitive control. Frontal neurophysiological markers that vary significantly between search and repetition are therefore assumed to represent changes in cognitive control. Following our previous work, the initial analyses below employ this search–repetition contrast as the index of cognitive control. Specifically, we contrast the beta in search and repetition trials in the “phase” model.

Changes in cognitive control can also be observed following certain types of feedback that engender a change in behavior or goal (Botvinick et al. 2001; Kerns et al. 2004). For example, an incorrect choice or signal-to-change should induce greater cognitive control than a correct choice. As such we also analyze the same data in a “response-to-feedback” model. Here, we contrast the beta power on the trial “after” the monkey has received each type of feedback to show how reactive cognitive control is represented in the oscillations.

In some tasks, cognitive control is expected to lead directly to a subsequent behavioral measure. For example, in a Stroop task, correct application of cognitive control should lead to a slowing in reaction time and subsequent correct response. Here stimulus, response, and control are tightly coupled. Because the PST task is a trial-and-error task in which response is not directly determined by stimulus, this coupling should be less strong or even absent, whereas cognitive control is still employed in response to informative feedback. We nevertheless test for this form of “predictive” cognitive control using the predictive model.

Therefore, the following modeling analyses use several statistical models to capture the variance created in beta oscillations during the task, and test for different behavioral explanations.

### Mixed-Effects Models

We observed modulations of beta power with task phase, within-session, and around pauses in work. To evaluate those modulations properly, trial-by-trial beta power measures were fitted with Linear Mixed-Effects models (Pinheiro and Bates 2000; Zuur et al. 2009). Such models allow us to analyze hierarchically organized data and to explicitly model variance inherent to repeated measures. In our data set, several sessions of recordings were used to analyze the within-session effect in each monkey. Characteristics such as the slope of power change over time could vary from one day to another. The random-effects terms in these models are specifically useful to capture this sort of variation. Meanwhile, the fixed effect can separately capture the presence of the slope in of itself. We produced models with 2 sets of fixed effects, the Phase model and the Response-to-feedback model. The data in the 2 models are the same; they simply treat the behavioral factors differently, allowing us to capture the variance in beta in different ways.

Mixed models are of the form Yi = β.Xi + b.Zi + ei where X and Z correspond to fixed- and random-effects design matrices, respectively, and e the random variations for each day i.

All statistical procedures were performed using R (R Development Core Team 2008, R foundation for Statistical computing) and the relevant packages (nlme, MASS).

#### Data Transformations

The “Phase” model included the following factors (and levels): Session, Phase (search/repetition), Task (PST2/PST4), Trial-type (Break, Incorrect, Correct), and the covariates “time” (time of target onset from the start of session, this is therefore within-session time) and RT. The “response-to-feedback” model is identical with the exception of phase and trial-type factors. These 2 factors are replaced by a previous trial feedback factor (PFB) referred to as PFB (Break, Incorrect, Correct, Switch), indicating the feedback that the monkey has just received. Here, the switch case refers to trials after a signal-to-change. Note that the first trial of the session and the first trial after the pause (where there was one) had to be removed from this analysis, as these trials do not follow any meaningful feedback.

The dependent variable Beta (trial-by-trial beta power measured in the time window of interest) was tested in a linear model to evaluate the need for a power transformation, that is, in particular to improve the “normality” of the data distribution. We computed and examined the profile log-likelihoods for the parameter of the Box–Cox power transformation (function boxcox in package MASS), which revealed the need to log transform the data before fitting a linear model adequately for both monkeys. Hence, log(Beta) was used as dependent variable in the following analyses.

In order to bring model coefficients within relatively similar ranges of values, “time” values were transformed into hours. Time values were then centered on the average time over all sessions, by simply subtracting each time value from the average time. RT were also centered to the mean RT value. This was used in order to reduce correlations between the intercept and slope estimates.

#### Model Selection

Models were first selected using data acquired on 1 test electrode in each monkey and then applied to all electrodes (see details later). The test electrodes were selected based on observation of a clear peak of Beta power on the power spectrum density on the contralateral side, using similar sites in both monkeys (dashed gray disks in Fig. 1C).

In a first series of analyses, we evaluated the effect of the above-mentioned covariates and factors on Beta power measured in completed trials (trials in which monkeys touched a target). In this case, we focused on all data acquired at the beginning of each session, before any pause made by the monkey (see below for a definition of pauses). Because our main objective was to test the effect of time, “time” was used in the initial full Phase model in interaction with each independent variable:

(1)
$log(Beta)=(β0+b0,S)+βϕPhase+βTrTrial-type+βTkTask+βlog(RT)log(RT)+(βt+b1,S)t+(βt:ϕ+b1,S)(t:Phase)+(βt:Tk+b1,S)(t:Task)+(βt:Tr+b1,S)(t:Trial-type)+(βt:log(RT)+b1,S)(t:log(RT))+ϵ,$
where the βi are fixed-effects and the bj random-effect coefficients, each of the latter assumed to be distributed as $N(0;sj2)$. The subscripts are coded as S—session, φ—Phase, Tr—Trial-type, RT—reaction time, Tk—task, and t—time. The terms Phase, Trial-type, and Task are factors and RT and time are covariates. A key feature of the model is that the random-effects capture variation across the multiple sessions. Specifically, they show the influence of random effects on the intercept and the slope of the log(Beta) change as a function of time. A second key feature is that the interaction of the factors with time will correspond to differences in slope across the factor levels.

The procedure to select the most appropriate model consisted in evaluating each component, starting from the most complete model.

The first step evaluated random effects by comparing models with and without specific random effect terms. Models were selected using AIC and Log Likelihood ratio tests (P < 0.05). We evaluated the random effects in a model in which all orders of interactions of the fixed effects were retained. We found that random slopes and intercepts associated with the Sessions needed to be retained (L.ratio test, P < 0.0001 in both monkeys). As such, the random effects were retained in all subsequent models.

The second step evaluated the contribution of fixed effects. We used the drop 1 function, repeatedly testing the effect of dropping the highest-order interaction fixed-effect term on the fit (Zuur et al 2008). Again, models were selected using AIC, and changes in AIC between models were tested using a chi-square test (P < 0.05). The principle of model selection was identical for Phase and Response-to-feedback models.

The selected model was fitted on all electrodes by incorporating the factor electrode as an overall interaction term. Finally, to test the validity of applying on all electrodes the model selected on only one, we proceeded in 2 further steps. We first tested whether adding the higher-order interactions to the selected model would reveal significant interactions of any terms with any of the electrodes. A forward selection procedure (using the add1 function in R) was used that adds terms in a fashion that respects the marginality of lower-order terms and evaluates the significance of added terms using a likelihood ratio test. No significant interaction with electrodes means that no model more complicated than the selected model is needed to fit the data arising from all the electrodes. In a second step, we again took the selected model with the factor electrode incorporated into it and tested whether dropping terms using the drop 1 function (Venables and Ripley 2002) would reveal significant interactions. This is a backward elimination procedure that respects the marginality of lower-order terms, and in this case, its application might reveal differential effects of fixed parameters across electrodes. In these data, such interactions are to be expected, revealing a functional organization captured by the electrode map. If the first step revealed significant interactions, we examined the statistical table resulting from the more complicated model with factor electrode.

#### Effect of Pauses

In a second series of analyses, within-session effects were also studied around short pauses that monkeys made spontaneously in some sessions. In order to observe the evolution of oscillatory activity and behavioral parameters around these events, trial-by-trial measures were aligned on pauses. For statistical analyses, we included all trials completed up to the onset of the 4 targets. This therefore included trials with breaks in fixation or in lever holding before the monkey could touch a target. Hence, for these analyses, we excluded the covariate RT, as not all trials had a reaction time. The way in which the 2 monkeys worked and paused differed slightly. In principle, we chose sessions with a pause of several minutes after a sustained period of work at the start of the session (after 40 min of work in monkey R and 25 min in monkey S). Sessions could contain none, one, or more pauses (monkey R: none 18/33, one 13/33, more 2/33; monkey S: none 10/36, one 16/36, more 10/36). We focused our analyses on the data acquired before and after the first pause in a session. This therefore concerned 15 sessions in monkey R and 26 sessions in monkey S. Pauses included in the analyses were of 8.1 min on average for monkey R (minimum: 2.9 min, sd = 5.1) and of 13.5 min on average for monkey S (minimum: 6.2 min, sd = 5.7 min). We first considered all trials including execution errors.

The initial model for this analysis around pauses was chosen on the basis of the model selection carried out on the first model mentioned in Equation (1), the outcome of which is described in “Results.” This allowed us to remove a number of interaction terms that had no significant influence. The Phase model selection was therefore initiated with:

(2)
$log(Beta)=(β0+b0,S+b0,S:Bk)+βTkTask+βTrTrial-type+βϕPhase+βBkBlock+βBk:ϕBlock:Phase+(βt+bt,S+bt,S:Bk0)time+(βt,S:Bk+bt,S+bt,S:Bk1)time:Block+ϵ,$
where the βi are fixed-effect and the bj random-effect coefficients, each of the latter assumed to be distributed as $N(0;sj2)$. The subscripts are coded as above and with Bk for Block. Block is a factor with 2 levels (0, 1) representing the block of trials before (0) and after (1) the pause in work. Again it is important to note a couple of key features of the model. As in the model described in Equation (1), the random-effects capture variation across the multiple sessions, but also the variation in the relationship between the pre- and post- pause responses (time:Block interaction). An interaction between Block and Phase corresponds to a difference in the intercept for different combinations of Block and Phase. An interaction of Block with time corresponds to a difference in slope between Block levels.

To test for the contribution of Reaction time to signal variance, we ran the same analyses on the subgroup of completed trials, i.e., including a touch on target.

#### Model Validation

Model validation was performed by checking that normalized residuals plotted against fitted values and factors did not show inhomogeneity or violations of independence.

The final best fitting model (see Results) was used to extract intercepts and slopes for each session and to provide global statistical evaluations. P-values obtained from Mixed models applied to each electrode were adjusted using Bonferroni correction.

## Results

### Behavior

It is important to recall the distinction between execution performance (successful completion of the trial regardless of outcome) and cognitive performance (optimal completion of the task itself).

Cognitive performance in the PST was stable across the different recording sessions (see Supplementary Fig. 1 for example). The monkeys had significant previous experience on this task prior to data collection for this study and should not be considered as being in a phase of learning about the task. Data presented in Figure 2 summarize behavior of the monkeys in the task. The low levels of nonoptimal choices (Fig. 2C) indicate that the monkeys were approaching optimality in the task, successfully completing search and repetition phases. Monkeys transitioned well from repetition back to search by taking into account the signal-to-change and changing their choice on the following trial (percentage of optimal transitions ± sd: monkey R: 94.19 ± 4.37%; monkey S: 75.72 ± 13.83%). Monkeys did show some execution errors as well as cognitive errors, and these were the starting point of our study of within-session changes.

Figure 2.

Behavioral effects within session and of cognitive control. (A) left panel, average evolution of the number of trials not initiated (“no start”) during sessions for both monkeys. Data are normalized in time to the start and end of sessions. The boxplot below the curves shows the median and deviation of the normalized time of the first pause of work in the session, this being the pause considered for analysis, again for each monkey. Right panel, median and dispersion of pause duration and time of pause relative to session onset for monkeys R and S. (B) Evolution of execution error rates and RT (left and right plots, respectively) as the session progresses. Data are grouped into 3 bins of trials (see Materials and Methods for details). (C) Evolution of cognitive performance within-session, represented by the proportion of nonoptimal choices in the search (left panel) and repetition (right panel) phases. Black and gray lines show the average across days (+/−SEM) for monkeys R and S, respectively. P-values represent one-way ANOVA main effects (factor bin of trials). As the session progresses, cognitive performance remains stable, whereas execution performance worsens. (D) RT and MT for both monkeys in both phases of the PST4 task only. (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001.

Figure 2.

Behavioral effects within session and of cognitive control. (A) left panel, average evolution of the number of trials not initiated (“no start”) during sessions for both monkeys. Data are normalized in time to the start and end of sessions. The boxplot below the curves shows the median and deviation of the normalized time of the first pause of work in the session, this being the pause considered for analysis, again for each monkey. Right panel, median and dispersion of pause duration and time of pause relative to session onset for monkeys R and S. (B) Evolution of execution error rates and RT (left and right plots, respectively) as the session progresses. Data are grouped into 3 bins of trials (see Materials and Methods for details). (C) Evolution of cognitive performance within-session, represented by the proportion of nonoptimal choices in the search (left panel) and repetition (right panel) phases. Black and gray lines show the average across days (+/−SEM) for monkeys R and S, respectively. P-values represent one-way ANOVA main effects (factor bin of trials). As the session progresses, cognitive performance remains stable, whereas execution performance worsens. (D) RT and MT for both monkeys in both phases of the PST4 task only. (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001.

### Behavioral Modulations within Session

Figure 2A–C present the evolution of execution and cognitive performance within-session. First, monkeys tended to miss more trial initiations (i.e., not touching the lever when available) as time passed in the session, with a peak toward the end of the session, the end corresponding to the final bonus reward delivery (Fig. 2A left). In several sessions, the animals even stopped working for several minutes, making a voluntary pause in work (see Materials and Methods). During pauses, monkeys stayed at rest without initiating trials, neither fixating nor touching the screen. The median duration and time of occurrence of the first pause in a session varied in the 2 monkeys but, for both animals, it occurred most often during the second half of the session and largely contributed to the peak in no start trials (Fig. 2A right). Reluctance to initiate trials can be associated with motivational changes and fatigue, which contribute to time-on-task effects.

To precisely evaluate the effect of time, we then restricted behavioral analyses to the first block of trials (up to the first pause, or to the end of session when no pause occurred). For both monkeys, progress in the session was also characterized by a significant increase of execution error rates (one-way ANOVA, factor bin of trials, monkey R: F2,93 = 27.21, P = 4.9 e−10; monkey S: F2,102 = 5.43, P = 5.8 e−3) and RT (monkey R: F2,93 = 4.01, P = 0.02; monkey S: F2,102 = 4.59, P = 0.01) (Fig. 2B). These within-session effects are landmark effects of time-on-task.

Despite the drop in execution performance during the session, both monkeys succeeded in keeping stable cognitive performance as indicated by a constant proportion of nonoptimal choices during the search phase (monkey R: F2,93 = 1.26, P = 0.29 ; monkey S: F2,102 = 1.15, P = 0.32) and the repetition phase (monkey R: F2,93 = 1.92, P = 0.15; monkey S: F2,102 = 1.34, P = 0.26) in PST4 during the course of the session (Fig. 2C). Stable cognitive performance was also observed for PST2 trials (“search”: monkey R: F2,93 = 1.33, P = 0.27 and monkey S: F2,102 = 0.28, P = 0.75; “repetition”: monkey R: F2,93 = 3.24, P = 0.04 and monkey S: F2,102 = 1.71, P = 0.18).

RT were slightly different over all sessions when comparing task versions in monkey S (two-way ANOVA, factor PST2/PST4, monkey R: F1,125 = 0.85, P = 0.36; monkey S: F1,137 = 4.5, P = 0.03) and significantly higher in search than repetition phases for monkey S too (Fig. 2D left; two-way ANOVA, factor search/repetition, monkey R: F1,125 = 0.13, P = 0.72; monkey S: F1,137 = 23.01, P = 4.1 e−6). MT were similar between PST2 and PST4 for both monkeys (two-way ANOVA, factor PST2/PST4, monkey R: F1,125 = 0.58, P = 0.45; monkey S: F1,137 = 1.81, P = 0.18). MT were significantly higher in search than repetition for monkey S (Fig. 2D right; two-way ANOVA, factor search/repetition, monkey R: F1,125 = 0.65, P = 0.42 ; monkey S: F1,137 = 47.52, P = 1.8 e−10).

In summary, we observed that execution performance declined in both monkeys within-session but cognitive performance showed no within-session effect.

### General Characteristics of Beta Oscillations

Recordings were made every day thanks to the chronically implanted array, and as we have already demonstrated, such recordings are stable across months (Vezoli and Procyk 2009). Supplementary Figure 1 underlines the stability of the recordings in this study over the individual sessions, showing that there is no practice-related modulation over time. TF analysis revealed beta oscillations during the execution of the PST (Fig. 3). Sustained beta oscillations were observed during the delay period (−1200 to −200 ms before the ON signal, Fig. 3A) when the monkey is fixating and holding touch on the screen. The power spectra revealed 2 identifiable peaks within the beta range for both monkeys (Fig. 3B). Although the average Beta power varied across sessions, the 2 peaks were clearly observed in most sessions (Supplementary Fig. 2). These 2 peaks are referred to here as Beta 1 and Beta 2 oscillations. Beta 1 and Beta 2 peaks were at 16 and 22 Hz for monkey R and at 14 and 28 Hz for monkey S (Fig. 3B). Both were located in a distributed frontal network, with a bias over the ipsilateral frontal cortex (Fig. 3C). This inter-individual difference in the peaks of power is worth noting. It is now clear that such individual differences in power spectra are to be expected (Buzsáki et al. 2013), and despite the different frequencies of these bands, we go on to show that equivalent peaks maintain equivalent properties (Fig. 3D and E). This property is further considered in the discussion.

Figure 3.

Description of beta oscillations. (A) Average TF representation of 2 contralateral electrodes (white dots in Panel C) aligned on target onset and target touch for both monkeys. The color scale shows the average power of oscillations. (B) Mean power spectra during the delay period (−1.2 to −0.2 s from ON) and post-touch period (0–0.6 s from Touch). We identified 2 beta frequency bands (beta 1 and beta 2) of interest from these plots (monkey R: 15–18 and 20–24 Hz; monkey S: 10–17 and 24–32 Hz). (C) Spatial representations of average beta power during the delay period. Note that monkey R is left-handed and monkey S right-handed. (D) Effect of task Phase (Search and Repeat) on the beta power. A power spectrum has been extracted from signal recorded in the delay for all trials in search (sea, magenta) and repetition (rep, blue). Note that the effect is most marked in the shaded region of beta 2. (E) Within-session effect on the overall power spectrum. A power spectrum has been extracted for signal recorded in the delay for all trials of the first block (before the first pause) separated in 3 terciles (bins 1, 2, and 3, see Materials and Methods). Again the effect is particularly clear in beta 2. All figures were derived from 1 representative session in both monkeys.

Figure 3.

Description of beta oscillations. (A) Average TF representation of 2 contralateral electrodes (white dots in Panel C) aligned on target onset and target touch for both monkeys. The color scale shows the average power of oscillations. (B) Mean power spectra during the delay period (−1.2 to −0.2 s from ON) and post-touch period (0–0.6 s from Touch). We identified 2 beta frequency bands (beta 1 and beta 2) of interest from these plots (monkey R: 15–18 and 20–24 Hz; monkey S: 10–17 and 24–32 Hz). (C) Spatial representations of average beta power during the delay period. Note that monkey R is left-handed and monkey S right-handed. (D) Effect of task Phase (Search and Repeat) on the beta power. A power spectrum has been extracted from signal recorded in the delay for all trials in search (sea, magenta) and repetition (rep, blue). Note that the effect is most marked in the shaded region of beta 2. (E) Within-session effect on the overall power spectrum. A power spectrum has been extracted for signal recorded in the delay for all trials of the first block (before the first pause) separated in 3 terciles (bins 1, 2, and 3, see Materials and Methods). Again the effect is particularly clear in beta 2. All figures were derived from 1 representative session in both monkeys.

Beta oscillations were also observed and modulated during the other periods of the trial. They were suppressed after target onset, when monkeys were allowed to make a saccade toward a selected target (Fig. 3A). This suppression [event-related beta desynchronization, ERD (Pfurtscheller and Lopes da Silva 1999)] remained until after the touch of the selected target. Beta oscillations reappeared after hand movement.

Inspection of data first revealed that delay-related beta oscillations were modulated between the search and repetition phases of the task suggesting an effect of cognitive control on beta power (Fig. 3D). This follows previous observations of prefrontal neuronal and evoked potential modulations using this task (Procyk et al. 2000; Procyk and Goldman-Rakic 2006; Quilodran et al. 2008; Vezoli and Procyk 2009).

As the within-session analysis revealed a time-on-task effect in execution performance (but notably not in cognitive performance), we wondered whether delay-related beta activity would show within-session variations correlated with time during the first block of trials. Indeed, as the session progressed, delay-related beta oscillations increased in power for both monkeys in particular for the Beta 2 oscillations (Fig. 3E). Therefore, a within-session effect on beta is present during the period of the trial in which beta also varies with cognitive control (see examples in Supplementary Fig. 3). This therefore potentially links the 2 phenomena, and we investigated this possibility using statistical modeling.

### Within-Session and Cognitive Control Modulations of Beta Power

#### Phase Model

To characterize the modulation of beta oscillations between sessions, within sessions, and by different key elements of the task, we performed linear mixed-effects modeling (see Materials and methods). We first conducted an exploratory analysis on one selected electrode for each monkey (Fig. 1). As fixed-effects, the initial full model included Time within-session and RT as covariates and Phase, Task, and Trial-type as two- and three-level factors, respectively. Sessions were treated as a grouping factor for the random effects (see Materials and Methods). Analyses were performed separately on measures for Beta 2 and Beta 1. We selected a linear mixed-effects model to describe these data by starting from a full model and successively testing the effect of dropping the highest-order interaction fixed effect term on the fits. The final model was therefore that model from which we were unable to remove any additional interactions because the remaining interactions had a significant effect on the fit.

Importantly, statistical modeling of Beta 2 showed that Time × Phase interaction was not significant (likelihood ratio test, monkey R: P = 0.37; monkey S: P = 0.93). There was no effect of RT or of the Trial-type with time (nonsignificant interactions in both monkeys). A Task × time interaction was significant in monkey S (P < 0.001). There was no main effect of Task in both monkeys (monkey R: P = 0.34, monkey S: P = 0.18). RT had a significant contribution in 1 monkey (monkey S: P = 0.11, monkey R: P < 0.001). Since removing RT had no significant effect on the other conclusions and had to be removed for the second analysis on pause, we excluded this covariate for both monkeys. These tests therefore permitted us to reject these factors and interactions as having a significant contribution to the measure of Beta 2, and therefore to construct a final model.

Although no interaction was found between them, Time and Phase (search vs. Repetition) had each made a very significant contribution in both monkeys to the modulation of Beta 2 oscillations, and so these terms were retained in the final model. We therefore tested the influence of these terms within the selected model. The effect of Phase revealed a significant reduction of Beta 2 power in Repetition compared with Search (Wald statistics, Repetition vs. Search, monkey R: t-value =− 10.04, monkey S: t-value =− 4.5, P < 0.0001 in both monkeys). The slope coefficient for time was significant (Wald statistics, monkey R: t-value = 11.9, P < 0.0001; monkey S: t-value = 14.8, P < 0.0001) with Beta 2 power increasing within-session.

The same analyses for power in the Beta 1 range provided identical results for monkey R (Wald statistics, monkey R, Phase: t-value =− 14.2, P < 0.0001, Time: t-value = 16.2, P < 0.0001) but no effect of Time or Phase for monkey S (Wald statistics, monkey S, Phase: t-value =− 1.1 P = 0.27, Time: t-value = 1.1, P = 0.27). The Beta 1 range was very close to the Beta 2 range in monkey R (Fig. 3B), and the dissociation might have been impossible. Because of this confound and of the absence of within-session and phase effects in monkey S, we only focused on the Beta 2 range in the rest of the study (referred to as Beta from here on).

Thus, the model selection approach on chosen electrodes showed that Beta power increases within-session over time and is modulated by task Phase and Trial-type but that there is no interaction between the influences of these factors. Hence, the modulation of Beta oscillations with cognitive control and the modulation of Beta within-session are both significant, but these influences are statistically independent.

To evaluate the effects over all electrodes, we tested a model including the factors found significant in each monkey and fitted to Beta power acquired on each electrode. P-values were corrected for multiple testing (Bonferroni correction). The validity of applying the selected model to all electrodes was tested with a double step procedure, in particular regarding the potential interaction between time and Phase (see Materials and Methods). The validation revealed that no more complicated model was needed for monkey R and revealed in monkey S a weak interaction effect (P = 0.02) for time and phase produced by 3 electrodes. Overall, the procedure revealed that the selected model with no interaction between time, Phase, and Trial-type explained the great part of the variance in data over all electrodes. The second step of validation showed moreover some dissociation between electrodes as revealed in the analyses presented later.

Slope of fit, intercept, and P-values were then extracted from the model fit and used to create maps presented in Figures 4 and 5. Figure 4 shows the results for the modulation by Phase. The mean power of Beta oscillations was almost always higher during search trials than during repetition trials, as shown on the contrasts between average measures for each session (Fig. 4A). Across electrodes, and for both monkeys, the major effect was a reduction of Beta power in repetition compared with search, as revealed by a systematically lower intercept for the fit for repetition data compared with the fit for search data (the difference REP-SEA was negative in the majority of cases). Mapping the differences in intercept revealed a global unidirectional change in Beta between search and repetition with a slight ipsilateral hemispheric bias (Fig. 4B).

Figure 4.

Modulation of delay beta oscillations by task Phase and Previous Feedback. (A) Distribution of the difference in mean log(Beta) calculated for each session and each monkey before the first pause. A negative difference indicates higher power in search than in repetition, so power decreases from search to repetition. (B) Spatial representations of the main effect of Phase for each monkey. The fixed effect of Phase is reported for each electrode and mapped onto the grid. The color scale represents the intercept difference between search and repetition (red is more negative, i.e., Beta in search is higher). Note that all electrodes show a significant effect between search and repetition. (C) Effect of previous feedback on intercept of log(Beta) as extracted from the Response-to-feedback model. Stars indicate level of significance compared with Correct feedback—in all cases, the Beta is increased compared with trials that follow correct feedback and so demand limited cognitive control. (D) Spatial representation of the difference between trials following Correct feedback and a Signal-to-change. The color grid represents the intercept difference Switch-Correct (positive values, i.e., Beta after Switch is higher). The effect is significant on all electrodes. Note that monkey R is left-handed and monkey S right-handed. (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001.

Figure 4.

Modulation of delay beta oscillations by task Phase and Previous Feedback. (A) Distribution of the difference in mean log(Beta) calculated for each session and each monkey before the first pause. A negative difference indicates higher power in search than in repetition, so power decreases from search to repetition. (B) Spatial representations of the main effect of Phase for each monkey. The fixed effect of Phase is reported for each electrode and mapped onto the grid. The color scale represents the intercept difference between search and repetition (red is more negative, i.e., Beta in search is higher). Note that all electrodes show a significant effect between search and repetition. (C) Effect of previous feedback on intercept of log(Beta) as extracted from the Response-to-feedback model. Stars indicate level of significance compared with Correct feedback—in all cases, the Beta is increased compared with trials that follow correct feedback and so demand limited cognitive control. (D) Spatial representation of the difference between trials following Correct feedback and a Signal-to-change. The color grid represents the intercept difference Switch-Correct (positive values, i.e., Beta after Switch is higher). The effect is significant on all electrodes. Note that monkey R is left-handed and monkey S right-handed. (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001.

Figure 5.

Changes in beta oscillations within-session. (A) Surface maps reconstructed with the slope of the main effect of time obtained from the linear mixed model, for monkeys R and S (left and right, respectively) and for both trial epochs (Delay and Post-Touch). Larger gray dots indicate electrodes with a significant slope. (B) Relationships between the level of Beta power and the within-session effect in the Delay (greens) and Post-Touch (white and gray) epochs for each monkey. The level of Beta power is estimated by the intercept, and the within-session effect is given by the slope of the regression. Note that the slope is always greater in the Delay period than the Post-Touch period. Also, there is no clear or stable relationship between beta power and slope, meaning that the size of the within-session effect does not depend on overall Beta power. (C) Histogram of the P-values from within-session slope effect for all electrodes measured for the beta power in delay (light and dark green) and post-touch (white and gray) epochs. Log of P-values are presented, with those above the statistical threshold (P > 0.05) represented on the left of the −1.3 limit (vertical dashed red line). Data are presented separately for the 2 monkeys (S and R).

Figure 5.

Changes in beta oscillations within-session. (A) Surface maps reconstructed with the slope of the main effect of time obtained from the linear mixed model, for monkeys R and S (left and right, respectively) and for both trial epochs (Delay and Post-Touch). Larger gray dots indicate electrodes with a significant slope. (B) Relationships between the level of Beta power and the within-session effect in the Delay (greens) and Post-Touch (white and gray) epochs for each monkey. The level of Beta power is estimated by the intercept, and the within-session effect is given by the slope of the regression. Note that the slope is always greater in the Delay period than the Post-Touch period. Also, there is no clear or stable relationship between beta power and slope, meaning that the size of the within-session effect does not depend on overall Beta power. (C) Histogram of the P-values from within-session slope effect for all electrodes measured for the beta power in delay (light and dark green) and post-touch (white and gray) epochs. Log of P-values are presented, with those above the statistical threshold (P > 0.05) represented on the left of the −1.3 limit (vertical dashed red line). Data are presented separately for the 2 monkeys (S and R).

Changes in Beta power during the delay were systematic across sessions and for both monkeys. The topographic maps in Figure 5A show the within-session effect (average slope of fit) for each monkey for the Beta measured in the delay and after the touch. These maps and the data extracted for each electrode (Fig. 5BC) revealed that the within-session effect during delay was strong and always positive, that is, Beta power increased with time. Beta changes across time (Fig. 5A) and between search and repetition phases (Fig. 4B) appeared somewhat dissociated in their topographic localization. Time-on-task variations appeared slightly more anterior and bilateral compared with search–repetition differences, and also more contralateral in monkey R.

Importantly, we tested whether the within-session variation of beta activity was specific to certain beta-related processes or reflected a general effect found in all recordings across the time of the session. We found that the effect was indeed specific to the delay period, as within-session modulations of beta power recorded after the touch were not consistent and much weaker for both monkeys. Figure 5 shows the results of mixed-effect models for each electrode for the Beta in Delay and after the touch (PostTouch). The panels show that the effect of time (slope) was much stronger in delay, and not related to the initial Beta power (intercept) (Fig. 5B) and that the effect of time was always significant in delay and rarely in post-touch (Fig 5C). This rules out, in particular, a global effect of time on the entire spectrum (shift of the power law).

#### Predictive Model

To explicitly address the question of whether increased beta power in the delay leads to a subsequently more optimal outcome on that trial, we replaced the “Trial-type” factor with a behavioral outcome factor: “Optimal.” This factor codes whether performance on the upcoming trial made optimal use of the feedback received on the previous trial. The factor therefore had 2 levels, optimal and nonoptimal, and the definition of optimality followed exactly that used in the behavioral analysis described in the Materials and Methods section. We applied the same model selection strategy to this model. In a model that retained terms for time and phase as before, subsequent optimality was also a significant predictor of delay beta power in monkey R (P = 0.02), but not in monkey S (P = 0.6). As such we are unable to claim that higher beta power is predictive of optimal responding, despite the fact that beta power strongly tracks task phase. To better understand the role of beta in this task, therefore, we tested whether there is a responsive rather than predictive link between beta power and cognitive control.

#### Response-to-Feedback Model

In order to capture the way in which beta oscillations responded to the changing cognitive control demands following different types of feedback, we also applied the Response-to-feedback model, using the same ECoG data but different behavior factors. We replaced the Phase and Trial-type factors with a single PFB, which described the feedback the monkey had received on the previous trial. Hence, the model tested how reactive cognitive control was expressed in beta oscillations following each feedback. This allows us in particular to test whether the incorrect feedback and signal-to-change do indeed induce increased cognitive control, as previously shown (Khamassi et al. 2015). The model was selected and tested in an identical fashion to the Phase model, on the Beta data in the delay period, and starting with the same selected electrodes.

A significant main effect of PFB was retained in both monkeys. Correct feedback should induce minimal cognitive control in the following trial, as the correct response need merely be repeated. In both monkeys, each of Incorrect, Switch, and Break feedback induced significantly increased Beta compared with Correct feedback (Fig. 4C, Wald statistics, in every case t-value > 6, P < 0.0001; excepting Correct vs. Break in monkey S: t-value = 2.1, P = 0.04). Hence, in all cases where feedback instructed a change of strategy or response, requiring the use of cognitive control, the Beta was increased significantly compared with the case of repeating the same correct response.

The main effect of time remained present in this model (Wald statistics, monkey R: t-value = 10.0, P < 0.0001; monkey S: t-value = 14.95, P < 0.0001). A time × PFB interaction also survived but only in monkey R (P = 0.017), and a main effect of Task survived in monkey S (P = 0.0006). RT made no contribution to the model following selection, and all other interactions were removed in the selection process.

We then applied the selected models to all electrodes. Intercepts and P-values were then extracted from the model fit and used to create Figure 4D. This figure shows the difference in log(Beta) between trials following a correct response and trials following a signal-to-change. There is clear evidence for reactive cognitive control being represented by Beta oscillations, with a significant increase in Beta on switch trials. The topography of this effect is comparable with the general cognitive control effect derived from the Phase model (Fig. 4B).

In summary, Beta power is high when cognitive control is required, both during cognitive control demanding phases of the task and immediately after feedback that required cognitive control. Beta power also increases within session, but the cognitive control and within-session effects do not interact. In addition, the behavior provided within-session effects in execution measures, but not in cognitive measures. This suggests these 2 effects, cognitive control and within-session, were independently expressed in the beta oscillations.

### Delay-Related Beta Oscillations around Pauses

As noted earlier, the motivational state of monkeys decreased while execution errors and RTs increased as the session progressed. This is a time-on-task effect. In some sessions, the monkeys made voluntary pauses for a few minutes before re-initiation of the task, quite possibly due to the drop in motivation. During these pauses, monkeys stayed at rest without initiating trials, neither fixating nor touching the screen. The interpretation of these pauses in the context of the time-on-task literature is unclear. We studied the effect of pauses on all measures in order to understand their impact on control and time-on-task.

Sessions with pauses in work were isolated (see Materials and Methods for details and Fig. 2A Right panels) and used to further investigate within-session effects at the level of trial series. We refer to within-session changes over time but restricted to a single block of work (before or after a pause) as “within-block” effects. Only data recorded before and after the first pause until the next pause or end of session were considered (see Materials and Methods). For descriptive purposes, single-trial measures of power in delay were aligned to the start of the first pause in each selected session before averaging (Fig. 6), thus isolating 2 blocks of work in each session—one before and one after the pause. The pattern of changes in beta oscillations around pauses is clearly illustrated in Figure 6A. As shown earlier, delay-related beta power increased significantly within-block prior to the pause. The power reached a maximum just before the onset of the pause for both monkeys. When the monkey started to work again, the beta power was lower, as if it had been reset to a level comparable with session start. On subsequent trials, during the second block, beta power increased again until the end of the block (Fig. 6A, but see also sessions with 2 pauses in Supplementary Fig. 4).

Figure 6.

Electrophysiological and behavioral changes after pauses. (A) Average power change aligned to pauses in work during the delay period. Power of beta oscillations drops significantly then increases again after pauses (monkey R, n = 15; monkey S, n = 26 sessions; see Materials and Methods for pause detection). (BD) Evolution of execution error rate (B), reaction time (C), and cognitive performance (D) throughout sessions and aligned to voluntary pauses for monkeys R and S (top and bottom, respectively). Gray bars represent the average measure (+sem) for each parameter that was used for statistical testing (see Materials and Methods for details). Asterisks indicate the significance level (Kruskall–Wallis test, factor “pre/post-pause,” using Bonferroni post-hoc correction): (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001. Execution and cognitive measures do not follow the same pattern as the beta oscillatory power.

Figure 6.

Electrophysiological and behavioral changes after pauses. (A) Average power change aligned to pauses in work during the delay period. Power of beta oscillations drops significantly then increases again after pauses (monkey R, n = 15; monkey S, n = 26 sessions; see Materials and Methods for pause detection). (BD) Evolution of execution error rate (B), reaction time (C), and cognitive performance (D) throughout sessions and aligned to voluntary pauses for monkeys R and S (top and bottom, respectively). Gray bars represent the average measure (+sem) for each parameter that was used for statistical testing (see Materials and Methods for details). Asterisks indicate the significance level (Kruskall–Wallis test, factor “pre/post-pause,” using Bonferroni post-hoc correction): (ns) P > 0.05, *P < 0.05, **P < 0.01, ***P < 0.001. Execution and cognitive measures do not follow the same pattern as the beta oscillatory power.

We further investigated how execution and cognitive measures exhibit a similar change around pauses. Neither execution error rate nor RT were modulated in the same way as beta power around pauses, specifically we did not observe a drop in errors or RT after the pause (Fig. 6BC). In fact, a linear mixed-effect model applied to RT showed that RT at the start of the second block were similar to those at the end of the first block and then decreased during the second block (see Fig. 6C and Supplementary Fig. 5). Also, the proportion of nonoptimal choices did not follow beta power changes (Fig. 6D). We evaluated the changes between the end of the first block and the beginning of the second one using a Kruskall–Wallis test (with Bonferroni post-hoc correction) and report significant comparisons on Figure 6. Statistical comparisons were made by taking the average of 30 trials for each session included (or the average of 2 problems for the cognitive measure), before and after pauses. Only a significant increase in RT was observed in monkey S (H = 4.68, 1 d.f., P = 0.03), but not in monkey R (H = 2.41, 1 d.f., P = 0.12). Other comparisons were not significant (“execution error rate,” monkey R: H = 0.17, 1 d.f., P = 0.68; monkey S: H = 0.96, 1 d.f., P = 0.33; “Pre- vs. Post-cognitive performance during search,” monkey R: H = 0.5, 1 d.f., P = 0.48; monkey S: H = 2.23, 1 d.f., P = 0.13; “Pre- vs. Post-cognitive performance during repetition,” monkey R: H = 0.29, 1 d.f., P = 0.59; monkey S: statistical testing could not be assessed due to zero inflated data, 106 of 116 problems with a value of zero, i.e., no error during repetition). None of the changes were comparable with the changes in beta, suggesting there was no direct relationship between execution or cognitive performance and beta power changes for either monkey.

#### Phase Model

In order to quantitatively assess this effect, and its variance across sessions, we varied the Phase model by including Block (before and after pause) as fixed and random factor. The Block effect was relevant in both cases to fit the data as shown by model selection (see Materials and Methods).

Only the Phase and the Time × Block fixed effects survived model selection, showing that the difference in Beta power between search and repetition remained stable even after the pause, but that the within-block effect was modified after the pause. We investigated these phenomena further by extracting fitted data and model coefficients for each session and each monkey. Figure 7 shows the key results. First, the drop in power after the pause was very reliable across sessions and monkeys (Fig. 7A left). In addition, the slope of fits reflecting the strength of the within-session effect was almost always stronger in the second block (after the pause) than in the first block (Fig. 7A right). In other words, after a drop during pauses, the increase of the Beta power with time was greater than at the beginning of the session.

Figure 7.

Effect of pauses in work on beta power drop. (A) The plot on the left presents the fitted values of log beta power at the start of the second block (after the pause), as a function of the values at the end of the first block (i.e., showing the drop in Beta power). The plot on the right compares the slope of the within-session effects in the second and first blocks of trials. (B and C). Dynamic of beta modulation around the pause for each session, as described by the model fit. The figures show the relationships between the drop in beta (indicated by a blue line) and the parameters of the pause, specifically the duration and the timing within the session of the pause. Black lines represent the linear fits for beta power both before and after the pause. This shows the increase of beta up to and after the pause. Log(Beta) power values are aligned at zero to equalize values at the start of each pause. Figures B and C show the same data with different alignments in time. (B) The longer the pause, the less the drop in Beta power—data are aligned on the time of pause to stress this effect, represented by the distribution of the red starting points. (C) The later the pause, the weaker the drop in Beta power—data are aligned on the start of the session to stress the timing of the pause within the session.

Figure 7.

Effect of pauses in work on beta power drop. (A) The plot on the left presents the fitted values of log beta power at the start of the second block (after the pause), as a function of the values at the end of the first block (i.e., showing the drop in Beta power). The plot on the right compares the slope of the within-session effects in the second and first blocks of trials. (B and C). Dynamic of beta modulation around the pause for each session, as described by the model fit. The figures show the relationships between the drop in beta (indicated by a blue line) and the parameters of the pause, specifically the duration and the timing within the session of the pause. Black lines represent the linear fits for beta power both before and after the pause. This shows the increase of beta up to and after the pause. Log(Beta) power values are aligned at zero to equalize values at the start of each pause. Figures B and C show the same data with different alignments in time. (B) The longer the pause, the less the drop in Beta power—data are aligned on the time of pause to stress this effect, represented by the distribution of the red starting points. (C) The later the pause, the weaker the drop in Beta power—data are aligned on the start of the session to stress the timing of the pause within the session.

This last element of results suggests that cumulated fatigue or effort, or the continuous change in motivation during work, induces slow evolving neural changes that impact on the production of beta oscillations and possibly on the effect of pauses. Thus, the time spent in work in the first block and the duration of pauses might contribute to the variance of the drop of power observed at pauses. We hence investigated the relationships between pause length or time of pause in sessions and the difference in power between the end of the first block and the beginning of the second. Figure 7B and C presents the data fitted by the above-mentioned mixed model. Fitted powers at the end the first block for each session are aligned to observe the variation in the size of power drop (symbolized with blue lines). Graphs show the effect of pause duration (left) and time of pause in sessions (right) on the distribution of drop in power. The data for both monkeys clearly show 2 important phenomena: 1) the longer the pause, the weaker the drop in power (Fig. 7B) and 2) the later the pause, the weaker the drop in power (Fig. 7C). These negative effects were tested in a multiple linear regression showing strong significance of both duration and time of pause on the power drop (P < 0.0001). There was no effect of power at the beginning and end of the first block. The slope of within-session change in power made a small contribution to the drop size only for one monkey (monkey R: P < 0.002, monkey S: P = 0.55). There was no correlation between timing of pauses and duration of pauses (monkey R: P = 0.59, monkey S: P = 0.97).

#### Response-to-Feedback Model

We also added the fixed and random factor Block to the Response-to-feedback model and selected it with the same procedure. Again Time × Block effects survived model selection, as did PFB. In monkey R, a time × PFB interaction survived selection, but not in monkey S. As in the original model, significantly lower Beta was measured in trials after Correct feedback than after other types of feedback (Wald statistics, in every case t-value > 4, P < 0.0001), and so the cognitive control response represented by changes in Beta was maintained after the pause.

In summary, pauses in work caused significant interruption of the within-session effect in delay-related beta oscillations, in a sense resetting it. By contrast, other measures that were modulated within-session were not modulated by the pauses in work.

## Discussion

In monkeys performing a test of cognitive control, we recorded beta oscillations that reflected the different cognitive control demands of the task: When cognitive control was required (during search, when shifting between problems, and after negative feedback), beta power was increased, notably during the delay period at the start of each trial. In this same delay period, beta oscillations also showed a significant increase in power within-session over time. Behaviorally, monkeys also showed within-session increases in response times and execution errors, and we regard these changes in execution measures to reflect a time-on-task effect. Despite this, cognitive performance on the task suffered no significant within-session decrement and therefore was resistant to the time-on-task effect. When the monkey made a voluntary pause in work during the session, we observed a significant reset of the beta power, and so an apparent re-initialization of the within-session effect. This effect was absent in the behavioral data. The magnitude of the beta reset was an inverse function of the timing of the pause in the session and the length of the pause. Finally, we observed no interaction between the cognitive control and within-session effects in beta oscillations during the delay period, in that the search–repetition difference in power was conserved despite the power increase during the session.

We propose that beta oscillations during delay therefore reflect multiple factors influencing cognitive control, one task-sensitive component and one time-sensitive component that, due to the effect of pauses, cannot be interpreted as a simple time-on-task effect.

### Beta and Cognitive Control

One approach to explain the relationship between cognitive functions and beta oscillations has been to relate them to top-down control of behavior (Buschman and Miller 2007; Siegel et al. 2012). Pesaran and colleagues demonstrated enhanced frontoparietal beta-band coherence in LFP during free decisions compared with instructed decisions (Pesaran et al. 2008). Free and instructed decisions require different cognitive control demands in the same way as the search and repetition periods of the current task. This proposed explanation accords with a generalized theory of beta oscillations in maintaining the “status-quo” proposed by Engel and Fries (2010). In the cognitive domain, these authors propose that such activity should be associated with the active maintenance of a cognitive set when the task involves a “strong endogenous top-down component.” Our finding of higher beta power in search seems to verify this proposal (Engel and Fries 2010). But, in contrast to these authors, we do not feel able to conclude that there is a unifying hypothesis of beta function. Our findings are too specific to permit this conclusion—the effects we report are limited to Beta 2 and to the delay period, and therefore, our interpretations do not apply to other instances of beta power recorded during the trial, for example after the touch.

LFP beta power in the pre-cue period of motor tasks, equivalent to the delay in the current task, has been reported in a number of studies (Kilavik et al. 2013). In human motor cortex, pre-cue beta power peaks before an informative but not a noninformative cue, supporting the idea that this is a top-down control signal that can be linked to cognitive elements of the task (Saleh et al. 2010). In the current task, we clearly demonstrate that beta power can be modulated by cognitive and motivational information during the delay period, but separately by motor action later in the trial.

Beta oscillations fluctuate depending on the cognitive control requirements, specifically those determined by the phase of the task (search/repetition) and by the outcome of the previous trial (INC/COR/SWI/BK). This is indeed predicted by the regulation models of cognitive control that account for variations in control in different situations, including not only tasks involving overriding of competing responses but also tasks with underdetermined responses like in the PST (Botvinick et al. 2001). One important instance of regulation occurs after errors. This is exactly what we observed. In the PST, shifting after error is the key to solve problems and optimal performance requires using errors appropriately. The animals did that perfectly, and their levels of beta oscillations reflect this. In this sense, we suggest that beta oscillations index cognitive control. Although beta power in the delay did not predict more optimal outcomes, nor longer RT, as might be expected of a cognitive control mechanism in a stimulus-response task driven by speed-accuracy trade off (Kerns et al. 2004), this was not necessarily expected in our case. In the PST, responses are underdetermined and driven by strategy not stimulus, and so a direct coupling between application of cognitive control (as indexed by beta power) and subsequent performance is not necessarily to be expected. Finally, in discussing the link between beta and cognitive control, we must remember that our evidence is correlational in nature, in common with most neurophysiological studies of cognitive control. Only direct experimental alterations of brain function, specifically focusing on beta oscillations, would be able to define a causal relationship between beta power, cognitive control, and performance.

### Beta Within-Session

At the same time, beta power also changed within the session, showing a striking increase over time. A simple and tempting interpretation is that this is a reflection of the behavioral time-on-task effect, which we have recorded through within-session increases in response times and execution errors. As such, one might posit that beta power is an index of general fatigue, linking to previous work in human EEG (Lafrance and Dumont 2000). But, this interpretation cannot be maintained, because of the crucial effect on beta power of pauses in work.

The evaluation of physiological and behavioral changes around pauses is a particularly important test that is rarely considered in the literature. Should the pause, for example, reset time-on-task decrements in performance in the case where the subject restarts work after the pause? Or should time-on-task effects maintain regardless of pauses? Variations in task are surely critical here. In our protocol, where the objective is fixed but work is self-paced, pauses and their related physiological changes are informative about the general state and cognition of the monkey within the context of a session that the monkey is motivated to finish. Note that although pauses could be experimentally imposed, such a manipulation would remove any possibility of understanding physiological reasons for pausing.

Our data show that beta power is profoundly influenced by pauses and that there is a de-correlation between execution parameters and the beta power either side of pauses (Fig. 6). If execution error rates or response times are an index of fatigue, the beta power is clearly not reflecting fatigue, and so is not a marker of the time-on-task effect as defined in the literature. Likewise, the pause effect on beta power permits rejection of several explanations of general change over the session, such as influences of reward satiation and the expectation of the bonus. Nevertheless, beta is modulated as a function of time, yet the task remains the same throughout the session. So while beta power changes during the session might not reflect time-on-task per se, they could reflect changes induced to counteract time-on-task perturbations, especially as our monkeys maintain cognitive performance throughout the session.

In some human research, cognitive control and execution error rates are modulated together across the session (Boksem et al. 2005). In our study, they are dissociated. A hypothesis for this dissociation is that monkeys have a strong overriding motivation to perform well on the cognitive task, to gain the final bonus reward more quickly. When motivation is manipulated in human subjects, time-on-task effects can be reversed (Lorist et al. 2009). Some subjects respond to increased motivation by increasing their accuracy, whereas others increase their response speed, but subjects do not do both (Boksem et al. 2006).

This influence of motivation returns us to the concept of attentional effort: a cognitive incentive that integrates explicit and implicit motivational forces (Sarter et al. 2006). A subject will increase attentional effort in order to maintain good performance, especially when highly motivated, and we posit that this is the case with the monkeys in the current experiment. In particular, attentional effort will be goal directed—monkeys will apply attentional effort in order to attain the final bonus reward, but attentional effort may not impact measures of general fatigue, such as the increasing response times. Hence, we hypothesize that the increasing beta power in the delay within-session is an index of the monkey's increasing attentional effort. The impact of attentional effort should be limited in some way, although note that we did not find a maximum value of beta power that induced pauses. Hence, the pause allows beta power and attentional effort reset: cognitive performance can be maintained after the pause with a lowered beta and presumably lowered attentional effort. The pause allows recovery of attentional effort, but not recovery from general fatigue; hence, the behavioral time-on-task effect remains (i.e., response times are not modulated around pauses). Such an interpretation might explain the dissociations between cognitive performance, execution performance, and beta oscillations.

Other interpretations of the within-session result should be considered, but they would seem to require that beta relates to a completely independent but time-sensitive function that we have not measured. We are, for the moment, unable to conceive of what such a function might be. Nevertheless, our interpretation demands experimental confirmation—in particular consideration of explicit manipulations of both fatigue and motivation in order to change the attentional effort applied to the task and record the resulting beta oscillations. We further note that studying pause effects in experiments targeting the neural correlates of fatigue and time-on-task would seem now to be essential.

### Multiple Roles of Beta Oscillations

So a single band of beta oscillations in the delay shows changes when the task demands more or less cognitive control, and when attentional effort is applied. It is established that different beta bands (as observed in our data and the data of others) have differential sensitivity in different moments of the trial, and this suggests that a large variety of mechanisms is expressed in the oscillations ranging from 12 to 30 Hz (Pfurtscheller et al. 1997). In addition to the roles cited earlier, a role in the motor system is well established (Pfurtscheller and Lopes da Silva 1999), and there is a clear link between beta oscillations and the pathophysiology of movement disorders (Brown 2007). Studies in visual cortical areas have sought to link low-frequency oscillations between 12 and 30 Hz, with a specific top-down role within the hierarchy of visual areas (Bosman et al. 2012; Bastos et al. 2014), and a specific localization of beta oscillations in the infragranular layers of cortex (Buffalo et al. 2011). These different roles are often differently localized or reflect different bands of “beta.” For example, several authors have already emphasized 2 sub-bands in the beta range (Beta 1 and Beta 2) that are associated with different neural mechanisms (Roopun et al. 2008; Cannon et al. 2013). Where our results contrast is that one single beta band (Beta 2) at one point in the task (the delay) in frontal cortex can be independently modified by different behavioral factors. We propose that this occurs because the 2 factors impinge on a single control mechanism.

Our data show interesting inter-individual variability for the beta power spectrum (Fig. 3). In both animals, 2 beta-bands were observed, close together in one monkey and well separated in the other. Yet, the effects of Phase and Time were observed for both animals on the highest frequency band, Beta 2. The literature provides interesting information regarding the relevance of inter-individual variability in power spectra (Buzsáki et al. 2013), a variability that should be taken into account when studying precise task-related variations in specific frequency bands (Pfurtscheller et al. 1997) and that can also be observed in LFPs (Kilavik et al. 2012). Brain rhythms are specific to individual brains and are at some level under genetic control, representing a robust heritable phenotype (De Gennaro et al. 2008; van Pelt et al. 2012). Importantly, our data show that although the exact Beta 2 peak differed between monkeys, the properties and modulations by cognitive challenge are identical, suggesting that functions are associated with a hierarchy of oscillatory bands but are independent of the exact frequency of operation.

Although the experiment was not designed to precisely locate functional dissociations within the frontal cortex, the reconstructed maps of effects show inhomogeneity hence functional organization. Although the electrode grids had different sizes in the 2 animals, they overlapped over the dorsomedial frontal cortex. The maps of the Phase effect (Fig. 4B) reveal for both monkeys a slight bias in the effects on the side ipsilateral to the hand used in the task, while relative to this, the Time effect appears to be slightly more anterior and bilateral (Fig. 5A). The largest grid showed effects over the dorsal arcuate sulcus but the description in one single monkey precludes strong conclusion. Finally, our analyses of ECoG signals do not avoid potential volume conduction effects that would alter anatomical resolution.

### Motivation and Cognitive Control

We propose that our results show a mechanism for the integration of motivational parameters into cognitive control. Beta oscillations index the implementation of cognitive control. Attentional effort acts to provide a general increase in beta over time. This is presumably necessary to combat a fatigue process, though our data do not show exactly what that might be. Crucially, this change in gain of beta allows for maintenance of the search–repetition difference necessary for the task. Motivation parameters such as attentional effort therefore act as modulators of cognitive control.

The alternative interpretation is 2 independent mechanisms each involving beta oscillations at identical frequencies and times, which we recorded as a single phenomenon on the surface of the brain. We posit that such a coincidence is unlikely. The dual influence on control interpretation is more plausible and more coherent with current theoretical positions.

The exertion of cognitive control is considered to be intrinsically costly and selected only in the presence of sufficient or adequate incentives (Westbrook et al. 2013; Kool and Botvinick 2014). In our case, decision to work or to pause might thus be based on the evaluation of the cost of exerting control in the PST in the face of fatigue, motivation, obtained and predicted outcomes, and distance to the final bonus reward. A recent proposition (Shenhav et al. 2013) integrates this cost-benefit analysis (including motivational factors) into control signal specification. Expected values of potential control signals are compared in order to select the identity and intensity of the control signal to be applied in a particular context. The specified control is then implemented, and we hypothesize that beta oscillations provide an index of this control implementation. Hence, beta modulation by 2 different factors reflects separated mechanisms that contribute to control specification. Independent inputs to control specification also echoes the dual mechanisms of control framework (Braver et al. 2007), albeit in a context where proactive and reactive mechanisms are employed concurrently (Braver 2012).

This interpretation leaves many open questions about the integration of motivation into cognitive control (Braver et al. 2014). Nevertheless, our findings here reiterate the suitability of beta oscillations as a contributing neural mechanism to these computations.

## Funding

This work was supported by Fondation de France, Agence National de la Recherche, Fondation pour la Recherche Médicale (J.V., F.M.S., M.C.M.F.), Fondation Caisse d'Epargne Rhône Alpes Lyon (J.V.), Fondation Neurodis (C.R.E.W.), and by the labex CORTEX ANR-11-LABX-0042. C.R.E.W. is funded by a Marie Curie Intra-European Fellowship (PIEF-GA-2010-273790). M.C.M.F. is funded by Ministère de l'enseignement et de la recherche. J.V. is currently funded by the LOEWE – NeFF project (Neuronale Koordination Forschungsschwerpunkt).

## Notes

We thank M. Valdebenito, M. Seon, and B. Beneyton for animal care and C. Nay for administrative support. Conflict of Interest: None declared.

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## Author notes

F.M.S. and C.R.E.W. contributed equally to this work (co-first authors).