Journal of Experimental Psychology: Human Perception and Performance 2015, Vol. 41, No. 2, 269 –276 © 2015 American Psychological Association 0096-1523/15/$12.00 http://dx.doi.org/10.1037/xhp0000026 OBSERVATION On the Independence of Visual Awareness and Metacognition: A Signal Detection Theoretic Analysis Barbara Jachs Manuel J. Blanco Imperial College London Universidad de Santiago de Compostela Sarah Grantham-Hill and David Soto Imperial College London Classically, visual awareness and metacognition are thought to be intimately linked, with our knowledge of the correctness of perceptual choices (henceforth metacognition) being dependent on the level of stimulus awareness. Here we used a signal detection theoretic approach involving a Gabor orientation discrimination task in conjunction with trial-by-trial ratings of perceptual awareness and response confidence in order to gauge estimates of type-1 (perceptual) orientation sensitivity and type-2 (metacognitive) sensitivity at different levels of stimulus awareness. Data from three experiments indicate that while the level of stimulus awareness had a profound impact on type-1 perceptual sensitivity, the awareness effect on type-2 metacognitive sensitivity was far lower by comparison. The present data pose a challenge for signal detection theoretic models in which both type-1 (perceptual) and type-2 (metacognitive) processes are assumed to operate on the same input. More broadly, the findings challenge the commonly held view that metacognition is tightly coupled to conscious states. Keywords: metacognition, visual awareness, perceptual decision making Persaud et al., 2011) and, in fact, metacognition has long been strongly coupled with higher-level cognition, namely, working memory, conscious awareness, and executive control processes (Shimamura, 2008). Accordingly, metacognitive ability ought to be dependent on factors that influence conscious awareness. For instance, the monitoring of the correctness of our perceptual decisions ought to be better when the perceptual saliency of the stimulus is stronger rather than weak. Recent studies have however challenged the traditional view that higher-level cognition, namely, reading, doing arithmetic, cognitive control, and working memory, are by necessity contingent on conscious awareness (Dutta, Shah, Silvanto, & Soto, 2014; Hassin, Bargh, Engell, & McCulloch, 2009; Pan, Lin, Zhao, & Soto, 2014; Sklar et al., 2012; Soto, Mäntylä, & Silvanto, 2010; Soto & Silvanto, 2014; van Gaal, Ridderinkhof, Scholte, & Lamme, 2010). Therefore here we sought to characterize more closely the relationship between perception, conscious awareness, and metacognition of perceptual decision making. We assessed how type-1 (perceptual) and type-2 (metacognitive) processing are influenced by levels of stimulus awareness, under conditions in which the stimulus input is held constant but awareness fluctuates across experimental trials. To assess the dependence/independence of awareness and metacognition, we used a Gabor orientation discrimination task in conjunction with different perceptual awareness scales (Overgaard, Timmermans, Sandberg, & Cleeremans, 2010) and response confidence ratings (see Figure 1 and Experimental Procedures for Experiment 1). The luminance of the Gabor was titrated in a Metacognition refers to our ability to reflect upon our own cognitive processes; for instance, to evaluate the quality of our perceptions, thoughts and actions. Intuitively, metacognitive processes are thought to be a key aspect of conscious awareness, and cognitive functions associated with reflection and introspection are indeed difficult to conceive independently of consciousness. Influential models of metacognition (Shimamura, 2008) highlight an interaction between first-order object-level processes (e.g., a task involving stimulus discrimination) and second-order monitoring processes that operate on the output of the first-order process; for instance, to provide a confidence estimate of the correctness of first-order perceptual choices. The contents of these second-order metacognitive processes are often assumed to reflect the contents of consciousness (Kunimoto, Miller, & Pashler, 2001; This article was published Online First February 9, 2015. Barbara Jachs, Department of Medicine, Division of Brain Sciences, Imperial College London; Manuel J. Blanco, Facultad de Psicología, Laboratorio de Percepción y Rendimiento Humano, Universidad de Santiago de Compostela; Sarah Grantham-Hill and David Soto, Department of Medicine, Division of Brain Sciences, Imperial College London. We thank Steve Fleming for sharing the code to compute the area under the type-2 ROC curve. Correspondence concerning this article should be addressed to David Soto, Imperial College London, Department of Medicine, Division of Brain Sciences, Charing Cross Campus, St. Dunstan’s Road, W6 8RP, London, UK. E-mail: [email protected] 269 JACHS, BLANCO, GRANTHAM-HILL, AND SOTO 270 Figure 1. Example of an experimental trial: sequence of events. precalibration stage using a 1-up 1-down staircase in order to present observers with stimuli near the threshold of conscious awareness. We derived receiver operating characteristics (ROC) curves associated with both type-1 performance (i.e., sensitivity to the Gabor orientation) and type-2 performance (i.e., sensitivity to the correctness of the type-1 perceptual decisions). The paradigm therefore allowed us to assess how awareness of the stimulus influences both type-1 perceptual and type-2 metacognitive sensitivity. Note that our key aim here was not to prove that metacognitive operations can be successfully deployed nonconsciously (i.e., above chance type-2 sensitivity to response correctness for truly subliminal items). We wondered instead whether type-2 sensitivity (metacognition) is indeed strongly coupled to stimulus awareness; were this the case, type-2 metacognitive sensitivity ought to covary with stimulus awareness in a similar fashion as type-1 perceptual sensitivity would be expected to covary with stimulus awareness. Notably, according to signal detection theoretic models (Galvin, Podd, Drga, & Whitmore, 2003) both type-1 and type-2 processes are assumed to operate on the same input, which, in the present experimental context, would reflect the output of neural channels in early visual cortex tuned to Gabor orientation (Hubel & Wiesel, 1974; Thomas & Shimamura, 1975). From this, it follows that any effect of awareness on performance should affect type-1 perceptual and type-2 metacognitive sensitivity to a similar extent. Type-2 sensitivity is often suboptimal (i.e., lower than what would be expected from the level of type-1 sensitivity), perhaps because not all of the information available for the type-1 decision is used for the type-2 metacognitive judgment (Maniscalco & Lau, 2012). Even within this constraint, however, it would be expected that awareness ought to influence type-1 and type-2 sensitivity to a similar degree. Experiment 1 Participants The participants were 13 healthy volunteers (7 male, 6 female; age range 22–30 years) who took part in return of £20. All participants were naïve as to the experimental hypothesis, had normal or corrected-to-normal vision, and provided written informed consent prior to the experiment. The study was approved by the West London Research Ethics Committee. Apparatus The stimuli were presented on a gamma calibrated CRT display (HP p1230, 1,600 ⫻ 1,200 pixels, 85 Hz refresh rate). The stim- ulus display and responses were controlled using PsychoPy (v.1.78.00) (Peirce, 2007), a psychophysics software written in Python (http://www.psychopy.org/). Experimental Procedures The experiment took place in a darkened room. Displays were viewed at a distance of approximately 90 cm. Each trial began with a fixation display (a central ⫹ printed in black) for 500 ms followed by a two-alternative forced choice (2AFC) discrimination task for the orientation of a Gabor patch (3 cm diameter) presented centrally on a gray background (luminance ⫽ 10.48 cd/m2). Figure 1 depicts the sequence of critical displays on a trial. Gabor orientation was 40° either to the left or right from the vertical; its spatial frequency was 0.1 cycles per pixel. The Gabor was presented for 35 ms during the experimental trials and was immediately followed by a circular backward mask of black and white random dots for 353 ms (11.34 cd/m2). Experimental trials were preceded by different task training and stimulus calibration phases (see below for further details). Observers were first exposed to a training phase with masked Gabors presented for 362 ms or for 35 ms, with a fixed luminance of 11.97cd/m2 in order to familiarize participants with the orientation discrimination task. Feedback about the orientation discrimination response was given on a trial by trial basis. Next, the luminance of the Gabor was calibrated using a 1-up: 1-down adaptive staircase. Observers were presented with a 35 ms masked Gabor and asked to report whether they could see the Gabor’s orientation or whether they were unaware of it. The luminance of the Gabor was reduced following orientation-aware trials and increased following orientation-unaware trials. Initial Gabor luminance was set to 11.97cd/m2. The percentage of aware responses was calculated on a trial by trial basis. Once the perceptual reports stabilized around the subjective awareness threshold (i.e., over 10 trials around 50% aware responses), we used the contrast measurements of the Gabor items across the last 10 trials to get an average, which was then used for the next procedural stage. Subsequently, observers received 30 training trials in the experimental task (see Figure 1) using 35 ms masked Gabors with the luminance level established in the prior calibration phase. Participants were required to: (a) report their level of awareness of the Gabor orientation (unaware, aware), (b) report the orientation of the Gabor (2AFC), and (c) to rate the confidence about the correctness of their responses on a scale of 1–3. Participants were instructed that confidence ratings should be conceived in a relative manner; accordingly, observers were instructed that the full range CONSCIOUS AWARENESS AND METACOGNITION of these relative confidence estimates ought to be equally used both on aware and unaware rated trials. Participants were encouraged to be as accurate as possible in their responses and reaction time was not emphasized. Each of the three response frames was presented during an unlimited time window until a response was collected. Prior to the experimental phase, the luminance of the Gabor was recalibrated by employing the procedure described above with the luminance output from the prior calibration as a starting point. Lastly, participants performed 10 blocks of each 50 experimental trials, as depicted in Figure 1. Signal Detection Theoretic (SDT) Analysis All data processing and analyses were completed using R (R Development Core Team, 2014) and Matlab. We used a receiveroperating-characteristic (ROC) analysis (Egan, 1975; Green & Swets, 1966) to measure type-1 and type-2 sensitivity. Regarding the type-1 perceptual sensitivity analyses, the “signal” and “noise” were defined as left and right oriented Gabor, respectively. A “hit” was therefore a correct response (“left”) to a left-oriented Gabor and a “correct rejection” was a correct response (“right”) to a right-oriented Gabor. A “false alarm” was an incorrect response (left) to a right-oriented Gabor and a “miss” was an incorrect response (right) to a left-oriented Gabor. To obtain the type-1 ROC curves, we plotted the probability of hits as a function of the probability of false alarms for all possible decision criteria. The different points in the ROC curve were obtained by calculating cumulative probabilities for hits and false alarms along a confidence continuum ranging from 3 (e.g., sure) to 1 (e.g., guess) in signal-present trials (left-oriented Gabor), and from 1 (e.g., guess) to 3 (e.g., sure) in noise trials (right-oriented Gabor). From simple Figure 2. 271 geometry, we computed the area under the ROC curve (Kornbrot, 2006) as a distribution-free measure of the discriminability of the two Gabors. Regarding the type-2 sensitivity analyses, the area under the ROC curve was calculated by plotting the cumulative probability of correct responses (either hit or correct rejection) and the cumulative probability of incorrect responses (either false alarm or miss) across the different levels of confidence. We estimated the area under the ROC curve as a distribution-free measure of the discriminability of correct and incorrect type-1 performance or metacognitive ability (Fleming, Weil, Nagy, Dolan, & Rees, 2010). We also computed type-1 d= and also meta-d= (Maniscalco & Lau, 2012), which is basically a parametric estimation of type-2 sensitivity predicted from the type-1 signal detection SDT model, done by fitting a type-1 SDT model to the observed type-2 performance data and estimating the type-2 ROC curves. Results and Discussion Figure 2 depicts the area under the type-1 and type-2 ROC curves. Notably, performance in the “unaware” state was significantly above chance levels (0.5) both for type-1 and type-2 sensitivity, t(12) ⫽ 6.698, p ⬍ .0001 and t(12 ⫽ 3.205, p ⫽ .007, respectively). Interestingly, while type-1 performance was better in the aware relative to the unaware state, t(12) ⫽ 6.292, p ⬍ .0001, type-2 performance was not significantly different across awareness states, t(12) ⫽ 0.545, p ⫽ .595. The above observations were further confirmed by means of an analysis of variance (ANOVA) with awareness (aware, unaware) and performance type (perceptual, metacognitive) as factors. There was a main effect of awareness F(1, 12) ⫽ 13.6 p ⫽ .0031) showing that overall performance was, overall, better in the aware Type-1 and type-2 ROC curves as a function of the level of awareness. JACHS, BLANCO, GRANTHAM-HILL, AND SOTO 272 state. There was also a main effect of performance type, showing that type-1 sensitivity outperforms type-2 sensitivity F(1, 12) ⫽ 88.87, p ⬍ .00001). Critically, there was a significant interaction between factors F(1, 12) ⫽ 24.39, p ⬍ .0003, in keeping with the observation that awareness effects were higher on type-1 relative to type-2 sensitivity. Type-2 sensitivity was similar in aware and unaware states, t(12) ⫽ 0.545, p ⫽ .595. Identical results were found with type-1 d= and meta-d= (Maniscalco & Lau, 2012): awareness state interacted with performance type, F(1, 12) ⫽ 11.17, p ⬍ .005, so that awareness effects were far higher on type-1 d= than on meta-d=; meta-d= was not different across awareness conditions, t(12) ⫽ 0.82, p ⫽ .428 (Figure 3). These results suggest that metacognition of perceptual decisionmaking, assessed by type-2 sensitivity scores from SDT, is not strongly dependent on the level of stimulus awareness. Notably, object perception, assessed by type-1 sensitivity was strongly dependent on stimulus awareness. Before delving into further discussion, we wished to replicate this pattern of results by using a more exhaustive measure of stimulus awareness. Experiment 2 was devised with this in mind. Experiment 2 Participants Eighteen new healthy volunteers (9 male; aged 20 –29 years) took part. One participant was excluded due to overall chance performance in the orientation discrimination task. Another participant was excluded because he had only 24 2-rating awareness trials, hence precluding accurate calculation n of type-2 sensitivity. One participant was excluded for not using the full range of the confidence scale (i.e., no 3-confidence ratings reported). However, the pattern of results remained unchanged when all data were analyzed. Experimental Procedures The experimental procedure was similar to Experiment 1, except that here we used a perceptual awareness scale following Sandberg, Bibby, Timmermans, Cleeremans, & Overgaard, 2011 (see their Experiment 2), which provides a more exhaustive measure of awareness than the binary scale used in Experiment 1. Awareness was rated by observers on a trial by trial basis, such that 1-rating corresponded to “no experience of the stimulus,” 2-rating corresponded to “a brief glimpse but no experience of the orientation,” and 3-rating signified “almost clear experience or clear experience of the Gabor orientation.” Results ROC analyses of type-1 and type-2 sensitivity were not performed on trials with reports of almost clear or vivid visual experience because these were a minority of the total and hence precluded accurate derivation of the area under the ROC curve. In keeping with Experiment 1, performance in the “unaware” state (e.g., trials with ratings of “No experience of the stimulus”) was significantly above chance levels (0.5) both for type-1 and type-2 sensitivity, t(14) ⫽ 5.15, p ⬍ .0001 and t(14 ⫽ 4.3, p ⬍ .0001, respectively). Figure 4 illustrates type-1 and type-2 ROC curves. An ANOVA of the areas under the ROC curves with awareness and performance type as factors showed the main effects of awareness, F(1, 14) ⫽ 15.2, p ⫽ .0016 and performance type, F(1, 14) ⫽ 35.81, p ⬍ .00001. More critically, replicating the findings from Experiment 1, there was a significant interaction between factors F(1, 14) ⫽ 24.85, p ⬍ .0001), indicating that the difference in sensitivity between aware and unaware states was stronger for type-1 relative to type-2 performance. We also note that type-2 sensitivity did not differ across awareness states, t(14) ⫽ 1.549, p ⫽ .143. The same interaction effect between awareness and performance type was found on meta-d=, F(1, 14) ⫽ 23.47, p ⬍ .0002 (Figure 5). Here, meta-d= results showed a significant awareness effect on type-2 sensitivity, t(14) ⫽ 2.834, p ⫽ .013. However, we note this result was absent in Experiment 1 and also in Experiment 3 below, and, in any case, it does not challenge our main conclusion that awareness effects are strongest on type-1 sensitivity and greatly reduced on type-2 sensitivity. Experiment 3 Figure 3. Type-1 d= and type-2 meta-d= scores as a function of the level of awareness. ROC analyses provide a measure of sensitivity which is biasfree from a SDT perspective; hence, type-2 sensitivity ought to be independent on a particular tendency of the individual to report (e.g.) high confidence. The same argument applies to type-1 d= and meta-d= (Maniscalco & Lau, 2012). However, it remains to be seen in the present study whether visual awareness could have had any effect on decision biases beyond the modulation of type-1 sensi- CONSCIOUS AWARENESS AND METACOGNITION Figure 4. 273 Type-1 and type-2 ROC curves as a function of the level of awareness. tivity. The present Experiment 3 tested for awareness effects on type-2 bias (e.g., the observer’s tendency to report high confidence). We note that the design of Experiments 1 and 2 did not allow us to derive a consistent SDT-based measurement of type-2 bias because there was an uneven number of three confidence ratings and the computation of type-2 bias can be biased with an odd number of ratings (Kornbrot, 2006). To provide an unbiased measure of type-2 bias we here used an even number of 2 ratings along a continuum of relative confidence. Participants Ten new healthy volunteers (5 male; aged 21–25 years) took part. Experimental Procedures The experimental procedure was similar to the previous experiments. The main difference is that the awareness and confidence scales were simplified to facilitate the computation of type-2 confidence biases. In reporting confidence, participants were asked to inform how confident there were about the correctness of the orientation response on a relative scale of 1 (relatively less)–2 (relatively more) confident. In reporting awareness, participants were asked to report “unawareness” when they had no experience of the Gabor or saw a brief glimpse but were not aware of the orientation, and to report “awareness” when they could see the Gabor’s orientation somewhat or almost clearly. There were eight blocks of 50 trials each. Signal Detection Theoretic (SDT) Analysis We used nonparametric assessments of type-2 sensitivity and type-2 bias because the parametric assumptions may not hold for type-2 data (Galvin et al., 2003). We used A= (Macmillan & Creelman, 1991) to derive a measure of both type-1 and type-2 sensitivities. For the type-1 sensitivity analyses, the hits and false alarms were defined as in the previous experiments. For the type-2 sensitivity analyses, the signal was the correct response and the noise the incorrect response. Accordingly, a type-2 hit was defined as a correct response (either a type-1 hit or a type-1 correct rejection) with high confidence and a type-2 false alarm was defined as an incorrect response (either a type-1 false alarm or a miss) with high confidence. Type-2 correct rejections were incorrect trials with low confidence and type-2 misses were correct trials with low confidence. We also report d=/meta-d= results (Maniscalco & Lau, 2012). To estimate the type-2 bias, we used B=k (Kornbrot, 2006), and also B”D (Donaldson, 1992) which has been shown to outperform other nonparametric estimates of bias in certain experimental settings (e.g., vigilance) (See, Warm, Dember, & Howe, 1997). Results and Discussion Analyses of type-1 and type-2 sensitivity confirmed the results found in the previous two experiments. Type-1 A= was higher on aware relative to unaware trials, t(9) ⫽ 4.126, p ⫽ .0025, which did not differ in terms of type-2 sensitivity, t(9) ⫽ 0.998, p ⫽ .344. Similar effects were found on d= and meta-d=. Type-1 d= was enhanced on aware relative to unaware trials, t(9) ⫽ 3.159, p ⫽ .011 but this was not the case for meta-d=, t(9) ⫽ 0.224, p ⫽ .827. Critically, this pattern of results was found in the absence of awareness effects on type-2 bias, t(9) ⫽ 0.025, p ⫽ .98, for B=k and t(9 ⫽ 0.2, p ⫽ .84, for B==D). These results are depicted in Figures 6 and 7. These data indicate that awareness effects occur in the absence of effects on type-2 decision biases. 274 JACHS, BLANCO, GRANTHAM-HILL, AND SOTO Figure 5. Type-1 d= and type-2 meta-d= scores as a function of the level of awareness. General Discussion We found that visual awareness had a profound effect on type-1 perceptual sensitivity but, intriguingly, the awareness effect on type-2 metacognitive sensitivity was far lower by comparison. Notably, metacognitive sensitivity was significantly above chance across awareness states. The disproportionate effect of awareness on type-1 relative to type-2 sensitivity was observed across three experiments, which varied the observer’s criteria to report the level of perceptual awareness. This pattern of results is newsworthy in several theoretical junctures. Traditionally, the information that is appraised in the metacognitive process is typically thought to reflect the contents of conscious visual experience (Kunimoto et al., 2001; Persaud, McLeod, & Cowey, 2007) and intuitively it is difficult to think how an observer can evaluate his or her responses to items independently of his or her level of awareness of the items in question. The present data suggests that the contents of metacognitive computations are dissociable from levels of stimulus awareness. Influential models (Shimamura, 2008) conceive metacognition as resulting from the interaction between perceptual processes operating on sensory representations (e.g., a feature discrimination task) and second-order (evaluative) processes that monitor the output of the object-level process (e.g., evaluation of the correctness of type-1 decisions). The present findings challenge this notion by showing that awareness can have distinctive effects on type-1 and type-2 processes. “Blindsight” patients report no visual experience for items presented in the visual field impaired by their lesion in primary visual cortex lesions but nevertheless can display astonishing high levels of perceptual sensitivity. Blindsight has provided remarkable insight into the relation between perception and awareness by showing that awareness may not be necessary for type-1 perceptual discrimination functions. Interestingly, there is some data suggesting that blindsight patients can sometimes report higher levels of decision confidence (e.g., by placing a higher wager) following correct than incorrect perceptual decision for targets presented in the “blind” visual field (Persaud et al., 2011; Persaud et al., 2007), which suggests that confidence ratings may be diagnostic of discrimination accuracy to some degree, even in the absence of awareness. To the best of our knowledge, only a recent study in healthy human observers assessed type-1 and type-2 sensitivity as a function of stimulus awareness (Charles, Van Opstal, Marti, & De- Figure 6. A= scores for the type-1 and type-2 task (left panel) and d=/meta-d= scores (right panel) as a function of the level of awareness. CONSCIOUS AWARENESS AND METACOGNITION 275 Figure 7. Type-2 decision bias scores: (B=k, left panel; B==D, right panel). Negative values of B= k reflect a relative bias toward lower confidence ratings while positive values correspond to higher confidence biases. B==D values equal to 0 indicates no bias; positive numbers represent a tendency report little confidence and negative numbers represent a tendency to report high confidence. haene, 2013). Charles and colleagues showed that type-2 metacognitive evaluation for nonconscious targets in a number comparison task could exceed chance levels. Unlike here, however, Charles et al. (2013) also found that type-2 metacognitive sensitivity was significantly higher than type-1 perceptual sensitivity. Typically, as we found here, type-2 sensitivity tends to be low (e.g., suboptimal) relative to type-1 sensitivity—that is, not all the information available for the type-1 process may be available for the secondorder metacognitive judgment (Maniscalco & Lau, 2012). Charles et al. (2013) rightly argued that higher type-2 sensitivity in their experimental protocol could reflect additional accumulation of information following the type-1 decision (Resulaj, Kiani, Wolpert, & Shadlen, 2009), which would continue to inform, therefore, the type-2 process. This would lead to errors or hits being greater acknowledged following the type-1 decision and hence leading to a boost in type-2 sensitivity. Our findings are in keeping with the Charles et al. (2013) study in that stimulus awareness does not appear to be a prerequisite for type-2 metacognitive sensitivity. Importantly, the present findings go beyond to demonstrate that type-1 and type-2 processes can dissociate in how they relate to stimulus awareness. The attenuated effect of awareness on type-2 sensitivity in the presence of a significant awareness effect on type-1 sensitivity suggests that type-2 metacognitive operations are not necessarily carried out on the same type of representation or follow a similar process to that underlying type-1 performance. These results, therefore, place critical constraints on extant signal detection theoretic frameworks, which postulate that type-1 and type-2 sensitivity share a common informational source which determines the sensitivity of type-2 decisions (Clifford, Arabzadeh, & Harris, 2008; Galvin et al., 2003; Maniscalco & Lau, 2012; Pleskac & Busemeyer, 2010). One limitation of the present study is that behavior was modeled by using a static analytical model of the decision process (i.e., SDT). Because SDT cannot capture the dynamics of the decision process, it may well be that the relationship between metacognition and awareness obey more complex rules than the degree of dependency or independency. To tackle this issue, dynamic models of the decision process such as drift diffusion or accumulator models (Brown & Heathcote, 2008; Ratcliff & McKoon, 2008) may be useful to better understand how awareness relates to type-1 and type-2 processes; however, any attempt to assess the role of awareness in this regard will be confronted with the difficulty of separating type-1 and type-2 processes because these are likely to overlap in time. Novel paradigms need to be developed in order to tackle this issue. The present findings challenge existing accounts of metacognition and its relation to perception and conscious awareness by suggesting that stimulus awareness and first-order perceptual processes are not necessarily key determinants in the computation of metacognitive judgments. 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The Journal of Neuroscience, 30, 4143– 4150. http://dx.doi.org/10.1523/JNEUROSCI .2992-09.2010 Received August 26, 2014 Revision received October 27, 2014 Accepted November 24, 2014 䡲
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