You will be presented with the abstract, introduction, and discussion section from a biomedical research article. Your task is to create a summary that a layperson can understand, capturing the essence of the research article. Keep essential scientific terms, but ensure that the language remains clear and the concepts are explained in an uncomplicated manner.

Title: Average Is Optimal: An Inverted-U Relationship between Trial-to-Trial Brain Activity and Behavioral Performance}
Article:
Abstract:
It is well known that even under identical task conditions, there is a tremendous amount of trial-to-trial variability in both brain activity and behavioral output. Thus far the vast majority of event-related potential( ERP) studies investigating the relationship between trial-to-trial fluctuations in brain activity and behavioral performance have only tested a monotonic relationship between them. However, it was recently found that across-trial variability can correlate with behavioral performance independent of trial-averaged activity. This finding predicts a U- or inverted-U- shaped relationship between trial-to-trial brain activity and behavioral output, depending on whether larger brain variability is associated with better or worse behavior, respectively. Using a visual stimulus detection task, we provide evidence from human electrocorticography( ECoG) for an inverted-U brain-behavior relationship: When the raw fluctuation in broadband ECoG activity is closer to the across-trial mean, hit rate is higher and reaction times faster. Importantly, we show that this relationship is present not only in the post-stimulus task-evoked brain activity, but also in the pre-stimulus spontaneous brain activity, suggesting anticipatory brain dynamics. Our findings are consistent with the presence of stochastic noise in the brain. They further support attractor network theories, which postulate that the brain settles into a more confined state space under task performance, and proximity to the targeted trajectory is associated with better performance.
Introduction:
An inverted-U relationship is well established between brain function and many neuromodulatory influences, including arousal[1], dopaminergic[2],[3], cholinergic[4] and noradrenergic[5],[6] systems, with both insufficient and excessive levels of neuromodulation causing impaired brain function and performance. Interestingly, the possibility that a similar inverted-U function might exist between trial-to-trial fluctuations of brain activity and behavioral performance is seldom tested( but see[7]–[10]). The vast majority of studies on the relationship between trial-to-trial brain activity and behavior have only investigated a monotonic relationship between them by, for example, comparing trial-averaged brain activity between different categories of behavioral performance( e. g., hits vs. misses) or computing the linear correlation between trial-to-trial brain activity and performance metrics[e. g., reaction times( RTs)]. These methods have been successfully applied to reveal influence on cognition/behavior by both pre-stimulus ongoing brain activity and post-stimulus brain responses in functional magnetic resonance imaging( fMRI)[11]–[15] and magnetoencephalography( MEG)[16],[17] signals from humans, as well as local field potentials( LFP)[18],[19] and neuronal spiking activity from primates[20]–[22]. Recently, it has been increasingly appreciated that across-trial brain variability can be modulated independently from trial-averaged brain activity[23]–[30]. Moreover, behaviorally relevant information can be encoded within across-trial variability but not trial-averaged activity[28],[30]. This phenomenon predicts the existence of a U- or inverted-U relationship between trial-to-trial brain activity and behavioral performance. For example, if trials with fast and slow reaction times are associated with a similar level of trial-averaged activity but fast trials have smaller across-trial variability, as observed previously[28],[30], then brain activity closer to the across-trial mean should be more likely to be associated with fast RTs. Notably, several previous studies have shown that pre-stimulus amplitude of brain oscillations in sensory cortices has an inverted-U relationship with behavioral performance: Intermediate amplitudes predict higher hit rate and faster reaction times[7]–[9]. In light of the prevalent phase-amplitude coupling in the human brain whereby lower-frequency phase modulates higher-frequency power[31],[32], we conjectured that such an inverted-U relationship might also manifest in the raw fluctuations of field potentials, which is dominated by low-frequency activity[31]. Theoretically, the existence of both monotonic and inverted-U relationships between trial-to-trial brain activity and behavioral performance accord with the consideration that there are two sources of brain variability: deterministic and stochastic. The deterministic source of variability arises from spontaneous brain activity related to overall brain functioning that varies from trial to trial[33]. Theoretical work further suggests that small differences in the initial state of a system can be deterministically amplified during responses to task[34]. The second source of variability is stochastic noise: Ion channel behavior is fundamentally indeterminate; ion channel noise contributes to synaptic noise, thence to membrane potential fluctuations and spike generation and propagation[35]–[37]. As inescapable as stochastic noise is, randomness at the behavioral level confers an evolutionary advantage in a competitive ecological environment[35]. As remarked by Alan Turing, “If a machine is expected to be infallible, it cannot also be intelligent”( 1947, Lecture to London Mathematical Society). Germane to the current thesis, the presence of stochastic noise predicts an inverted-U relationship between trial-to-trial brain activity and behavioral performance: Under a large amount of noise, brain activity will be scattered across a wide range; under low noise, activity will remain close to the center “targeted” value. Even though the presence of stochastic noise is evolutionarily advantageous and beneficial in contexts such as stochastic resonance[38], gambling[35], and probabilistic decision making[39], under a specific task condition it could still degrade performance( e. g., musicians train for many years to attain motor consistency and precision)[36]. Thus, the presence of stochastic noise in the brain should impose an inverted-U relationship between trial-to-trial brain activity and performance. Using electrocorticography( ECoG) in patients undergoing invasive brain monitoring for neurosurgical treatment, we found strong evidence for such a phenomenon in the human brain.
Discussion:
In summary, consistent with earlier studies[7]–[9], the present results provide strong evidence for an inverted-U relationship between trial-to-trial brain activity and behavioral performance in the human brain, such that moderate activity predicts better behavioral performance( more hits and shorter RTs), whereas both very low and very high activity levels are associated with degraded performance( more misses and longer RTs). While these previous studies have focused on the amplitude of alpha and mu oscillations in sensory cortices, the present study extends the inverted-U relationship to the raw fluctuations of field potentials( similar to single-trial ERPs) outside the sensory cortex. Specifically, when the contralateral hand was used for motor output, we found that the inverted-U relationship between trial-to-trial ECoG activity and hit rate was most pronounced around the stimulus onset( Fig. 4A) and was relatively localized to a subset of electrodes( Fig. 8 A–C). By contrast, the inverted-U relationship between ECoG activity and response speed was strongest around behavioral responses( Fig. 4B) and was more distributed across all electrodes( Fig. 8D). Interestingly, when the ipsilateral hand was used for motor output instead, the inverted-U relationship between ECoG activity and hit rate was most pronounced around behavioral responses( Fig. 5A), and that between ECoG activity and response speed was less robust and more sporadic in time( Fig. 5B). The Laplacian montage of ECoG approximates transcortical recording, such that increased cortical excitability manifests as more negative ECoG signals. Thus, the inverted-U relationship between trial-to-trial ECoG activity and behavioral performance suggests that both very low and very high cortical activity, manifesting as most positive and most negative ECoG signals respectively, are associated with compromised performance, while intermediate activity levels are associated with better performance. These findings support the notion that a higher level of stochastic noise, which scatters the brain activity across a wider range, is associated with degraded performance under a specific task condition. Importantly, such an effect is not contradictory to a potentially beneficial role of stochastic noise during development or evolution[35],[48]. For example, young adulthood is associated with larger brain variability as compared with both childhood and aging, and at the same time more accurate and consistent behavioral responses[49]–[51]. We think that these observations are complementary instead of contradictory to the present results, as both a wider dynamic range at rest and the ability to quickly settle into the desired state during task should be associated with better function. Thus, across developmental stages, larger brain variability is an index of a wider dynamic range and a greater repertoire of potential brain states[48]. On the other hand, during task processing, the ability of the brain to quickly settle into a particular task state is highly desirable and predictive of better performance. Indeed, post-stimulus brain responses appear to be more variable in patients with autism[27] and schizophrenia[52]. An inverted-U brain-behavior relationship is consistent with the present( Figs. 3B & 7B) and earlier[28],[30] findings showing that better behavioral performance can be accompanied by smaller trial-to-trial variability, even without any correlation with trial-averaged activity. An inverted-U relationship has also been reported between trial-to-trial neuronal firing rate and movement speed in the macaque premotor cortex[29]. In addition to the different recording modalities and species, the present results extend this previous finding in several directions by showing: i) the inverted-U relationship is present in both post-stimulus brain responses and pre-stimulus ongoing activity up to 500 ms before the stimulus onset; ii) the inverted-U relationship had largely separate spatial localizations from the monotonic brain-behavior relationship( Fig. 6); and iii) the spatiotemporal patterns of the inverted-U relationship differ between performance metrics( hit rate vs. RT) and motor output( contralateral vs. ipsilateral)( Figs. 4, 5 & 8), suggesting functional specificity. The difference in spatial localization for the inverted-U vs. monotonic brain-behavior relationships is consistent with our earlier observation that variability-based analysis results follow a different spatial distribution from mean-based analysis results[30]. It is worth noting that the exact spatial localizations of the quadratic and monotonic brain-behavior relationships in our electrode-by-electrode analysis( Fig. 6) should not be over-interpreted. This is partly because the spatial localizations revealed by ECoG in neurosurgical patients are subject to limited electrode coverage( especially under Laplacian montage) as well as heterogeneous spatial sampling from subject to subject( Fig. 1C). More importantly, as revealed in our analysis on RT( Fig. 8D), there is a significant amount of behaviorally relevant information distributed among non-significant electrodes. Our PCA analysis also suggests that the inverted-U relationship with RT is distributed amongst the top PCs( Fig. 4B). These results are consistent with a recent fMRI study showing that with sufficient signal-to-noise ratio, over 95% of the brain is involved in a simple visual attention task[47]. Lastly, a limitation of the present study is that the primary( visual) sensory regions were not sampled by the ECoG electrodes( see Fig. 1C), hindering a direct comparison with earlier studies on this topic[7]–[9]. Nonetheless, our results in somatosensory/motor regions are consistent with earlier neurophysiological studies in the macaque[23],[29]. The traditional framework in neuroscience surmises that brain responses during task are the superposition of noise-like ongoing activity and task-evoked activity. This framework predicts variability increase after task onset[30] and a monotonic relationship between trial-to-trial brain activity and behavioral performance. Our findings of stimulus-induced variability reduction and an inverted-U brain-behavior relationship cannot be accommodated within this traditional framework. Instead, our results are readily embraced by attractor-network[53]–[55] and liquid-state machine[56]–[58] theories. These theories predict that as the network settles into a particular state or trajectory during task processing, across-trial variability decreases[55],[59]. The faster the system converges onto this state, the more similar its activity will be across trials, predicting a correlation between fast RT and smaller across-trial variability( see Fig. 7B herein and Ref[28]–[30]). Moreover, because the presence of stochastic noise scatters brain activity across a wider range than the targeted state, the closer the brain activity is to the targeted trajectory, the better the behavioral performance, consistent with the inverted-U relationship we observed. Notably, these ideas have close parallels to the “optimal-subspace hypothesis” developed in the context of motor preparation[60]. While the attractor-network framework provides potential explanations for our observation of an inverted-U relationship between post-stimulus brain activity and performance, what could account for the presence of such a relationship at or before the stimulus onset? One potential explanation for our results might be provided by the sampling-based Bayesian framework[61]. This idea proposes that the brain activity trajectory through the multidimensional state space samples different potential states; the distribution of the pre-stimulus samples constitutes the prior of its internal model, and that of the post-stimulus samples constitutes the posterior of the model. Accordingly, pre-stimulus activity closer to the across-trial mean would represent cortical states that are a priori more probable( assuming a unimodal distribution). Speculatively, this “most probable” state might also be the most “ready” state, and thus be associated with better performance. Another, not mutually exclusive, explanation lies in the framework of stochastic resonance – a nonlinear effect whereby an optimal level of noise facilitates the detection of a weak stimulus[62],[63]. This framework has been invoked previously to explain the inverted-U relationship between pre-stimulus amplitude of brain oscillations and task performance[7]. Since low-frequency activity phase modulates higher-frequency power[31],[32], such a mechanism might explain our results pertaining to the raw fluctuations of broadband signals as well. In addition, a theoretical model utilizing input-output nonlinearity to explain an inverted-U relationship between pre-stimulus oscillatory power and ERP has been proposed[8]. Needless to say, the exact mechanisms of the inverted-U brain-behavior relationship we uncovered in the pre-stimulus period await future investigations. In particular, elucidation of the interaction between higher-frequency brain oscillations and lower-frequency raw signal fluctuations( such as the slow-cortical potentials)[31],[32],[64],[65] in the context of inverted-U brain-behavior relationship might provide clues to the underlying mechanism. In conclusion, our results are in line with recent theoretical frameworks suggesting that the brain is an active nonlinear dynamical system whose activity trajectory embodies information processing[48],[56],[57],[66]–[69]. Interestingly, the inverted-U and monotonic relationships between brain activity and behavioral performance were largely segregated in their spatial localizations( Fig. 6). While the presence of stochastic noise in the brain could impose an inverted-U relationship between brain activity and behavioral performance, it is tempting to speculate that the monotonic relationship might have a larger contribution from the deterministic source of brain variability. The underlying mechanisms of these two dissociable types of brain-behavior relationships should be an important topic for future experimental and theoretical studies.
The human brain is notoriously “noisy” . Even with identical physical sensory inputs and task demands , brain responses and behavioral output vary tremendously from trial to trial . Such brain and behavioral variability and the relationship between them have been the focus of intense neuroscience research for decades . Traditionally , it is thought that the relationship between trial-to-trial brain activity and behavioral performance is monotonic: the highest or lowest brain activity levels are associated with the best behavioral performance . Using invasive recordings in neurosurgical patients , we demonstrate an inverted-U relationship between brain and behavioral variability . Under such a relationship , moderate brain activity is associated with the best performance , while both very low and very high brain activity levels are predictive of compromised performance . These results have significant implications for our understanding of brain functioning . They further support recent theoretical frameworks that view the brain as an active nonlinear dynamical system instead of a passive signal-processing device .