Scale-specific dynamics of large-amplitude bursts in EEG capture

behaviorally meaningful variability

March 17, 2020

Kanika Bansal1,2,*, Javier O. Garcia1,3, Nina Lauharatanahirun 1,4, Sarah F. Muldoon5, PaulSajda2,6, Jean M. Vettel1,3,7

1 U.S. Combat Capabilities Development Command Army Research Laboratory, Aberdeen Proving Ground,MD 21005, USA2 Department of Biomedical Engineering, Columbia University, New York, NY 10027, USA3 Department of Biomedical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA4 Annenberg School of Communication, University of Pennsylvania, Philadelphia, PA 19104, USA5 Mathematics Department, CDSE Program, and Neuroscience Program, University at Buffalo, SUNY, Buf-falo, NY 14260, USA6Data Science Institute, Columbia University, New York, NY 10027, USA7 Department of Psychological and Brain Sciences, University of California, Santa Barbara, CA 93106 , USA

*Correspondence should be addressed to K.B. (phy.kanika@gmail.com).

Abstract

Cascading large-amplitude bursts in neural activity, termed avalanches, are thought to provide insight intothe complex spatially distributed interactions in neural systems. In human neuroimaging, for example,avalanches occurring during resting-state show scale-invariant dynamics, supporting the hypothesis thatthe brain operates near a critical point that enables long range spatial communication. In fact, it hasbeen suggested that such scale-invariant dynamics, characterized by a power-law distribution in theseavalanches, are universal in neural systems and emerge through a common mechanism. While the analysisof avalanches and subsequent criticality is increasingly seen as a framework for using complex systemstheory to understand brain function, it is unclear how the framework would account for the omnipresentcognitive variability, whether across individuals and/or tasks. To address this, we analyzed avalanchesin the EEG activity of healthy humans during rest as well as two distinct task conditions that varied incognitive demands and produced behavioral measures unique to each individual. In both rest and taskconditions we observed that avalanche dynamics demonstrate scale-invariant characteristics, but differin their specific features, demonstrating individual variability. Using a new metric we call normalizedengagement, which estimates the likelihood for a brain region to produce high-amplitude bursts, wealso investigated regional features of avalanche dynamics. Normalized engagement showed not onlythe expected individual and task dependent variability, but also scale-specificity that correlated withindividual behavior. Our results suggest that the study of avalanches in human brain activity provides atool to assess cognitive variability. Our findings expand our understanding of avalanche features and aresupportive of the emerging theoretical idea that the dynamics of an active human brain operate close toa critical-like region and not a singular critical-state.

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1 Introduction

Cognition is believed to require a widespread coordination of spatiotemporal neural activity. Though suchcoordination appears to be ubiquitous across tasks and conditions, the underlying principles of how thiscoordination occurs and how it may relate to individualized behavior are not yet well understood. Previousstudies have proposed that cascading large-amplitude bursts in neural activity, also known as avalanches,provide a novel marker of characteristic complex dynamics that relate to brain function [1–9]. In terms ofanalysis of avalanches in the human brain activity, the focus has been on resting state activity, where severalgroups have demonstrated power-law probability distributions of avalanche sizes and durations [3, 4, 7, 10].Power-law distributions are interesting in that they imply the absence of a characteristic scale of activity– i.e., scale-invariance. Systems with scale-invariant characteristics demonstrate efficient integration andsegregation of information both locally and globally. Another observed attribute of neural avalanches hasbeen that their branching process – i.e., how the dynamics evolve over time – demonstrates a balance betweenongoing and upcoming neural activity [11], which is thought to be indicative of a macroscopic balance inexcitation and inhibition [12]. Interestingly, these statistical features of avalanche dynamics in resting stateat the macro-scale (i.e., measured fMRI, MEG, and EEG) were found consistent with what has been observedin smaller scale neuronal assemblies [1, 13–15] and in vivo studies [8, 16–19]. These observations of braindynamics, based on analyses adopted from statistical physics [20,21], have been the basis for the hypothesisthat the brain operates near criticality [1, 22, 23], a special point in system’s dynamical phase space, thatseparates order from disorder, providing for scale-invariance and subsequently, dynamical and functionaldiversity [24–27].

Despite these observations that critical-like features appear in experimental recordings across systems,questions surrounding the ‘criticality’ hypothesis have not been fully explored. For example, the effect ofstimulus and task-evoked activity on avalanche dynamics has only been partially investigated [5, 28] andis not well understood [29]. Additionally, the proposition that a single universality class exists and servesas a unifying mechanism for observed scale-invariance and criticality [15, 30] theoretically require identicalscaling features and a single critical point for all neural systems. However, given the variability of neuralsystems, compared to more traditional physical systems studied using this analytical approach (e.g. magneticsystems) [31], the ‘universality’ proposition fails to provide an explanation for the variability often observedin the study of neural avalanches [32–34]. Existence of criticality requires a delicate balance in system’sdynamics and a single critical point requires a fine tuning of parameters to achieve this balance. Such afine tuning appears unlikely in a complex system like the brain, considering the inherent nonstationarityof brain processes [35] and the inhomogeneity of neuronal elements [36]. Moreover, a global organizationof avalanches, probed by studying the probability distribution of avalanche sizes and durations, does notprovide insight into the spatiotemporal cascading dynamics itself, which is of neuroscientific importance.

Here, we aim to address several of these issues by asking how previously observed scale-invariant, near-critical dynamics of avalanches in the ‘resting’ brain (i.e., no controlled task) is related to state changes duringstimulus-driven cognitive processing. We examined avalanches of neuronal activity from multi-channel scalpEEG, while participants underwent three sequential experimental conditions (Figure 1A). The conditionssystematically varied in cognitive complexity, ranging from (i) resting state (eyes open), (ii) passive viewing ofemotionally charged images, and (iii) active viewing of negatively charged images before rating the emotionalintensity. Emotional responses are ubiquitous in our everyday lives and have been shown to affect brain ac-tivity by predominantly engaging neural activity in frontal and parietal regions of the brain at distinguishabletimescales [37, 38]. Our relatively simple experimental design allowed us to investigate avalanche propertiesas a function of cognitive complexity, and enabled us to consider aspects of the ‘criticality’ hypothesis as itrelates to behaviorally meaningful variability.

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2 Methods

2.1 Participants

36 healthy adults were recruited with average age 32.2±7. This study was carried out in accordance with theaccredited Institutional Review Board at US Army Research Laboratory and conducted in compliance withthe US Army Research Laboratory Human Research Protection Program (32 Code of Federal Regulations219 and Department of Defense Instruction 3216.01). All participants gave informed, written consent.

2.2 Experimental design

Participants performed three sequential experimental conditions (Figure 1A). The conditions systematicallyvaried in cognitive complexity, ranging from (i) resting state (eyes open) with no explicit task, (ii) passiveviewing of emotionally charged images with no explicit judgment, and (iii) active viewing of emotionallycharged images before rating the emotional intensity. For passive viewing, subjects viewed images withpositive, negative, and neutral valence. For the active viewing task, only negatively charged images wereshown. Participants used the numeric keypad on the keyboard to rate their emotional intensity in response toeach image, for a total of 60 images, on a scale ranging from 1 (low emotional intensity) to 9 (high emotionalintensity). Experimental timelines for these tasks are shown in Figure 1A and further details can be foundin reference [39].

2.3 EEG data acquisition and pre-processing

Continuous EEG recordings were captured via the Biosemi ActiveTwo EEG system (Amsterdam, Nether-lands) equipped with standard Ag/AgCl electrodes from 64 sites on the scalp. Reference electrodes wereplaced on the mastoids. VEOG and HEOG external electrodes were used around the eyes during passiveviewing and active viewing to ensure that our analysis was not affected by eye-blinks (see SupplementaryFigure S1). Raw EEG measurements were pre-processed using in-house software in MATLAB (Mathworks,Inc., Natick, MA, USA) and the EEGLAB toolbox [40]. The pre-processing pipeline consisted of four steps(the PREP approach, [41]): (1) resampling the raw EEG to 256 Hz; (2) line noise removal via a frequency-domain (multitaper) regression technique to remove 60 Hz and harmonics present in the signal; (3) a robustaverage reference with a Huber mean; and (4) artifact subspace reconstruction to remove residual artifact(the standard deviation cutoff parameter was set to 10).

2.4 Identification of avalanches in the EEG activity

In microscopic brain imaging data, avalanches are identified as spatiotemporal clusters of events which areseparated by windows of inactivity [5, 7, 10]. Here, using 3 minutes of recorded data for each participantand condition, we first identified events as positive and negative excursions beyond a chosen threshold of 3standard deviations for each EEG sensor (Figure 1B) [4, 8]. Next, to identify avalanches, we looked for acontinuous cascade of events across all sensors such that all the consecutive events are separated by a timespan not larger than the correlation window ∆t (Figure 1C). The correlation window was selected in anadaptive manner for each individual by calculating the average inter-event-interval for all the consecutiveevents that occurred across all the sensors [4, 7, 8]. The observed mean ∆t was 28 ± 4 ms. The size of anavalanche (S) was determined as the total number of events within the avalanche. Avalanches of the samesize can have different spatiotemporal spreads, as demonstrated by the orange cluster and the purple clusterin Figure 1C, (both have a size S = 11).

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2.5 Power-law fitting and quality of fit

To evaluate the global-scale (whole-brain) organization of avalanches, we used a maximum likelihood methodto fit a head and tail truncated power-law to the avalanche distributions as described previously [8,42]. Thefitting function used was P (S) = S−τ (

∑xmax

xminx−τ )−1. Here, τ is a fitting parameter and is the exponent

of the power-law. For fitting τ , values between 1 and 5 were tried with a step size of 0.01. Another fittingparameter is xmin which represented the lower bound of the fit. We restricted its value to be < 15. Finally,xmax here denotes the upper bound of the fit and its value was chosen as the maximum avalanche sizefor which the avalanche size distribution showed a significant fit to a power-law. To ensure the validityof the fitted power-law, we tested the quality of the fit by computing the quality factor q [8, 43, 44]. Forthis computation, we used an established approach [43] and constructed 1000 synthetic data sets which hadthe same number of observations as the fitted experimental data and were drawn from an ideal power-lawwith the same fitting parameters as the experimental data. We then calculated Kolmogorov-Smirnov (KS)statistics between synthetic data sets and their own power-law fit models. q is the fraction of these syntheticKS-statistics which were greater than the KS-statistics for the experimental data. A power-law fit wasdeemed significant with a conservative criterion of q ≥ 0.1 [8, 43].

(A)

≤ ∆tAvalanches(B) EEG sensor activity100 ms

Time

3SD

- 3SD

Passive viewing (PV)

Active viewing (AV)

Image1 Image2--

1.5 s 1.5 s

Image1 Image1Attend/reinterpret

1 s 4.5 s

. . .

1 s 2 s

Emotional rating (1-9)

2 s

. . .

--

View

(C)

Time

EEG

sen

sor

. . .

Figure 1: Research design. (A) EEG was recorded during three different conditions that systematicallyvaried in cognitive complexity. These conditions included a resting state and two task states which werepassive viewing (PV) of emotionally charged images with no explicit judgment and active viewing (AV) ofnegatively charged images before rating the emotional intensity on a scale from 1 (low) to 9 (high). Timeline of tasks was as shown here. (B)-(C) Avalanches were extracted from the EEG recordings of each task.An avalanche was identified as a cluster of events (activity beyond ±3 SD of the mean, black dots) acrossall sensors, such that the temporal gap between any two consecutive events was not more than the size ofthe correlation window ∆t. Size (S) of an avalanche was defined as the number of events in the avalanchecluster. As shown in C, observed avalanches varied in their spatiotemporal spread.

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2.6 Calculating branching parameter

We extracted another feature of avalanches termed the ‘branching parameter’ (σ) which denotes the averageratio of the number of events in the second and the first half of the observed avalanches [1, 5]. For each

participant and condition, σ = 1/N∑Ni=1 n

iT2/n

iT1. Here, i represents an avalanche, N is the total number of

avalanches in the given data segment, n represents the number of events, and T2 and T1 denote the secondand the first half of a given avalanche.

2.7 Comparing observed avalanche features between conditions

We used a paired t-test to assess if computed global-level avalanche features demonstrate significant groupdifferences due to the change in experimental condition. These features included fitted power-law exponentsand branching parameters.

2.8 Calculating normalized engagement

We analyzed localized features of avalanche dynamics by calculating the ‘normalized engagement’ (NE) ofeach EEG sensor in producing avalanches. We defined engagement as the average number of ‘events’ that agiven sensor contributes to observed avalanches. If Ns is the total number of avalanches under considerationand ni is the total number of events observed on a sensor i during these avalanches, the engagement of thesensor Ei = ni/Ns. We computed normalized engagement by normalizing each Ei by the maximum valueof Ei across sensors, and consequently, obtained values bounded between 0 and 1. For each subject andcondition, we calculated NEs during all the observed avalanches as well as during avalanches with specificranges of sizes namely short (1-10 events), moderate (11-100 events), and persistent (101-1000 events).

2.9 Identifying task-evoked changes in avalanche dynamics

We used NE to identify regions of interest (ROIs) which showed significant task-evoked changes in avalanchedynamics. ROIs were those EEG sensors for which the distributions of NE values were significantly differentbetween rest and active viewing, as per a paired t-test (uncorrected). To extract ROIs for the regressionmodel (see below) and figures presented here, we used a significance level (α) of 0.05. However, to test therobustness of our findings, different α values (between 0.02 and 0.07) were used.

2.10 Statistical analysis

In order to test a relationship between avalanche dynamics and emotional ratings reported during the activeviewing task, multiple regression analyses were conducted. The emotional rating (Y ) for each participant wascalculated as the average rating reported across all trials. For predictors in the regression models, we usedaverage NE values across the identified ROIs for different ranges of avalanche sizes i.e., for short avalanches(Rs), for moderate avalanches (Rm), and for persistent avalanches (Rp). Prior to multiple regression analysis,all the predictors were mean-centered and tested to be normally distributed using the Shapiro-Wilk’s test(p > 0.02). In order to test the independent and interactive effects among the predictors on emotionalratings, main effects, pairwise interactions, and the three-way interaction term were included in the modelas shown below.

Y = 1 +Rp +Rm +Rs +Rp ∗Rm +Rp ∗Rs +Rm ∗Rs +Rp ∗Rm ∗Rs. (1)

To probe the interaction effects for observed significant interactions, we conducted simple slope analysesto compare high (> 0.5 SD) and low (< −0.5 SD) values of the moderator in relation to the mean.

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(A)

Avalanche size (S)100 101 102 103

10-1

10-2

10-3

10-4

100

Prob

abili

ty

xmin xmax

PV AVRest PV AVRest

Expo

nent

(τ)

Rest-PV

Rest-AV

PV-AV

(B) (C) (D)

Chan

ge in

exp

onen

t

3

2.5

2

1.5

0.5

0-0.5

-1-1.5

1*

*

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1000

2000

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x max

*****

Figure 2: Probability distributions of avalanche sizes fit to power laws. (A) We tested if the probabilitydistribution of avalanche sizes for a given subject and condition fits a power-law such that P (S) ∼ S−τ . Inthe example here, the circles show the cumulative probability distribution of avalanche size for the restingstate condition of one participant. The dotted line shows the fitted power-law. Here, xmin and xmax denotethe lower and upper bound of the fit. (B) We observed distributed values of fitted power-law exponent(τ) for different participants across all conditions. We also observed a decreasing trend in exponent valueswith increasing cognitive complexity of task conditions. (C) Pairwise difference in exponent values betweenconditions showed distributed non-zero values, indicating within subject variability in exponents, and there-fore avalanche distributions, across task conditions. Difference of exponents is significantly more prominentbetween resting and task conditions as compared to the difference between PV and AV conditions. (D) Weobserved a significant decrease in xmax for the two task conditions as compared to the rest, indicating thatlarge size avalanches during task conditions significantly deviate from their resting state distributions. Here,* and ** denote a significant difference on paired t-test with p-value ≤0.01 and ≤0.001 respectively.

3 Results

3.1 Global-scale avalanche features vary between individuals and tasks

In our first analysis, we examined how the global, whole-brain functional activity, is potentially representedthrough EEG avalanche dynamics, and varies across our three experimental conditions. Previous findingshave shown that the probability distribution of avalanche sizes during resting state fits a power-law, suchthat P (S) ∼ S−τ , where τ is a positive valued exponent [3, 4, 7, 10]. We examined if the distributions ofavalanche sizes, derived from EEG, fit the power-law behavior both for resting state as well as the two taskconditions. As shown in Figure 2A, in our data (circles), avalanche sizes spanned a little over two ordersof magnitude; therefore, we fit the data to a truncated power-law (see Methods) [8, 42, 43, 45]. A fittedpower-law is shown by the dashed line. Here, xmin and xmax represent the lower and upper bounds of thefit, describing the minimum and maximum values of avalanche size that can be fitted through power-lawprobability dynamics. To test the goodness of fit [44], for each participant and each condition, we calculatedthe quality of the fit factor (q) as described by Clauset et al. [43] (see Methods). We used a conservativecriterion and deemed the fit significant if q ≥ 0.1 [8, 43].

We observed a distribution of the fitted power-law exponent τ across participants for all three conditions,as shown in Figure 2B (individual values for τ and q are shown in Supplementary Figure S2). While acrossparticipants and conditions we found the avalanche distributions to fit a power-law, the exponent significantlyvaried between individuals. As shown in Figure 2B, exponents for the resting task varied between the range∼ 1.5 to ∼ 3 across subjects. A similar variability was observed for the passive viewing and active viewingconditions. We also observed a slight decreasing trend in the exponent values for increasing task complexity,

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σRest σRest σPV

σ PV σ AV σ AV

(B) (C) (D)

r = 0.57 r = 0.53 r = 0.51p<0.001 p<0.001 p=0.001

0.8 1 1.2

1.2

1

0.80.8

1

1.2

PV AVRest

(A)

Bran

chin

g pa

ram

eter

(σ) 1.2

1

0.8

1.2

1

0.8

0.8 1 1.2 0.8 1 1.2

**

Figure 3: Estimated branching parameters. (A) The branching parameter (σ) varies across participantsand conditions and indicates an increasing trend with increasing cognitive complexity. Here, * denotes asignificant difference on paired t-test with p-value ≤0.01. (B)-(D) Despite the variability within and betweenparticipants, we observed a significant positive correlation in branching parameter between conditions. Here,r denotes the Pearson’s correlation coefficient and p denotes the associated p-value.

with a significant difference between rest and passive viewing (t(34) = 2.84, p = 0.008).In Figure 2C, we plot the pairwise difference in exponents within an individual for each pairing of the

experimental conditions. Notably, all of the conditions show non-zero differences. This variability in theexponent suggests that the global scale-invariant organization may shift based on the cognitive complexityof the task. An interesting trend was a decrease in the change in exponents as the task complexity increased– i.e., we observed significantly higher differences between rest and task conditions (Rest-PV, Rest-AV) thanbetween the two task conditions (PV-AV) (t(34) = 2.62, p = 0.01; t(34) = 2.84, p = 0.008).

In addition to the variability observed in the exponent values of the power-law fits, we also observed thatxmax, which represents the upper bound of the fit, decreases from rest to task conditions, seen in Figure2D (rest to PV t(34) = 3.63, p < 0.001 and rest to AV t(34) = 3.75, p < 0.001; also see SupplementaryFigure S3). Collectively, these results indicate that EEG-derived avalanches that are spatially and temporallydistributed, demonstrate significant power-law dynamics for both rest and our two task conditions, thoughthe form of the power laws varies significantly across both individuals and conditions.

3.2 Avalanche dynamics vary between individuals and task conditions, but ina correlated manner

We computed the branching parameter (σ) to further assess EEG-derived avalanche dynamics and investigatewhether the system was in a state of criticality. Branching parameter values demonstrated similar variabilityas the power-law exponents, both across participants and conditions. As shown in Figure 3A, we observedthat the branching parameter show significant increase from the rest to passive viewing (t(35) = −2.76, p =0.009) and to active viewing (t(35) = −2.99, p = 0.005). The medians of these values in each experimentalcondition are close to the theoretical prediction of 1, suggesting the system is close to a critical state [46].

While we observe variability in the values of the branching parameter across individuals, there are clearlysignificant correlations within an individual between parameters across different experimental conditions.Figures 3B-D compare within-individual branching parameter values between conditions. For all pairingsof conditions, we found a significant positive correlation between the branching parameter values (rest andpassive viewing r = 0.57, p < 0.001; rest and active viewing r = 0.53, p < 0.001; passive viewing and activeviewing r = 0.51, p = 0.001).

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Results thus far indicate a consistent interpretation, namely EEG activity shows evidence of the brainbeing at a near-critical state, as quantified via the observed power-law distributions and branching parametervalues for the avalanche activity. However, neither of these measures suggests a universality class, and bothreveal the sensitivity of these measures to individual differences between participants.

Rest Passive viewing

Active viewing

<Normalized engagement>

(B)

(A)

Aval

anch

e si

ze

Short(1-10)

Moderate(11-100)

Persistent(101-1000)

0.70.60.50.40.3

Figure 4: Localized avalanche features change with task conditions. We calculated normalized engagement(NE) as the normalized average frequency of each sensor for contributing events to observed avalanches. (A)Subject averages of NE (denoted by <>) for each sensor across different conditions show a systematic shiftfrom parietal to frontal activity as cognitive complexity increases (i.e. from resting state to active viewing).(B) NE shifts are specific to avalanche size. Subject averages for short avalanches (1-10 events) show similartopologies for all three conditions. However, one sees a shift in the topology between conditions for moderate(11-100 events) and persistent (101-1000 events) avalanches.

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3.3 Changes in task complexity result in localized changes in avalanche dynam-ics

We next examined whether avalanche dynamics, defined locally, relate to the task complexity that variesacross experimental conditions. Specifically, we characterized the EEG sensors located at spatially distinctpositions on the scalp using a metric we term ‘normalized engagement’ (NE, see Methods). Larger NE valuesindicate more frequent high amplitude activity on the sensor.

We observed differences in the spatial distribution of large NE values across the three experimentalconditions. Figure 4A, shows the group average of these distributions for three task conditions. We findthat larger NE values systematically shifted from posterior areas of the scalp to frontal areas as the taskcomplexity increased from resting state to passive and then active viewing.

Next we considered these spatial distributions as a function of avalanche size. We binned avalanchesinto three scales based on their sizes (short, moderate and persistent) and recomputed the NE measuresas a function of task complexity. Figure 4B displays these results and shows that different avalanche sizesare associated with a different spatial distribution of normalized engagement across the scalp. For shortavalanche sizes, there is no substantial difference between the spatial distributions across task conditions.However, for persistent avalanches, there is a clear shift in the spatial distribution of large NE values whencomparing the rest and task conditions. Importantly, the shift shows that as the task becomes more complex(active viewing) there is a substantial engagement in both frontal and parietal sensors. Additional analyses,investigating the frequency-specificity of these results, showed that the effects were sustained in EEG activitybelow 20 Hz, indicating they were unlikely linked to muscle artifact and EMG contamination [47,48]. Moreinterestingly, for persistent avalanches, the spatial distribution disassociated across frequencies, with occipitalpatterns expressed in the alpha band activity (8-12 Hz) while the frontal patterns were largely in the thetaband activity (4-7Hz) (see supplementary Figures S4).

Resting state EEG is characterized by strong alpha oscillations in occipito-parietal cortex [49,50]. Addi-tionally, it has been shown that visual stimuli and emotional judgments typically result in high theta activityin frontal brain regions [51, 52]. Importantly, persistent avalanche dynamics provide links between frontaland occipito-parietal activity in a way that is consistent with other findings showing that the coordinationof these networks is important for executive function and behavior [37,38].

3.4 Variability of task evoked localized responses in avalanche activity is pre-dictive of individual behavioral response

We used multiple regression analyses to investigate whether the localized variability in avalanche dynamicscorrelates with subject level differences in behavior, measured through self-reported emotional ratings duringactive viewing condition. EEG sensors which showed significant task-evoked change in NE values (using apaired t-test with α = 0.05, see Methods) are highlighted in Figure 5A. We found 27 sensors for persistentavalanches, 23 for moderately sized avalanches (see Figure 5A), and only five sensors (two frontal and threeparietal) for short avalanches (not shown in Figure 5A). We call these sensors ‘regions of interest’ (ROIs).

We used a linear regression model (Equation 1) to correlate emotional ratings (Y ) with average NEsacross ROIs for each scale of the avalanche dynamics (Rp for persistent, Rm for moderate, and Rs forshort), and the model findings are detailed in Table 1. We found three significant relationships: (i) a maineffect showing that the average NE of the ROIs for persistent avalanche activity (Rp) is positively relatedto emotional rating (β = 4.07 and p = 0.02); (ii) another main effect showing that the average NE ofthe ROIs for moderate avalanche activity (Rm) is negatively related to emotional rating (β = −3.68 andp = 0.05); and (iii) an interaction effect between ROIs engagement for persistent and moderate avalancheactivity (β = −33.54 and p = 0.04).

As shown in Figures 5B-C, to probe the observed significant interaction effect, we conducted an analysis

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Linear regression model: Y ~ 1 + Rp + Rm + Rs + Rp*Rm + Rp*Rs + Rm*Rs + Rp*Rm*Rs

Estimated coefficients:

Estimate (β) Standard error t-Stat. p-value

InterceptRp

Rm

Rs

Rp:Rm

Rp:Rs

Rm:Rs

Rp:Rm:Rs

3.32 0.21 15.88 1.56e-15

4.07 1.60 2.55 0.02-3.68 1.84 -2.00 0.05

-2.14 1.91 -1.12 0.27

-33.54 15.54 -2.16 0.04

22.09 15.80 1.40 0.17

30.54 17.19 1.78 0.09

38.20 155.09 0.25 0.81

R-Squared: 0.49F-Statistics vs. constant model: 3.91, p-value: 0.004

Table 1: Results from the regression model described by Equation 1 to assess the relationship between local-ized avalanche features and emotional ratings reported by the participants during active viewing task. Here,Y represents the mean emotional rating for each individual, Rp, Rm, and Rs represent average normalizedengagement (NE) values of regions of interest for persistent, moderate, and short avalanches respectively. Inthe comprehensive model, we included main effects, pairwise interactions, and three-way interaction terms.Results for each model term are presented in different rows of the table and significant effects are highlightedin the bold text. An interpretation of model findings is discussed in the text and Figure 5.

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-0.2 -0.1 0 0.11

6

5

4

3

2

10

5

0

β = 10.64*(B) (C)(A)Regions of interest

For persistent

avalanches (ROIp)

For moderate

avalanches (ROIm)

β w

eigh

ts fo

rEm

otio

nal r

atin

g an

dAv

. NE

of R

OI p

(Rp)

Emot

iona

l rat

ing

Av. NE of ROIm (Rm)

Low High

p = 0.002

Rp

Figure 5: Avalanche dynamics correlate with subject specific emotional ratings in active viewing task. (A)Set of regions (EEG sensors marked in red) which showed significantly different NE values between restand active viewing for persistent (left) and moderate (right) avalanches. Using a regression model, wefound that average NEs across these regions of interest (Rp for persistent avalanches and Rm for moderateavalanches), were predictive of self reported emotional ratings by participants. In our model, in addition tothe main effects of Rp and Rm on emotional rating, we also found a significant interaction effect betweenthese quantities. Details of the model are presented in Equation 1 and Table 1. In (B)-(C) we probe thisinteraction effect by assessing the relationship between emotional rating and Rp (predictor) through linearregression for low and high values of the moderator (Rm). We observed a positive relationship betweenRp and emotional rating for low values of Rm (β = 10.64, p = 0.002, R2 = 0.59), whereas no significantrelationship was found between Rp and emotional rating for high values of Rm (β = 1.74, p = 0.47). Here,error bars denote ±1 standard error and dotted lines denote 95% confidence interval.

of these slopes (βs), comparing high and low engagement (assessed by NE) of the ROIs in the avalancheactivity in relation to mean. We observed that engagement of the ROIs in persistent avalanche activityshows a positive relationship with emotional rating when the engagement in moderate avalanche activity islow (β = 10.64 and p = 0.002, R2 = 0.59). Whereas, this relationship disappears when the engagement inmoderate avalanche activity is high (β = 1.74, p = 0.47). This suggests that localized avalanche dynamicscapture spatiotemporial coordinated activity that are predictive of subject experience and behavior.

4 Discussion

We investigated avalanche features in the EEG time series as a way to characterize brain states acrossindividuals and tasks of varying complexity. For the global organization of avalanches, we observed power-law behavior and scale-invariance in the resting state condition as well as in the passive and active viewingconditions. These findings support previous studies that have investigated resting state brain activity [3,4,7],as well as studies where there is a presence of a stimulus, both for humans [5, 9] and non-human primates[28,53]. The results also suggest that the large-scale neural dynamics within the brain maintain a critical-likestate [18, 22, 23] for different conditions and that this state may be important for optimizing informationprocessing capabilities within the brain [24–26,29].

Though the ‘critical-like’ state was prevalent across conditions and subjects, the corresponding power-law exponents, (τ), displayed substantial variability across individuals and between conditions within anindividual. The estimated values in macroscopic experimental data deviate from the exponent value ofτ = 1.5 reported in multiple organisms as well as in in-vitro experiments [1,7,8,28,54]. The estimated value

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of τ can vary as a function of study parameters, e.g., the distance between recording sensors, the chosenthreshold for identifying large-amplitude events, and the size of the correlation window ∆t [7, 16, 19]. Sincethe first two parameters were fixed during the study, they did not contribute to the observed variability inexponent. The third parameter was adaptively defined for each individual and condition as the mean inter-event-interval [7,8] which allowed a uniform interpretation of estimated avalanche features across individualsand conditions. Observed variability in the exponent can therefore be attributed to individual differences inavalanche dynamics.

The absence of a single-valued exponent to describe the avalanche dynamics likely indicates that the scale-invariant organization we see in the EEG is not fine tuned to a single “universal” state, but instead, variesbased on the underlying functional dynamics [34]. Therefore, our results suggest that models for criticalityin neural systems may need to account for robust individual and task related differences [36, 55, 56]. Forexample, Moretti et al. suggested that the inherent hierarchical-modular architecture and heterogeneityof cortical networks can replace a singular critical point by an extended critical-like region such that theexponents may vary to capture unique functional connectivity of different neural systems and cognitivestates [33, 34]. Despite the variability we see, the observed exponent values do distribute within a similarrange across the three experimental conditions, which further suggests a flexible, yet functionally orderedorganization within the brain, characteristic of a complex system.

Surprisingly, concurrent with the maintained global scale-invariance, we observed localized features ofavalanches to show not only a task-dependent regional patterning, but also the scale-specific features. Wefound that the avalanches with relatively large sizes (moderate and persistent) carried meaningful informationabout the task-dependent changes within the brain. Using a metric that quantifies the likelihood of differentbrain regions to engage in avalanches, we identified a set of ROIs which were predictive of individual behavior,i.e. emotional rating, through a regression model that also included interaction terms relating the differentscales of avalanche sizes. We found these ROIs to be located within the frontal as well as occipito-parietalregions of the brain. Previous research has also highlighted the activation of these areas during the processingof emotional stimuli [37, 38,57].

We used a data-driven approach to identify these ROIs and required that they show a significant change oftheir engagement in producing avalanches, following the change in experimental condition from rest to activeviewing. To assess a significant change in engagement, we used a paired t-test with α = 0.05. Importantly,the findings of our regression model were qualitatively robust for a range of α (0.02 to 0.07). We observedhigher average engagement of ROIs in producing persistent avalanches to be indicative of higher emotionalrating.

Combining our findings across the global and regional scales of the EEG dynamics, we propose thatthe macro-scale dynamics of the neural activity operates close to criticality whilst simultaneously rapidlychanging to match behavioral goals [58]. Neurophysiological mechanisms for the brain to adaptively maintainits macroscopic organization near criticality are not well understood. However, it appears likely that suchan adaptive mechanism is characteristic of healthy human brains [59]. Indeed, it has been previously shownthat the features of criticality are more consistently disrupted in the interictal activity of epilepsy patients[6], where, a localized or global inability of the brain to regain its balance may cause uncontrolled activity orseizures. A significant departure from a critical-like state has also been reported during sustained wakefulnessover several hours, which reverses back upon the recovery of sleep [10], a necessity for the healthy brainfunction [60]. Scale-invariant avalanche dynamics have also been found important during developmentalstages of the brain [61] and during recovery after brain insult [62].

We believe that the analysis of macroscopic avalanches can provide useful insight into the temporalevolution of brain activity and might even provide biomarkers when the activity becomes abnormal. However,the study of avalanches within the human brain also presents a number of challenges. Avalanches estimatedin EEG recordings allow only a limited neurophysiological interpretation since the EEG represents largepopulation neural activity measured at the scalp, and suffers from volume conduction distortion and artifacts

12

due to the high electrical conductivity of the scalp. Often, source localization is used to identify uniquesources in the brain given the measured scalp EEG activity and to rid the data of the artifacts due tovolume conduction. However, effective and accurate localization of signal sources is a field of research initself and the analysis of avalanches in such data would require careful consideration and further work.

4.1 Conclusions

We observed that similar to the resting state activity, EEG-derived avalanches in task-evoked, stimulus-driven activity demonstrate power-law probability distributions and scale-invariance, characteristic to globalorganization in a complex system near criticality. Global avalanche dynamics however varied between in-dividuals, as represented by the exponents of the fitted power-laws. From the analysis of the branchingparameters, this global dynamics within an individual seemed to be correlated across experimental condi-tions. Analysis of localized (regional) avalanche dynamics showed correlation with behavioral measure, andthis correlation was driven by a spatiotemoporal interaction of the avalanches. In general, we believe theanalysis of macroscopic avalanches in the EEG provides a straightforward yet effective way to measure thestate of the brain, both in health and disease.

5 Data availability

Data is accessible upon request as far as allowed by the security policy and guidelines established with theethics committee of the US Army Research Laboratory Human Research Protection Program. Requestsshould be addressed to K. Bansal.

6 Author contributions

K.B. conceived the idea of this research, implemented the analysis, prepared figures, and wrote the initialdraft. J.M.V. secured the funding and contributed in performing the EEG experiments. J.O.G. helped withthe EEG data pre-processing and data visualization. N.L. helped with the statistical modeling. P.S. andS.F.M. provided supervision. All authors contributed in reviewing and editing the manuscript.

7 Acknowledgment

This research was sponsored by the US Army Research Laboratory and was accomplished under CooperativeAgreement Number W911NF-16-2-0158. The views and conclusions contained in this document are those ofthe authors and should not be interpreted as representing the official policies, either expressed or implied, ofthe Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduceand distribute reprints for Government purposes notwithstanding any copyright notation herein.

References

[1] J. M. Beggs, D. Plenz, Neuronal avalanches in neocortical circuits., The Journal of neuroscience 23 (35)(2003) 11167–77. doi:10.1523/JNEUROSCI.23-35-11167.2003.

[2] M. Fukunaga, S. G. Horovitz, P. van Gelderen, J. A. de Zwart, J. M. Jansma, V. N. Ikonomidou, R. Chu,R. H. Deckers, D. A. Leopold, J. H. Duyn, Large-amplitude, spatially correlated fluctuations in BOLD

13

fMRI signals during extended rest and early sleep stages, Magnetic Resonance Imaging 24 (8) (2006)979–992. doi:10.1016/j.mri.2006.04.018.

[3] E. Tagliazucchi, P. Balenzuela, D. Fraiman, D. R. Chialvo, Criticality in large-scale brain fmri dynamicsunveiled by a novel point process analysis, Frontiers in Physiology 3 (February) (2012) 1–12. doi:

10.3389/fphys.2012.00015.

[4] O. Shriki, J. Alstott, F. Carver, T. Holroyd, R. N. A. Henson, M. L. Smith, R. Coppola, E. Bullmore,D. Plenz, Neuronal Avalanches in the Resting MEG of the Human Brain, Journal of Neuroscience33 (16) (2013) 7079–7090. doi:10.1523/JNEUROSCI.4286-12.2013.

[5] O. Arviv, A. Goldstein, O. Shriki, Near-Critical Dynamics in Stimulus-Evoked Activity of the HumanBrain and Its Relation to Spontaneous Resting-State Activity, Journal of Neuroscience 35 (41) (2015)13927–13942. doi:10.1523/JNEUROSCI.0477-15.2015.

[6] O. Arviv, M. Medvedovsky, L. Sheintuch, A. Goldstein, O. Shriki, Deviations from Critical Dynamicsin Interictal Epileptiform Activity, Journal of Neuroscience 36 (48) (2016) 12276–12292. doi:10.1523/JNEUROSCI.0809-16.2016.

[7] V. Priesemann, M. Valderrama, M. Wibral, M. Le Van Quyen, Neuronal Avalanches Differ from Wake-fulness to Deep Sleep Evidence from Intracranial Depth Recordings in Humans, PLoS ComputationalBiology 9 (3) (2013) e1002985. doi:10.1371/journal.pcbi.1002985.

[8] W. L. Shew, W. P. Clawson, J. Pobst, Y. Karimipanah, N. C. Wright, R. Wessel, Adaptation to sensoryinput tunes visual cortex to criticality, Nature Physics 11 (8) (2015) 659–663. doi:10.1038/nphys3370.

[9] J. M. Palva, A. Zhigalov, J. Hirvonen, O. Korhonen, K. Linkenkaer-Hansen, S. Palva, Neuronallong-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws,Proceedings of the National Academy of Sciences 110 (9) (2013) 3585–3590. doi:10.1073/pnas.

1216855110.

[10] C. Meisel, E. Olbrich, O. Shriki, P. Achermann, Fading Signatures of Critical Brain Dynamics duringSustained Wakefulness in Humans, Journal of Neuroscience 33 (44) (2013) 17363–17372. doi:10.1523/JNEUROSCI.1516-13.2013.

[11] F. Lombardi, H. J. Herrmann, C. Perrone-Capano, D. Plenz, L. De Arcangelis, Balance between excita-tion and inhibition controls the temporal organization of neuronal avalanches, Physical Review Letters108 (22) (2012) 228703. doi:10.1103/PhysRevLett.108.228703.

[12] S. S. Poil, R. Hardstone, H. D. Mansvelder, K. Linkenkaer-Hansen, Critical-state dynamics of avalanchesand oscillations jointly emerge from balanced excitation/inhibition in neuronal networks, Journal ofNeuroscience 32 (29) (2012) 9817–9823. doi:10.1523/JNEUROSCI.5990-11.2012.

[13] A. Mazzoni, F. D. Broccard, E. Garcia-Perez, P. Bonifazi, M. E. Ruaro, V. Torre, On the dynamics ofthe spontaneous activity in neuronal networks, PLoS ONE 2 (5) (2007) e439. doi:10.1371/journal.

pone.0000439.

[14] V. Pasquale, P. Massobrio, L. L. Bologna, M. Chiappalone, S. Martinoia, Self-organization and neuronalavalanches in networks of dissociated cortical neurons, Neuroscience 153 (4) (2008) 1354–1369. doi:

10.1016/j.neuroscience.2008.03.050.

14

[15] N. Friedman, S. Ito, B. A. Brinkman, M. Shimono, R. E. Deville, K. A. Dahmen, J. M. Beggs, T. C.Butler, Universal critical dynamics in high resolution neuronal avalanche data, Physical Review Letters108 (20) (2012) 208102. doi:10.1103/PhysRevLett.108.208102.

[16] T. Petermann, T. C. Thiagarajana, M. A. Lebedev, M. A. L. Nicolelis, D. R. Chialvo, D. Plenz,Spontaneous cortical activity in awake monkeys composed of neuronal avalanches, Proc Natl Acad Sci106 (37) (2009) 15921–15926. doi:10.1073/pnas.0904089106.

[17] E. D. Gireesh, D. Plenz, Neuronal avalanches organize as nested theta- and beta/gamma-oscillationsduring development of cortical layer 2/3, Proceedings of the National Academy of Sciences of the UnitedStates of America 105 (21) (2008) 7576–7581. doi:10.1073/pnas.0800537105.

[18] A. Ponce-Alvarez, A. Jouary, M. Privat, G. Deco, G. Sumbre, Whole-Brain Neuronal Activity DisplaysCrackling Noise Dynamics, Neuron 100 (6) (2018) 1446–1459.e6. doi:10.1016/j.neuron.2018.10.045.

[19] S. R. Miller, S. Yu, D. Plenz, The scale-invariant, temporal profile of neuronal avalanches in relation tocortical γoscillations, Scientific Reports 9 (1) (2019) 1–14. doi:10.1038/s41598-019-52326-y.

[20] J. P. Sethna, K. A. Dahmen, C. R. Myers, Crackling noise, Nature 410 (6825) (2001) 242–250. doi:

10.1038/35065675.

[21] J. M. Beggs, N. Timme, Being Critical of Criticality in the Brain, Frontiers in Physiology 3 (2012) 163.doi:10.3389/fphys.2012.00163.

[22] K. Linkenkaer-Hansen, V. V. Nikouline, J. M. Palva, R. J. Ilmoniemi, Long - Range Temporal Correla-tions and Scaling Behavior in Human Brain Oscillations, Journal of Neuroscience 21 (2001) 1370–1377.doi:10.1523/JNEUROSCI.21-04-01370.2001.

[23] L. Cocchi, L. L. Gollo, A. Zalesky, M. Breakspear, Criticality in the brain: A synthesis of neurobiology,models and cognition, Progress in Neurobiology 158 (2017) 132–152. doi:10.1016/j.pneurobio.2017.07.002.

[24] C. Haldeman, J. M. Beggs, Critical branching captures activity in living neural networks and maxi-mizes the number of metastable states, Physical Review Letters 94 (5) (2005) 058101. doi:10.1103/

PhysRevLett.94.058101.

[25] J. M. Beggs, The criticality hypothesis: How local cortical networks might optimize information pro-cessing, Philosophical Transactions of the Royal Society A: Mathematical, Physical and EngineeringSciences 366 (1864) (2008) 329–343. doi:10.1098/rsta.2007.2092.

[26] W. L. Shew, H. Yang, T. Petermann, R. Roy, D. Plenz, Neuronal avalanches imply maximum dynamicrange in cortical networks at criticality, Journal of Neuroscience 29 (49) (2009) 15595–15600. doi:

10.1523/JNEUROSCI.3864-09.2009.

[27] W. L. Shew, D. Plenz, The Functional Benefits of Criticality in the Cortex, The Neuroscientist 19 (1)(2013) 88–100. doi:10.1177/1073858412445487.

[28] S. Yu, T. L. Ribeiro, C. Meisel, S. Chou, A. Mitz, R. Saunders, D. Plenz, Maintained avalanchedynamics during task-induced changes of neuronal activity in nonhuman primates, eLife 6 (2017) e27119.doi:10.7554/eLife.27119.001.

[29] D. Papo, Functional significance of complex fluctuations in brain activity: From resting state to cognitiveneuroscience, Frontiers in Systems Neuroscience 8 (JUNE) (2014) 112. doi:10.3389/fnsys.2014.

00112.

15

[30] A. J. Fontenele, N. A. De Vasconcelos, T. Feliciano, L. A. Aguiar, C. Soares-Cunha, B. Coimbra, L. DallaPorta, S. Ribeiro, A. J. Rodrigues, N. Sousa, P. V. Carelli, M. Copelli, Criticality between CorticalStates, Physical Review Letters 122 (20) (2019) 454934. doi:10.1103/PhysRevLett.122.208101.

[31] J. M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford University Press, Oxford, 1992.

[32] G. Hahn, A. Ponce-Alvarez, C. Monier, G. Benvenuti, A. Kumar, F. Chavane, G. Deco, Y. Fregnac,Spontaneous cortical activity is transiently poised close to criticality, PLOS Computational Biology13 (5) (2017) e1005543. doi:10.1371/journal.pcbi.1005543.

[33] N. Dehghani, N. G. Hatsopoulos, Z. D. Haga, R. A. Parker, B. Greger, E. Halgren, S. S. Cash,A. Destexhe, Avalanche Analysis from Multielectrode Ensemble Recordings in Cat, Monkey, andHuman Cerebral Cortex during Wakefulness and Sleep, Frontiers in Physiology 3 (2012) 302. doi:

10.3389/fphys.2012.00302.

[34] M. Yaghoubi, T. de Graaf, J. G. Orlandi, F. Girotto, M. A. Colicos, J. Davidsen, Neuronal avalanchedynamics indicates different universality classes in neuronal cultures, Scientific Reports 8 (1) (2018)3417. doi:10.1038/s41598-018-21730-1.

[35] A. Y. Kaplan, A. A. Fingelkurts, A. A. Fingelkurts, S. V. Borisov, B. S. Darkhovsky, Nonstationarynature of the brain activity as revealed by EEG/ MEG: Methodological, practical and conceptualchallenges, Signal Processing 85 (2005) 2190–2212. doi:10.1016/j.sigpro.2005.07.010.

[36] P. Moretti, M. A. Munoz, Griffiths phases and the stretching of criticality in brain networks, NatureCommunications 4 (1) (2013) 2521. doi:10.1038/ncomms3521.

[37] J. T. Buhle, J. A. Silvers, T. D. Wager, R. Lopez, C. Onyemekwu, H. Kober, J. Weber, K. N. Ochsner,Cognitive Reappraisal of Emotion: A Meta-Analysis of Human Neuroimaging Studies, Cerebral Cortex24 (11) (2014) 2981–2990. doi:10.1093/cercor/bht154.

[38] N. Kohn, S. Eickhoff, M. Scheller, A. Laird, P. Fox, U. Habel, Neural network of cognitive emotionregulation an ale meta-analysis and macm analysis, NeuroImage 87 (2014) 345 – 355. doi:10.1016/

j.neuroimage.2013.11.001.

[39] H. Roy, N. Wasylyshyn, D. P. Spangler, K. R. Gamble, D. Patton, J. R. Brooks, J. O. Garcia, J. M. Vet-tel, Linking emotional reactivity between laboratory tasks and immersive environments using behaviorand physiology, Frontiers in Human Neuroscience 13 (2019) 54. doi:10.3389/fnhum.2019.00054.

[40] A. Delorme, S. Makeig, Eeglab: an open source toolbox for analysis of single-trial eeg dynamics includingindependent component analysis, Journal of Neuroscience Methods 134 (1) (2004) 9 – 21. doi:10.1016/j.jneumeth.2003.10.009.

[41] N. Bigdely-Shamlo, T. Mullen, C. Kothe, K. M. Su, K. A. Robbins, The PREP pipeline: Standardizedpreprocessing for large-scale EEG analysis, Frontiers in Neuroinformatics 9 (JUNE) (2015) 1–19. doi:10.3389/fninf.2015.00016.

[42] A. Klaus, S. Yu, D. Plenz, Statistical Analyses Support Power Law Distributions Found in NeuronalAvalanches, PLoS ONE 6 (5) (2011) e19779. doi:10.1371/journal.pone.0019779.

[43] A. Clauset, C. R. Shalizi, M. E. J. Newman, POWER-LAW DISTRIBUTIONS IN EMPIRICAL DATA,SIAM Rev. 51 (4) (2009) 661–703. doi:10.1137/070710111.

16

[44] J. Touboul, A. Destexhe, Can power-law scaling and neuronal avalanches arise from stochastic dynam-ics?, PLoS ONE 5 (2) (2010) e8982. doi:10.1371/journal.pone.0008982.

[45] S. Yu, A. Klaus, H. Yang, D. Plenz, Scale-Invariant Neuronal Avalanche Dynamics and the Cut-Off inSize Distributions, PLoS ONE 9 (6) (2014) e99761. doi:10.1371/journal.pone.0099761.

[46] V. Priesemann, M. Wibral, M. Valderrama, R. Propper, M. Le Van Quyen, T. Geisel, J. Triesch,D. Nikolic, M. H. Munk, Spike avalanches in vivo suggest a driven, slightly subcritical brain state,Frontiers in Systems Neuroscience 8 (JUNE) (2014) 108. doi:10.3389/fnsys.2014.00108.

[47] S. D. Muthukumaraswamy, High-frequency brain activity and muscle artifacts in MEG/EEG: a reviewand recommendations, Frontiers in Human Neuroscience 7 (2013) 138. doi:10.3389/fnhum.2013.

00138.

[48] I. Goncharova, D. McFarland, T. Vaughan, J. Wolpaw, EMG contamination of EEG: spectral andtopographical characteristics, Clinical Neurophysiology 114 (9) (2003) 1580–1593. doi:10.1016/

s1388-2457(03)00093-2.

[49] R. I. Goldman, J. M. Stern, J. J. Engel, M. S. Cohen, Simultaneous EEG and fMRI of the alpha rhythm,NeuroReport 13 (18) (2002) 2487–2492. doi:10.1097/01.wnr.0000047685.08940.d0.

[50] Basar2012, A review of alpha activity in integrative brain function: Fundamental physiology, sensorycoding, cognition and pathology, International Journal of Psychophysiology 86 (1) (2012) 1–24. doi:

10.1016/j.ijpsycho.2012.07.002.

[51] J. F. Cavanagh, M. J. Frank, Frontal theta as a mechanism for cognitive control, Trends in CognitiveSciences 18 (8) (2014) 414–421. doi:10.1016/j.tics.2014.04.012.

[52] M. Ertl, M. Hildebrandt, K. Ourina, G. Leicht, C. Mulert, Emotion regulation by cognitive reappraisal- The role of frontal theta oscillations, NeuroImage 81 (2013) 412–421. doi:10.1016/j.neuroimage.

2013.05.044.

[53] N. Tomen, D. Rotermund, U. Ernst, Marginally subcritical dynamics explain enhanced stimulus dis-criminability under attention, Frontiers in Systems Neuroscience 8 (AUG) (2014) 151. doi:10.3389/

fnsys.2014.00151.

[54] G. Hahn, T. Petermann, M. N. Havenith, S. Yu, W. Singer, D. Plenz, D. Nikolic, Neuronal avalanchesin spontaneous activity in vivo, Journal of Neurophysiology 104 (6) (2010) 3312–3322. doi:10.1152/

jn.00953.2009.

[55] R. V. Williams-Garcıa, M. Moore, J. M. Beggs, G. Ortiz, Quasicritical brain dynamics on a nonequi-librium Widom line, Physical Review E 90 (6) (2014) 1–8. doi:10.1103/PhysRevE.90.062714.

[56] V. Priesemann, O. Shriki, Can a time varying external drive give rise to apparent criticality in neuralsystems?, PLOS Computational Biology 14 (5) (2018) e1006081. doi:10.1371/journal.pcbi.1006081.

[57] T. Baumgartner, M. Esslen, L. Jancke, From emotion perception to emotion experience: Emotionsevoked by pictures and classical music, International Journal of Psychophysiology 60 (1) (2006) 34–43.doi:10.1016/j.ijpsycho.2005.04.007.

[58] Y. Karimipanah, Z. Ma, J.-e. K. Miller, R. Yuste, R. Wessel, Neocortical activity is stimulus- andscale-invariant, PLOS ONE 12 (5) (2017) e0177396. doi:10.1371/journal.pone.0177396.

17

[59] P. Massobrio, L. de Arcangelis, V. Pasquale, H. J. Jensen, D. Plenz, Criticality as a signature of healthyneural systems, Frontiers in Systems Neuroscience 9 (2015) 22. doi:10.3389/fnsys.2015.00022.

[60] S. Banks, D. F. Dinges, Behavioral and physiological consequences of sleep restriction, Journal of ClinicalSleep Medicine 3 (5) (2007) 519–528. doi:10.5664/jcsm.26918.

[61] K. K. Iyer, J. A. Roberts, L. Hellstrom-Westas, S. Wikstrom, I. Hansen Pupp, D. Ley, S. Vanhatalo,M. Breakspear, Cortical burst dynamics predict clinical outcome early in extremely preterm infants,Brain 138 (8) (2015) 2206–2218. doi:10.1093/brain/awv129.

[62] J. A. Roberts, K. K. Iyer, S. Finnigan, S. Vanhatalo, M. Breakspear, Scale-free bursting in humancortex following hypoxia at birth., The Journal of neuroscience : the official journal of the Society forNeuroscience 34 (19) (2014) 6557–72. doi:10.1523/JNEUROSCI.4701-13.2014.

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Supplementary information

EEG

Sen

sor

Ext

...

Time (s)4 8 12 16 20 24

FP1

AF7

AF3

Blinks Blinks

Event

102

10-2

10010-4

100

Prob

abili

ty

Avalanche size (S)

Overlapping events with blinks:

RemovedNot removed

(B)

(A)

Figure S1: During passive viewing and active viewing conditions, we monitored eye-activity from an externalchannel, placed close to the eyelid, which allowed us to specifically track eye-blinks and their impact on eventsand avalanches. (A) In addition to the EEG data preprocessing steps, in order to ensure there are no eye-blinks related artifacts in event distributions, we removed all the events in the frontal channels that showedan overlap with an eye-blink. (B) In general, global probability distribution of avalanche sizes remainedlargely unchanged before and after the removal of events which overlapped with eye-blinks.

19

Expo

nent

(τ)

Fit q

ualit

y (q

)

0.5

1

00

1

2

3Rest PV AV

s1s2

s3

s4

s5

s6

s7s8 s9 s10

s11s12 s13

s14 s15 s16 s17s18 s19

s20 s21

s22s23

s24

s25

s26

s27 s28s29

s30

s31s32

s33 s34s35 s36

Figure S2: We tested if avalanche size distributions fit to the power-law behavior for each participant andcondition. To assess the goodness of a power-law fit, we calculated quality of the fit factor (q). We deemedthe fit significant if q ≥ 0.1. Here, we show the fitted power-law exponent (τ) and fit quality factor obtainedfor different participants and conditions. A significant power-law fit was obtained for all the participantsexpect one (s26), whose data did not show a significant fit within the tested range of parameters under ourconservative significance criterion.

Prob

abili

ty

RestPVAV

100 101 102 103

100

10-1

10-2

10-3

10-4

102 103

Avalanche size (S)

10-5

Figure S3: Probability distributions of avalanche sizes calculated for avalanches observed across all the par-ticipants for three different conditions. Distributions show more pronounced differences between conditionsfor avalanches of relatively higher sizes.

20

Shor

t(1

-10)

Mod

erat

e(1

1-10

0)Pe

rsis

tent

(101

-100

0)

Rest Active viewing

0.70.60.50.40.3<Normalized engagement>

< 20 Hz

(A)Rest Active viewing

Alpha band (8-12 Hz)

(B)Rest Active viewing

Theta band (4-7 Hz)

(C)

Figure S4: Scale dependence of normalized engagement (NE) of EEG sensors in avalanches for filtered EEGdata. In order to understand the change of NE values with changing task conditions, we compared theseresults within a more traditional EEG analysis framework, and analyzed NEs for EEG activity extractedin particular frequency ranges that are shown to have distinct functional purposes. (A) First, in order toensure that the elevation in frontal NEs during task performance condition is not due to any muscle or EMGartifacts and represents neuronal responses, we filtered out the high frequency activity from EEG data thatcarries the largest impact of such artifacts [47,48]. We applied a 20 Hz lowpass filter (6th order Butterworth)to the EEG signal and then calculated NE values for the filtered data. We still observed similar frontal andoccipito-parietal changes of NE values between rest and active viewing task as discussed in the context ofFigure 4. (B)-(C) Posterior changes in persistent avalanche activity are dominantly represented in alphaband activity while frontal changes are dominantly represented in theta activity.

21