TABLE 5.

Summary of cognition-related criticality literature.

Study	Study population	Modality	Analysis	Main findings
Lai et al., 2010	30 male adult subjects with autism or Asperger’s syndrome, 33 age- and IQ-matched male adult controls	fMRI during resting-state	Hurst exponent	• Study examined complexity of endogenous, low-frequency neurophysiological processes in patients with ASD compared to control patients. Study confirmed that spontaneous BOLD signal fluctuations in the brain, specifically in regions implicated as atypical in previous autism neuroimaging studies, had small but significant decrease in Hurst exponents in the autistic compared with neurotypical group. This finding indicated a shift-to-randomness of brain oscillations in the autistic brain. • Though the meaning of the Hurst exponent ins limited by our understanding of neuronal and blood-supply sources to the measured BOLD signal, nevertheless fractal scaling may serve as indicator of organizational properties of local neural circuits.
Altamura et al., 2012	12 healthy adults	Response times to working memory and response tasks	Probability density functions, power-law estimation	• Power law-like behavior was noted in the upper tails of the CDF of response times for working memory tasks. This finding possibly reflects emergence of scale-free behavior in time series as an adaptation to increased cognitive requirements. Increasing cognitive load could shift random behavior to scale-free behavior near a critical point.
Dimitriadis et al., 2013	23 children with reading difficulties, 27 age- and IQ-matched children	MEG during resting-state	DFA	• Study examined MEG in children with reading difficulties compared to children without reading difficulties. Children with reading difficulties had decreased overall network organization across all frequency bands (global efficiency decrease) and a decrease in temporal correlations between sensors covering the left temporoparietal region. Study suggested that the specific parameters of SOC vary systematically in presence of reading difficulties. Both groups exhibited scale-free global network connectivity dynamics.
Tinker and Velazquez, 2014	15 children with high-functioning autism, 16 neurotypical children (ages 7−16 years old)	MEG during two executive function tasks	power-law estimation	• Study examined scaling of phase synchrony in MEG in patients with ASD compared to controls. Power-law scaling of phase synchrony was not common in either group. Its frequency of occurrence diminished with increased cognitive load/effort as children performed more difficult tasks. Power law distribution coexisted with other distributions (e.g., exponential) suggesting a sign of the metastability of brain dynamics.
Fagerholm et al., 2015	18 healthy adults	EEG-fMRI during rest and a visuomotor cognitive task	Power-law estimation*, shape analysis	• Study examined combined EEG and fMRI in healthy volunteers during rest and cognitive task. Resting-state EEG cascades were associated with approximate power-law distribution, while task state was associated with subcritical dynamics. Decreased response times during the cognitive task were associated with better approximation of a power-law form of cascade distribution. Findings suggest that resting-state was associated with near-critical dynamics while focused cognitive state induced subcritical dynamics with a lower dynamic range to reduce interference with task (i.e. promoting task performance).
Euler et al., 2016	54 healthy adults	EEG at rest and during a working memory task	DFA	• Study finds evidence of inverse relation between theta band LRTC and working memory performance−higher scaling exponent was related to poorer cognitive performance. Authors suggest that since elevated LRTC have been noted in epilepsy, increases in LRTC are not always beneficial.
Cohen, 2016	21 healthy adults	EEG during action adjustment task	Demeaned fluctuation analysis (DMA)	• Real-time error correction has been correlated to an idiosyncratic electrophysiological signature called midfrontal theta. This study found that midfrontal theta is a transient but non-phase-locked response modulated by task performance over three time scales, including scale-free-like fluctuations over many 10 s. The phasic midfrontal theta brain response to errors or error corrections is modulated by slow fluctuations in criticality.
Simola et al., 2017	27 healthy adults	Response times during a Go/NoGo task	Autocorrelation, spectral density, DFA	• Response time fluctuations in the Go/NoGO task exhibited a power law frequency scaling, autocorrelations and LRTCs, with LRTC scaling exponents negatively correlated with the commission error rates. Finding suggested that LRTCs co-exist with cognitive flexibility which is in line with the criticality hypothesis. LRTC scaling exponents were uncorrelated to the mean response time (MRT), suggesting that performance variables derive from distinct processes than brain criticality. Understanding the individual variation in scale-free behavioral dynamics may improve utility of neuropsychiatric assessment in ADHD.
Irrmischer et al., 2018a	28 meditation-trained healthy adults, 21 meditation-naïve healthy adults	EEG during eyes-closed rest and meditation	Spectral density, DFA	• Study evaluated EEG from meditation practitioners and meditation-naive participants from independent labs. In practitioners, but not in controls, meditation strongly suppressed LRTC of oscillations relative to eyes-closed rest, across all frequency bands and scalp locations. Sustained practice led to reduction in LRTC during meditation after 1 year of additional training. Practice also impacted normal waking brain dynamics as reflected in increased LRTC during eyes-closed rest state, indicating an alteration beyond merely meditation. Authors suggested that meditation-induced release of GABA may lead to subcritical regime.
Irrmischer et al., 2018b	57 healthy adults	EEG during eyes-open, eyes-closed, and temporal expectancy task	Spectral density, DFA	• High levels of alpha band LRTC in sensorimotor region during rest predicted good reaction-time performance in attention task. During task execution, fast reaction times were associated with high-amplitude beta and gamma oscillations with low LRTC. • Authors hypothesize that focus and attention move the neural system from near-criticality optimized for environmental and internal demands, to a state of reduced input propagation but increased attentional stability, leading to suppression of LRTC.
Jia et al., 2018	35 children with ASD (ages 4−9 years old), 31 age- and gender-matched neurotypical children	Functional near-infrared spectroscopy (fNIRS) while watching a cartoon	DFA	• The hemoglobin concentration signals (i.e., oxy-Hb and deoxy-Hb) of young children with ASD and normal children were recorded via fNIRS while watching a cartoon. DFA exponents of young children with ASD were significantly smaller over left temporal region for oxy-Hb signal, and over bilateral temporo-occipital regions for deoxy-Hb signals, indicating a shift-to-random-ness of brain oscillations in children with ASD. Testing the relationship between age and DFA exponents revealed that this association could be modulated by autism. • Studying the temporal structure of brain activity via fNIRS technique may provide physiological indicators for autism. Authors speculated about a connection with SOC, though functional significance of DFA exponent is unclear. LRTC could play a role in evaluating disease progression in ASD.
Bongers et al., 2019	22 healthy university students	EEG during computerized learning and resting-state	Irregular Resampling Auto-spectral Analysis (IRASA), power-law estimation	• Study identified power law exponent of fractal signal during continuous EEG of computerized chemistry learning. Mixed power increase of broadband frequencies, which reflected an overall increase in fractal power, was seen during learning. A low power law exponent with increased band power of the fractal component seemed to correlate to high learning gains.
Kwok et al., 2019	41 healthy children (ages 4−6)	High-density EEG during eyes-open and eyes-closed	Spectral density, DFA	• Study used resting state EEG of children with typical development to explore relation between alpha (7−10 hz) oscillations and oral language ability. Higher language scores were correlated with lower alpha power and increased temporal correlations. Findings further demonstrated existence of critical state dynamics as important for language acquisition.
Ezaki et al., 2020	138 healthy adults	Resting-state fMRI; IQ scores	Correlation between spin-glass susceptibility and performance IQ score	• Study added support to criticality hypothesis by showing moderate but clear correlation between IQ scores and distance from criticality at an individual level using dynamic fMRI signals. A model of criticality using spin glasses was compared to data from healthy adults with a range of fluid intelligence IQs. Human fMRI data was found to be within paramagnetic phase close to the boundary with the spin-glass (SG) phase if using the framework of the Ising model. High fluid intelligence was associated with proximity to boundary between paramagnetic and SG phases. SG phase yields chaotic dynamics in spin systems, consistent with idea of enhanced computational performance “at the edge of chaos.”
Ouyang et al., 2020	210 healthy adults	EEG during eyes-open, eyes-closed resting-state, and object recognition task	Structural equation modeling; fitting oscillations and one-over-f (FOOOF) methodology; IRASA	• The goal of this study was to investigate how individual differences in cognitive processing speeds could be predicted by the power spectrum of resting-state EEG signals. Alpha oscillations were not significantly associated with cognitive processing speed once the 1/f noise was eliminated by SEM. Variation in 1/f was revealed to robustly predict cognitive processing speed in eyes open and eyes closed. Slope of the power law decaying function was most predictive of between-person processing speed.

Asterisk (*) represents power-law estimations that meet criteria equivalent to or more stringent than Clauset et al. (2009). ASD, autism spectrum disorder; BOLD, blood oxygenation level-dependent; CDF, cumulative distribution function.