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Changes in arousal state and task performance alter the power-law exponent in the SCP range recorded by electrocorticography in humans ( He et al., 2010). The SCPs are the low-frequency (<5 Hz) component of broadband field potentials that exhibit a 1/ f-type power spectrum. Two well-studied forms of scale-free neural dynamics are the slow cortical potentials (SCPs He et al., 2010) and amplitude fluctuations of brain oscillations ( Linkenkaer-Hansen et al., 2001). In the brain, scale-free dynamics are prominent across multiple observational levels ( He, 2014) and manifest in human behavioral output ( Gilden, 2001).
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D, Group-average ( n = 19) conditional probability of behavioral response given stimulus β, color-coded by the proportion of response β at each stimulus-β level. Sequences of two different overall range were presented (two left columns, large fluctuation range two right columns, small range), to demonstrate that trend strength (i.e., autocorrelation) is independent from overall range. C, Visual instruction presented to the subjects, showing example stimulus sequences at different β levels. B, Power spectra of stimulus sequences, averaged across the six examples at each β level. A, Lagged autocorrelation function for each class of stimulus sequences, averaged across the six examples at each β level. Stimuli characteristics and behavioral performance. Loudness and pitch fluctuations of natural soundscapes, such as urban and rural environmental noise ( De Coensel et al., 2003), speech, and music ( Voss and Clarke, 1975), also exhibit 1/ f-type temporal power spectra. Time-varying natural images (i.e., natural movies) typically follow a P( f) ∝ 1/ f β -type temporal power spectrum ( Dong and Atick, 1995). In dynamics with a larger β, trends tend to persist over longer periods of time ( Fig. In the temporal domain, scale-free dynamics are characterized by a P( f) ∝ 1/ f β temporal power spectrum, where f is the temporal frequency and the power-law exponent β captures the strength of autocorrelation in the signal over time.
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In the spatial domain, it is well documented that natural images follow a P( f) ∝ 1/ f β spatial power spectrum, where f is the spatial frequency ( Field, 1987). Many natural stimuli exhibit scale-free temporal or spatial patterns, such that no particular temporal or spatial periodicity predominates ( Mandelbrot, 1999). These findings reveal interrelations among different scale-free neural and physiological dynamics and initial evidence for the involvement of scale-free neural dynamics in the processing of natural stimuli, which often exhibit scale-free dynamics. In addition, across individuals, long-range temporal correlation of both SCP and α-oscillation amplitude predicted subjects’ discrimination performance in the auditory task, albeit through antagonistic relationships. We observed that long-range temporal correlation (captured by the power-law exponent β) in SCPs positively correlated with that of heartbeat dynamics across time within an individual and negatively correlated with that of α-amplitude fluctuations across individuals.
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We recorded simultaneous magnetoencephalography and electrocardiography in healthy subjects in the resting state and while performing a discrimination task on scale-free dynamical auditory stimuli that followed different scale-free statistics. However, the exact relationships among these scale-free neural and physiological dynamics remain unclear. In addition, scale-free dynamics characterize normal human physiology such as heartbeat dynamics. Two extensively studied forms of scale-free neural dynamics in the human brain are slow cortical potentials (SCPs)-the low-frequency (<5 Hz) component of brain field potentials-and the amplitude fluctuations of α oscillations, both of which have been shown to carry important functional roles. Such activity often exhibits a 1/ f-type power spectrum, in which power falls off with increasing frequency following a power-law function: P( f) ∝ 1/ f β, which is indicative of scale-free dynamics. Neural activity recorded at multiple spatiotemporal scales is dominated by arrhythmic fluctuations without a characteristic temporal periodicity.