Links between aperiodic signal components, neural ‘variability’, and ‘noise’

Brain activity is naturally variable at multiple spatio-temporal scales (Faisal, Selen, &

Wolpert, 2008). This variability includes both periodic and irregular fluctuations at the level of population signals, and may index latent dynamic regimes that are considered important for healthy, efficient and flexible neural function (Breakspear, 2017). However, the mapping between neural variability moment-to-moment, trial-by-trial, and the multiple proxy measures thereof often remains unclear in application (Dinstein, Heeger, & Behrmann, 2015; Doiron et al., 2016;

Garrett et al., 2013a; but see B. J. He, 2011; Kumral et al., 2020). As a result, the notion of neuro-behavioral variability (and associated functional interpretations) may encompass a wide variety of metrics that potentially index different aspects of neural dynamics (cf. Garrett et al., 2015;

Shafiei et al., 2019)²⁶. Project 2 provides a unifying perspective on time series irregularity (or

25 Any generative caveats regarding the latent neural nature (cf. inhalation, muscle sources) or intrinsic origin (cf. entrainment; Obleser & Kayser, 2019) of rhythms at the level of observed time series naturally also apply to rhythm detection.

26 Given that metrics vary in their descriptive order (mean, total variation, variance structure, variance and phase interactions), lower-order indices should be controlled for when specific claims are to be made about the unique relevance of a higher-order index, e.g., using surrogate analyses (as highlighted in Project 2). These two studies illustrate how interpretations may diverge depending on whether overall signal variation or entropy are considered, even if effects largely converge given the strong anticorrelation between these indices.

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‘complexity’) and aperiodic slopes (and rhythms) in the frequency domain. It thereby indicates previously underappreciated links between measurements of signal complexity and variance structure (Garrett et al., 2013a) that may bridge disparate findings. In particular, a strong link of temporal irregularity to aperiodic slopes is appealing, given that such slopes may provide a bona fide index of neural excitability (see Section 1.6) and have conceptually been associated with the stochasticity (i.e., ‘noise’²⁷ level) of neural firing via links to mass synaptic and membrane potential flux (Voytek & Knight, 2015).

Functionally, two alternative expectations exist regarding the role of noise for information processing. While overwhelming intrinsic noise constrains the reliability of computations (for a review see Faisal et al., 2008), intermediate levels of random input can benefit neural processing via stochastic facilitation (Garrett, McIntosh, & Grady, 2011; Garrett et al., 2013b; McDonnell &

Ward, 2011; Stein, Gossen, & Jones, 2005). As such, elevated stochasticity may contribute to a state of ‘stable flexibility’ that characterizes a balance between reliable stimulus responses and large dynamic range (Dinstein et al., 2015; Garrett et al., 2013a). Such a suggestion is conceptually similar to the notion of ‘critical’ dynamics (Beggs, 2008; Palva & Palva, 2018)²⁸ that operate at the boundary of order and disorder (Stanley, 1971) (e.g., at the transition between periodic and chaotic regimes; Breakspear, 2017). Importantly, networks that are critically balanced between excitation and inhibition theoretically (Kinouchi & Copelli, 2006; Peterson & Voytek, 2015; Shew

27 The notion of noise can only be defined with reference to a target signal of interest; e.g.,

“Random or unpredictable fluctuations and disturbances that are not part of a signal.” (Faisal et al., 2008, p. 292) Given that there is no canonical model of a brain ‘signal’ (e.g., Buzsáki, 2019), the definition of ‘noise’ for brain function is non-trivial outside of computational models that implement a clear operational definition of both components (e.g., with regards to the neural

‘representation’ of experimentally measurable external variables). I use the term ‘noise’ here to refer to the level of (largely scale-free) stochasticity of synaptic inputs and neural firing, albeit those components may constitute signals (a) in the brain itself, and as such (b) for experimenters recording those signals.

28 Power-law dynamics have been observed across a range of systems, although phenomenological similarity does not imply mechanistic equality (Stumpf & Porter, 2012). Scale-free dynamics have been proposed as a signature of self-organized criticality (e.g., Bak, Tang, &

Wiesenfeld, 1987; Beggs, 2008; de Arcangelis, Perrone-Capano, & Herrmann, 2006; De Los Rios &

Zhang, 1999; Lin & Chen, 2005; Mandelbrot, 1999; Markovic & Gros, 2014), as an emergent property of dynamically interacting systems. However, the inference of such principles from power-law dynamics has received criticism (for a review see Beggs & Timme, 2012) and the applicability of such broad models to electrophysiological features (Touboul & Destexhe, 2017) remains unclear.

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& Plenz, 2013) and empirically support efficient, large, and dynamic information transfer (Deneve

& Machens, 2016; H. D. Yang, Shew, Roy, & Plenz, 2012; Y. G. Yu, Migliore, Hines, & Shepherd, 2014;

S. L. Zhou & Yu, 2018). At a global network level, such critical states may facilitate the exploration of different network attractors (Cocchi, Gollo, Zalesky, & Breakspear, 2017; Palva & Palva, 2018) during rested wakefulness (Deco & Jirsa, 2012; Lynn, Cornblath, Papadopoulos, Bertolero, &

Bassett, 2020), whereas specific networks may stabilize activity when ‘expected uncertainty’

(Friston, Breakspear, & Deco, 2012) regarding upcoming events decreases during specific tasks (Fagerholm et al., 2015; Hellyer et al., 2014; Lynn et al., 2020). By controlling the number of concurrently relevant feature attractors during attention, Project 3 similarly proposes that E-I regulation fine-tunes dynamic range during attentional states, although the determination of whether optimal excitability regimes for sensory processing exist (e.g., McGinley, David, et al., 2015) and how or when they are instantiated requires further work.

In parallel with the power-law (1/f) appearance of broadband time series, narrowband-filtered (i.e., putatively rhythmic) EEG or MEG signals also exhibit long-range temporal correlations (Hansen et al., 2001; Monto et al., 2008; Poil, van Ooyen, & Linkenkaer-Hansen, 2008) in their amplitude fluctuations. Narrowband amplitudes depend on their past values with a probability falling off according to a power-law²⁹. This amplitude autocorrelation further argues against stationary rhythms with constant amplitude, and – like broadband 1/f slopes – has been proposed to covary with cortical excitability (Bruining et al., 2020; Stephani et al., 2020). A unified perspective on these narrow- and broadband characteristics emerges from the observation that E-I balance gives rise to spatial power-law distributions of spreading activity ('neuronal avalanches'; Beggs & Plenz, 2003; Shew, Yang, Yu, Roy, & Plenz, 2011) at short time scales (Lombardi et al., 2017; Poil, Hardstone, Mansvelder, & Linkenkaer-Hansen, 2012), that are nested within emerging alpha rhythms at longer times scales (Poil et al., 2012). Similarly, injection of empirical alpha-band signals (including their autocorrelative amplitude structure) into large-scale mean field models can emulate BOLD-like signals (Schirner et al., 2018), indicating close (but likely non-exclusive) links between the 1/f appearance of BOLD signals and the scale-free

29 Others have noted bimodality in alpha power distributions at rest to argue that cortical dynamics stochastically switch between an aperiodic and a rhythmic fix-point regime (Freyer, Aquino, Robinson, Ritter, & Breakspear, 2009; Freyer et al., 2011), although the continuous vs.

discrete nature of rhythmic amplitude fluctuations remains unresolved. Given that these results are more generally based exclusively on narrowband-filtered fluctuations, the characteristics of the ‘low-amplitude’ episodes deserve further attention, as the absence of a rhythm conceptually differs from the continued presence of rhythmicity, albeit of decreased amplitude.

43 distribution of alpha-band amplitudes. This provides an interesting perspective on potential generative links between alpha rhythms and aperiodic slopes, and may partially account for the robustly observed empirical covariation between them (see next section).