A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f Scaling in Coordinated Physiological and Cognitive Processes

Abstract

Time series of human performances present fluctuations around a mean value. These fluctuations are typically considered as insignificant, and attributable to random noise. Over recent decades, it became clear that temporal fluctuations possess interesting properties, however, one of which the property of fractal 1/fscaling. 1/fscaling indicates that a measured process extends over a wide range of timescales, suggesting an assembly over multiple scales simultaneously. This paper reviews neurological, physiological, and cognitive studies that corroborate the claim that 1/fscaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/fscaling are confronted with these reviewed studies. It is concluded that 1/fscaling in living systems appears to reflect their genuine complex nature, rather than constituting a coincidental side-effect. The consequences of fractal dynamics extending from the small spatial and temporal scales (e.g., neurons) to the larger scales of human behavior and cognition, are vast, and impact the way in which relevant research questions may be approached. Rather than focusing on specialized isolable subsystems, using additive linear methodologies, nonlinear dynamics, more elegantly so, imply a complex systems methodology, thereby exploiting, rather than rejecting, mathematical concepts that enable describing large sets of natural phenomena.

Making sense of the noise: Replication difficulties of Correll’s (2008) modulation of 1/f noise in a racial bias task

“…For instance, alternative scaling methods could be used to examine 1/f noise such as detrended fluctuation analysis (DFA) or standardized dispersion analysis (SDA), which have been argued to yield more robust results with relatively short time-series data (Hasselman, 2013). Of more theoretical importance, however, we did consistently observe general patterns of 1/f noise in each of our conditions across both samples -successfully replicating general 1/f noise results observed in past research (Torre et al, 2011;Wijnants, 2014;Wijnants et al, 2012) and as originally observed in specific conditions of Correll's prior work (i.e., Correll, 2008, Study 1 and control condition of Study 2; Correll, 2011). Consequently, it is important to emphasize that though our results challenge Correll's (2008) theoretical account that 1/f noise in racial bias tasks reflects an effortful deliberative process, our results corroborate the fact that 1/f noise does indeed emerge in implicit racial bias tasks.…”

“…Correll (2008) investigated the potentially meaningful fluctuations in RTs across trials using an approach referred to as 1/f noise, which refers to non-random patterns of long-range correlations that manifest as waves in the fluctuations of RTs over time (Gilden, 2001;Gilden, Thornton, & Mallon, 1995; but see Wagenmakers, van der Maas, & Farrell, 2012). In recent years, 1/f noise -also known as flicker noise or pink noise -has been documented in a wide number of biological and physical systems including the fluctuations in tide heights, heartbeat, and firings of single neurons (Gilden, 2001;Press, 1978; for a review see Wijnants, 2014). From this perspective, the sequence of raw RTs can be represented as a complex waveform which can be decomposed into simpler component waves via a Fast Fourier transform (FFT).…”

Detrended fluctuation analysis in a simple spreadsheet as a tool for teaching fractal physiology

“…The connection between fractals and human physiology was popularized to a large extent by publications in the American Physiological Society journals in the 1990s (16 -19, 21). In subsequent years, "fractal-based" analyses of output signals in physiology and behavior have developed in parallel on both sides of the Atlantic, in the U.S. (4,22,37,38) and in Europe (5,7,28,39). A major, must-read article has given scientific impetus to ongoing and emerging ideas in 2002 (12).…”

The Temporal Structure of State Self-Esteem Variability During Parent–Adolescent Interactions: More Than Random Fluctuations

“…Any point in a fractal process, therefore, possesses the "dynamic memory" of all preceding points of the process and is therefore embedded in the historical context of the system Diniz et al, 2011). The presence of pink noise is also significant in that it indicates a balance between order and chaos (Wijnants, 2014), which characterizes healthy and well-coordinated systems (Herman, Giladi, Gurevich, & Hausdorff, 2005;. Indeed, pink noise lies on a continuum between white noise and Brown noise (see Figure 1), which we will describe below.…”

“…While the fractal properties of SSE across real time have not been examined to date, there is an abundance of evidence that real-time cognitive and motor processes reveal pink noise (for a review, see Wijnants, 2014). Moreover, there is rising evidence that pink noise is also displayed in socio-emotional processes, such as trial-by-trial reaction times in racial-bias tasks (Correll, 2008), short conversational storytelling sessions (Butner, Pasupathi, & Vallejos, 2008), and mood across the long term (from 1 to 2.5 years) (Gottschalk, Bauer, & Peter, 1995).…”