Maarten L. Wijnants

Contemporary theories of 1/f noise in motor control

1/f noise has been discovered in a number of time series collected in psychological and behavioral experiments. This ubiquitous phenomenon has been ignored for a long time and classical models were not designed for accounting for these long-range correlations. The aim of this paper is to present and discuss contrasted theoretical perspectives on 1/f noise, in order to provide a comprehensive overview of current debates in this domain. In a first part, we propose a formal definition of the phenomenon of 1/f noise, and we present some commonly used methods for measuring long-range correlations in time series. In a second part, we develop a theoretical position that considers 1/f noise as the hallmark of system complexity. From this point of view, 1/f noise emerges from the coordination of the many elements that compose the system. In a third part, we present a theoretical counterpoint suggesting that 1/f noise could emerge from localized sources within the system. In conclusion, we try to draw some lines of reasoning for going beyond the opposition between these two approaches.

An interaction-dominant perspective on reading fluency and dyslexia

The background noise of response times is often overlooked in scientific inquiries of cognitive performances. However, it is becoming widely acknowledged in psychology, medicine, physiology, physics, and beyond that temporal patterns of variability constitute a rich source of information. Here, we introduce two complexity measures (1/f scaling and recurrence quantification analysis) that employ background noise as metrics of reading fluency. These measures gauge the extent of interdependence across, rather than within, cognitive components. In this study, we investigated dyslexic and non-dyslexic word-naming performance in beginning readers and observed that these complexity metrics differentiate reliably between dyslexic and average response times and correlate strongly with the severity of the reading impairment. The direction of change in the introduced metrics suggests that developmental dyslexia resides from dynamical instabilities in the coordination among the many components necessary to read, which could explain why dyslexic readers score below average on so many distinct tasks and modalities.

A trade-off study revealing nested timescales of constraint

This study investigates human performance in a cyclic Fitts task at three different scales of observation, either in the presence (difficult condition) or in the absence (easy condition) of a speed–accuracy trade-off. At the fastest scale, the harmonicity of the back and forth movements, which reflects the dissipation of mechanical energy, was measured within the timeframe of single trials. At an intermediate scale, speed and accuracy measures were determined over a trial. The slowest scale pertains to the temporal structure of movement variability, which evolves over multiple trials. In the difficult condition, reliable correlations across each of the measures corroborated a coupling of nested scales of performance. Participants who predominantly emphasized the speed-side of the trade-off (despite the instruction to be both fast and accurate) produced more harmonic movements and clearer 1/f scaling in the produced movement time series, but were less accurate and produced more random variability in the produced movement amplitudes (vice versa for more accurate participants). This implied that speed–accuracy trade-off was accompanied by a trade-off between temporal and spatial streams of 1/f scaling, as confirmed by entropy measures. In the easy condition, however, no trade-offs nor couplings among scales of performance were observed. Together, these results suggest that 1/f scaling is more than just a byproduct of cognition. These findings rather support the claim that interaction-dominant dynamics constitute a coordinative basis for goal-directed behavior.

A review of theoretical perspectives in cognitive science on the presence of scaling in coordinated physiological and cognitive processes

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/f scaling. 1/f scaling 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/f scaling is most clearly present in healthy, well-coordinated activities. Prominent hypotheses about the origins of 1/f scaling are confronted with these reviewed studies. It is concluded that 1/f scaling 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.

Dyslexic and skilled reading dynamics are self-similar

The shape of a word pronunciation time distribution supplies information about the dynamic interactions that support reading performance. Speeded word-naming pronunciation and response time distributions were collected from 20 sixth grade Dutch students with dyslexia and 23 age-matched controls. The participants’ pronunciation times were modeled and contrasted with a lognormal inverse power-law mixture distribution. Identical contrasts were also conducted on the same participants’ response time distributions derived from flanker, color-naming, and arithmetic tasks. Results indicated that children with dyslexia yield slower, broader, and more variable pronunciation time distributions than their age-matched counterparts. This difference approximated a self-similar rescaling between the two group’s aggregate pronunciation time distributions. Moreover, children with dyslexia produced similar, but less prominent trends toward slower and more variable performance across the three non-reading tasks. The outcomes support a proportional continuum rather than a localized deficit account of dyslexia. The mixture distribution’s success at describing the participants’ pronunciation and response time distributions suggests that differences in proportional contingencies among low-level neurophysiological, perceptual, and cognitive processes likely play a prominent role in the etiology of dyslexia.

Does sample rate introduce an artifact in spectral analysis of continuous processes

Spectral analysis is a widely used method to estimate 1/fα noise in behavioral and physiological data series. The aim of this paper is to achieve a more solid appreciation for the effects of periodic sampling on the outcomes of spectral analysis. It is shown that spectral analysis is biased by the choice of sample rate because denser sampling comes with lower amplitude fluctuations at the highest frequencies. Here we introduce an analytical strategy that compensates for this effect by focusing on a fixed amount, rather than a fixed percentage of the lowest frequencies in a power spectrum. Using this strategy, estimates of the degree of 1/fα noise become robust against sample rate conversion and more sensitive overall. Altogether, the present contribution may shed new light on known discrepancies in the psychological literature on 1/fα noise, and may provide a means to achieve a more solid framework for 1/fα noise in continuous processes.

Progress in reading and spelling of dyslexic children is not affected by executive functioning.

Although poor reading and spelling skills have been associated with weak skills of executive functioning (EF), its role in literacy is not undisputed. Because EF has different theoretical underpinnings, methods of analysis and of assessing, it has led to varying and often contrasting results in its effects in children with dyslexia. The present study has two goals. The first goal is to establish the relationship between a large number of EF tasks and reading and spelling skills in a large number of Dutch dyslexic children (n = 229). More interesting, however, is the second aim. To what extent do EF skills predict progress in reading and spelling in dyslexic children who attended a remediation programme? The results revealed small, but significant relationships between EF and reading and spelling skills, but no relationships between EF and progress in reading and spelling. It is concluded that training EF skills is unlikely to enhance reading and spelling skills.

From the Role of Context to the Measurement Problem: The Dutch Connection Pays Tribute to Guy Van Orden

The call for a daisy chain of replications by Daniel Kahneman (as cited in Yong, 2012) to combat the recent credibility problems of psychological science touches upon the issue that Guy dealt with ever since he started his academic career and that we acknowledge as one of his major contributions. After coming to terms with the fact that psycholinguistics (with strong roots in information-processing theory) never accepted the dogma of falsification, Guy advanced a different approach. Applying the so-called ideal strategy manipulation in his experiments, he showed that psycholinguistic effects are fundamentally context sensitive. Any subtle change in an experiment may cause the effect to appear, diminish, or to even disappear. This analysis of psycholinguistics in particular and psychological science in general leads us to believe that just replicating experiments will not easily solve the current crisis in psychology. We believe this crisis to be one of theory evaluation, allowing the scientific description of cognitive behavior as a linearly decomposable system to prevail in the face of anomalies and empirical falsification.

What Enables Novel Thoughts? The Temporal Structure of Associations and Its Relationship to Divergent Thinking

The aim of the current study is to enhance our understanding of cognitive creativity, specifically divergent thinking, by employing an interdisciplinary methodological approach. By integrating methodology from computational linguistics and complex systems into creativity research, the current study aims to shed light on the relationship between divergent thinking and the temporal structure of semantic associations. In complex systems, temporal structures can be described on a continuum from random to flexible-stable and to persistent. Random structures are highly unpredictable, persistent structures are highly predictable, and flexible-stable structures are in-between, they are partly predictable from previous observations. Temporal structures of associations that are random (e.g., dog–graveyard–north pole) or persistent (e.g., dog–cat–rat) are hypothesized to be detrimental to divergent thinking. However, a flexible-stable structure (e.g., dog–police–drugs) is hypothesized to be related to enhanced divergent thinking (inverted-U). This notion was tested (N = 59) in an association chain task, combined with a frequently used measure of divergent thinking (i.e., Alternative Uses Test). Latent Semantic Analysis from computational linguistics was used to quantify the associations, and methods from complex systems in form of Power Spectral Density analysis and detrended fluctuation analysis were used to estimate the temporal structure of those associations. Although the current study does not confirm that a flexible-stable (vs. random/persistent) temporal structure of associations is related to enhanced divergent thinking skills, it hopefully challenges fellow researchers to refine the recent methodological developments for assessing the (temporal) structure of associations. Moreover, the current cross-fertilization of methodological approaches may inspire creativity researchers to take advantage of other fields’ ideas and methods. To derive a theoretically sound cognitive theory of creativity, it is important to integrate research ideas and empirical methods from a variety of disciplines.

A comment on "Measuring fractality" by Stadnitski (2012).

In a recent publication Stadnitski (2012) presented an overview of methods to estimate fractal scaling in time series, outlined as an accessible tutorial1. The publication was set-up as a comparison between monofractal and ARFIMA methods, and promotes ARFIMA to distinguish between spurious and genuine 1/f noise, shedding light on “the problem that the log–log power spectrum of short-memory ARMA (p, q) processes can resemble the spectrum of 1/f noise.” Stadnitski proposes an analytic strategy that consists of fitting 18 models to any time series. Nine of the models are ARMA (p, q) models, with p and q varying from 0 to 2, that do not contain long-range correlations. The remaining ARFIMA (p, d, q) models add to the ARMA models a fractional integration parameter d. As laid-out by the author, given a genuine fractal series, ARFIMA models should present a better fit than ARMA counterparts. Based on this logic, Stadnitski (2012) evaluates one simple reaction time (SRT) series, and concludes it is not a genuine fractal signal. This conclusion is intriguing, because it was previously argued that SRT series typically present genuine 1/f scaling (Van Orden et al., 2003; Wagenmakers et al., 2004). In this commentary, iteratively refined spectral surrogates (Schreiber and Schmitz, 1996) were generated from the Van Orden et al. (2003) SRT series. This procedure is known to follow the original spectrum more closely than alternative procedures. Next, the performance of a monofractal method (DFA) was compared with the performance of ARFIMA modeling. Using the R-code made available in the Stadnitski tutorial, it is evaluated whether monofractal methods are indeed “distinctly inferior” to the ARFIMA method. AIC and BIC for nine possible ARMA models and nine ARFIMA models were calculated (see Table ​Table1).1). For the ten surrogate series, AIC showed best fits for the ARMA (2,0,0), ARMA (0,0,2), ARFIMA (1, d, 0) and (2, d, 2) model once, and six times for the ARFIMA (0, d, 0) model. BIC favored the ARMA (1,0,0) and (2,0,0) model and the ARFIMA (1,d,0) model once, and the ARFIMA (0, d, 0) model seven times. Given that “the smallest AIC or BIC indicates the best model,” the d parameter was estimated for the best fitting models (for the favored ARMA models, d = 0). Next, the 10 surrogate series were analyzed using DFA (converted to d), to allow for a comparison between the ARFIMA and monofractal methodologies2. Table 1 Values of the information criteria AIC and BIC for the surrogate time series are shown at the left-hand side. The targeted scaling exponent and the estimated scaling exponents from the various methods are shown on the right-hand side. As pointed out by Stadnitski, “good estimators are unbiased, i.e., their means equal the true parameter value.” The summed absolute difference between the estimated d-values from the surrogates and the original data was 3.86 for AIC, 3.87 for BIC, and 1.27 for DFA. Hence, DFA equaled the target parameters much more closely. DFA approached the target d-values more closely than ARFIMA in ten out of ten cases. Hence, the claim that monofractal methods are inferior to ARFIMA methods is not supported. Contrary, this analysis shows that monofractal methods in fact provide much better estimates. This conclusion is discrepant to Stadnitskis conclusion. Stadnitski simulated a short-memory ARIMA (1,0,1) model and a long-memory ARFIMA (1, d, 1) model, and concluded that ARFIMA methods were less biased and more precise than, and therefore superior to, monofractal estimators. Here, spectral surrogates were constructed, and ARFIMA and DFA estimates were compared to the original target parameters. Here, the ARFIMA methodology was more biased than monofractal estimators. So how should one go about this discrepancy? Accuracy concerns aside, it may be concluded that the issue raised by Stadnitski is in fact a theoretical, rather than a statistical one. By realizing that “goodness-of-fit alone cannot serve up counterexamples that falsify theories” (Gilden, 2009, p. 1463), it is argued that fitting ARFIMA algorithms to the data is not sufficient in itself to distinguish between genuine and spurious scaling properties. The true challenge should be “to compare the empirical accuracy of theoretical predictions in a program of strong inference” (Hasselman, 2012, p. 4). That is, although often implicit, there must exist specific ontological intuitions that motivate researchers to fit ARFIMA models. As it stands, however, this inherent theoretical motivation is still to take up the challenge against theoretical predictions corroborated by fractal perspectives (see Diniz et al., 2011), like the ubiquity of 1/f scaling, consistent changes away from 1/f scaling with pathological conditions and aging (Goldberger et al., 2002; Hausdorff, 2007), consistent changes toward 1/f scaling in more skilled performances (Wijnants et al., 2009, 2012a,b), no bending at the low-frequencies in a power spectrum when longer time series are collected (Van Orden et al., 2005), and so forth. In short, spurious 1/f scaling “becomes an extraordinary hypothesis that would itself require extraordinary evidence” (Van Orden et al., 2003, p. 19), evidence that cannot come from goodness-of-fit alone, to convince that the preferred models are also theoretically viable, and consequently to be preferred methodologically.