Provenance of correlations in psychological data

1/f laws found in non-human music

A compelling question at the intersection of physics, neuroscience, and evolutionary biology concerns the extent to which the brains of various species evolved to encode regularities of the physical world. It would be parsimonious and adaptive, for example, for brains to evolve an innate understanding of gravity and the laws of motion, and to be able to detect, auditorily, those patterns of noises that ambulatory creatures make when moving about the world. One such physical regularity of the world is fractal structure, generally characterized by power-law correlations or 1/f ^β spectral distributions. Such laws are found broadly in nature and human artifacts, from noise in physical systems, to coastline topography (e.g., the Richardson effect), to neuronal spike patterns. These distributions have also been found to hold for the rhythm and power spectral density of a wide array of human music, suggesting that human music incorporates regularities of the physical world that our species evolved to recognize and produce. Here we show for the first time that 1/f^β laws also govern the spectral density of a wide range of animal vocalizations (music), from songbirds, to whales, to howling wolves. We discovered this 1/f^β power-law distribution in the vocalizations within all of the 17 diverse species examined. Our results demonstrate that such power laws are prevalent in the animal kingdom, evidence that their brains have evolved a sensitivity to them as an aid in processing sensory features of the natural world.

Temporal Structure in Sensorimotor Variability: A Stable Trait, But What For?

Human performance shows substantial endogenous variability over time, and this variability is a robust marker of individual differences. Of growing interest to psychologists is the realisation that variability is not fully random, but often exhibits temporal dependencies. However, their measurement and interpretation come with several controversies. Furthermore, their potential benefit for studying individual differences in healthy and clinical populations remains unclear. Here, we gather new and archival datasets featuring 11 sensorimotor and cognitive tasks across 526 participants, to examine individual differences in temporal structures. We first investigate intra-individual repeatability of the most common measures of temporal structures - to test their potential for capturing stable individual differences. Secondly, we examine inter-individual differences in these measures using: (1) task performance assessed from the same data, (2) meta-cognitive ratings of on-taskness from thought probes occasionally presented throughout the task, and (3) self-assessed attention-deficit related traits. Across all datasets, autocorrelation at lag 1 and Power Spectra Density slope showed high intra-individual repeatability across sessions and correlated with task performance. The Detrended Fluctuation Analysis slope showed the same pattern, but less reliably. The long-term component (d) of the ARFIMA(1,d,1) model showed poor repeatability and no correlation to performance. Overall, these measures failed to show external validity when correlated with either mean subjective attentional state or self-assessed traits between participants. Thus, some measures of serial dependencies may be stable individual traits, but their usefulness in capturing individual differences in other constructs typically associated with variability in performance seems limited. We conclude with comprehensive recommendations for researchers.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42113-022-00162-1.

Stochastic modeling of Lévy-like human eye movements

The standard model of visual search dynamics is Brownian motion. However, recent research in cognitive science reveals that standard diffusion processes seem not to be the appropriate models of human looking behavior. In particular, experimental results confirm that the superdiffusive Lévy-type dynamics appears in this context. In this paper, we analyze the diffusive properties of human eye movement in a language comprehension task. We propose a model that is a combination of a Markov chain with a finite number of states and a Lévy walk. Our model fits well the experimental data and allows one to investigate the properties of the visual search dynamics using numerical simulations.

Central Auditory Tests to Track Cognitive Function in People With HIV: Longitudinal Cohort Study

Background

The development of neurocognitive deficits in people infected with HIV is a significant public health problem. Previous cross-sectional studies have shown that performance on central auditory tests (CATs) correlates with cognitive test results in those with HIV, but no longitudinal data exist for confirmation. We have been performing longitudinal assessments of central auditory and cognitive function on a cohort of HIV-positive and HIV-negative individuals in Dar es Salaam, Tanzania to understand how the central auditory system could be used to study and track the progress of central nervous system dysfunction.

Objective

The goal of the project was to determine if CATs can track the trajectory of cognitive function over time in people diagnosed with HIV.

Methods

Tests of peripheral and central auditory function as well as cognitive performance were performed on 382 individuals over the course of 3.5 years. Visits were scheduled every 6 months. CATs included tests of auditory temporal processing (gap detection) and speech perception in noise (Hearing in Noise Test and Triple Digit Test). Cognitive tests included the Montreal Cognitive Assessment (MoCA), Test of Variables of Attention (TOVA), and subtests from the Cogstate battery. HIV-positive subjects were divided into groups based on their CAT results at their final visit (bottom 20%, top 20%, middle 60%). Primary analyses focused on the comparison between HIV-positive individuals that performed worse on CATs (bottom 20%) and the overall HIV-positive group (middle 60%). Data were analyzed using linear mixed-effect models with time as the main fixed effect.

Results

The group with the worst (bottom 20%) CAT performance showed a difference in trajectory for the MoCA (P=.003), TOVA (P<.048), and Cogstate (P<.046) over the course of the study period compared to the overall HIV-positive group. A battery of three CATs showed a significant difference in cognitive trajectory over a relatively short study period of 3.5 years independent of age (bottom 20% vs HIV-positive group).

Conclusions

The results of this study support the ability for CATs to track cognitive function over time, suggesting that central auditory processing can provide a window into central nervous system performance. CATs can be simple to perform, and are relatively insensitive to education and socioeconomic status because they only require repeating sentences, numbers, or detecting gaps in noise. These tests could potentially provide a time-efficient, low-cost method to screen for and monitor cognitive decline in patients with HIV, making them a useful surveillance tool for this major public health problem.

Behavior Stability and Individual Differences in Pavlovian Extended Conditioning

How stable and general is behavior once maximum learning is reached? To answer this question and understand post-acquisition behavior and its related individual differences, we propose a psychological principle that naturally extends associative models of Pavlovian conditioning to a dynamical oscillatory model where subjects have a greater memory capacity than usually postulated, but with greater forecast uncertainty. This results in a greater resistance to learning in the first few sessions followed by an over-optimal response peak and a sequence of progressively damped response oscillations. We detected the first peak and trough of the new learning curve in our data, but their dispersion was too large to also check the presence of oscillations with smaller amplitude. We ran an unusually long experiment with 32 rats over 3,960 trials, where we excluded habituation and other well-known phenomena as sources of variability in the subjects' performance. Using the data of this and another Pavlovian experiment by Harris et al. (2015), as an illustration of the principle we tested the theory against the basic associative single-cue Rescorla–Wagner (RW) model. We found evidence that the RW model is the best non-linear regression to data only for a minority of the subjects, while its dynamical extension can explain the almost totality of data with strong to very strong evidence. Finally, an analysis of short-scale fluctuations of individual responses showed that they are described by random white noise, in contrast with the colored-noise findings in human performance.

Co-actors Exhibit Similarity in Their Structure of Behavioural Variation That Remains Stable Across Range of Naturalistic Activities

Human behaviour, along with any natural/biological behaviour, has varying degrees of intrinsic 'noise' or variability. Many studies have shown that the structure or patterning of this variability is sensitive to changes in task and constraint. Furthermore, two or more humans interacting together often begin to exhibit similar structures of behavioural variability (i.e., the patterning of their behavioural fluctuations becomes aligned or matched) independent of any moment-to-moment synchronization (termed complexity matching). However, much of the previous work has focused on a subset of simple or contrived behaviours within the context of highly controlled laboratory tasks. In the current study, individuals and pairs performed five self-paced (unsupervised), semi-structured activities around a university campus. Empatica E4 wristbands and iPhones were used to record the participants' behavioural activity via accelerometers and GPS. The results revealed that the structure of variability in naturalistic human behaviour co-varies with the task-goal constraints, and that the patterning of the behavioural fluctuations exhibited by co-acting individuals does become aligned during the performance of everyday activities. The results also revealed that the degree of complexity matching that occurred between pairs remained invariant across activity type, indicating that this measure could be employed as a robust, task-independent index of interpersonal behaviour.

Fractal properties and short-term correlations in motor control in cycling: influence of a cognitive challenge

Fluctuations in cyclic tasks periods is a known characteristic of human motor control. Specifically, long-range fractal fluctuations have been evidenced in the temporal structure of these variations in human locomotion and thought to be the outcome of a multicomponent physiologic system in which control is distributed across intricate cortical, spinal and neuromuscular regulation loops. Combined with long-range correlation analyses, short-range autocorrelations have proven their use to describe control distribution across central and motor components. We used relevant tools to characterize long- and short-range correlations in revolution time series during cycling on an ergometer in 19 healthy young adults. We evaluated the impact of introducing a cognitive task (PASAT) to assess the role of central structures in control organization. Autocorrelation function and detrending fluctuation analysis (DFA) demonstrated the presence of fractal scaling. PSD in the short range revealed a singular behavior which cannot be explained by the usual models of even-based and emergent timing. The main outcomes are that (1) timing in cycling is a fractal process, (2) this long-range fractal behavior increases in persistence with dual-task condition, which has not been previously observed, (3) short-range behavior is highly persistent and unaffected by dual-task. Relying on the inertia of the oscillator may be a way to distribute more control to the periphery, thereby allocating less resources to central process and better managing additional cognitive demands. This original behavior in cycling may explain the high short-range persistence unaffected by dual-task, and the increase in long-range persistence with dual-task.

Complexity matching and coordination in individual and dyadic performance

Complexity matching is a measure of coordination based on information exchange between complex networks. To date, studies have focused mainly on interpersonal coordination, but complexity matching may generalize to interacting networks within individuals. The present study examined complexity matching in a double, coordinated Fitts' perceptual-motor task with comparable individual and dyadic conditions. Participants alternated touching targets with their left and right hands in the individual condition, or analogously with the left hand of one partner and the right hand of another in the dyadic condition. In Experiment 1, response coupling was manipulated by making targets drift either randomly or contingently based on prior responses. Here, drift refers to the variability in the target movements between response locations. Long-range correlations in time series of inter-response intervals exhibited complexity matching between the left and right hands of dyads and individuals. Response coupling was necessary for complexity matching in dyads but not individuals. When response coupling was absent in the dyadic condition, the degree of complexity matching was significantly reduced. Experiment 2 showed that the effect of coupling was due to interactions between left and right responses. Results also showed a weak, negative relationship between complexity matching and performance as measured by total response time. In conclusion, principles and measures of complexity matching apply similarly within and between individuals, and perceptual-motor performance can be facilitated by loose response coupling.

The Over-Extended Mind? Pink Noise and the Ethics of Interaction-Dominant Systems

There is a growing recognition within cognitive enhancement and neuroethics debates of the need for greater emphasis on cognitive artefacts. This paper aims to contribute to this broadening and expansion of the cognitive-enhancement and neuroethics debates by focusing on a particular form of relation or coupling between humans and cognitive artefacts: interaction-dominance. We argue that interaction-dominance as an emergent property of some human-cognitive artefact relations has important implications for understanding the attribution and distribution of causal and other forms of responsibility as well as agency relating to the actions of human-cognitive artefact couplings. Interaction-dominance is both indicated and constituted by the phenomenon of "pink noise". Understanding the role of noise in this regard will establish a necessary theoretical groundwork for approaching the ethical and political dimensions of relations between human cognition and digital cognitive artefacts. We argue that pink noise in this context plays a salient role in the practical, ethical, and political evaluation of coupling relations between humans and cognitive artefacts, and subsequently in the responsible innovation of cognitive artefacts and human-artefact interfaces.

Temporal fractals in movies and mind

Fractal patterns are seemingly everywhere. They can be analyzed through Fourier and power analyses, and other methods. Cutting, DeLong, and Nothelfer (2010) analyzed as time-series data the fluctuations of shot durations in 150 popular movies released over 70 years. They found that these patterns had become increasingly fractal-like and concluded that they might be linked to those found in the results of psychological tasks involving attention. To explore this possibility further, we began by analyzing the shot patterns of almost twice as many movies released over a century. The increasing fractal-like nature of shot patterns is affirmed, as determined by both a slope measure and a long-range dependence measure, neither of which is sensitive to the vector lengths of their inputs within the ranges explored here. But the main reason for increased long-range dependence is related to, but not caused by, the increasing vector length of the shot-series samples. It appears that, in generating increasingly fractal-like patterns, filmmakers have systematically explored dimensions that are important for holding our attention-shot durations, scene durations, motion, and sound amplitude-and have crafted fluctuations in them like those of our endogenous attention patterns. Other dimensions-luminance, clutter, and shot scale-are important to film style but their variations seem not to be important to holding viewers' moment-to-moment attention and have not changed in their fractional dimension over time.

Decomposing Multifractal Crossovers

Physiological processes-such as, the brain's resting-state electrical activity or hemodynamic fluctuations-exhibit scale-free temporal structuring. However, impacts common in biological systems such as, noise, multiple signal generators, or filtering by transport function, result in multimodal scaling that cannot be reliably assessed by standard analytical tools that assume unimodal scaling. Here, we present two methods to identify breakpoints or crossovers in multimodal multifractal scaling functions. These methods incorporate the robust iterative fitting approach of the focus-based multifractal formalism (FMF). The first approach (moment-wise scaling range adaptivity) allows for a breakpoint-based adaptive treatment that analyzes segregated scale-invariant ranges. The second method (scaling function decomposition method, SFD) is a crossover-based design aimed at decomposing signal constituents from multimodal scaling functions resulting from signal addition or co-sampling, such as, contamination by uncorrelated fractals. We demonstrated that these methods could handle multimodal, mono- or multifractal, and exact or empirical signals alike. Their precision was numerically characterized on ideal signals, and a robust performance was demonstrated on exemplary empirical signals capturing resting-state brain dynamics by near infrared spectroscopy (NIRS), electroencephalography (EEG), and blood oxygen level-dependent functional magnetic resonance imaging (fMRI-BOLD). The NIRS and fMRI-BOLD low-frequency fluctuations were dominated by a multifractal component over an underlying biologically relevant random noise, thus forming a bimodal signal. The crossover between the EEG signal components was found at the boundary between the δ and θ bands, suggesting an independent generator for the multifractal δ rhythm. The robust implementation of the SFD method should be regarded as essential in the seamless processing of large volumes of bimodal fMRI-BOLD imaging data for the topology of multifractal metrics free of the masking effect of the underlying random noise.

Criticality in the brain: A synthesis of neurobiology, models and cognition

Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.

Cortical localization of phase and amplitude dynamics predicting access to somatosensory awareness

Neural dynamics leading to conscious sensory perception have remained enigmatic in despite of large interest. Human functional magnetic resonance imaging (fMRI) studies have revealed that a co-activation of sensory and frontoparietal areas is crucial for conscious sensory perception in the several second time-scale of BOLD signal fluctuations. Electrophysiological recordings with magneto- and electroencephalography (MEG and EEG) and intracranial EEG (iEEG) have shown that event related responses (ERs), phase-locking of neuronal activity, and oscillation amplitude modulations in sub-second timescales are greater for consciously perceived than for unperceived stimuli. The cortical sources of ER and oscillation dynamics predicting the conscious perception have, however, remained unclear because these prior studies have utilized MEG/EEG sensor-level analyses or iEEG with limited neuroanatomical coverage. We used a somatosensory detection task, magnetoencephalography (MEG), and cortically constrained source reconstruction to identify the cortical areas where ERs, local poststimulus amplitudes and phase-locking of neuronal activity are predictive of the conscious access of somatosensory information. We show here that strengthened ERs, phase-locking to stimulus onset (SL), and induced oscillations amplitude modulations all predicted conscious somatosensory perception, but the most robust and widespread of these was SL that was sustained in low-alpha (6-10 Hz) band. The strength of SL and to a lesser extent that of ER predicted conscious perception in the somatosensory, lateral and medial frontal, posterior parietal, and in the cingulate cortex. These data suggest that a rapid phase-reorganization and concurrent oscillation amplitude modulations in these areas play an instrumental role in the emergence of a conscious percept.

Spectral convergence in tapping and physiological fluctuations: coupling and independence of 1/f noise in the central and autonomic nervous systems

When humans perform a response task or timing task repeatedly, fluctuations in measures of timing from one action to the next exhibit long-range correlations known as 1/f noise. The origins of 1/f noise in timing have been debated for over 20 years, with one common explanation serving as a default: humans are composed of physiological processes throughout the brain and body that operate over a wide range of timescales, and these processes combine to be expressed as a general source of 1/f noise. To test this explanation, the present study investigated the coupling vs. independence of 1/f noise in timing deviations, key-press durations, pupil dilations, and heartbeat intervals while tapping to an audiovisual metronome. All four dependent measures exhibited clear 1/f noise, regardless of whether tapping was synchronized or syncopated. 1/f spectra for timing deviations were found to match those for key-press durations on an individual basis, and 1/f spectra for pupil dilations matched those in heartbeat intervals. Results indicate a complex, multiscale relationship among 1/f noises arising from common sources, such as those arising from timing functions vs. those arising from autonomic nervous system (ANS) functions. Results also provide further evidence against the default hypothesis that 1/f noise in human timing is just the additive combination of processes throughout the brain and body. Our findings are better accommodated by theories of complexity matching that begin to formalize multiscale coordination as a foundation of human behavior.

Manual choice reaction times in the rate-domain

Over the last 150 years, human manual reaction times (RTs) have been recorded countless times. Yet, our understanding of them remains remarkably poor. RTs are highly variable with positively skewed frequency distributions, often modeled as an inverse Gaussian distribution reflecting a stochastic rise to threshold (diffusion process). However, latency distributions of saccades are very close to the reciprocal Normal, suggesting that "rate" (reciprocal RT) may be the more fundamental variable. We explored whether this phenomenon extends to choice manual RTs. We recorded two-alternative choice RTs from 24 subjects, each with 4 blocks of 200 trials with two task difficulties (easy vs. difficult discrimination) and two instruction sets (urgent vs. accurate). We found that rate distributions were, indeed, very close to Normal, shifting to lower rates with increasing difficulty and accuracy, and for some blocks they appeared to become left-truncated, but still close to Normal. Using autoregressive techniques, we found temporal sequential dependencies for lags of at least 3. We identified a transient and steady-state component in each block. Because rates were Normal, we were able to estimate autoregressive weights using the Box-Jenkins technique, and convert to a moving average model using z-transforms to show explicit dependence on stimulus input. We also found a spatial sequential dependence for the previous 3 lags depending on whether the laterality of previous trials was repeated or alternated. This was partially dissociated from temporal dependency as it only occurred in the easy tasks. We conclude that 2-alternative choice manual RT distributions are close to reciprocal Normal and not the inverse Gaussian. This is not consistent with stochastic rise to threshold models, and we propose a simple optimality model in which reward is maximized to yield to an optimal rate, and hence an optimal time to respond. We discuss how it might be implemented.

A Review of Theoretical Perspectives in Cognitive Science on the Presence of 1/f 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.

Interactive rhythmic cue facilitates gait relearning in patients with Parkinson's disease

To develop a method for cooperative human gait training, we investigated whether interactive rhythmic cues could improve the gait performance of Parkinson's disease patients. The interactive rhythmic cues ware generated based on the mutual entrainment between the patient's gait rhythms and the cue rhythms input to the patient while the patient walked. Previously, we found that the dynamic characteristics of stride interval fluctuation in Parkinson's disease patients were improved to a healthy 1/f fluctuation level using interactive rhythmic cues and that this effect was maintained in the short term. However, two problems remained in our previous study. First, it was not clear whether the key factor underpinning the effect was the mutual entrainment between the gait rhythms and the cue rhythms or the rhythmic cue fluctuation itself. Second, it was not clear whether or not the gait restoration was maintained longitudinally and was relearned after repeating the cue-based gait training. Thus, the present study clarified these issues using 32 patients who participated in a four-day experimental program. The patients were assigned randomly to one of four experimental groups with the following rhythmic cues: (a) interactive rhythmic cue, (b) fixed tempo cue, (c) 1/f fluctuating tempo cue, and (d) no cue. It has been reported that the 1/f fluctuation of stride interval in healthy gait is absent in Parkinson's disease patients. Therefore, we used this dynamic characteristic as an evaluation index to analyze gait relearning in the four different conditions. We observed a significant effect in condition (a) that the gait fluctuation of the patients gradually returned to a healthy 1/f fluctuation level, whereas this did not occur in the other conditions. This result suggests that the mutual entrainment can facilitate gait relearning effectively. It is expected that interactive rhythmic cues will be widely applicable in the fields of rehabilitation and assistive technology.

Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto- and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics.

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

Spectral analysis is a widely used method to estimate 1/f^α 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/f^α 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/f^α noise, and may provide a means to achieve a more solid framework for 1/f^α noise in continuous processes.

Dynamics of cognition

The application of dynamical systems methods and concepts to cognitive phenomena has broadened the range of testable hypotheses and theoretical narratives available to cognitive scientists. Most research in cognitive dynamics tests the degree to which observed cognitive performance is consistent with one or another core phenomena associated with complex dynamical systems, such as tests for phase transitions, coupling among processes, or scaling laws. Early applications of dynamical systems theory to perceptual-motor performance and developmental psychology paved the way for more recent applications of dynamical systems analyses, models, and theoretical concepts in areas such as learning, memory, speech perception, decision making, problem solving, and reading, among others. Reviews of the empirical results of both foundational and contemporary cognitive dynamics are provided. WIREs Cogn Sci 2012. doi: 10.1002/wcs.1200 For further resources related to this article, please visit the WIREs website.

Measuring fractality

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.

Infra-slow fluctuations in electrophysiological recordings, blood-oxygenation-level-dependent signals, and psychophysical time series

Converging electrophysiological and neuroimaging data show that mammalian brain dynamics are governed by spontaneous modulations of neuronal activity levels in cortical and subcortical structures. The time scales of these fluctuations form a continuum from seconds to tens and hundreds of seconds corresponding to slow (0.1-1Hz), infra-slow (0.01-0.1Hz), and "ultradian" (<0.01Hz) frequency bands, respectively. We focus here on the spontaneous neuronal dynamics in the infra-slow frequency band, infra-slow fluctuations (ISFs), and explore their electrophysiological substrates and behavioral correlates. Although electrophysiological ISFs and the associated infra-slow modulations of fast (here, >1Hz) neuronal activities have been recognized on numerous occasions since late 50's, a resurgence in interest towards this frequency band has been driven by a discovery that ISFs in blood-oxygenation-level dependent (BOLD) signals are correlated among specific constellations of brain regions, which constitute intrinsic connectivity networks and define the dynamic architecture of spontaneous brain activity at large. Importantly, electrophysiological and BOLD signal ISFs are directly correlated both with ISFs in amplitudes of fast neuronal activities and with ISFs in behavioral performance. Moreover, both electrophysiological and neuroimaging data suggest that the apparently scale-free ISFs may arise from more local quasi-periodic infra-slow oscillations with a contribution of time-scale-specific cellular-level mechanisms. We conclude that ISFs in electrophysiological recordings, BOLD signals, neuronal activity levels, and behavioral time series are likely to reflect the same underlying phenomenon; a superstructure of interacting and transiently oscillatory ISFs that regulate both the integration within and decoupling between concurrently active neuronal communities.

1/f Noise in human color vision: the role of S-cone signals

We examine the functional role of S-cone signals on reaction time (RT) variability in human color vision. Stimuli were selected along red-green and blue-yellow cardinal directions and at random directions in the isoluminant plane of the color space. Trial-to-trial RT variability was not statistically independent but correlated across experimental conditions and exhibited 1/f noise spectra with an exponent close to unity in most of the cases. Regarding contrast coding, 1/f noise for random chromatic stimuli at isoluminance was similar to that for achromatic stimuli, thus suggesting that S-cone signals reduce variability of higher order color mechanisms. If we regard spatial coding, the effect of S-cone density in the retina on RT variability was investigated. The magnitude of 1/f noise at 16 min of arc (S-cone free zone) was higher than at 90 min of arc in the blue-yellow channel, and it was similar for the red-green channel. The results suggest that S-cone signals are beneficial and they modulate 1/f noise spectra at postreceptoral stages. The implications related to random multiplicative processes as a possible source of 1/f noise and the optimal information processing in color vision are discussed.

Visual motion with pink noise induces predation behaviour

Visual motion cues are one of the most important factors for eliciting animal behaviour, including predator-prey interactions in aquatic environments. To understand the elements of motion that cause such selective predation behaviour, we used a virtual plankton system where the predation behaviour in response to computer-generated prey was analysed. First, we performed motion analysis of zooplankton (Daphnia magna) to extract mathematical functions for biologically relevant motions of prey. Next, virtual prey models were programmed on a computer and presented to medaka (Oryzias latipes), which served as predatory fish. Medaka exhibited predation behaviour against several characteristic virtual plankton movements, particularly against a swimming pattern that could be characterised as pink noise motion. Analysing prey-predator interactions via pink noise motion will be an interesting research field in the future.

Aging and motor variability: a test of the neural noise hypothesis

Experimental tests of the neural noise hypothesis of aging, which holds that aging-related increments in motor variability are due to increases in white noise in the perceptual-motor system, were conducted. Young (20-29 years old) and old (60-69 and 70-79 years old) adults performed several perceptual-motor tasks. Older adults were progressively more variable in their performance outcome, but there was no age-related difference in white noise in the motor output. Older adults had a greater frequency-dependent structure in their motor variability that was associated with performance decrements. The findings challenge the main tenet of the neural noise hypothesis of aging in that the increased variability of older adults was due to a decreased ability to adapt to the constraints of the task rather than an increment of neural noise per se.

Dimensionality Analysis of the Thought Suppression Inventory: Combining EFA, MSA, and CFA

The Thought Suppression Inventory (TSI; Rassin, European Journal of Personality 17: 285-298, 2003) was designed to measure thought intrusion, thought suppression and successful thought suppression. Given the importance to distinguish between these three aspects of thought control, the aim of this study was to scrutinize the dimensionality of the TSI. In a sample of 333 Dutch senior citizins, we examined (1) the dimensionality of the TSI using various procedures such as PAF, Mokken scale analysis (MSA) and CFA, and (2) the scale properties of the TSI. PAF favored a two factor solution, however, MSA and CFA suggested that three dimensions most adequately capture the structure of the TSI. Although all scales obtained at least medium scalability coefficients, several items were identified that are psychometrically unsound and may benefit from rewording or replacement. The findings suggest that the TSI is a three-dimensional questionnaire as originally proposed by Rassin (European Journal of Personality 17: 285-298, 2003) measuring thought intrusion, thought suppression, and successful thought suppression.

Extended Stevens' power law

An extension of the Stevens' power law, widely used in psychophysics to relate a physical magnitude of a stimulus (e.g. taste, luminance, weight, sound pressure) with the corresponding experienced magnitude (saltiness, brightness, heaviness, loudness etc.) has been proposed. It takes into account the fact that psychophysical functions are basically of a sigmoid and not power-like type. To model the stimulus-response relationship the S-shaped Gompertz function converted to the power form by the mapping procedure is employed. It provides the extended Stevens' power law y(C) = k(C)C(n(C)) with the scaling factor k(C) and exponent n(C) as function of the stimulus magnitude C. The model will be used in determination of the saltiness and brightness stimulus-response power function correctly reproducing the experimental psychophysical data in a wide range of the stimuli applied. It will be proven that the extended Stevens' power law belongs to the class of self-similar and allometric processes of the fractal nature.

Causality, criticality, and reading words: distinct sources of fractal scaling in behavioral sequences

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition.

Motor imagery may incorporate trial-to-trial error

The authors tested for 1/f noise in motor imagery (MI). Participants pointed and imagined pointing to a single target (Experiment 1), to targets of varied size (Experiment 2), and switched between pointing and grasping (Experiment 3). Experiment 1 showed comparable patterns of serial correlation in actual and imagined movement. Experiment 2 suggested increased correlation for MI and performance with increased task difficulty, perhaps reflecting adaptation to a more complex environment. Experiment 3 suggested a parallel decrease in correlation with task switching, perhaps reflecting discontinuity of mental set. Although present results do not conclusively reveal 1/f fluctuation, the emergent patterns suggest that MI could incorporate trial-to-trial error across a range of constraints.

Data series embedding and scale invariant statistics

Data sequences acquired from bio-systems such as human gait data, heart rate interbeat data, or DNA sequences exhibit complex dynamics that is frequently described by a long-memory or power-law decay of autocorrelation function. One way of characterizing that dynamics is through scale invariant statistics or "fractal-like" behavior. For quantifying scale invariant parameters of physiological signals several methods have been proposed. Among them the most common are detrended fluctuation analysis, sample mean variance analyses, power spectral density analysis, R/S analysis, and recently in the realm of the multifractal approach, wavelet analysis. In this paper it is demonstrated that embedding the time series data in the high-dimensional pseudo-phase space reveals scale invariant statistics in the simple fashion. The procedure is applied on different stride interval data sets from human gait measurements time series (Physio-Bank data library). Results show that introduced mapping adequately separates long-memory from random behavior. Smaller gait data sets were analyzed and scale-free trends for limited scale intervals were successfully detected. The method was verified on artificially produced time series with known scaling behavior and with the varying content of noise. The possibility for the method to falsely detect long-range dependence in the artificially generated short range dependence series was investigated.

Attention and the evolution of Hollywood film

Reaction times exhibit a spectral patterning known as 1/f, and these patterns can be thought of as reflecting time-varying changes in attention. We investigated the shot structure of Hollywood films to determine if these same patterns are found. We parsed 150 films with release dates from 1935 to 2005 into their sequences of shots and then analyzed the pattern of shot lengths in each film. Autoregressive and power analyses showed that, across that span of 70 years, shots became increasingly more correlated in length with their neighbors and created power spectra approaching 1/f. We suggest, as have others, that 1/f patterns reflect world structure and mental process. Moreover, a 1/f temporal shot structure may help harness observers' attention to the narrative of a film.

Estimating long-range dependence in time series: an evaluation of estimators implemented in R

Recent studies have shown that many physiological and behavioral processes can be characterized by long-range correlations. The Hurst exponent H of fractal analysis and the fractional-differencing parameter d of the ARFIMA methodology are useful for capturing serial correlations. In this study, we report on different estimators of H and d implemented in R, a popular and freely available software package. By means of Monte Carlo simulations, we analyzed the performance of (1) the Geweke-Porter-Hudak estimator, (2) the approximate maximum likelihood algorithm, (3) the smoothed periodogram approach, (4) the Whittle estimator, (5) rescaled range analysis, (6) a modified periodogram, (7) Higuchi's method, and (8) detrended fluctuation analysis. The findings-confined to ARFIMA (0, d, 0) models and fractional Gaussian noise-identify the best estimators for persistent and antipersistent series. Two examples combining these results with the step-by-step procedure proposed by Delignières et al. (2006) demonstrate how this evaluation can be used as a guideline in a typical research situation.

Global Model Analysis of Cognitive Variability

Residual fluctuations produced in typical experimental methodologies are examined as correlated noises. The effective range of the correlations was assessed by determining whether the decay over look‐back time is better described as a power law or exponential. Both of these decay laws contain free parameters and it is argued that it is not possible to distinguish their models on the basis of simple measures of goodness‐of‐fit. Global analyses that evaluate models on the basis of how well they generalize are conducted. The models are examined in terms of three constructs that all bear on generalization: cross‐validity, flexibility, and representativeness. Quantitative assessment of a large ensemble of data suggests that the correlations decay over time as a power law. The conclusion is that human residual fluctuation is a correlated fractal.

Dispersion of response times reveals cognitive dynamics

Trial-to-trial variation in word-pronunciation times exhibits 1/f scaling. One explanation is that human performances are consequent on multiplicative interactions among interdependent processes-interaction dominant dynamics. This article describes simulated distributions of pronunciation times in a further test for multiplicative interactions and interdependence. Individual participant distributions of approximately 1,100 word-pronunciation times were successfully mimicked for each participant in combinations of lognormal and power-law behavior. Successful hazard function simulations generalized these results to establish interaction dominant dynamics, in contrast with component dominant dynamics, as a likely mechanism for cognitive activity.

Lévy-like diffusion in eye movements during spoken-language comprehension

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.