Experimental control of scaling behavior: what is not fractal?

From Cognitive Agents to Cognitive Systems: Theoretical, Methodological, and Empirical Developments of van Gelder's (1998) "Dynamical Hypothesis"

Over two decades have passed since the publication of van Gelder's (1998) "dynamical hypothesis." In that paper, van Gelder proposed that cognitive agents were not digital computers-per the representational computational approach-but dynamical systems. The evolution of the dynamical hypothesis was driven by parallel advances in three areas. Theoretically, a deeper understanding of genetics, biology, neuroscience, and cognitive science inspired questions about how systems within each domain dynamically interact and extend their effects across spatiotemporal scales. Methodologically, more sophisticated and domain-general tools allowed researchers to discover, model, and quantify system dynamics, structure, and patterns across multiple scales to generate a more comprehensive system-level understanding of behaviors. Empirically, we can analyze a system's behavior while preserving its natural dynamics, revealing evidence that the reductionist approach leads to an incomplete understanding of the components and the overall system. Researchers have traditionally reduced a complex system into its component processes and assumed that the parts can be recombined to explain the whole. These three advances fundamentally altered our understanding of a "cognitive agent:" How their behaviors are driven by long-range coordination across multiple processes, how the interdependent and nested structure of interacting variables produces behaviors that are greater than the sum of its parts, and how environmental constraints shape adaptive yet stable behavioral patterns.

Multifractality in stride-to-stride variations reveals that walking involves more movement tuning and adjusting than running

Introduction: The seemingly periodic human gait exhibits stride-to-stride variations as it adapts to the changing task constraints. The optimal movement variability hypothesis (OMVH) states that healthy stride-to-stride variations exhibit "fractality"-a specific temporal structure in consecutive strides that are ordered, stable but also variable, and adaptable. Previous research has primarily focused on a single fractality measure, "monofractality." However, this measure can vary across time; strideto-stride variations can show "multifractality." Greater multifractality in stride-tostride variations would highlight the ability to tune and adjust movements more. Methods: We investigated monofractality and multifractality in a cohort of eight healthy adults during self-paced walking and running trials, both on a treadmill and overground. Footfall data were collected through force-sensitive sensors positioned on their heels and feet. We examined the effects of self-paced walking vs. running and treadmill vs. overground locomotion on the measure of monofractality, α-DFA, in addition to the multifractal spectrum width, W, and the asymmetry in the multifractal spectrum, WAsym, of stride interval time series. Results: While the α-DFA was larger than 0.50 for almost all conditions, α-DFA was higher in running and locomoting overground than walking and locomoting on a treadmill. Similarly, W was greater while locomoting overground than on a treadmill, but an opposite trend indicated that W was greater in walking than running. Larger WAsym values in the negative direction suggest that walking exhibits more variation in the persistence of shorter stride intervals than running. However, the ability to tune and adjust movements does not differ between treadmill and overground, although both exhibit more variation in the persistence of shorter stride intervals. Discussion: Hence, greater heterogeneity in shorter than longer stride intervals contributed to greater multifractality in walking compared to running, indicated by larger negative WAsym values. Our results highlight the need to incorporate multifractal methods to test the predictions of the OMVH.

The nonlinearity of pupil diameter fluctuations in an insight task as criteria for detecting children who solve the problem from those who do not

Insights, characterized by sudden discoveries following unsuccessful problem-solving attempts, are fascinating phenomena. Dynamic systems perspectives argue that insight arises from self-organizing perceptual and motor processes. Entropy and fractal scaling are potential markers for emerging new and effective solutions. This study investigated whether specific features associated with self-organization in dynamical systems can distinguish between individuals who succeed and those who fail in solving insight tasks. To achieve this, we analyzed pupillary diameter fluctuations of children aged 6 to 12 during the 8-coin task, a well-established insight task. The participants were divided into two groups: successful (n = 24) and unsuccessful (n = 43) task completion. Entropy, determinism, recurrence ratio, and the β scaling exponent were estimated using Recurrence Quantification and Power Spectrum Density analyses. The results indicated that the solver group exhibited more significant uncertainty and lower predictability in pupillary diameter fluctuations before finding the solution. Recurrence Quantification Analysis revealed changes that went unnoticed by mean and standard deviation measures. However, the β scaling exponent did not differentiate between the two groups. These findings suggest that entropy and determinism in pupillary diameter fluctuations can identify early differences in problem-solving success. Further research is needed to determine the exclusive role of perceptual and motor activity in generating insights and investigate these results' generalizability to other tasks and populations.

Multifractal roots of suprapostural dexterity

Visually guided postural control emerges in response to task constraints. Task constraints generate physiological fluctuations that foster the exploration of available sensory information at many scales. Temporally correlated fluctuations quantified using fractal and multifractal metrics have been shown to carry perceptual information across the body. The risk of temporally correlated fluctuations is that stable sway appears to depend on a healthy balance of standard deviation (SD): too much or too little SD entails destabilization of posture. This study presses on the visual guidance of posture by prompting participants to quietly stand and fixate at distances within, less than, and beyond comfortable viewing distance. Manipulations of the visual precision demands associated with fixating nearer and farther than comfortable viewing distance reveals an adaptive relationship between SD and temporal correlations in postural fluctuations. Changing the viewing distance of the fixation target shows that increases in temporal correlations and SD predict subsequent reductions in each other. These findings indicate that the balance of SD within stable bounds may depend on a tendency for temporal correlations to self-correct across time. Notably, these relationships became stronger with greater distance from the most comfortable viewing and reaching distance, suggesting that this self-correcting relationship allows the visual layout to press the postural system into a poise for engaging with objects and events. Incorporating multifractal analysis showed that all effects attributable to monofractal evidence were better attributed to multifractal evidence of nonlinear interactions across scales. These results offer a glimpse of how current nonlinear dynamical models of self-correction may play out in biological goal-oriented behavior. We interpret these findings as part of the growing evidence that multifractal nonlinearity is a modeling strategy that resonates strongly with ecological-psychological approaches to perception and action.

Irregular Metronomes as Assistive Devices to Promote Healthy Gait Patterns

Older adults and people suffering from neurodegenerative disease often experience difficulty controlling gait during locomotion, ultimately increasing their risk of falling. To combat these effects, researchers and clinicians have used metronomes as assistive devices to improve movement timing in hopes of reducing their risk of falling. Historically, researchers in this area have relied on metronomes with isochronous interbeat intervals, which may be problematic because normal healthy gait varies considerably from one step to the next. More recently, researchers have advocated the use of irregular metronomes embedded with statistical properties found in healthy populations. In this paper, we explore the effect of both regular and irregular metronomes on many statistical properties of interstride intervals. Furthermore, we investigate how these properties react to mechanical perturbation in the form of a halted treadmill belt while walking. Our results demonstrate that metronomes that are either isochronous or random break down the inherent structure of healthy gait. Metronomes with statistical properties similar to healthy gait seem to preserve those properties, despite a strong mechanical perturbation. We discuss the future development of this work in the context of networked augmented reality metronome devices.

Stochastic Resonance Reduces Sway and Gait Variability in Individuals With Unilateral Transtibial Amputation: A Pilot Study

Sub-threshold (imperceptible) vibration, applied to parts of the body, impacts how people move and perceive our world. Could this idea help someone who has lost part of their limb? Sub-threshold vibration was applied to the thigh of the affected limb of 20 people with unilateral transtibial amputation. Vibration conditions tested included two noise structures: pink and white. Center of pressure (COP) excursion (range and root-mean-square displacements) during quiet standing, and speed and spatial stride measures (mean and standard deviations of step length and width) during walking were assessed. Pink noise vibration decreased COP displacements in standing, and white noise vibration decreased sound limb step length standard deviation in walking. Sub-threshold vibration positively impacted aspects of both posture and gait; however, different noise structures had different effects. The current study represents foundational work in understanding the potential benefits of incorporating stochastic resonance as an intervention for individuals with amputation.

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.

Do intentionality constraints shape the relationship between motor variability and performance?

The aim of this experiment was to assess if the previously supported relationship between the structure of motor variability and performance changes when the task or organismic constraints encourage individuals to adjust their movement to achieve a goal. Forty-two healthy volunteers (aged 26.05 ± 5.02 years) performed three sets of cyclic pointing movements, 600 cycles each. Every set was performed under different conditions: 1) without a target; 2) with a target; 3) with a target and a financial reward. The amount of performance variability was analysed using the standard deviation of the medial-lateral (ML) and anterior-posterior (AP) axes and the bivariate variable error. The structure of the variability was assessed by Detrended Fluctuation Analysis (DFA) of the following time series: the coordinate values of the endpoint in ML, AP axes and resultant distance (RD), the hand orientation and the movement time. The performance of the task constrained with a target, or a target and reward, required higher implication to adjust an individual’s movements to achieve the task goal, showing a decrease in dispersions and lower autocorrelation. Under the condition without a target, variability dispersion was positively related to autocorrelation of the movement values from ML axis and RD time series, and negatively related to the values from the hand orientation time series. There was a loss of the relationship between variability structure and performance when the task was constrained by the target and the reward. That could indicate different strategies of the participants to achieve the objective. Considering the results and previous studies, the relationship between variability structure and performance could depend on task constraints such as feedback, difficulty or the skill level of participants and it is mediated by individual constraints such as implication or intentionality.

Scaling Behavior of Ionic Transport in Membrane Nanochannels

Ionic conductance in membrane channels exhibits a power-law dependence on electrolyte concentration ( G ∼ c^α). The many scaling exponents, α, reported in the literature usually require detailed interpretations concerning each particular system under study. Here, we critically evaluate the predictive power of scaling exponents by analyzing conductance measurements in four biological channels with contrasting architectures. We show that scaling behavior depends on several interconnected effects whose contributions change with concentration so that the use of oversimplified models missing critical factors could be misleading. In fact, the presence of interfacial effects could give rise to an apparent universal scaling that hides the channel distinctive features. We complement our study with 3D structure-based Poisson-Nernst-Planck (PNP) calculations, giving results in line with experiments and validating scaling arguments. Our findings not only provide a unified framework for the study of ion transport in confined geometries but also highlight that scaling arguments are powerful and simple tools with which to offer a comprehensive perspective of complex systems, especially those in which the actual structure is unknown.

Transitions in persistence of postural dynamics depend on the velocity and structure of postural perturbations

The sensorimotor system prefers sway velocity information when maintaining upright posture. Sway velocity has a unique characteristic of being persistent on a short time-scale and anti-persistent on a longer time-scale. The time where the transition from persistence to anti-persistence occurs provides information about how sway velocity is controlled. It is, however, not clear what factors affect shifts in this transition point. This research investigated postural responses to support surface movements of different temporal correlations and movement velocities. Participants stood on a force platform that was translated according to three different levels of temporal correlation. White noise had no correlation, pink noise had moderate correlation, and sine wave movements had very strong correlation. Each correlation structure was analyzed at five different average movement velocities (0.5, 1.0, 2.0, 3.0, and 4.0 cm·s^-1), as well as one trial of quiet stance. Center of pressure velocity was analyzed using fractal analysis to determine the transition from persistent to anti-persistent behavior, as well as the strength of persistence. As movement velocity increased, the time to transition became longer for the sine wave and shorter for the white and pink noise movements. Likewise, during the persistent time-scale, the sine wave resulted in the strongest correlation, while white and pink noise had weaker correlations. At the highest three movement velocities, the strength of persistence was lower for the white noise compared to pink noise movements. These results demonstrate that the predictability and velocity of support surface oscillations affect the time-scale threshold between persistent and anti-persistent postural responses. Consequently, whether a feedforward or feedback control is utilized for appropriate postural responses may also be determined by the predictability and velocity of environmental stimuli. The study provides new insight into flexibility and adaptability in postural control. This information has implications for the design of rehabilitative protocols in neuromuscular control.

Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG

Humans are high-dimensional, complex systems consisting of many components that must coordinate in order to perform even the simplest of activities. Many behavioral studies, especially in the movement sciences, have advanced the notion of soft-assembly to describe how systems with many components coordinate to perform specific functions while also exhibiting the potential to re-structure and then perform other functions as task demands change. Consistent with this notion, within cognitive neuroscience it is increasingly accepted that the brain flexibly coordinates the networks needed to cope with changing task demands. However, evaluation of various indices of soft-assembly has so far been absent from neurophysiological research. To begin addressing this gap, we investigated task-related changes in two distinct indices of soft-assembly using the established phenomenon of EEG repetition suppression. In a repetition priming task, we assessed evidence for changes in the correlation dimension and fractal scaling exponents during stimulus-locked event-related potentials, as a function of stimulus onset and familiarity, and relative to spontaneous non-task-related activity. Consistent with predictions derived from soft-assembly, results indicated decreases in dimensionality and increases in fractal scaling exponents from resting to pre-stimulus states and following stimulus onset. However, contrary to predictions, familiarity tended to increase dimensionality estimates. Overall, the findings support the view from soft-assembly that neural dynamics should become increasingly ordered as external task demands increase, and support the broader application of soft-assembly logic in understanding human behavior and electrophysiology.