Didier Delignières

Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al.

We propose in this paper a reassessment of the original data of Hausdorff et al. (Hausdorff JM, Purdon PL, Peng C-K, Ladin Z, Wei JY, Goldberger AR. J Appl Physiol 80: 1448-1457, 1996). We confirm, using autoregressive fractionally integrated moving average modeling, the presence of genuine fractal correlations in stride interval series in self-paced conditions. In contrast with the conclusions of the authors, we show that correlations did not disappear in metronomic conditions. The series of stride intervals presented antipersistent correlations, and 1/f fluctuations were evidenced in the asynchronies to the metronome. We show that the super central pattern generator model (West B, Scafetta N. Phys Rev E Stat Nonlin Soft Matter Phys 67: 051917, 2003) allows accounting for the experimentally observed correlations in both self-paced and metronomic conditions, by the simple setting of the coupling strength parameter. We conclude that 1/f fluctuations in gait are not overridden by supraspinal influences when walking is paced by a metronome. The source of 1/f noise is still at work in this condition, but expressed differently under the influence of a continuous coupling process.

Influence of physical exercise on simple reaction time: effect of physical fitness.

The influence of physical fitness and energy expenditure on a simple reaction time task performed during exercise was investigated. Two groups of 10 subjects were used, one was composed of trained middle-distance runners and one of students who had no regular physical training. The subjects performed a simple reaction time task while pedalling on a cycloergometer at different relative power output corresponding to 20, 40, 60, and 80% of their own maximal aerobic power and immediately after exercise. During exercise, the results showed a decrease in cognitive performance for both groups whereas no significant effect was found after exercise. A significant effect of physical fitness on simple reaction time was noted during exercise. The data are interpreted in terms of optimization of performance focusing particularly on the relations between energy cost of the physical task and attentional demand.

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.

SELECTIVE EFFECTS OF PHYSICAL EXERCISE ON CHOICE REACTION PROCESSES

The aim of the present study was to examine the effects of an exercise of moderate intensity (60% of maximal aerobic power) on specific information-processing mechanisms. 22 students completed 3 10-min. exercise bouts on a bicycle ergometer. Concomitantly, participants performed six manual choice-reaction tasks manipulating task variables (Signal Intensity, Stimulus–Response Compatibility, and Time Uncertainty) on two levels. Reaction tests, randomly ordered, were administered at rest and during exercise. A significant underadditive interaction between Time Uncertainty and exercise was found for the highest quartiles of the distribution of reaction times. No other interaction effects were obtained for the other variables. These results reasonably support that moderate aerobic exercise showed selective rather than general influences on information processing.

On Discontinuities in Motor Learning: A Longitudinal Study of Complex Skill Acquisition on a Ski-Simulator

Abstract The qualitative behavioral reorganizations that occurred during the acquisition of a complex motor skill were examined. Five novice participants practiced for 39 sessions of ten 1-min trials on a modified version of the ski-simulator. Analyses focused on the motion of the apparatus platform, modeled as a self-sustained oscillator. At the beginning of the experiment, all participants adopted a behavior that could be modeled with a highly nonlinear stiffness function and a Rayleigh damping function. The behavior in the final part of the experiment was captured by a qualitatively different model, with a linear stiffness function and a van der Pol damping behavior. The transition from the initial to the final model was gradual and was marked in most cases by an abrupt increase of oscillation frequency. During the transition stage, the 2 damping behaviors seemed alternately exploited within each trial. The results are discussed in the framework of the dynamical systems approach to motor coordination and learning, considering motor skill acquisition as a phase transition.

Transition from persistent to anti-persistent correlations in postural sway indicates velocity-based control.

The displacement of the center-of-pressure (COP) during quiet stance has often been accounted for by the control of COP position dynamics. In this paper, we discuss the conclusions drawn from previous analyses of COP dynamics using fractal-related methods. On the basis of some methodological clarification and the analysis of experimental data using stabilogram diffusion analysis, detrended fluctuation analysis, and an improved version of spectral analysis, we show that COP velocity is typically bounded between upper and lower limits. We argue that the hypothesis of an intermittent velocity-based control of posture is more relevant than position-based control. A simple model for COP velocity dynamics, based on a bounded correlated random walk, reproduces the main statistical signatures evidenced in the experimental series. The implications of these results are discussed.

Inter-limb coordination in swimming: Effect of speed and skill level

The aim of this study was to examine the effects of swimming speed and skill level on inter-limb coordination and its intra-cyclic variability. The elbow-knee continuous relative phase (CRP) was used as the order parameter to analyze upper-lower limbs coupling during a complete breaststroke cycle. Twelve recreational and 12 competitive female swimmers swam 25m at a slow speed and 25m at maximal speed. Underwater and aerial side views were mixed and genlocked with an underwater frontal view. The angle, angular velocity, and phase were calculated for the knee and elbow by digitizing body marks on the side view. Three cycles were analyzed, filtered, averaged, and normalized in percentage of the total cycle duration. The competitive swimmers showed greater intra-cyclic CRP variability, indicating a combination of intermediate phase and in-phase knee-elbow coupling within a cycle. This characteristic was more marked at slow speed because more time was spent in the glide period of the stroke cycle, with the body completely extended. Conversely, because they spent less time in the glide, the recreational swimmers showed lower intra-cyclic CRP variability (which is mostly in the in-phase coordination mode), resulting in superposition of contradictory actions (propulsion of one limb during the recovery of the other limb).

Detection of long-range dependence and estimation of fractal exponents through ARFIMA modelling

We evaluate the performance of autoregressive, fractionally integrated, moving average (ARFIMA) modelling for detecting long-range dependence and estimating fractal exponents. More specifically, we test the procedure proposed by Wagenmakers, Farrell, and Ratcliff, and compare the results obtained with the Akaike information criterion (AIC) and the Bayes information criterion (BIC). The present studies show that ARFIMA modelling is able to adequately detect long-range dependence in simulated fractal series. Conversely, this method tends to produce a non-negligible rate of false detections in pure autoregressive and moving average (ARMA) series. Generally, ARFIMA modelling has a bias favouring the detection of long-range dependence. AIC and BIC gave dissimilar results, due to the different weights attributed by the two criteria to accuracy and parsimony. Finally, ARFIMA modelling provides good estimates of fractal exponents, and could adequately complement classical methods, such as spectral analysis, detrended fluctuation analysis or rescaled range analysis.

Unraveling the finding of 1/ f β noise in self-paced and synchronized tapping: a unifying mechanistic model

Abstract1/fβ noise has been revealed in both self-paced and synchronized tapping sequences, without being consistently taken into consideration for the modeling of underlying timing mechanisms. In this study we characterize variability, short-range, and long-range correlation properties of asynchronies and inter-tap intervals collected in a synchronization tapping experiment, attesting statistically the presence of 1/fβ noise in asynchronies. We verify that the linear phase correction model of synchronization tapping in its original formulation cannot account for the empirical long-range correlation properties. On the basis of previous accounts of 1/fβ noise in the literature on self-paced tapping, we propose an extension of the original synchronization model by modeling the timekeeping process as a source of 1/fβ fluctuations. Simulations show that this ‘1/f-AR synchronization model’ accounts for the statistical properties of empirical series, including long-range correlations, and provides an unifying mechanistic account of 1/fβ noise in self-paced and synchronization tapping. This account opens the original synchronization framework to further investigations of timing mechanisms with regard to the serial correlation properties in performed time intervals.

1/fβ fluctuations in bimanual coordination: an additional challenge for modeling

We analyzed the correlation structure of discrete relative phase (DRP) series in bimanual in-phase and anti-phase coordination by associating a number of fractal methods and using discrete rather than continuous relative phase measurement. ARFIMA/ARMA modeling provided statistical evidence for the presence of long-range correlation, and the series were unambiguously characterized as 1/fβ noise. Diverging accounts of bimanual coordination are defended in the literature. Since the evidence for 1/fβ noise provides new insight into the properties of stability in coordination, it should be considered as an empirical criterion for determining which mechanisms are likely to be engaged in bimanual coordination models. We discussed some implications for studying the neural basis of coordination, and we tested the performance of three current models in accounting for 1/fβ noise in DRP. None of these models was proven to generate the expected correlation structure.