Relative Roughness: An Index for Testing the Suitability of the Monofractal Model

Fractal analyses have become very popular and have been applied on a wide variety of empirical time series. The application of these methods supposes that the monofractal framework can offer a suitable model for the analyzed series. However, this model takes into account a quite specific kind of fluctuations, and we consider that fractal analyses have been often applied to series that were completely outside of its relevance. The problem is that fractal methods can be applied to all types of series, and they always give a result, that one can then erroneously interpret in the context of the monofractal framework. We propose in this paper an easily computable index, the relative roughness (RR), defined as the ratio between local and global variances, that allows to test for the applicability of fractal analyses. We show that RR is confined within a limited range (between 1.21 and 0.12, approximately) for long-range correlated series. We propose some examples of empirical series that have been recently analyzed using fractal methods, but, with respect to their RR, should not have been considered in the monofractal model. An acceptable level of RR, however, is a necessary but not sufficient condition for considering series as long-range correlated. Specific methods should be used in complement for testing for the effective presence of long-range correlations in empirical series

Theories and models for 1/f b noise in human movement science

a b s t r a c t Human motor behavior is often characterized by long-range, slowly decaying serial correlations or 1/f b noise. Despite its prevalence, the role of the 1/f b phenomenon in human movement research has been rather modest and unclear. The goal of this paper is to outline a research agenda in which the study of 1/f b noise can contribute to scientific progress. In the first section of this article we discuss two popular perspectives on 1/f b noise: the nomothetic perspective that seeks general explanations, and the mechanistic perspective that seeks domain-specific models. We believe that if 1/f b noise is to have an impact on the field of movement science, researchers should develop and test domain-specific mechanistic models of human motor behavior. In the second section we illustrate our claim by showing how a mechanistic model of 1/f b noise can be successfully integrated with currently established models for rhythmic self-paced, synchronized, and bimanual tapping. This model synthesis results in a unified account of the observed longrange serial correlations across a range of different tasks

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce the same tapping performance while being deprived from 0, 1, 2, or 3 sensory feedbacks simultaneously (auditory and/or visual and/or tactile). Whereas tapping performance was not statistically different across groups, the number of brain networks involved and the degree of multifractality of the inter-tap interval series were significantly correlated, increasing as a function of feedback deprivation. Our findings provide first evidence that concomitant changes in brain modularity and multifractal properties characterize adaptations underlying unchanged performance. We discuss implications of our findings with respect to the degeneracy properties of complex systems, and the entanglement of adaptability and effective adaptation

Long-Range Correlation in Synchronization and Syncopation Tapping: A Linear Phase Correction Model

We propose in this paper a model for accounting for the increase in long-range correlations observed in asynchrony series in syncopation tapping, as compared with synchronization tapping. Our model is an extension of the linear phase correction model for synchronization tapping. We suppose that the timekeeper represents a fractal source in the system, and that a process of estimation of the half-period of the metronome, obeying a random-walk dynamics, combines with the linear phase correction process. Comparing experimental and simulated series, we show that our model allows accounting for the experimentally observed pattern of serial dependence. This model complete previous modeling solutions proposed for self-paced and synchronization tapping, for a unifying framework of event-based timing

Persistent fluctuations in stride intervals under fractal auditory stimulation

Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.Commission of the European Community and the Netherlands Organisation for Scientific Research

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

Timing absolu et relatif dans les coordinations bimanuelles (contribution de l'analyse des corrélations sérielles et implications pour la modélisation)

MONTPELLIER-BU Médecine UPM (341722108) / SudocMONTPELLIER-BU STAPS (341722109) / SudocMONTPELLIER-BU Médecine (341722104) / SudocSudocFranceF

Vers une nécessaire prise en compte de la complexité : variabilité et fractalité dans la motricité rythmique

Coming to the Necessary Consideration of Complexity : Variability and Fractality in Rhythmic Motor behavior. The variability of systems’ behavior has been for a long time considered as random fluctuation. A number of recent works have shown, however, that this variability had a characteristic temporal structure, and especially 1/f-type fractal correlations. This kind of fluctuation is considered the natural signature of complex systems, and questions the models classically adopted for taking into account the processes under study. We give some examples in the domain of rhythmical movement, and consider the theoretical consequences of the consideration of these fluctuations in performance. In readable English…La variabilité du comportement des systèmes a longtemps été considérée comme relevant de fluctuations aléatoires. Un certain nombre de travaux récents ont cependant montré que cette variabilité possédait une structure temporelle caractéristique, et en particulier des corrélations fractales de type 1/f. Ce type de fluctuation est considéré comme la signature naturelle des systèmes complexes, et questionne les modèles classiquement adoptés pour rendre compte des processus étudiés. Nous donnons ici un certain nombre d’exemples dans le cadre de la motricité rythmique et envisageons les conséquences théoriques de la prise en compte de ces fluctuations de performance.Delignières Didier, Torre Kjerstin. Vers une nécessaire prise en compte de la complexité : Variabilité et fractalité dans la motricité rythmique. In: Intellectica. Revue de l'Association pour la Recherche Cognitive, n°52, 2009/2. Sport de haute performance et cognition. pp. 41-54