Degeneracy and long-range correlations

Degeneracy is a ubiquitous property of complex adaptive systems, which refers to the ability of structurally different components to perform the same function in some conditions and different functions in other conditions. Here, we suppose a causal link between the level of degeneracy in the system and the strength of long-range correlations in its behavior. In a numerical experiment, we manipulated degeneracy through the number of networks available in a model composed of a chain of correlated networks over which a series of random jumps are performed. Results showed that correlations in the outcome series increased with the number of available networks, and that a minimal threshold of degeneracy was required to generate long-range correlations. We conclude that degeneracy could underlie the presence of long-range correlations in the outcome series produced by complex systems. In turn, we suggest that quantifying long-range correlations could allow to assess the level of degeneracy of the system. Degeneracy affords a maybe more intuitive way than former hypotheses for understanding the effects of complexity on essential properties such as robustness and adaptability

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

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

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

The PARAChute project: remote monitoring of posture and gait for fall prevention

Falls in the elderly are a major public health problem due to both their frequency and their medical and social consequences. In France alone, more than two million people aged over 65 years old fall each year, leading to more than 9 000 deaths, in particular in those over 75 years old (more than 8 000 deaths). This paper describes the PARAChute project, which aims to develop a methodology that will enable the detection of an increased risk of falling in community-dwelling elderly. The methods used for a remote noninvasive assessment for static and dynamic balance assessments and gait analysis are described. The final result of the project has been the development of an algorithm for movement detection during gait and a balance signature extracted from a force plate. A multicentre longitudinal evaluation of balance has commenced in order to validate the methodologies and technologies developed in the project

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

Contains fulltext : 50308.pdf (publisher's version ) (Closed access)In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control

Émotion et performance sportive

Delignières Didier. Émotion et performance sportive. In: Les Cahiers de l'INSEP, n°22, 1998. Entraînement mental et sport de haute performance. pp. 107-119