Restoring Walking Complexity in Older Adults Through Arm-in-Arm Walking: Were Almurad et al.'s (2018) Results an Artifact?

The analysis of stride series revealed a loss of complexity in older people, which correlated with the falling propensity. A recent experiment evidenced an increase of walking complexity in older participants when they walked in close synchrony with a younger companion. Moreover, a prolonged experience of such synchronized walking yielded a persistent restoration of complexity. This result, however, was obtained with a unique healthy partner, and it could be related to a particular partner's behavior. The authors' aim was to replicate this important finding using a different healthy partner and to compare the results to those previously obtained. The authors successfully replicated the previous results: synchronization yielded an attraction of participants' complexity toward that of their partner and a restoration of complexity that persisted in two posttests, 2 and 6 weeks after the end of the training sessions. This study shows that this complexity restoration protocol can be applied successfully with another partner, and allows us to conclude that it can be generalized.

Interpersonal Synchronization Processes in Discrete and Continuous Tasks.

Three frameworks have been proposed to account for interpersonal synchronization: The information processing approach argues that synchronization is achieved by mutual adaptation, the coordination dynamics perspective supposes a continuous coupling between systems, and complexity matching suggests a global, multi-scale interaction. We hypothesized that the relevancy of these models was related to the nature of the performed tasks. 10 dyads performed synchronized tapping and synchronized forearm oscillations, in two conditions: full (participants had full information about their partner), and digital (information was limited to discrete auditory signals). Results shows that whatever the task and the available information, synchronization was dominated by a discrete mutual adaptation. These results question the relevancy of the coordination dynamics perspective in interpersonal coordination.

Biases in the Simulation and Analysis of Fractal Processes.

Fractal processes have recently received a growing interest, especially in the domain of rehabilitation. More precisely, the evolution of fractality with aging and disease, suggesting a loss of complexity, has inspired a number of studies that tried, for example, to entrain patients with fractal rhythms. This kind of study requires relevant methods for generating fractal signals and for assessing the fractality of the series produced by participants. In the present work, we engaged a cross validation of three methods of generation and three methods of analysis. We generated exact fractal series with the Davies-Harte (DH) algorithm, the spectral synthesis method (SSM), and the ARFIMA simulation method. The series were analyzed by detrended fluctuation analysis (DFA), power spectral density (PSD) method, and ARFIMA modeling. Results show that some methods of generation present systematic biases: DH presented a strong bias toward white noise in fBm series close to the 1/f boundary and SSM produced series with a larger variability around the expected exponent, as compared with other methods. In contrast, ARFIMA simulations provided quite accurate series, without major bias. Concerning the methods of analysis, DFA tended to systematically underestimate fBm series. In contrast, PSD yielded overestimates for fBm series. With DFA, the variability of estimates tended to increase for fGn series as they approached the 1/f boundary and reached unacceptable levels for fBm series. The highest levels of variability were produced by PSD. Finally, ARFIMA methods generated the best series and provided the most accurate and less variable estimates.

Complexity Matching: Restoring the Complexity of Locomotion in Older People Through Arm-in-Arm Walking.

The complexity matching effect refers to a maximization of information exchange, when interacting systems share similar complexities. Additionally, interacting systems tend to attune their complexities in order to enhance their coordination. This effect has been observed in a number of synchronization experiments, and interpreted as a transfer of multifractality between systems. Finally, it has been shown that when two systems of different complexity levels interact, this transfer of multifractality operates from the most complex system to the less complex, yielding an increase of complexity in the latter. This theoretical framework inspired the present experiment that tested the possible restoration of complexity in older people. In young and healthy participants, walking is known to present 1/f fluctuations, reflecting the complexity of the locomotion system, providing walkers with both stability and adaptability. In contrast walking tends to present a more disordered dynamics in older people, and this whitening was shown to correlate with fall propensity. We hypothesized that if an aged participant walked in close synchrony with a young companion, the complexity matching effect should result in the restoration of complexity in the former. Older participants were involved in a prolonged training program of synchronized walking, with a young experimenter. Synchronization within the dyads was dominated by complexity matching. We observed a restoration of complexity in participants after 3 weeks, and this effect was persistent 2 weeks after the end of the training session. This work presents the first demonstration of a restoration of complexity in deficient systems.

Complexity matching in side-by-side walking.

Interpersonal coordination represents a very common phenomenon in daily-life activities. Three theoretical frameworks have been proposed to account for synchronization processes in such situations: the information processing approach, the coordination dynamics perspective, and the complexity matching effect. On the basis of a theoretical analysis of these frameworks, we propose three statistical tests that could allow to distinguish between these theoretical hypotheses: the first one is based on multifractal analyses, the second and the third ones on cross-correlation analyses. We applied these tests on series collected in an experiment where participants were instructed to walk in synchrony. We contrasted three conditions: independent walking, side-by-side walking, and arm-in-arm walking. The results are consistent with the complexity matching hypothesis.

Multifractal signatures of complexity matching.

The complexity matching effect supposes that synchronization between complex systems could emerge from multiple interactions across multiple scales and has been hypothesized to underlie a number of daily-life situations. Complexity matching suggests that coupled systems tend to share similar scaling properties, and this phenomenon is revealed by a statistical matching between the scaling exponents that characterize the respective behaviors of both systems. However, some recent papers suggested that this statistical matching could originate from local adjustments or corrections, rather than from a genuine complexity matching between systems. In the present paper, we propose an analysis method based on correlation between multifractal spectra, considering different ranges of time scales. We analyze several datasets collected in various situations (bimanual coordination, interpersonal coordination, and walking in synchrony with a fractal metronome). Our results show that this method is able to distinguish between situations underlain by genuine statistical matching and situations where statistical matching results from local adjustments.

Learning, motor skill, and long-range correlations.

Long-range correlations have been evidenced in a number of experiments, generally using overlearned and overpracticed tasks. The authors hypothesized that long-range correlation could represent the byproduct of learning. They analyzed the series of periods produced by a group of expert and a group of novices during prolonged trials on a ski simulator. Results showed a very low variability in expert's series, as compared to novices. Fractal analyses showed that fluctuations were significantly more structured and correlated in experts. These results suggest that learning could be conceived as the progressive installation of complexity in the system.

'Human paced' walking: followers adopt stride time dynamics of leaders.

Isochronous cueing is widely used in gait rehabilitation even though it alters the stride-time dynamics toward anti-persistent rather than the persistent, fractal fluctuations characteristic of human walking. In the present experiment we tested an alternative cueing method: pacing by a human. To this end, we formed sixteen pairs of walkers based on their preferred stride frequency. Each pair consisted of a designated "leader" and a "follower" who was instructed to synchronize his or her steps to those of the leader. Heel strike times were detected with tiny footswitches, and Detrended Fluctuation Analysis (DFA) was applied to estimate fractal exponents of stride-time series. To ensure that the stride-time dynamics of the follower matched those of the leader, the latter was structurally modified by artificial cueing via either an isochronous metronome or a fractal metronome, in contrast to self-paced walking. Mean relative phases between followers and leaders were close to 0°, confirming that followers effectively synchronized their footfalls with those of the leaders. Mean fractal exponents were not statistically different between followers and leaders in any condition and highly correlated, suggesting that followers matched their stride-time structure to that of leaders. Our results open perspectives for alternative, more natural cueing protocols for gait rehabilitation.

Persistent coordination patterns in a complex task after 10 years delay: subtitle: how validate the old saying "once you have learned how to ride a bicycle, you never forget!".

Motor learning studies have for a long time focused on performance variables (in terms of speed or accuracy) in assessing learning, transfer and retention of motor skills. We argue, however, that learning essentially resides in changes in coordination variables (in terms of qualitative organization of behavior) and that relevant tests for assessing the effectiveness of learning and retention should consider these variables. The aim of this experiment was to test the retention of a complex motor skill, after a long-term delay. Ten years ago, five participants were involved in an experiment during which they practiced for 39 sessions of ten 1-min trials on a ski-simulator. All participants volunteered for a retention test, ten years after, for one session of ten 1-min trials. Analyses focused on the oscillations of the platform of the simulator. Performance was assessed in terms of amplitude and frequency. Coordination was accounted for by an analysis of dynamical properties of the motion of the platform, and especially the nature of the damping function that was exploited for sustaining the limit cycle dynamics. Results showed a significant decrement in performance variables. In contrast, all participants adopted from the first trial onwards the coordination mode they learned 10years ago. These results confirm the strong persistence of coordination modes, once acquired and stabilized in the behavioral repertoire. They also support the importance of coordination variables for a valid assessment of learning and retention.

Strong anticipation: complexity matching in interpersonal coordination.

A subtle coordination occurs within complex systems, between multiple nested sub-systems. This intra-system coordination can be detected by the presence of 1/f fluctuations produced by the system. But coordination can occur also between systems. Interpersonal coordination has been studied from a local point of view until now, focusing on macroscopic interactions. But the recent concept of strong anticipation introduced by Dubois (Lect Notes Comput Sci 2684:110-132, 2003) suggests that interactions could occur on multiple levels between complex systems. The hypothesis is that time series in interpersonal synchronization present a matching of the complexity index (fractal exponent). Moreover, it is argued that this matching is not a consequence of short-term adaptations but reveals a global coordination between participants. Eleven pairs of participants oscillated a hand-held pendulum in the in-phase pattern for 11 min, in three conditions where the coupling strength was manipulated by the perceptual feedbacks. The results show a high correlation between fractal exponents irrespective of the coupling strength, and a very low percentage of local cross-correlations between time series appear at lag 0 and lag 1. These results suggest that interpersonal coordination, and more globally synchronization of participants with natural environments, is based on non-local time scales.

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.

Fractal fluctuations and complexity: current debates and future challenges.

Complexity is perhaps one of the less properly understood concepts, even within the scientific community. Recent theoretical and experimental advances, however, based on the close relationship between the complexity of the system and the presence of 1/f fluctuations in its macroscopic behavior, have opened new domains of investigation, which consider fundamental questions as well as more applied perspectives. These approaches allow a better understanding of how essential macroscopic functions could emerge from complex interactive networks. In this review we present the current state of the theoretical debate about the origins of 1/f fluctuations, with special focus on recent hypotheses that establish a direct link between complexity and fractal fluctuations. Further, we clarify some lines of opposition, especially between idiosyncratic versus nomothetic conceptions, and global versus componential approaches. Finally, we discuss the deep questioning that this approach can generate with regard to current theories of motor control and psychological processes, as well as some future developments which may be evoked, especially in the domain of physical medicine and rehabilitation.

Complexity, coordination, and health: avoiding pitfalls and erroneous interpretations in fractal analyses.

BACKGROUND AND OBJECTIVE: The analysis of fractal fluctuation has become very popular because of the close relationships between health, adaptability, and long-range correlations. 1/f noise is considered a "magical" threshold, characterizing optimal functioning, and a decrease or conversely and increase of serial correlations, with respect to 1/f noise, is supposed to sign a kind of disadaptation of the system. Empirical results, however, should be interpreted with caution. In experimental series, serial correlations often present a complex pattern, resulting from the combination of long-range and short-term correlated processes. We show, in the present paper, that an increase in serial correlations cannot be directly interpreted as an increase in long-range correlations. MATERIAL AND METHODS: Eleven participants performed four walking bouts following 4 individually determined velocities (slow, comfortable, high, and critical). Series of 512 stride intervals were collected under each condition. The strength of serial correlation was measured by the detrended fluctuation analysis. The effective presence of 1/f fluctuation was tested through ARFIMA modeling. RESULTS: The strength of serial correlations tended to increase with walking velocity. However, the ARFIMA modeling showed that long-range correlations were significantly present only at slow and comfortable velocities. CONCLUSIONS: The strength of correlations, as measured by classical methods, cannot be considered as predictive of the genuine presence of long-range correlations. Sometimes systems can present the moderate levels of effective long-range correlations, whereas in others cases, series can present high correlation levels without being long-range correlated.

Event-based and emergent timing: dichotomy or continuum? A reply to Repp and Steinman (2010).

B. H. Repp and S. R. Steiman (2010) suggested that event-based and emergent timing, usually conceived as mutually exclusive modes of timing, could in fact coexist in a single activity. According to this point of view, rhythmic activities could exploit mixtures of control modes, in which the relative importance of event-based and emergent components could depend on task characteristics. This point of view, in the opinion of the authors of the present article, corresponds to a fundamental misunderstanding of the theoretical basis of the event-based and emergent distinction, and is not supported by any experimental evidence. However, they present some new results that could support new lines of reasoning for the future developments of research in this domain.

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.

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.

Oscillating in synchrony with a metronome: serial dependence, limit cycle dynamics, and modeling.

We analyzed serial dependencies in periods and asynchronies collected during oscillations performed in synchrony with a metronome. Results showed that asynchronies contain 1/f fluctuations, and the series of periods contain antipersistent dependence. The analysis of the phase portrait revealed a specific asymmetry induced by synchronization. We propose a hybrid limit cycle model including a cycle-dependent stiffness parameter provided with fractal properties, and a parametric driving function based on velocity. This model accounts for most experimentally evidenced statistical features, including serial dependence and limit cycle dynamics. We discuss the results and modeling choices within the framework of event-based and emergent timing.

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).

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.