Complexity matching in side-by-side walking

A B S T R A C T When two people synchronize their rhythmic behaviors (e.g., finger tapping; walking) they match one another not only at a local scale of beat-to-beat intervals, but also at a global scale of the complex (fractal) patterns of variation in their interval series. This " complexity matching " had been demonstrated in a variety of timing behaviors, but the current study was designed to address two important gaps in previous research. First, very little was known about complexity matching outside of synchronization tasks. This was important because different modes are associated with differences in the strength of coordination and the fractal scaling of the task performance. Second, very little was known about the dynamics of the asynchrony series. This was important because asynchrony is a variable directly quantifying the coordination between the two timing behaviors and the task goal. So, the current study explored complexity matching in both synchronized and syncopated finger tapping tasks, and included analyses of the fractal scaling of the asynchrony series. Participants completed an interpersonal finger tapping task, in both synchronization and syncopation conditions. The magnitude of variation and the exact power law scaling of the tapping intervals were manipulated by having one participant tap in time with a metronome. Complexity matching was most stable when there was sufficient variation in the task behavior and when a persistent scaling dynamic was presented. There were, however, several interesting differences between the two coordination modes, in terms of the heterogeneity of the complexity matching effect and the scaling of the asynchronies. These findings raised a number of important points concerning how to approach and understand the interaction of inherently complex systems.

Journal of Motor Behavior, 2020

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.

Experimental Brain Research, 2012

A subtle coordination occurs within complex systems, between multiple nested sub-systems. This intrasystem 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: 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 handheld 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 crosscorrelations 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.

Neuroscience Letters, 2008

We examined how people synchronize their leg movements while walking side-by-side on a treadmill. Walker pairs were either instructed to synchronize their steps in in-phase or in antiphase or received no coordination instructions. Frequency and phase analysis revealed that instructed in-phase and antiphase coordination were equally stable and independent of walking speed and the difference in individually preferred stride frequencies. Without instruction we found episodes of frequency locking in three pairs and episodes of phase locking in four pairs, albeit not always at (or near) 0 • or 180 • . Again, we found no difference in the stability of in-phase and antiphase coordination and no systematic effects of walking speed and the difference in individually preferred stride frequencies. These results suggest that the Haken-Kelso-Bunz model for rhythmic interlimb coordination does not apply to interpersonal coordination during gait in a straightforward manner. When the typically involved parameter constraints are relaxed, however, this model may largely account for the observed dynamical characteristics.

There is a growing consensus that a fuller understanding of social cognition depends on more systematic studies of real-time social interaction. Such studies require methods that can deal with the complex dynamics taking place at multiple interdependent temporal and spatial scales, spanning sub-personal, personal, and dyadic levels of analysis. We demonstrate the value of adopting an extended multi-scale approach by re-analyzing movement time-series generated in a study of embodied dyadic interaction in a minimal virtual reality environment (a perceptual crossing experiment). Reduced movement variability revealed an interdependence between social awareness and social coordination that cannot be accounted for by either subjective or objective factors alone: it picks out interactions in which subjective and objective conditions are convergent (i.e., elevated coordination is perceived as clearly social, and impaired coordination is perceived as socially ambiguous). This finding is consistent with the claim that interpersonal interaction can be partially constitutive of direct social perception. Clustering statistics (Allan Factor) of salient events revealed fractal scaling. Complexity matching defined as the similarity between these scaling laws was significantly more pronounced in pairs of participants as compared to surrogate dyads. This further highlights the multi-scale and distributed character of social interaction and extends previous complexity matching results from dyadic conversation to non-verbal social interaction dynamics. Trials with successful joint interaction were also associated with an increase in local coordination. Consequently, a local coordination pattern emerges on the background of complex dyadic interactions in the PCE task and makes joint successful performance possible.

We examined how people synchronize their leg movements while walking side-by-side on a treadmill. Walker pairs were either instructed to synchronize their steps in in-phase or in antiphase or received no coordination instructions. Frequency and phase analysis revealed that instructed in-phase and antiphase coordination were equally stable and independent of walking speed and the difference in individually preferred stride frequencies. Without instruction we found episodes of frequency locking in three pairs and episodes of phase locking in four pairs, albeit not always at (or near) 0 • or 180 • . Again, we found no difference in the stability of in-phase and antiphase coordination and no systematic effects of walking speed and the difference in individually preferred stride frequencies. These results suggest that the Haken-Kelso-Bunz model for rhythmic interlimb coordination does not apply to interpersonal coordination during gait in a straightforward manner. When the typically involved parameter constraints are relaxed, however, this model may largely account for the observed dynamical characteristics.

Human Movement Science, 2019

Complexity matching is a measure of coordination based on information exchange between complex networks. To date, studies have focused mainly on interpersonal coordination, but complexity matching may generalize to interacting networks within individuals. The present study examined complexity matching in a double, coordinated Fitts' perceptual-motor task with comparable individual and dyadic conditions. Participants alternated touching targets with their left and right hands in the individual condition, or analogously with the left hand of one partner and the right hand of another in the dyadic condition. In Experiment 1, response coupling was manipulated by making targets drift either randomly or contingently based on prior responses. Here, drift refers to the variability in the target movements between response locations. Longrange correlations in time series of inter-response intervals exhibited complexity matching between the left and right hands of dyads and individuals. Response coupling was necessary for complexity matching in dyads but not individuals. When response coupling was absent in the dyadic condition, the degree of complexity matching was significantly reduced. Experiment 2 showed that the effect of coupling was due to interactions between left and right responses. Results also showed a weak, negative relationship between complexity matching and performance as measured by total response time. In conclusion, principles and measures of complexity matching apply similarly within and between individuals, and perceptual-motor performance can be facilitated by loose response coupling.

Rhythmic coordination with stimuli and other people’s movements containing variable or unpredictable fluctuations might involve distinct processes: detecting the fluctuation structure and tuning to or matching the structure’s temporal complexity. This framework predicts that global tuning and local parameter adjustments (e.g., position, velocity or phase) can operate independently during coordination (Marmelat & Delignières, 2012). Alternatively, we propose that complexity matching is a result of local phase adjustments during coordination (Delignières & Marmelat, 2014; Torre, Varlet, & Marmelat, 2013). The current study examined this relationship in a rhythmic interpersonal coordination task. Dyads coordinated swinging pendulums that differed in their uncoupled frequencies (detuning). We predicted that frequency detuning would require increased local corrections to maintain the intended phase pattern (in phase). This was expected to yield a relative phase shift accompanied by a change in period complexity and matching. Experimental data and numerical modeling of the pendulum dynamics confirmed our predictions. Increased relative phase shifts occurred simultaneously with increased dissociation between individuals’ movement period complexity. This provided evidence that global complexity matching is intricately linked to local movement adjustments and is not a distinct coordination mechanism. These findings are considered with respect to dynamical and computational approaches to interpersonal coordination.

Neuroscience Letters, 2005

Most studies about human locomotion only tend to consider single subjects walking alone in a stationary environment. Nevertheless, human subjects have often to plan and generate their locomotor trajectories according to one another's displacements. Therefore, in the present study we address the question of the interpersonal coordination when pairs of subjects walk simultaneously. Six pairs of subjects walking face to face, backwards and forwards on a 8 m × 2 m track were involved in our experiment. Within each pair, the leader (L) was required to break the initial interpersonal distance whereas the follower (F) had to maintain this distance constant (1, 2 or 3 m). We measured their position and analyzed their travelled distance, the time course of their linear displacement, and the kinematics parameters of their steps. Our results show that F travels smaller distances than L and that even if they are highly correlated, some temporal delays exist between displacements of L and F with greater values when the interpersonal distance increases (from 1 to 3 m). These results are discussed in terms of high level imitation, i.e. bidirectional interactions with mutual influences of each subject on one another.

Frontiers in Physiology, 2018

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.