Interaction patterns and individual dynamics shape the way we move in synchrony

Spontaneous movement synchrony as an exogenous source for interbrain synchronization in cooperative learning

Learning through cooperation with conspecifics-'cooperative learning'-is critical to cultural evolution and survival. Recent progress has established that interbrain synchronization (IBS) between individuals predicts success in cooperative learning. However, the likely sources of IBS during learning interactions remain poorly understood. To address this dearth of knowledge, we tested whether movement synchrony serves as an exogenous factor that drives IBS, taking an embodiment perspective. We formed dyads of individuals with varying levels of prior knowledge (high-high (HH), high-low (HL), low-low (LL) dyads) and instructed them to collaboratively analyse an ancient Chinese poem. During the task, we simultaneously recorded their brain activity using functional near-infrared spectroscopy and filmed the entire experiment to parse interpersonal movement synchrony using the computer-vision motion energy analysis. Interestingly, the homogeneous groups (HH and/or LL) exhibited stronger movement synchrony and IBS compared with the heterogeneous group. Importantly, mediation analysis revealed that spontaneous and synchronized body movements between individuals contribute to IBS, hence facilitating learning. This study therefore fills a critical gap in our understanding of how interpersonal transmission of information between individual brains, associated with behavioural entrainment, shapes social learning. This article is part of the theme issue 'Minds in movement: embodied cognition in the age of artificial intelligence'.

How and Why People Synchronize: An Integrated Perspective

Academic AbstractInterpersonal synchrony, the alignment of behavior and/or physiology during interactions, is a pervasive phenomenon observed in diverse social contexts. Here we synthesize across contexts and behaviors to classify the different forms and functions of synchrony. We provide a concise framework for classifying the manifold forms of synchrony along six dimensions: periodicity, discreteness, spatial similarity, directionality, leader-follower dynamics, and observability. We also distill the various proposed functions of interpersonal synchrony into four interconnected functions: reducing complexity and improving understanding, accomplishing joint tasks, strengthening social connection, and influencing partners' behavior. These functions derive from first principles, emerge from each other, and are accomplished by some forms of synchrony more than others. Effective synchrony flexibly adapts to social goals and more synchrony is not always better. Our synthesis offers a shared framework and language for the field, allowing for better cross-context and cross-behavior comparisons, generating new hypotheses, and highlighting future research directions.

Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

You, me, and us: Maintaining self-other distinction enhances coordination, agency, and affect

Coordinating our actions with others changes how we behave and feel. Here, we provide evidence that interacting with others rests on a balance between self-other integration and segregation. Using a group walking paradigm, participants were instructed to synchronize with a metronome while listening to the sounds of 8 virtual partners. By manipulating the similarity and synchronicity of the partners' steps to the participant's own, our novel auditory task disentangles the effects of synchrony and self-other similarity and examines their contribution to both collective and individual awareness. We measured temporal coordination (step timing regularity and synchrony with the metronome), gait patterns, and subjective reports about sense of self and group cohesion. The main findings show that coordination is best when participants hear distinct but synchronous virtual others, leading to greater subjective feelings of agency, strength, dominance, and happiness.

Social and nonlinear dynamics unite: musical group synchrony

Synchronization, the human tendency to align behaviors in time with others, is necessary for many survival skills. The ability to synchronize actions with rhythmic (predictable) sound patterns is especially well developed in music making. Recent models of synchrony in musical ensembles rely on pairwise comparisons between group members. This pairwise approach to synchrony has hampered theory development, given current findings from social dynamics indicating shifts in members' influence within larger groups. We draw on social theory and nonlinear dynamics to argue that emergent properties and novel roles arise in musical group synchrony that differ from individual or pairwise behaviors. This transformational shift in defining synchrony sheds light on successful outcomes as well as on disruptions that cause negative behavioral outcomes.

Rhythmic modulation of visual discrimination is linked to individuals' spontaneous motor tempo

The impact of external rhythmic structure on perception has been demonstrated across different modalities and experimental paradigms. However, recent findings emphasize substantial individual differences in rhythm-based perceptual modulation. Here, we examine the link between spontaneous rhythmic preferences, as measured through the motor system, and individual differences in rhythmic modulation of visual discrimination. As a first step, we measure individual rhythmic preferences using the spontaneous tapping task. Then we assess perceptual rhythmic modulation using a visual discrimination task in which targets can appear either in-phase or out-of-phase with a preceding rhythmic stream of visual stimuli. The tempo of the preceding stream was manipulated over different experimental blocks (0.77 Hz, 1.4 Hz, 2 Hz). We find that visual rhythmic stimulation modulates discrimination performance. The modulation is dependent on the tempo of stimulation, with maximal perceptual benefits for the slowest tempo of stimulation (0.77 Hz). Most importantly, the strength of modulation is also linked to individuals' spontaneous motor tempo. Individuals with slower spontaneous tempi show greater rhythmic modulation compared to individuals with faster spontaneous tempi. This finding suggests that different tempi affect the cognitive system with varying levels of efficiency and that self-generated rhythms impact our ability to utilize rhythmic structure in the environment for guiding perception and performance.

Playing the mirror game in virtual reality with an autonomous character

Perceptual-motor synchronisation in human groups is crucial in many activities, from musical ensembles to sports teams. To this aim, the mirror game, where partners are asked to imitate each other's movements or gestures, is one of the best available experimental paradigms to study how humans engage in joint tasks and how they tend to synchronise their behaviour. However, to date, virtual reality characters do not engage in motor synchronisation with human users. In this work, we explored to what extent an autonomous virtual character and a human that play the mirror game in virtual reality can synchronise their behaviour. We created a full-body version of the mirror game with an autonomous virtual character, whose movements were driven by a model based on coupled oscillators. Participants engaged in a joint imitation task with a virtual player animated with one of three options: a model that included a small coupling, a model with no coupling, or another human. Behavioural measures and subjective reports suggest that participants were unable to distinguish the condition of small coupling from the engagement with an avatar driven by another human participant.

Endogenous rhythms influence musicians' and non-musicians' interpersonal synchrony

Individuals display considerable rate differences in the spontaneous production of rhythmic behaviors (such as speech, gait, dance). Temporal precision in rhythmic behavior tends to be highest at individuals’ spontaneous production rates; musically trained partners with similar spontaneous rates show increased synchrony in joint tasks, consistent with predictions based on intrinsic frequencies of coupled oscillators. We address whether partner-specific influences of intrinsic frequencies are evidenced in musically trained and untrained individuals who tapped a familiar melody at a spontaneous (uncued) rate individually. Each individual then synchronized with a partner from the same musicianship group at an initially cued rate that matched the partners’ spontaneous rates. Musically trained partners showed greater synchrony in joint tapping than musically untrained partners. Asynchrony increased in both groups as the partners’ difference in individual spontaneous rates increased, with greater impact for musically untrained pairs. Recurrence quantification analysis confirmed that musically untrained individuals demonstrated greater determinism (less flexibility) in their tapping than musically trained individuals. Furthermore, individuals with greater determinism in solo performances demonstrated reduced synchrony in joint performances. These findings suggest that musicians’ increased temporal flexibility is associated with decreased endogenous constraints on production rate and greater interpersonal synchrony in musical tasks.

Spatiotemporal patterns of firearm acquisition in the United States in different presidential terms

This study develops mathematical tools and approaches to investigate spatiotemporal patterns of firearm acquisition in the U.S. complemented by hypothesis testing and statistical analysis. First, state-level and nation-level instant background check (BC) data are employed as proxy of firearm acquisition corresponding to 1999-2021. The relative-phase time-series of BC in each U.S. state is recovered and utilized to calculate the time-series of the U.S. states' synchronization degree. We reveal that U.S. states present a high-level degree of synchronization except in 2010-2011 and after 2018. Comparing these results with respect to a sitting U.S. president provides additional information: specifically, any two presidential terms are characterized by statistically different synchronization degrees except G. W. Bush's first term and B. H. Obama's second term. Next, to detail variations of BC, short-time Fourier transform, dimensionality reduction techniques, and diffusion maps are implemented within a time-frequency representation. Firearm acquisition in the high frequency band is described by a low-dimensional embedding, in the form of a plane with two embedding coordinates. Data points on the embedding plane identify separate clusters that signify state transitions in the original BC data with respect to different time windows. Through this analysis, we reveal that the frequency content of the BC data has a time-dependent characteristic. By comparing the diffusion map at hand with respect to a presidential term, we find that at least one of the embedding coordinates presents statistically significant variations between any two presidential terms except B. H. Obama's first term and D. J. Trump's pre-COVID term. The results point at a possible interplay between firearm acquisition in the U.S. and a presidential term.

Collective Rhythm as an Emergent Property During Human Social Coordination

The literature on social interactions has shown that participants coordinate not only at the behavioral but also at the physiological and neural levels, and that this coordination gives a temporal structure to the individual and social dynamics. However, it has not been fully explored whether such temporal patterns emerge during interpersonal coordination beyond dyads, whether this phenomenon arises from complex cognitive mechanisms or from relatively simple rules of behavior, or which are the sociocultural processes that underlie this phenomenon. We review the evidence for the existence of group-level rhythmic patterns that result from social interactions and argue that the complexity of group dynamics can lead to temporal regularities that cannot be predicted from the individual periodicities: an emergent collective rhythm. Moreover, we use this interpretation of the literature to discuss how taking into account the sociocultural niche in which individuals develop can help explain the seemingly divergent results that have been reported on the social influences and consequences of interpersonal coordination. We make recommendations on further research to test these arguments and their relationship to the feeling of belonging and assimilation experienced during group dynamics.

Modeling Frequency Reduction in Human Groups Performing a Joint Oscillatory Task

In human groups performing oscillatory tasks, it has been observed that the frequency of participants' oscillations reduces when compared to that acquired in solo. This experimental observation is not captured by the standard Kuramoto oscillators, often employed to model human synchronization. In this work, we aim at capturing this observed phenomenon by proposing three alternative modifications of the standard Kuramoto model that are based on three different biologically-relevant hypotheses underlying group synchronization. The three models are tuned, validated and compared against experiments on a group synchronization task, which is a multi-agent extension of the so-called mirror game.

A metastable attractor model of self-other integration (MEAMSO) in rhythmic synchronization

Human interaction is often accompanied by synchronized bodily rhythms. Such synchronization may emerge spontaneously as when a crowd's applause turns into a steady beat, be encouraged as in nursery rhymes, or be intentional as in the case of playing music together. The latter has been extensively studied using joint finger-tapping paradigms as a simplified version of rhythmic interpersonal synchronization. A key finding is that synchronization in such cases is multifaceted, with synchronized behaviour resting upon different synchronization strategies such as mutual adaptation, leading-following and leading-leading. However, there are multiple open questions regarding the mechanism behind these strategies and how they develop dynamically over time. Here, we propose a metastable attractor model of self-other integration (MEAMSO). This model conceptualizes dyadic rhythmic interpersonal synchronization as a process of integrating and segregating signals of self and other. Perceived sounds are continuously evaluated as either being attributed to self-produced or other-produced actions. The model entails a metastable system with two particular attractor states: one where an individual maintains two separate predictive models for self- and other-produced actions, and the other where these two predictive models integrate into one. The MEAMSO explains the three known synchronization strategies and makes testable predictions about the dynamics of interpersonal synchronization both in behaviour and the brain. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

Spontaneous emergence of leadership patterns drives synchronization in complex human networks

Synchronization of human networks is fundamental in many aspects of human endeavour. Recently, much research effort has been spent on analyzing how motor coordination emerges in human groups (from rocking chairs to violin players) and how it is affected by coupling structure and strength. Here we uncover the spontaneous emergence of leadership (based on physical signaling during group interaction) as a crucial factor steering the occurrence of synchronization in complex human networks where individuals perform a joint motor task. In two experiments engaging participants in an arm movement synchronization task, in the physical world as well as in the digital world, we found that specific patterns of leadership emerged and increased synchronization performance. Precisely, three patterns were found, involving a subtle interaction between phase of the motion and amount of influence. Such patterns were independent of the presence or absence of physical interaction, and persisted across manipulated spatial configurations. Our results shed light on the mechanisms that drive coordination and leadership in human groups, and are consequential for the design of interactions with artificial agents, avatars or robots, where social roles can be determinant for a successful interaction.

Dynamic Input Deep Learning Control of Artificial Avatars in a Multi-Agent Joint Motor Task

In many real-word scenarios, humans and robots are required to coordinate their movements in joint tasks to fulfil a common goal. While several examples regarding dyadic human robot interaction exist in the current literature, multi-agent scenarios in which one or more artificial agents need to interact with many humans are still seldom investigated. In this paper we address the problem of synthesizing an autonomous artificial agent to perform a paradigmatic oscillatory joint task in human ensembles while exhibiting some desired human kinematic features. We propose an architecture based on deep reinforcement learning which is flexible enough to make the artificial agent interact with human groups of different sizes. As a paradigmatic coordination task we consider a multi-agent version of the mirror game, an oscillatory motor task largely used in the literature to study human motor coordination.

Bridging the gap between emotion and joint action

Our daily human life is filled with a myriad of joint action moments, be it children playing, adults working together (i.e., team sports), or strangers navigating through a crowd. Joint action brings individuals (and embodiment of their emotions) together, in space and in time. Yet little is known about how individual emotions propagate through embodied presence in a group, and how joint action changes individual emotion. In fact, the multi-agent component is largely missing from neuroscience-based approaches to emotion, and reversely joint action research has not found a way yet to include emotion as one of the key parameters to model socio-motor interaction. In this review, we first identify the gap and then stockpile evidence showing strong entanglement between emotion and acting together from various branches of sciences. We propose an integrative approach to bridge the gap, highlight five research avenues to do so in behavioral neuroscience and digital sciences, and address some of the key challenges in the area faced by modern societies.

The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind

This article presents a brief retrospective on the Haken-Kelso-Bunz (HKB) model of certain dynamical properties of human movement. Though unanticipated, HKB introduced, and demonstrated the power of, a new vocabulary for understanding behavior, cognition and the brain, revealed through a visually compelling mathematical picture that accommodated highly reproducible experimental facts and predicted new ones. HKB stands as a harbinger of paradigm change in several scientific fields, the effects of which are still being felt. In particular, HKB constitutes the foundation of a mechanistic science of coordination called Coordination Dynamics that extends from matter to movement to mind, and beyond.

Collective music listening: Movement energy is enhanced by groove and visual social cues

The regularity of musical beat makes it a powerful stimulus promoting movement synchrony among people. Synchrony can increase interpersonal trust, affiliation, and cooperation. Musical pieces can be classified according to the quality of groove; the higher the groove, the more it induces the desire to move. We investigated questions related to collective music-listening among 33 participants in an experiment conducted in a naturalistic yet acoustically controlled setting of a research concert hall with motion tracking. First, does higher groove music induce (1) movement with more energy and (2) higher interpersonal movement coordination? Second, does visual social information manipulated by having eyes open or eyes closed also affect energy and coordination? Participants listened to pieces from four categories formed by crossing groove (high, low) with tempo (higher, lower). Their upper body movement was recorded via head markers. Self-reported ratings of grooviness, emotional valence, emotional intensity, and familiarity were collected after each song. A biomechanically motivated measure of movement energy increased with high-groove songs and was positively correlated with grooviness ratings, confirming the theoretically implied but less tested motor response to groove. Participants' ratings of emotional valence and emotional intensity correlated positively with movement energy, suggesting that movement energy relates to emotional engagement with music. Movement energy was higher in eyes-open trials, suggesting that seeing each other enhanced participants' responses, consistent with social facilitation or contagion. Furthermore, interpersonal coordination was higher both for the high-groove and eyes-open conditions, indicating that the social situation of collective music listening affects how music is experienced.

Unifying Large- and Small-Scale Theories of Coordination

Coordination is a ubiquitous feature of all living things. It occurs by virtue of informational coupling among component parts and processes and can be quite specific (as when cells in the brain resonate to signals in the environment) or nonspecific (as when simple diffusion creates a source–sink dynamic for gene networks). Existing theoretical models of coordination—from bacteria to brains to social groups—typically focus on systems with very large numbers of elements (N→∞) or systems with only a few elements coupled together (typically N = 2). Though sharing a common inspiration in Nature’s propensity to generate dynamic patterns, both approaches have proceeded largely independent of each other. Ideally, one would like a theory that applies to phenomena observed on all scales. Recent experimental research by Mengsen Zhang and colleagues on intermediate-sized ensembles (in between the few and the many) proves to be the key to uniting large- and small-scale theories of coordination. Disorder–order transitions, multistability, order–order phase transitions, and especially metastability are shown to figure prominently on multiple levels of description, suggestive of a basic Coordination Dynamics that operates on all scales. This unified coordination dynamics turns out to be a marriage of two well-known models of large- and small-scale coordination: the former based on statistical mechanics (Kuramoto) and the latter based on the concepts of Synergetics and nonlinear dynamics (extended Haken–Kelso–Bunz or HKB). We show that models of the many and the few, previously quite unconnected, are thereby unified in a single formulation. The research has led to novel topological methods to handle the higher-dimensional dynamics of coordination in complex systems and has implications not only for understanding coordination but also for the design of (biorhythm inspired) computers.

Leadership and tempo perturbation affect coordination in medium-sized groups

In marching bands, sports, dance and virtually all human group behaviour, we coordinate our actions with others. Coordinating actions in time and space can act as a social glue, facilitating bonding among people. However, much of our understanding about coordination dynamics is based on research into dyadic interactions. Little is known about the nature of the sensorimotor underpinnings and social bonding outcomes of coordination in medium-sized groups-the type of groups, in which most everyday teamwork takes place. In this study, we explored how the presence of a leader and an unexpected perturbation influence coordination and cohesion in a naturalistic setting. In groups of seven, participants were instructed to walk in time to an auditory pacing signal. We found that the presence of a reliable leader enhanced coordination with the target tempo, which was disrupted when the leader abruptly changed their movement tempo. This effect was not observed on coordination with the group members. Moreover, participants' perceptions of being a follower and group cooperativeness increased in the presence of a leader. This study extends our knowledge about coordination beyond previous work on dyads. We discuss our results in light of sensorimotor coupling and social cohesion theories of coordination in groups.

Moving in unison after perceptual interruption

Humans interact in groups through various perception and action channels. The continuity of interaction despite a transient loss of perceptual contact often exists and contributes to goal achievement. Here, we study the dynamics of this continuity, in two experiments involving groups of participants ([Formula: see text]) synchronizing their movements in space and in time. We show that behavioural unison can be maintained after perceptual contact has been lost, for about 7s. Agent similarity and spatial configuration in the group modulated synchronization performance, differently so when perceptual interaction was present or when it was memorized. Modelling these data through a network of oscillators enabled us to clarify the double origin of this memory effect, of individual and social nature. These results shed new light into why humans continue to move in unison after perceptual interruption, and are consequential for a wide variety of applications at work, in art and in sport.

Herding in human groups is related to high autistic traits

Herding is ubiquitous throughout all social life forms, providing beneficial outcomes. Here, we examine whether herding emerges spontaneously in human groups and whether it adheres to the core principles of herding observed in the animal kingdom. Using a computerized paradigm involving the movements of circles, we tested the emergence of spontaneous and intentional herding of 136 participants assigned into groups of four participants. Herding was assessed by measuring directional synchrony in the movements of the circles, level of cohesion, and separation between circles. We found that human groups tend to spontaneously herd, particularly in terms of directional synchrony, supporting the notion of a human herding instinct. We further asked whether individuals with high traits of Autism Spectrum Disorder (ASD) exhibit differences in their herding tendencies. Results indicated that individuals with high ASD traits showed greater social separation from the group, compared to individuals with low ASD traits. Moreover, we found diminished spontaneous synchrony, but intact instructed synchrony in the high vs. the low ASD traits group. We contend that humans spontaneously herd with their group and suggest that the spontaneous tendency to synchronize with others is diminished in individuals with high ASD traits, though it is recovered when synchronization is intentional.

Synchronization of complex human networks

The synchronization of human networks is essential for our civilization and understanding its dynamics is important to many aspects of our lives. Human ensembles were investigated, but in noisy environments and with limited control over the network parameters which govern the network dynamics. Specifically, research has focused predominantly on all-to-all coupling, whereas current social networks and human interactions are often based on complex coupling configurations. Here, we study the synchronization between violin players in complex networks with full and accurate control over the network connectivity, coupling strength, and delay. We show that the players can tune their playing period and delete connections by ignoring frustrating signals, to find a stable solution. These additional degrees of freedom enable new strategies and yield better solutions than are possible within current models such as the Kuramoto model. Our results may influence numerous fields, including traffic management, epidemic control, and stock market dynamics.

Topological portraits of multiscale coordination dynamics

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge in both theoretical and empirical realms. The present work shows how integrating approaches from computational algebraic topology and dynamical systems may help us meet this challenge. In particular, we focus on the application of multiscale topological analysis to coordinated rhythmic processes. First, theoretical arguments are introduced as to why certain topological features and their scale-dependency are highly relevant to understanding complex collective dynamics. Second, we propose a method to capture such dynamically relevant topological information using persistent homology, which allows us to effectively construct a multiscale topological portrait of rhythmic coordination. Finally, the method is put to test in detecting transitions in real data from an experiment of rhythmic coordination in ensembles of interacting humans. The recurrence plots of topological portraits highlight collective transitions in coordination patterns that were elusive to more traditional methods. This sensitivity to collective transitions would be lost if the behavioral dynamics of individuals were treated as separate degrees of freedom instead of constituents of the topology that they collectively forge. Such multiscale topological portraits highlight collective aspects of coordination patterns that are irreducible to properties of individual parts. The present work demonstrates how the analysis of multiscale coordination dynamics can benefit from topological methods, thereby paving the way for further systematic quantification of complex, high-dimensional dynamics in living systems.

Staying Together: A Bidirectional Delay-Coupled Approach to Joint Action

To understand how individuals adapt to and anticipate each other in joint tasks, we employ a bidirectional delay-coupled dynamical system that allows for mutual adaptation and anticipation. In delay-coupled systems, anticipation is achieved when one system compares its own time-delayed behavior, which implicitly includes past information about the other system's behavior, with the other system's instantaneous behavior. Applied to joint music performance, the model allows each system to adapt its behavior to the dynamics of the other. Model predictions of asynchrony between two simultaneously produced musical voices were compared with duet pianists' behavior; each partner performed one voice while auditory feedback perturbations occurred at unpredictable times during live performance. As the model predicted, when auditory feedback from one musical voice was removed, the asynchrony changed: The pianist's voice that was removed anticipated (preceded) the actions of their partner. When the auditory feedback returned and both musicians could hear each other, they rapidly returned to baseline levels of asynchrony. To understand how the pianists anticipated each other, their performances were fitted by the model to examine change in model parameters (coupling strength, time-delay). When auditory feedback for one or both voices was removed, the fits showed the expected decrease in coupling strength and time-delay between the systems. When feedback about the voice(s) returned, the coupling strength and time-delay returned to baseline. These findings support the idea that when people perform actions together, they do so as a coupled bidirectional anticipatory system.

Discovering the topology of complex networks via adaptive estimators

Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.

Multi-layer adaptation of group coordination in musical ensembles

Group coordination passes through an efficient integration of multimodal sources of information. This study examines complex non-verbal communication by recording movement kinematics from conductors and two sections of violinists of an orchestra adapting to a perturbation affecting their normal pattern of sensorimotor communication (rotation of half a turn of the first violinists’ section). We show that different coordination signals are channeled through ancillary (head kinematics) and instrumental movements (bow kinematics). Each one of them affect coordination either at the inter-group or intra-group levels, therefore tapping into different modes of cooperation: complementary versus imitative coordination. Our study suggests that the co-regulation of group behavior is based on the exchange of information across several layers, each one of them tuned to carry specific coordinative signals. Multi-layer sensorimotor communication may be the key musicians and, more generally humans, use to flexibly communicate between each other in interactive sensorimotor tasks.

Social information and spontaneous emergence of leaders in human groups

Understanding the dynamics of social networks is the objective of interdisciplinary research ranging from animal collective behaviour to epidemiology, political science and marketing. Social influence is key to comprehending emergent group behaviour, but we know little about how inter-individual relationships emerge in the first place. We conducted an experiment where participants repeatedly performed a cognitive test in a small group. In each round, they were allowed to change their answers upon seeing the current answers of other members and their past performance in selecting correct answers. Rather than following a simple majority rule, participants granularly processed the performance of others in deciding how to change their answers. Toward a network model of the experiment, we associated a directed link of a time-varying network with every change in a participant's answer that mirrored the answer of another group member. The rate of growth of the network was not constant in time, whereby links were found to emerge faster as time progressed. Further, repeated interactions reinforced relationships between individuals' performance and their network centrality. Our results provide empirical evidence that inter-individual relationships spontaneously emerge in an adaptive way, where good performers rise as group leaders over time.

Plasticity in leader-follower roles in human teams

In humans, emergence of leaders and followers is key to group performance, but little is known about the whys and hows of leadership. A particularly elusive question entails behavioral plasticity in leadership across social contexts. Addressing this question requires to eliminate social feedback between focal individuals and their partners in experiments that could illuminate the spontaneous emergence of social roles. We investigated plasticity in leader-follower roles in cooperation, where members choose the task toward a shared goal, and coordination, where members adjust their actions in real time based on social responsiveness. Through a computer-programmed virtual partner, we demonstrate adaptive plasticity in leader-follower roles. Humans increased their followership to cooperate when the partner led more in the choice of the task, whereas they showed only weak leadership when the partner followed more. We leveraged the information-theoretic notion of transfer entropy to quantify leadership and followership in coordination from their movements. When exhibiting stronger followership in task cooperation, humans coordinated more with the partner's movement, with greater information being transferred from the partner to humans. The evidence of behavioral plasticity suggests that humans are capable of adapting their leader-follower roles to their social environments, in both cooperation and coordination.

A Novel Computer-Based Set-Up to Study Movement Coordination in Human Ensembles

Existing experimental works on movement coordination in human ensembles mostly investigate situations where each subject is connected to all the others through direct visual and auditory coupling, so that unavoidable social interaction affects their coordination level. Here, we present a novel computer-based set-up to study movement coordination in human groups so as to minimize the influence of social interaction among participants and implement different visual pairings between them. In so doing, players can only take into consideration the motion of a designated subset of the others. This allows the evaluation of the exclusive effects on coordination of the structure of interconnections among the players in the group and their own dynamics. In addition, our set-up enables the deployment of virtual computer players to investigate dyadic interaction between a human and a virtual agent, as well as group synchronization in mixed teams of human and virtual agents. We show how this novel set-up can be employed to study coordination both in dyads and in groups over different structures of interconnections, in the presence as well as in the absence of virtual agents acting as followers or leaders. Finally, in order to illustrate the capabilities of the architecture, we describe some preliminary results. The platform is available to any researcher who wishes to unfold the mechanisms underlying group synchronization in human ensembles and shed light on its socio-psychological aspects.

A Novel Computer-Based Set-Up to Study Movement Coordination in Human Ensembles

Existing experimental works on movement coordination in human ensembles mostly investigate situations where each subject is connected to all the others through direct visual and auditory coupling, so that unavoidable social interaction affects their coordination level. Here, we present a novel computer-based set-up to study movement coordination in human groups so as to minimize the influence of social interaction among participants and implement different visual pairings between them. In so doing, players can only take into consideration the motion of a designated subset of the others. This allows the evaluation of the exclusive effects on coordination of the structure of interconnections among the players in the group and their own dynamics. In addition, our set-up enables the deployment of virtual computer players to investigate dyadic interaction between a human and a virtual agent, as well as group synchronization in mixed teams of human and virtual agents. We show how this novel set-up can be employed to study coordination both in dyads and in groups over different structures of interconnections, in the presence as well as in the absence of virtual agents acting as followers or leaders. Finally, in order to illustrate the capabilities of the architecture, we describe some preliminary results. The platform is available to any researcher who wishes to unfold the mechanisms underlying group synchronization in human ensembles and shed light on its socio-psychological aspects.