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<reference>
Emergent togetherness in collaborative dance improvisation:
neural and motor synchronization reveal a coupling-decoupling
paradox
Yago Emanoel Ramos12, Raphael Silva do Rosário1, Adriana de Faria Gehres3, Maria João Alves45,
Ana Maria Leitão⁴⁵, Cecília Bastos da Costa Accioly6, Fatima Wachowicz⁶, Ivani Lúcia Oliveira de
Santana7, José Garcia Vivas Miranda1*

Abstract
Collective improvisation in dance provides a rich natural laboratory for studying
emergent coordination in coupled neuro-motor systems. Here, we investigate how
training shapes spontaneous synchronization patterns in both movement dynamics and
brain signals during collaborative performance. Using a dual-recording protocol
integrating 3D motion capture and hyperscanning EEG, participants engaged in free,
interaction-driven, and rule-based improvisation before and after a program of
generative dance, grounded in cellular-automata. Motor behavior was modeled through
a time-resolved α-exponent derived from Movement Element Decomposition scaling
between mean velocity and displacement, revealing fluctuations in energetic strategies
and degrees of freedom. Synchronization events were quantified using Motif
Synchronization (biomechanical data) and multilayer Time-Varying Graphs (neural
data), enabling the detection of nontrivial lead-lag dependencies beyond zero-lag
entrainment. Results indicate that training produced an intriguing dissociation: interbrain synchronization increased, particularly within the frontal lobe, while interpersonal
motor synchrony decreased. This opposite trend suggests that enhanced participatory
sense-making fosters neural alignment while simultaneously expanding individual
motor explorations, thereby reducing coupling in movement. Our findings position
collaborative improvisation as a complex dynamical regime in which togetherness
emerges not from identical motor outputs but from shared neural intentionality
distributed across multilayer interaction networks, exemplifying the couplingdecoupling paradox, whereby increasing inter-brain synchrony supports the exploration
of broader and mutually divergent motor trajectories. These results highlight the
nonlinear nature of social coordination, offering new avenues for modeling creative
joint action in human systems.
Keywords: Motif-synchronization, Time-varying graphs, Movement
decomposition, Togetherness, Brain functional networks, Generative dance.

1

Physics Institute, Federal University of Bahia, Salvador, Brazil.
Physics Department, Federal University of Pernambuco, Recife, Brazil.
3
Superior School of Physical Education, University of Pernambuco, Recife, Brazil.
4
Faculty of Human Kinetics, University of Lisbon, Lisbon, Portugal.
5
Institute of Ethnomusicology - Centre for Studies in Music and Dance, Lisbon, Portugal.
6
Dance School, Federal University of Bahia, Salvador, Brazil.
7
Department of Performing Arts, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
*
vivas@ufba.br
2

element

1. Introduction
Movement synchrony refers to the temporal and spatial alignment of performers,
a process tightly linked to social perception (intuition of social relationships) and
aesthetic appreciation in dance (Cross et al., 2024). Studies show that moving in
synchrony increases feelings of affiliation (Hove & Risen, 2009), collective enjoyment
Vicary et al., 2017), and predicts pro-social effects (von Zimmermann et al., 2018).
According to Orgs et al. (2024), in dance observation (within a video/fMRI context),
higher degrees of movement synchrony between performers are associated with greater
neural synchrony among spectators, which is interpreted as an indicator of shared
aesthetic experience. Group-based coordination also shapes dancers’ internal
experience: distributed patterns of movement coupling enhance feelings of liking and
group affiliation among performers (von Zimmermann et al., 2018). Neuroscientifically,
these phenomena engage the action-observation network, mirror-neuron systems, and
predictive motor pathways. As reviewed by Ribeiro et al. (2024), observing dance
engages visual processing streams (dorsal and ventral visual pathways) that project to
parietal and premotor cortices, activating the action observation network. These neural
mechanisms support motor resonance and embodied processing during dance
observation, potentially facilitating interpersonal coordination and contributing to the
social and aesthetic impact of synchronized movement.
Physiological evidence further demonstrates the embodied nature of
synchronization (Noy et al., 2015). In improvisational tasks such as the mirror game,
there exist moments of togetherness, which by Gesbert et al. (2022) define as the
experience of being and acting together, characterized by tight kinematic alignment and
subjective reports of shared flow. It fits within what De Jaegher & Di Paolo (2007)
describe as participatory sense-making. Noy et al. (2015) showed that synchronized
motion elicits shared physiological arousal (e.g., heart rate and respiration), reinforcing
collective engagement and flow during reciprocal interaction. An fMRI hyperscanning
study of dancers found distinct patterns of social network activation in leaders vs.
followers, although it did not directly measure brain-to-brain synchrony (Basso et al.,
2021; Chauvigné & Brown, 2018; Chauvigné et al., 2018). Taken together, these
findings suggest that synchronization goes beyond movement alone. Moments of
togetherness often emerge during synchronized creative processes, such as the
improvisational mirror game, in which performers experience a sense of unity and flow
through tightly coupled movements (Gesbert et al., 2022). These findings situate group
coordination as not only a physical phenomenon but also an embodied, interdependent
social process.
In addition, within group-based coordination, leadership dynamics often
influence the degree of synchrony achieved: leaders tend to guide timing and
complexity of movement, while followers exhibit predictive and reactive adjustments
(Basso et al., 2021). This role differentiation is critical, as it balances flexibility with
structured coordination. In dance improvisation, for instance, shifts between leader and
follower create opportunities for creativity while maintaining collective engagement.
While significant advances have been made, open questions remain regarding how
large-scale ensemble synchrony, cultural variations, and long-term training shape the
neural computations that underpin coordinated movement. Together, current evidence
suggests that dance synchrony serves as a rich subject for understanding how brains and
bodies coordinate to produce shared aesthetic and social experience.

To study motor and neural synchronization, the present research offers a
combination of approaches to study collaborative performance through motif-based
neural and motor synchronization. The study conducted by Miranda et al. (2018)
investigated the formation process of complex hand movements and found that complex
movements can be decomposed into a combination of simpler reaching movements, a
method known as Movement Element Decomposition (MED). This decomposition
revealed a scale-free relationship between mean velocity and displacement,
characterized by an optimal exponent α=2/3. Recent studies on the energy balance of
human movement suggest that this α exponent can vary. For instance, differences have
been observed when comparing the dominant and non-dominant hands of right-handed
individuals during writing (Ramos et al., 2025a). Additionally, this exponent may
exhibit unique alterations across different movement directions, such as when assessing
balance in the mediolateral and anteroposterior directions (Fialho et al., 2025).
Furthermore, Ramos et al. (2025b) demonstrated that the value of the α exponent varies
over time during fine motor tasks, with more significant variation occurring in the
dominant hand. This emphasizes the reduction of degrees of freedom (Bernstein, 1967)
in motor executions with the non-dominant hand. These findings encourage us to
investigate other circumstances in which this optimization index may be altered. We
hypothesize that collaborative dance, as a genuinely creative motor task, may exhibit
dynamics of α that explore differing degrees of freedom. We expect these movement
dynamics to change and become interrelated. To investigate this, we will measure how
the α index varies over time and how it may synchronize between subjects improvising
together under various types of interaction stimuli.
The coordination of human movement is fundamentally defined by Bernstein's
Degrees of Freedom (DoF) Problem (Bernstein, 1967), which addresses the redundancy
inherent in the sensorimotor system, in which numerous joints and muscles can be
orchestrated to achieve a single task goal. The central challenge for the Central Nervous
System is managing this high-dimensional space of possibilities, a process typically
solved through the temporary formation of synergies, functional groupings of DoF that
simplify control (Latash & Turvey, 1996). Motor learning is, therefore, a progression
from initially "freezing" DoF to reduce complexity toward"freeing" and "exploiting" of
redundant DoF, allowing for increased flexibility and adaptability in movement
(Vereijken et al., 1992). Mastery over DoF dictates the complexity and dimensionality
of motor output.
We hypothesize that in interactive, creative tasks, deliberately increasing
explored DoF, which reflects greater individual movement complexity, will disrupt
simpler, low-dimensional coordination solutions. This disruption may lead to reduced
interpersonal movement synchronization between participants, even when they are
performing together.
Synchronization in collaborative dance offers a unique lens through which to
explore how humans coordinate their actions to create shared aesthetic and social
experiences. By bridging neuroscience, principles of motor control, and biomechanics,
our study aims to deepen our understanding of how creative motor tasks like
improvisational dance shape neural and motor synchronization.
This study employs an experimental approach that combines EEG measurements
and movement in collaborative dance, pioneering the investigation of neural
synchronization during the process of group improvisation in dance.

1.1 From a physical perspective:
(i) Collaborative improvisation can be framed as a high-dimensional complex system in
which neural oscillations and motor trajectories constitute coupled dynamical variables
evolving across multiple temporal scales. Such multiscale interactions are characteristic
of biological coordination and other high-dimensional dynamical systems operating far
from equilibrium (Haken et al., 1983; Kelso, 1995).
(ii) Fluctuations in movement strategies, captured here through the α-exponent,
resemble local power-law relations commonly found in scale-invariant processes (Bak,
1996; Stanley et al., 1999). Likewise, motif-based neural synchronization characterizes
transient coherence patterns analogous to metastable states in coupled oscillator
networks (Breakspear et al., 2010; Rabinovich et al., 2008). These metastable regimes
have been proposed as key computational principles in neural and cognitive dynamics.
(iii) The collective behavior emerging from these interactions may thus be interpreted as
spontaneous organization within a nonlinear multilayer network, where coordination
does not arise from fixed coupling rules but from continuous transitions among
attractor-like states (Arenas et al., 2008; Boccaletti et al., 2014). This theoretical bridge
positions improvisational dance as a natural experiment for studying self-organization,
criticality, and information flow in complex adaptive systems (Bar-Yam, 2004;
Pikovsky et al., 2001), offering a physical lens for interpreting the neuro-motor
signatures of togetherness.

2. Experimental Protocol and Data Acquisition
The experiment was conducted in two sessions: before and after a movement
interaction program called Generative Dance through Agent Modelling (GDAM). This
program translates computational models into scores for collective improvisation, and
emphasizes principles of complexity theory (Leitão et al. 2025). Participants were
instructed to move freely, utilizing only two basic movement states: undulating (wavy)
or rectilinear (straight-line) movements with both hands.
Each experimental session involved four participants. The participants were
seated at the four sides of a table, with written movement instructions placed in front of
them.
Motion Capture: Four participants wore gloves equipped with infrared markers
on both hands. Movement was captured using an OptiTrack Motion Capture system
featuring 17 cameras, providing 3D spatial data with 1mm precision and a sample rate
of 120Hz. The origin of the coordinate system was positioned on the floor and aligned
with the center of the table. See Fig. 1 for an illustration of the setup.
Electroencephalography (EEG): Simultaneously, neural activity was recorded.
Due to resource constraints, only two of the four participants wore EEG caps during
each experimental session. EEG recordings were obtained using a 64-channel system
(Neuvo 64-channel Amplifier - Compumedics), following the International 10-20
System. The Cz electrode served as the reference, and data were acquired at a sampling
rate of 1000 Hz. 64 channels were divided into two caps, excluding non-cortical
regions, configured to record 28 channels per individual, covering the following

locations: FP1, FP2, F3, F4, F5, F7, F8, Fz, FC1, FC2, T3, T4, T5, T6, C3, C4, Cz,
CP1, CP2, CP5, CP6, P3, P4, Pz, P9, P10, O1, O2, Oz.
For data processing, EEGLAB, a MATLAB toolbox, was utilized. The data
were filtered using a bandpass filter between 0.5 and 48 Hz. The continuous data were
then segmented into 1.28 s epochs. Subsequently, epochs in which the signal exceeded a
threshold of +/- 100 μV were automatically rejected as containing artifacts. Following
these automated procedures, a final visual inspection was performed, and any remaining
artifact-contaminated epochs were manually removed.
The tasks were performed in the following order:
1. (FM) Free Movement (2 min): Participants were instructed to move purely
according to their own volition, without constraint or consideration for the other
participants. This task served as an individual baseline for unconstrained motor
dynamics.
2. (DM) Dependent Movement (2 min): In this phase, participants were encouraged to
actively consider the movements of the other participants and decide how they would
integrate or respond to these movements. The specific nature of the interaction (e.g.,
imitation, opposition, synchronization) was left entirely to the subjects' choice.
3. (RM) Rule-Based Movement (6 min): This task introduced specific, structured rules
(Wolfram rules, see Fig. 2.), see for movement, effectively simulating a cellular
automaton algorithm. Movement became dependent on the state (movement states:
undulating or rectilinear) of a participant's neighbors. Initial State: Each participant was
given an initial movement configuration (either rectilinear or undulating). Rule
Changes: The period of the rule was 30 seconds. At the end of each period, the
“observe” command was given, during which participants had 10 seconds to identify
the neighbors’ configuration on the rule sheet and understand what their next
configuration would be. The observing process was carried out continuously, without
interrupting the movement. After that, the “act” command was given, which
corresponded to the transition to the next rule, which was then followed until the next
“act” command.

Fig. 1. Protocol setup illustration, including two subjects wearing EEG caps. Sheets on the table contain
transition rules such as those in Fig 2.

2.1 Wolfram rules

In the RM task, 4 Wolfram rules were used for two-dimensional cellular
automata with four cells. Formally, let n denote the number of binary cells (where 0 or 1
represents a pattern of undulating or rectilinear movements) in a local neighborhood,
here n = 4: the focal cell σ and its three neighbors σ r ,σ f ,σ l (right, front and left
respectively). A transition rule is completely specified by the 2n bits d k = φ ( b k ), where {
b k ; k = 0 … 2n − 1} is the lexicographic ordering of all length-n binary vectors. For
example:
b 0 = {0,0,0,0},
b1 = {0,0,0,1},
…,
b( 2 −1 ) = b15 = {1,1,1,1}
n

Each integer N (N represents a code of a Wolfram rule) can be written as a
sequence of binary digits d k , each representing the next state for a specific
neighborhood configuration b k . The Wolfram integer code N φ associated with the rule φ
is given by the binary-to-integer map:
2n −1

N φ = ∑ d k ⋅ 2k
k =0

So that the binary expansion of N φ recovers the truth table of φ bit by bit.
Conversely, given an integer N with binary digits d k (where d k ∈ {0,1}).
This one-to-one correspondence endows the finite set of Boolean local maps.
Under bitwise comparison rules, it permits systematic enumeration and algebraic
manipulation of rule classes (in our case, undulating or rectilinear movements, which
place nonlinear constraints on the b k ). In the specific 2-D diamond-neighborhood model
used for choreographic objects, the case n = 4 yields distinct local rules and makes the
Wolfram code a convenient scalar index for exploring properties such as symmetric
attractors, reversible cycles, and sensitivity to perturbation (Leitão et al., 2023), giving
an application to emergent collective dynamics.

Fig. 2. Wolfram rule 37102 for configurations of being undulating (dusty purple) or rectilinear (cream) in
the next step as a function of their neighbours (Leitão et al., 2023).

3. Biomechanical data segmentation and processing
Based on the work of Miranda et al. (2018), it has been shown that there exists
an exponent linking mean velocity and displacement in reaching movements ⟨ V ⟩ ∝ D α
. This relationship can be extended to more complex movements by decomposing the
velocity components into zero-crossings, thereby generating sub-movements that
preserve the same dynamic properties. The exponent α is an index associated with the
energetic dynamics of movement and can be interpreted as an indicator of the motor
strategy employed.
The methodology proposed in this study aims to identify synchronized motor
patterns among different participants. To this end, the entire movement is considered for
the computation of the α index, in contrast to previous approaches (Fialho et al., 2025;
Miranda et al., 2018; Ramos et al., 2025a, 2025b). This work introduces a single α index
derived from the combined movement of two distinct body parts, in our case, the left
and right hands, as illustrated in Fig. 3. This approach aims to represent movement as a
whole, encompassing the three components of three-dimensional movement.
The computation of the exponent α was based on a time series approach, as
developed by Ramos et al. (2025b), who introduced a temporal sequence of α values to
infer temporal and sequential variations of this parameter during task execution. In the
present study, α is computed within 20-second windows using a sliding window method
with frame-by-frame updates, according to the following formula:
α ( t ) = ( α 1 — 20 f , α 2 — ( 20 f + 1) , … , α ( n - 20 f ) — n )

(1)

Where n represents the total number of recorded movement frames, and f is the
sampling rate. α i — j represents the value of α is computed from the movement
occurring between frames i and j. From the resulting α time series, we extract features
that enable the analysis of motor behavior synchrony between participants on a pairwise
basis.
The α exponent is related to the energy balance of the system, being a highly
important index for studying motor dynamics, unlike velocity or acceleration, which do
not represent the energy dynamics in their entirety, as they do not take into account the
temporal component of the movement (Ramos et al., 2025b).

Fig. 3. Application of the MED method to the motion analysis of both hands combined. (A) and (B) show
the velocity components over time for the left (red) and right (blue) hand, respectively. ( C) illustrates the
3D spatial trajectories from which these velocity data were derived. (D) demonstrates the power-law
relationship between <V> and D for each sub-movement, presented on a log-log scale.

3. Motif Synchronization
The study of synchronization has gained substantial traction in recent decades,
particularly through the use of the Kuramoto model (Kuramoto, 1975, 1984), which has
become a canonical framework for describing collective behavior in populations of
coupled phase oscillators. Numerous extensions of the model have been proposed to
account for heterogeneity, network structure, and time delays (Acebrón et al., 2005;
Arenas et al., 2008; Rodrigues et al., 2016). These formulations have enabled profound
theoretical insights into phase locking, critical transitions, and emergent coherence in
complex systems. Despite its analytical power, however, the Kuramoto model presents
intrinsic limitations when applied directly to real-world time series generated by
interacting individuals.
In empirical settings, especially those involving biological or behavioral data
from multiple persons, synchronized activity may be driven by shared sensory input,
contextual cues, or global environmental fluctuations. Since the Kuramoto model
assumes a predefined coupling function and does not infer influence or directionality
from the data, instantaneous or near-zero-lag synchrony may reflect external common
drivers rather than genuine inter-individual interaction (Breakspear et al., 2010;
Pikovsky et al. 2001). Even in delay-coupled variants of Kuramoto dynamics (Earl &
Strogatz, 2003; Yeung & Strogatz, 1999), time delays are modeled, not estimated, and
the framework remains fundamentally phenomenological rather than data-driven.
Additionally, extracting phase information from noisy, broadband, or non-stationary

signals, such as EEG or behavioral time series, introduces methodological ambiguities
that further compromise the interpretability of synchronization measures based on the
Kuramoto model (Kralemann et al., 2008).
For these reasons, and given our primary objective of characterizing how
individuals influence one another within collective dynamics, we adopt an alternative
approach: the Motif-Synchronization method introduced by Rosário et al. (2015), which
has been applied in a wide range of contexts for synchronized time series analysis, from
the progression of epidemics to neural dynamics (Fernandes et al., 2024; de O. Toutain
et al., 2023; Saba et al., 2022; Sousa et al., 2024; Thaise et al., 2024; Toutain et al.,
2020; ). Instead of relying on phase representations, Motif-Synchronization transforms
each time series into an ordinal sequence of three-point motifs that encode local patterns
of increases and decreases in the signal. Synchronization is then quantified by
computing the proportion of identical motifs occurring across two time series at specific
positive time lags, which allows for the detection of lead-lag relationships and
directional information flow (see Fig. 4). By evaluating this similarity over time, we
construct Time-Varying Graphs (TVGs).
A connection between two nodes is established whenever the proportion of
identical motifs exceeds a similarity threshold ( S c ). In the present study, we set S c = 0.7
as a standard criterion, meaning that at least 70% of the observed motif transitions must
be structurally identical for two time series to be considered synchronized. This
threshold reflects a stringent regime of structural coincidence, well above chance levels,
ensuring that detected links represent statistically meaningful synchronization rather
than random overlap. Robustness analyses confirmed that the global network topology
and all reported results remain qualitatively stable for thresholds in the range (
S c ∈ [ 0.5 , 0.9 ] ), indicating that the choice of S c = 0.7 does not bias the conclusions.
This framework is particularly advantageous in empirical contexts where zerolag synchrony may arise from shared perceptual events or global inputs rather than
genuine inter-individual coupling. By explicitly incorporating temporal delays in the
motif-matching process, the method distinguishes between trivial stimulus-driven
synchrony and temporally structured dependencies that more accurately reflect interindividual influence. As a result, it provides a more reliable account of information flow
between participants while avoiding the confounds inherent in phase-based or modelassumed synchronization frameworks.

Fig. 4. Motif synchronization method in neural signals for a certain window. The process must be
repeated window by window in a sliding sequence to obtain a TVG.

3.1 Biomechanical synchronization
Biomechanical synchronization was measured from the subjects' α time series,
using motif synchronization. We sought the sequence of correlated motifs in 1s
windows (120 frames), considering delays of up to 4 frames, thereby obtaining a
synchronization graph for each time frame. In the end, we produced a composite graph
containing all pairwise synchronizations between individuals, as shown in Fig. 5.
Because our time scales are significantly shorter than those for information processing
and motor response generation, we treat the graphs as undirected.
From this 6-edge graph, we analyzed the proportion of synchronized moments
of that same edge (pair of individuals) throughout all tasks.

Fig. 5. Biomechanical synchronization graph in a α time series. Each node represents a player in Fig. 1.

3.2 Multilayer synchronization in neural data
To assess neural synchronization between pairs of individuals, a combined
methodological approach was employed: Motif Synchronization and the multilayer
TVG analysis proposed by Sousa et al. (2024). This work presents a methodology for
constructing TVGs based on the quasi-simultaneous counting of micropatterns, referred
to as motifs, among all possible pairs of EEG signals from each subject. This approach
is considered appropriate for representing neural activity, given that the brain exhibits
complex, continuous, and connectionist dynamics even under minimal external
stimulation, such as during the resting state.
The study by Sousa et al. (2024) presents an innovative approach that
characterizes synchronization between pairs of TVGs by identifying simultaneous
connections in the networks constructed for different individuals. The method relies on
the Incidence-Fidelity (IFij) index, which is computed as the product of the Incidence
index, representing the number of occurrences of the same edge in both TVGs divided
by the total time instants, and the Fidelity index, which represents the proportion of
times an edge appears simultaneously in both TVGs relative to the total number of its
occurrences. Mathematically, the Incidence-Fidelity index for two TVGs, G and F, is
expressed as follows:
I Fi , j = I i , j × Fi , j

(2)

,where:
Γ

∑ aGi , j ( t s ) aiF, j ( t s )

I i , j = s=1

(3)

Γ

and:
Γ

Fi , j =

∑ aGi , j ( t s ) aiF, j ( t s )
Γ

∑a
s=1

,where:

G
i, j

s=1
Γ

Γ

(t s) + ∑ a (t s) - ∑ a
s=1

F
i, j

s=1

G
i, j

(4)
F
i, j

(t s) a (t s)

x

ai , j ( t s ) = {1 , if ∃ an edge e i , j ∈ theframe t s do TVG x . s = 1,2 , … Γ ; 0 , otherwise }
(5)

This method results in a weighted network, in which the weights associated with
the edges correspond to the IF of each link. See Fig. 6.

Fig. 6. Example of calculating synchronization indices in a multilayer network for an edge: (a) Multilayer
network with 5 vertices in each layer and TVG lifetime equal to 3. (b) Fidelity and Incidence Network for
the considered TVGs. (c) Incidence-Fidelity Network.

The Incidence-Fidelity network for a pair of TVGs aims to avoid
misinterpretations of synchronization values when analyzed in isolation. For instance,
an edge that occurs infrequently but is always simultaneous in both networks may show
high Fidelity values, even if it appears only once throughout the TVGs. Thus, the
Incidence-Fidelity index measures synchronization between networks by considering
both the temporal extent of the TVGs and their individual edge frequencies, ensuring
that the maximum interlayer synchronization value effectively corresponds to the
highest synchronization recorded between the TVGs.
The Incidence-Fidelity networks were constructed for each pair of individuals.
To assess whether the identified edges could arise by randomness, additional IncidenceFidelity networks were generated with randomized edges for each pair of TVGs.The
highest Incidence-Fidelity value obtained was adopted as only edges with weights
exceeding this threshold were retained for analysis.
To compare engagement across tasks, we also examined the mean edge weight
distribution of the Incidence networks and compared these distributions before and after
GDAM using the Mann-Whitney statistical test.

4. Brain synchronization results
For the EEG data, the direct comparison between tasks before and after the
GDAM showed no significant effect, F(1, 8) = 0.216, p = .654, η²ₚ = .026. In contrast,
the relative EEG analysis revealed a significant effect, F(1, 8) = 10.787, p = .011, η²ₚ =
.574, indicating a marked change in the relative neural activity patterns between tasks
after the GDAM in the comparison between the tasks FM and DM (p=0.01). Post-Hoc
analysis is available in Table 1.

In order to compare the mean edge incidence distributions, Mann-Whitney U
tests were conducted to compare PRE (1) and POS (2) conditions across the three tasks
(FM, DM, and RM). Results indicated a significant difference for FM (U = 344,717.5; Z
= 6.97; p < .001) and RM (U = 402,018.0; Z = 13.74; p < .001), with the POS condition
showing higher mean ranks (FM: M₁ = 678.52, M₂ = 834.48; RM: M₁ = 602.73, M₂ =
910.27). In contrast, no significant difference was observed for DM (U = 270,162.0; Z =
–1.84; p = .195), although PRE exhibited slightly higher mean ranks (M₁ = 777.14; M₂
= 735.86). A Bonferroni correction was applied to control for Type I error. (See Fig. 3.).

Fig. 7. Distribution of edge Incidence values across tasks (FM, DM, RM) before (PRE, blue) and after
(POS, red) the GDAM. Violin plots represent the distribution of edge incidence values within each
condition, with horizontal dashed lines indicating the median. Insets show the ΔWeighted Degree (POSPRE) topographic maps.

The comparison of the mean edge incidence distributions revealed greater
synchronization in the POS condition for the FM and RM tasks, with a prominent effect
in the frontal region, as illustrated by the insets showing the variation of the weighted
degree across electrodes in Fig. 7.

5. Biomechanical synchronization results
The statistical analyses revealed a significant effect for the biomechanical
measures when comparing performance directly before and after the GDAM, F(1, 70) =
5.233, p = .025, η²ₚ = .070, indicating a change in biomechanical performance following
the GDAM. However, when analyzing the relative changes between tasks, no
significant difference was observed, F(1, 70) = 0.006, p = .940, η²ₚ = .000, suggesting
that the proportional relationship between tasks remained consistent across sessions.
Mean
Difference
(PRE-POS)

95% Confidence Interval for
Difference
P value
Std. Error

Lower
Bound

Upper
Bound

EEG (PRE: 5 pairs, POS: 5 pairs)
FM

0.08

0.08

0.36

-0.11

0.27

DM

-0.06

0.06

0.37

-0.19

0.08

RM

-0.1

0.07

0.2

-0.27

0.06

Relative increase in EEG

DM,FM

-.083*

0.03

0.01

-0.14

-0.03

RM,FM

-0.11

0.06

0.13

-0.25

0.04

RM,DM

-0.02

0.05

0.66

-0.14

0.09

Biomechanics (PRE: 42 pairs, POS: 30 pairs)
FM

3.099*

1.46

0.04

0.19

6.01

DM

0.19

1.31

0.89

-2.42

2.8

RM

3.550*

1.46

0.02

0.64

6.46

Relative increase in biomechanics
DM,FM

-0.12

0.11

0.27

-0.33

0.1

RM,FM

0.05

0.11

0.64

-0.17

0.28

RM,DM

0.08

0.11

0.45

-0.13

0.3

*. The mean difference is significant at the .05 level. Correction for multiple comparisons: Bonferroni.
Table 1. Statistical comparisons between measurements before and after the GDAM.

The post-hoc analyses revealed a decrease in motor synchronization for the FM
and RM tasks after the GDAM (see Table 1 and Fig. 8). However, no significant
differences were found when comparing the variation of these measures (Δ/sum)
between the PRE and POS conditions, as also observed in the EEG analyses (see Fig.
9). This suggests consistency in synchronization patterns across tasks within the same
day, with no significant differences between tasks when comparing PRE and POS
sessions.

Fig. 8. Ratio of motor-synchronized frames between pairs before and after the GDAM.

Fig. 9. Relative increase in synchronization between tasks, comparing pairs before and after the GDAM.
(A): motor synchronization; (B) Brain synchronization.

6. Discussion
Neural behavior
The results suggest that frontal lobe synchronization between individuals does
not directly reflect explicit social interaction, but rather alignment in internal executive
and intentional processes. Both free improvisation and rule-based improvisation
demand greater autonomous generation of motor strategies, monitoring, inhibition, and
decision-making under uncertainty, elements inherent to a genuine sense of
togetherness. These processes rely on the prefrontal cortex (Badre, 2008; Bari &
Robbins, 2013; Krawczyk, 2002), especially the right prefrontal region (Aron et al.,
2004, 2014). This neural engagement leads to increased inter-individual coupling in
these areas. In contrast, explicit interaction conditions reduce decisional autonomy and
shift cognitive focus toward sensorimotor and parietal networks, resulting in decreased

shared frontal involvement and, consequently, no increase in synchronization in this
region.

Opposite trends and DoF
The results indicate increased neural synchrony between individuals after the
GDAM program, while motor synchrony decreased. A similar dissociation, this
opposite effect between neural and motor behavior, was also reported by Ramos et al.
(2025b), who observed higher permutation entropy in neural data during writing with
the non-dominant hand, whereas permutation entropy of motor data was higher in the
dominant hand. The connection between this finding and ours suggests an inverse
relationship between brain and motor dynamics, which may indicate greater activity
efficiency: in our case, the more synchronized the brain, the less synchronized the
hands. This pattern reflects an expansion of motor degrees of freedom (a behavior of
increased DoF), as participants enhanced their experience in collective improvisation,
enabling a broadening of their range of possibilities during generative dance. Such
expansion enables more diverse and flexible compositions, which are not necessarily
identical across individuals (Himberg et. al, 2018; Tseng et. al, 2021). Despite this
increase in motor variability, neural synchronization simultaneously intensified,
indicating that the sense of togetherness is maintained even as motor behaviors
diversify.

7. Conclusion
This study highlights modern techniques in movement analysis and
synchronization modeling and is pioneering in characterizing the nonlinear dynamics
underlying generative dance through simultaneously recorded neural and motor data.
Our findings demonstrate that the participatory sense emerging during collaborative
improvisation is supported by a complex, multilayer network of neural interactions
shaped by training. These interactions reveal signatures of metastability, selforganization, and coupling, indicating that togetherness emerges not from simple motor
imitation, but from coordinated transitions across attractor-like states in shared neurocognitive space.
Importantly, the observed dissociation between increased inter-brain
synchronization and reduced motor synchrony after training suggests a reorganization of
the system’s degrees of freedom: performers expand the dimensionality of their motor
manifolds even as their neural dynamics become more coherent. This couplingdecoupling paradox is a hallmark of complex adaptive systems, in which global
coherence coexists with local divergence. This dynamic can be situated within Araújo’s
(2009) ecological model of decisional behavior, particularly its third phase of action
calibration within the perceptual–motor system. The post-training dissociation between
neural and motor synchrony indicates that performers operate in this calibration phase,
fine-tuning their actions in relation to shared intentions and contextual affordances
rather than converging on uniform motor outputs. Increased neural coherence thus
reflects stabilized collective intentionality, while motor divergence expresses the
adaptive expansion of individual action possibilities. Thus, togetherness in generative
dance cannot be reduced to aligned or mirrored movements; rather, it reflects an

emergent property of a multimodal, dynamical system in which neural intentionality,
creative exploration, and interpersonal influence continuously reorganize.
By integrating physical concepts such as metastability, scale-invariant structure,
and nonlinear network dynamics into the study of collective improvisation, this work
positions dance as an experimental model for examining self-organization and
information flow in adaptive systems. Beyond the artistic domain, these findings
provide a conceptual and methodological framework for investigating coordination and
emergent collective behavior in broader biological, cognitive, and social systems.

Funding
National Council for Scientific and Technological Development (CNPq) and Brazilian
Federal Agency for Support and Evaluation of Graduate Education (CAPES) provided
financial support for this project: Jose Garcia Vivas Miranda (grant CNPq nº
308758/2021-8), Adriana de Faria Gehres (grant CNPq nº 420222/2022-7) and Yago
Emanoel Ramos (PhD scholarship CAPES nº 88887.203818/2025-00). Additional
funding was provided by the Portuguese Foundation for Science and Technology
(FCT): Maria João Alves (FCT Multiannual Funding UIDB/00472/2020) and Ana
Maria Leitão (FCT PhD grant 2021.07216.BD).

Ethics approval
The experimental protocol was approved by the Ethics Committee of the Physics
Institute of Federal University of Bahia, Certificate of Presentation for Ethical
Approval: 73085523.0.0000.8035, in accordance with the Declaration of Helsinki.

CRediT
Yago Emanoel Ramos: Writing - original draft, Investigation, Data Curation, Formal
Analysis, Software, Conceptualization, Methodology; Raphael Rosário: Writing original draft, Software, Conceptualization, Formal Analysis, Validation, Investigation,
Methodology; Adriana de Faria Gehres: Writing - review & editing, Supervision,
Methodology, Conceptualization, Project administration; Maria João Alves: Writing review & editing, Conceptualization, Formal Analysis, Methodology, Validation,
Investigation, Supervision; Ana Maria Leitão: Conceptualization, Validation,
Investigation, Methodology; Cecília Bastos da Costa Accioly: Writing - review &
editing, Methodology, Conceptualization; Fatima Wachowicz: Writing - review &
editing, Supervision, Methodology, Conceptualization, Investigation; Ivani Lúcia
Oliveira de Santana: Writing - review & editing, Methodology; José Garcia Vivas
Miranda: Writing - review & editing, Data Curation, Supervision, Methodology,
Software, Formal Analysis, Validation, Investigation, Conceptualization, Resources.
Declaration of competing interest
The authors declare no conflict of interest.

Data availability
Data will be made available on request.

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</reference>

<statements>
1. Fitts & Posner's cognitive→associative→autonomous stages and Bernstein's freeze→release→exploit degrees-of-freedom progression prescribe what feedback to give when: concise cues and DoF-freezing for novices; variability, timing, and efficiency refinement for advanced learners.
2. Bernstein (1967): coordination is mastering redundant degrees of freedom (DoF)—freeze, then release, then exploit reactive forces/passive dynamics—supported empirically by ski-simulator and baseball-batting studies.
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.