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Behavioral Impact of Unisensory and Multisensory Audio-Tactile Events: Pros and Cons for Interlimb Coordination in Juggling


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Recent behavioral neuroscience research revealed that elementary reactive behavior can be improved in the case of cross-modal sensory interactions thanks to underlying multisensory integration mechanisms. Can this benefit be generalized to an ongoing coordination of movements under severe physical constraints? We choose a juggling task to examine this question. A central issue well-known in juggling lies in establishing and maintaining a specific temporal coordination among balls, hands, eyes and posture. Here, we tested whether providing additional timing information about the balls and hands motions by using external sound and tactile periodic stimulations, the later presented at the wrists, improved the behavior of jugglers. One specific combination of auditory and tactile metronome led to a decrease of the spatiotemporal variability of the juggler's performance: a simple sound associated to left and right tactile cues presented antiphase to each other, which corresponded to the temporal pattern of hands movement in the juggling task. A contrario, no improvements were obtained in the case of other auditory and tactile combinations. We even found a degraded performance when tactile events were presented alone. The nervous system thus appears able to integrate in efficient way environmental information brought by different sensory modalities, but only if the information specified matches specific features of the coordination pattern. We discuss the possible implications of these results for the understanding of the neuronal integration process implied in audio-tactile interaction in the context of complex voluntary movement, and considering the well-known gating effect of movement on vibrotactile perception.
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Behavioral Impact of Unisensory and Multisensory
Audio-Tactile Events: Pros and Cons for Interlimb
Coordination in Juggling
Gregory Zelic, Denis Mottet, Julien Lagarde*
Movement To Health, EuroMov, Montpellier 1 University, Montpellier, France
Recent behavioral neuroscience research revealed that elementary reactive behavior can be improved in the case of cross-
modal sensory interactions thanks to underlying multisensory integration mechanisms. Can this benefit be generalized to
an ongoing coordination of movements under severe physical constraints? We choose a juggling task to examine this
question. A central issue well-known in juggling lies in establishing and maintaining a specific temporal coordination
among balls, hands, eyes and posture. Here, we tested whether providing additional timing information about the balls and
hands motions by using external sound and tactile periodic stimulations, the later presented at the wrists, improved the
behavior of jugglers. One specific combination of auditory and tactile metronome led to a decrease of the spatiotemporal
variability of the juggler’s performance: a simple sound associated to left and right tactile cues presented antiphase to each
other, which corresponded to the temporal pattern of hands movement in the juggling task. A contrario, no improvements
were obtained in the case of other auditory and tactile combinations. We even found a degraded performance when tactile
events were presented alone. The nervous system thus appears able to integrate in efficient way environmental information
brought by different sensory modalities, but only if the information specified matches specific features of the coordination
pattern. We discuss the possible implications of these results for the understanding of the neuronal integration process
implied in audio-tactile interaction in the context of complex voluntary movement, and considering the well-known gating
effect of movement on vibrotactile perception.
Citation: Zelic G, Mottet D, Lagarde J (2012) Behavioral Impact of Unisensory and Multisensory Audio-Tactile Events: Pros and Cons for Interlimb Coordination in
Juggling. PLoS ONE 7(2): e32308. doi:10.1371/journal.pone.0032308
Editor: Paul L. Gribble, The University of Western Ontario, Canada
Received July 26, 2011; Accepted January 26, 2012; Published February 27, 2012
Copyright: ß2012 Zelic et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This research was supported by SKILLS, an Integrated Project (FP6-IST contract #035005) of the Commission of the European Community. The funders
had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail:
In everyday natural situations the combination or integration of
multiple senses is essential for an adapted goal directed behavior
[1–8]. The efficiency of multimodal integration is demonstrated by
the improvement of detection, reaction, and discrimination [9–
15]. Recently it was found that an added sound can interfere with
the opponent’s perception of the ball in tennis, showing that
multisensory integration may play a strategic role also in more
ecological settings [16]. Yet little is known about how cross-modal
environments can contribute to the ongoing coordination of limbs
in complex tasks [17–19]. In this study we examine multisensory
processes defined neither by detection or discrimination, nor by
behavioral reactions after the presentation of cross-modal stimuli,
but involved when perception and action come together in
ongoing coordination. The coordination of movements has a
pervasive functional role in elementary behaviors [20–23] (e.g.
grasping, reaching, pointing, upright standing, walking, chewing,
speech production, to name a few), in daily actions (see [24] for an
illustration), but also at the work place, in performing music and
arts, or in sports [25–27]. Such coordination typically involves
multiple joints, and requires dynamic and reciprocal information
exchanges between brain, body and the environment [22,23,28–
31]. Though intrinsically multisensory (i.e. combining vision,
audition, touch, and proprioception), interlimb coordination is in
many cases very dependent upon the use of vision. Here we are
interested in the advantage audio-tactile stimuli, which leave the
optical array invariant, may provide to specify, guide, and enhance
coordination. Despite the recent increase of interest for audio-
tactile multimodal integration its impact on behavior is still poorly
documented (for a review see [32]).
It is well known that detection of tactile events is reduced during
the execution of movements, a gating effect [33–36], which varies
during the time course of movement [37]. If the information
provided by external tactile events can hardly be detected when
movements are produced, then one may predict that audio-tactile
stimuli are not likely to improve coordination skills. However in
the present study the tactile detection was not achieved without a
functional relation to the movement produced; rather the stimuli
endorsed the role of carrying over relevant information to enhance
an ongoing coordination. Moreover vibrotactile stimuli have been
successfully used to direct attention in driving tasks [38].
Therefore, on the basis of these previous studies, the efficiency
of audio-tactile events to drive the coordination of movements
remains an open question.
We selected the so-called three balls cascade juggling trick, for
which the tactile suppression phenomena has recently being
demonstrated [39], as test case in the present study. The three
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balls cascade is among the simplest and the most studied juggling
tricks [40–43] and will be denoted juggling in the present paper.
Juggling represents a very challenging and high-dimensional
coordination problem. On the perception side, vision is cardinal
to dynamically couple the hands to the balls pattern [40,44,45]
and involves significant neural plasticity [46,47]. On the
movement side, juggling requires the patterning of precise and
fast hand movements [41,42]: the juggling pattern is periodic and
characterized by an invariant relative timing, where the throwing
action parameterizes the parabolic trajectories of the ball [43]. In
terms of coordination, juggling is mainly characterized by a 1:3
frequency ratio between the hand movement and a ball cycle
[41,42]. This notably entails forming and maintaining multi-
frequency relations among movements of hands, eyes and posture
[40,43–45,48–50]. Proficiency in juggling is readily identified by
co-variations among the trajectories of the hands and the limbs
combined with a decrease in variability of balls trajectories in time
and space [42,51,52], which contributed to depict learning to
juggle as the formation of a ‘‘spatial clock’’ [43].
What type of external periodic stimulations could improve the
performance at juggling?
Sensory stimulation can increase the robustness of elementary
coordination against internal biological noise or external pertur-
bation [23,53,54]. This increase in robustness was accompanied
by a decrease in variability of limbs trajectories, a phenomenon
referred to as ‘‘anchoring’’, which indicates higher stability of the
coordination pattern [55–58]. In the case of interlimb coordina-
tion, the stabilization effect was even more pronounced when the
frequency of the stimuli was twice the frequency of the movement
of the limbs [59]. Periodic stimuli carrying information about the
tempo provide global frequency information, but also local relative
timing information specifically defined by phase difference
[54,60]. As juggling is a rhythmical skill, such external timing
information should be beneficial to the juggler. However, a simple
auditory metronome failed to stabilize juggling [61], which
indicates that the multi-frequency nature of the juggling calls for
more than a mere metronome.
To provide the juggler with two metronomes without
overloading vision, we assumed that non-visual cross-modal
pairings matching the multi-frequency nature of juggling would
be the best stimuli to improve the stability of the coordination.
Accordingly, we focused our study on audio- tactile parings.
Previously important principles underlying the combination of
sensory cues from different modalities have been discovered,
notably that integration takes place according to a statistical
optimal rule [62]. However to the best of our knowledge, only
anecdotal evidence of an advantage of cross-modal stimuli over
uni-modal parings was provided for this class of multi-frequency
coordination in a bimanual task [63]. This corresponds to a case
where cross- modal pairing may be adequate because the task
requires segregation to move the hands at two distinct frequencies.
In the present study, our prediction that one can stabilize the
juggling coordination with adequate external sensory stimulations
was tested using periodic audio-tactile stimuli, respectively
presented at the ears and at the wrists, and providing specific
tempo. Because balls and hands frequencies are core to the
multiple component coordination in juggling, we chose to
associate each sensory modality to one of these main components.
The frequencies of the tactile metronome and of the auditory
metronome were thus scaled to match, respectively, the tempo of
the hands and the tempo of the balls. In one condition, the
metronome frequencies were multiplied by two to examine the
generalization of the parametric stabilization to an audio-tactile
pairing [59,64] (see also [65]). Finally, in one audio-tactile
condition, the tactile stimuli were presented alternatively at each
wrist, so to match the antiphase movement of the two hands in
juggling [23,53,54].
Seven right-handed students (five males, mean = 23.5 yr,
SD = 2.5 yr) from the Montpellier 1 University participated in
this study. Each participant signed an informed consent form
approved by the Institutional Review Board (IRB) of the
Montpellier 1 University (UFR STAPS).
Because of the very low natural variability of expert jugglers
[66] and because novices cannot juggle in a sustained fashion, we
ran a preliminary test to identify intermediate-level jugglers:
participants performed a three-ball cascade, while keeping feet
inside a 2 meters circle. They were deemed intermediate-level
jugglers if they could succeed for at least 20 seconds, but failed
before 60 seconds. Seven volunteers were selected out of thirteen
Data were collected using a Vicon 3D motion recording system
at a 100-Hz sampling rate. The system was calibrated according to
the manufacturer’s instructions prior to data collection. Two
reflective markers were taped on the dorsal head of the 3
metacarpal, to record the left and right hand movements. The
three balls were covered with reflective tape and defined as
markers, to record the movements of the balls.
Thanks to additional markers fixed on each shoulder, we had
able to follow the rotation and translation movement of the subject
in the environment during the task. To homogenize the set of
trials, we realized a projection of the data, first recorded in the lab
frame, into a new reference frame relative to the subject (center at
the top of the sternum – O , with antero-posterior – ~
xx, transversal
yy, vertical axes ~
zz), fixed in time, and defined as the mean
position of the participant on the trial.
The vibrotactile metronome consisted in 80 ms square wave
pulses (vibration carrier frequency: 100 Hz). The stimulation was
delivered with a DC motor (weight: 42 g) strapped on the ventral
part of each wrist. Preliminary tests showed that the time to reach
100 Hz was less than 5 ms.
The auditory metronome consisted in 80 ms square wave pulses
(tone carrier frequency: 300 Hz) delivered to headphones fixed on
top of the auricles. Headphones also played white noise in order to
isolate the subject from the noise emitted by the vibrotactile
We wanted to compare the effect of metronomes that differed in
modality (tactile, auditory or audio-tactile), frequency (simple or
double) and, in the case of simple frequency metronomes, in the
phasing of the stimuli (in-phase or anti-phase).
Running the full crossing of the three factors in a repeated
measure design would necessitate multiple sessions per participant.
As a consequence, we selected the most interesting metronome
conditions. Because metronomes that beat twice per movement
generally provide a better guidance [59], we selected such a double
frequency metronome in the three modalities (Multi. Doub., Tact.
Doub., Audio. Doub.). Then, to reproduce the natural relative
phase between the hands movement in juggling [23,53,54,67], we
added the simple audio-tactile metronome with anti-phase tactile
stimuli on each wrist (Multi. Anti.) and its in-phase counterpart
(Multi. Simp.). Finally, we included a baseline control condition
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with no metronomes, to get a total of 6 experiment conditions
(Table 1).
More precisely, because the juggling is the assembly of two
frequencies within a single task [41,48,52], we set up the tactile
metronome to the hand frequency (Vhand) and the auditory
metronome to the ball frequency (Vball). Hand frequency was the
inverse of the average period of time between two consecutive
throws by the same hand. Ball frequency was defined as one-third
of hand frequency, because one hand takes care of three balls in
the selected juggling pattern [41]. In the multimodal conditions,
the phasing between the audio and the tactile stimuli corresponded
to the average phasing between the motion of one ball and the
motion of one hand along the vertical axis, that is, the two stimuli
were set with identical initial phases (see Figure 1, panel B).
We used a repeated measures design, where each participant had
to juggle in each one of the 6 metronome conditions. The order of the
metronome conditions was randomized across participants. In each
metronome condition, participants had to perform a bloc of 5 trials.
The experimental session started with a preliminary trial to
record the preferred juggling frequency of each participant. Then,
during 10 minutes, the participant was familiarized with the 6
metronome conditions. After this familiarization, the participant
performed a block of 5 trials in each one of the 6 metronome
conditions, for a total of 30 experimental trials.
No instructions to synchronize with the stimuli were given, and
participants were instructed to start juggling after the metronome
Table 1. Experimental conditions and characteristics of the metronomes.
Sensory Modality Structure Auditory frequency Tactile frequency (and phasing) Label
Audio-tactile Simple Vball Vhand (P= 0) Multi. Simp.
Audio-tactile Simple Vball Vhand (P=p) Multi. Anti.
Audio-tactile Double 2*Vball 2*Vhand (P= 0) Multi. Doub.
Tactile Double - 2*Vhand (P= 0) Tact. Doub.
Audio Double 2*Vball - Audio. Doub.
- - - - Control
The sensory modalities (multimodal – solid line frame – vs. tactile or auditory unimodal) and the metronome parameters have been manipulated. We distinguished
simple metronome from double metronome (dashed frame) for which the tactile and auditory metronome have been set equal to or twice the hands and balls
frequency respectively. In one of the simple, multimodal metronome, the vibrotactile stimuli were presented in antiphase at the wrists (Multi. Anti, P=p). Otherwise
P= 0 indicates that the vibrotactile stimuli were presented simultaneously.
Figure 1. Representative juggling behavior in the frontal plane ~
zzðÞ.(A) Motion of balls (solid line) and left hand movement (dashed line) in
the frontal plane are presented with the localization of throws and catches (respectively circles and squares). Please note that throws and catches
points and balls trajectories are not exactly coincident because the passive marker was placed on the back of the hand. (B) Representative time series
of position of one ball and of position of the left hand are respectively represented in solid and in dashed lines.
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The task was to juggle as regularly as possible for the duration of
a trial: 20 to 30 s (in some conditions, two jugglers were only able
to complete 3 trials lasting more than 20 sec.).
For each participant individually, the frequencies of the
metronomes were set at her/his preferred hands frequency (or
twice the preferred frequency in the Doub. conditions).
Data processing and analysis
The marker data were dual passed through a second-order
Butterworth filter (fourth-order) with a low-pass cutoff frequency
of 8 Hz prior to further data processing.
From the vertical velocity profiles of balls, we identified the
moments of throw and catch: a positive velocity peak denotes a
throw, and a negative velocity peak denotes a catch.
We then used the average period of time between two
consecutive throws by the same hand to compute the hand
frequency (Vhand).
We addressed the organization of the juggling by analyzing the
variability of the juggling pattern among the metronome
conditions. Variability was computed as the within-trial stan-
dard-deviation of the variables of interest, using directional
statistics for angular values [68]. The variables, listed in Table 2
and schematized in Figure 2, measured the performance in three
aspects of variability that are key to sustained juggling: timing,
bimanual coordination, and throw.
First, because the timing of balls events seems to be the focus of
control in intermediate and expert jugglers [52], we examined the
within-trial variability of ball flight duration. The ball flight time
(BFT) is the period between a throw and the consecutive catch by
the other hand (Table 2 and Figure 2). Variability in BFT is here
used as a global indicator of the stability of the coordination
involved to sustain juggling. We also investigated the within-trial
variability of the time spend with a ball in hand. The so-called K-
ratio (K) is the percentage of a cycle duration with the ball in hand
Table 2. Dependant variables.
Label Name Definition Computation
BFT Ball flight time Time duration between the throw of a ball
and its consecutive catch
K K-ratio Proportion of time with the hand loaded (TL - i.e.,
with ball in hand) in a juggling cycle
with TL~Tthrow{Tcatch
DBT Distance between throws Euclidean distance between two consecutive points
of throws in the vertical plane
DBTy~LHythrow{RHythrow DBTz~LHzthrow {RHzthrow
ThVel Throw velocity Norm of the velocity vector at time of throw in the
plane of ball flight ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(dBxthrow)2z(dBythrow )2z(dBzthrow)2
ThAngle Throw angle Angle of the velocity vector at time of throw
in the plane of ball flight tan{1(dBzthrow)
(dBxthrow)2z(dBythrow )2
FSI Frequency synchronization
Difference between the hand frequency and
the metronome frequency
Vhand {Vmetronome
PSI Phase synchronization index Dispersion of the relative phase (mean(cos(Q)))2z(mean(sin(Q)))2
DT Dwell time Percentage of phase locking episodes dQ
with ea limit value and Nsamples the
number of values in a trial
We analyzed the within-trial standard-deviation of the dependant variables listed in this table. The first two variables (BTF, K) are used to assess the juggling
performance in time. The third variable (DBT) addresses the spatial aspects of the coordination between hands in the transversal axis (DBTy) and in the vertical axis
(DBTz). Two variables (ThVel, ThAngle) focus on the throwing, which is key to sustained juggling. Note that, though the juggling was performed in 3D space, ThAngle
refers to the elevation angle in the plane of ball flight. The three last variables (FSI, PSI, DT) were used to assess the synchronization of the participant with the
metronome. Hand frequency (Vhand) was the inverse of the average period of time between two consecutive throws by the same hand. The metronome frequency
(Vmetronome) was the inverse of the period of the metronome.
In the equations of the computation column : T is the time ; Hx, Hy, Hz are the coordinates of the hand ; Bx, By, Bz are the coordinates of the ball ; indices specify the
juggling events (i.e., catch, throw) ; d indicates the differential, so that dQ
is the differential of Q at time of throw ; L/R refers to the left/right hand ; Qis the relative
phase between hand position along the vertical axis and the metronome.
Figure 2. Juggling pattern in the frontal plane ~
trajectories are represented with a double line, and ball trajectories with
a single line. Ball trajectories are presented during ball flight time (BFT) :
the trajectory of a ball thrown by the left hand is drawn with a solid line,
the trajectory of a ball thrown by the right hand is drawn with a dashed
line (see Table 2 for variables details).
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(Table 2). The K-ratio is a key variable in the temporal structure of
the juggling [43,55,61].
Second, we addressed the organization of the juggling in space
via the within-trial variability of the distance between two
consecutive throws in the vertical plane (DBTz, see Table 2).
Because two consecutive throws involve the two hands, these
variables render a global measure of the between-hand coordina-
tion in space.
Finally, we captured the organization of the throwing behavior
via the within-trial variability of the tossing: The tossing angle and
velocity fully determines the trajectories of a ball (ThAngle and
ThVel, see Table 2 and Figure 2).
Synchronization to metronome
Synchronization of the hands to the metronome should result in
systematic frequency relations (i.e., frequency locking) and, if the
coupling is strong enough, in systematic phase relations (i.e., phase
locking) between the hands and the metronome [69].
Frequency locking was easy to assess from a frequency
synchronization index (FSI) computed from the difference
between the observed hand frequency and the frequency of the
metronome (see Table 2).
Phase locking necessitated a more sophisticated approach. For
each hand, the instantaneous phase was estimated using the
Hilbert’s transform of the vertical positions time series [70]. The
periodic variability arising from the specific coordinates used to
extract the instantaneous phase [71,72] was reduced by the
method proposed by Kralemann et al. [73]. The relative phase
between a hand and the metronome was obtained by probing the
value of the hand’s phase at times of stimuli onsets, which is
tantamount to using the metronome as a stroboscope to read the
hand’s phase time-series. To measure the strength of the phase
synchronization, we computed a synchronization index PSI (see
[74], for a theoretical presentation). The value of PSI is zero in the
absence of synchronization, corresponding to a uniform distribu-
tion of relative phase. The value of PSI is one for perfect
synchronization, corresponding to a distribution concentrated
around a single peak [75]. This phase synchronization index is
formally analog to the dispersion of the relative phase distribution
[68] and was calculated using the following formulae:
where PSI is the phase synchronization index and wis the relative
phase between the position of the hand along the vertical axis and
the metronome.
Furthermore, we calculated the dwell time of the relative phase
([23], chap.4). The dwell time was introduced in the case of
intermittent phase locking [58], and can be used to assess
tendencies toward phase synchronization [76]. We calculated the
dwell time from the time series of the slope of the relative phase
(i.e., relative phase velocity). A slope close to zero corresponds to
an episode of stationary phase locking [19]. A tendency toward
synchrony is revealed by alternating episodes of large and small
values of the slope, which indicates episodes of change and dwell in
relative phase. The dwell time is the importance of the small slope
episodes expressed as a percentage of the total length of the trial:
the larger the dwell time the stronger the tendency to synchronize.
Operationally, to minimize the effect of noise after differencia-
tion of the relative phase, we smoothed the time series of slope
with a 4-points moving-average before calculating the proportion
of time spent in small-slope episodes (i.e., episodes where the
absolute value of relative phase velocity was lower than a limit
value). We tried four different limit values for a small-slope episode
(0.1, 0.15, 0.2, and 0.25 rd/s). The dwell time (DT) is the time
spent in small-slope episodes divided by the total duration of the
trial and multiplied by 100 to get a percentage.
Statistical analysis
To assess the significance of the effects of the metronomes on
the juggling performance, we analyzed the variability of the
juggling and, in a second step, focused on the synchronization to
the metronomes, in relation to the juggling performance.
All analyses of variance were complemented with Tukey HSD
tests for post-hoc mean comparisons, and we reported the raw F
values and degrees of freedom, but pvalues after Huynh-Feldt
correction for non spherical variance.
In all statistical analyses, the significance level was set at .05.
Effect of the metronomes on the variability of juggling
behavior. Participants clearly differed in their level of variability
in the control condition, which corresponded to differences in their
juggling experience, despite the inclusion test and criteria.
Accordingly, to improve the sensibility and reliability of our
analysis to distinguish the five metronomes conditions, we
subtracted for each subject his/her mean variability measured in
the control condition to the variability measured in the
metronomes conditions, and this for each given variable. Thus
in this part of the analysis all variables were baseline corrected.
To examine the effect the 5 metronome conditions on the
juggling performance, we ran a global analysis of variance with
repeated measures (ANOVA). Moreover, in order to test for
significance against the baseline level, we compared the juggling
performance under each metronome condition against the
hypothetical mean of zero, the latter corresponding to the
baseline level of variability, using a one sample t-test. As we
emphasized the sensitivity of the analysis, we did not use a
Bonferroni-Sidak correction [77,78] and kept the pvalue
threshold set at .05.
Entrainment to the metronomes. To globally address the
issue of synchronization, we analyzed the timing of the juggler’s
hand relative to the metronome beats, using an ANOVA with
repeated measures, as previously.
In a last step, being aware that mean frequency differences
between movements and the metronome presented (FSI) varied
between subjects, we further examined the phase synchronisation
to the metronomes in each participant individually. We ran a
within-participant statistical analysis using a surrogate approach to
distinguish true phase synchronization from values obtained by
chance. One type of synchronization, a weak synchronization, can
indeed be expressed by a correspondence between the mean
frequencies while phase synchronization is absent [22,69]. For
instance consider the fact that oscillatory movement may
comprise, except for perfectly harmonic movement, alternating
slow and fast evolution within a period. In such a case periodic
stimuli onsets would necessarily happen more often during the
slow parts, introducing a concentration of the relative phase
distribution, directly increasing the synchronization index and
dwell time. The phase synchronization variables would differ from
zero but this won’t indicate an underlying sensori-motor phase
synchronization process. In this case rejecting the presence of
phase synchronization requires a specific approach. We then
tested the hypothesis of phase synchronisation by comparing the
observed distributions of the synchronization index and dwell time
to surrogates distributions of the same quantities. The surrogates
were generated under the null hypothesis of values obtained by
chance in the absence of coupling to the metronome. To this end
we computed a relative phase between the movements recorded in
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the control condition and a metronome generated from those used
in the other conditions. Moreover the time between the start of the
movement and the first stimulus onset was randomly drawn from a
Gaussian distribution, so as to get for the initial time shift a
duration between 0 and the actual period of the metronome used
for a given subject. By taking 1000 random initial period in
different runs we computed for each individual 1000 phase
synchronization indexes and dwell times (see appendix S1).
Because larger values indicate better synchronization in the
surrogate distributions obtained for each participant, we took the
95 percentiles as the threshold value to get a p value of 0.05 for
significant synchronization [79].
Finally, we analyzed the correlation between the synchroniza-
tion indexes and the variability of the juggling pattern, with the
prediction that better synchronization to the metronome would
render lower variability in the juggling pattern.
Figure 1 A–B presents a representative sample of the recorded
data, which clearly demonstrates the variability in hands move-
ments, onsets of throws and catches, and in the ball’s trajectories.
Throwing movement
The first step in the analysis of the data was to examine whether
the temporal information carried out by the external metronome
affected the throwing action. The ANOVA applied on the
variability of the initial angle at throws (ThAngle) was inconclu-
The ANOVA on the variability of the velocity at throws (ThVel)
indicated an effect of the metronome condition (Figure 3; F
= 3.03, p = .037). It especially showed that the velocity
variability with the antiphase audio-tactile metronome (Multi.
Anti.) was smaller than the variability obtained with the unimodal
tactile metronome (Tact. Doub.).
In addition the t-test comparison showed a variability of the
velocity at throws in the unimodal tactile condition (Tact. Doub.)
significantly larger than zero (t
= 2.13, p = .042).
Temporal organization of the juggling coordination
The ANOVA applied on the averages of variability of the K-
ratio was inconclusive.
The ANOVA on the variability of the balls flight time (BFT)
revealed a significant effect of the metronome condition (Figure 4;
4, 24
= 3.60, p = .030). It evidenced a smaller variability of the
Figure 3. Variability of throw velocity (ThVel) for each metronome condition. The average variability for each individual in the control
condition defined the individual baseline variability, which was subtracted to the individual’s average variability in each metronome condition. Thus,
the zero corresponds to the baseline variability without metronome. Negative values indicates smaller variability than in the control condition. Error
bars represent inter-participant standard deviation. The grey bar indicates a significant increase in the variability of throw velocity in the Tact. Doub.
metronome condition.
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BFT in the antiphase audio-tactile condition (Multi. Anti.) than in
the unimodal tactile condition (Tact. Doub.).
Spatial variability of the juggling coordination
The ANOVA on the variability of the vertical distance between
two consecutives throws (DBTz) also showed a significant effect of
the metronome condition (Figure 5; F
4, 24
= 3.62, p = .019). The
antiphase audio-tactile condition (Multi. Anti.) decreased the
DBTz variability when compared to the in-phase audio-tactile
condition (Multi. Simp.). In addition, let us remark that post hoc
comparisons suggested, with a probability very close to the
threshold for significance (p = .051), that this variability was
smaller with the audio-tactile double metronome (Multi. Doub.)
than with the audio-tactile simple metronome (Multi. Simp.).
Finally, t-tests showed that the variability of DBTz reached in
the antiphase audio-tactile condition (Multi. Anti.) was signifi-
cantly smaller than the zero baseline level corresponding to the
control condition (t
=22.24, p = .033).
Entrainment to the metronome
The ANOVA on the frequency synchronization index (FSI) was
not conclusive.
In addition, neither the ANOVA on the phase synchronization
index (PSI) nor the ANOVA on the dwell times (DT) showed a
significant effect of the metronome conditions.
However, as the differences between the actual average hand
frequency and the metronome frequency varied between partic-
ipants, this may have overridden the detection of differences in
phase synchronization between metronomes conditions. The
individual statistical analysis based on surrogates didn’t revealed
significant phase synchronization neither for the PSI, nor for the
DT, except for the DT in one participant and this in all conditions
but the Audio Double condition.
This confirmed that phase synchronization between the hands
and the metronome was not present in the various metronomes
conditions and that only a frequency relationship was maintained.
Finally a Pearson’s correlation analysis indicated that the
variability of the juggling pattern increased with the FSI. This
was evidenced for BFT (R
= 12%, p = .037), ThVel (R
= 25%,
p = .002), and DBTz (R
= 56%, p = 10
). Moreover, we found
that the frequency difference (FSI) affected the variability of DBTz
in the case of the antiphase audio-tactile metronome (R
= 40%,
p = 2*10
) more than in the other conditions (R
= 12% to 28%,
.002,p,.051; see Table 3).
Figure 4. Variability of ball flight time (BFT) for each metronome condition. Zero corresponds to the baseline variability without
metronome, and the error bars represent inter-participant standard deviation. The lack of grey bars indicate no significant difference from baseline
variability: the metronomes did not influence significantly the BFT.
Sound-Touch Facilitation of Movement Coordination
PLoS ONE | 7 February 2012 | Volume 7 | Issue 2 | e32308
Our goal was to examine whether auditory and tactile
metronomes, presented together or separately, can influence the
behavioral variability of a challenging inter-limb coordination.
The question addressed here is that of multimodal integration, and
its potentially useful role to convey information from the
environment to enhance an ongoing coordination. Recently,
rhythmic neuronal mechanisms underlying audio-tactile cross-
sensory interactions shed a new light on multimodal integration. It
was shown that somatosensory input in auditory cortex reset the
phase of ongoing auditory cortical oscillations which subsequently
enhanced the auditory response [80]. Whether similar mecha-
nisms may account for the present findings is certainly speculative,
but it suggests that rhythmic paradigms involving interlimb
coordination may provide a new look to the understanding of
multimodal integration phenomena, departing from concepts of
simple redundancy [81] or statistical rules [62]. We below discuss
how the multiple timing information provided by the audio-tactile
metronomes might be integrated to influence the stability of
coordination patterns in juggling.
A tactile metronome can destabilize sensorimotor
We found that a tactile metronome, presented synchronously at
the wrists, increased the variability of the velocity at the throws
when compared to the baseline variability measured in the
absence of a metronome (Tact Doub in Figure 3). This detrimental
effect of the tactile metronome on a local component of the
Figure 5. Variability of the vertical distance between consecutives throws (DBTz) for each metronome condition. Zero corresponds to
the baseline variability without metronome, and the error bars represent inter-participant standard deviation. The grey bar indicates a significant
decrease in the variability of the vertical distance between consecutives throws in the Multi. Anti. metronome condition.
Table 3. Correlation scores between the vertical distance
variability (DBTz) and the relation to the metronomes (FSI).
Multi. Simp. Multi. Anti. Multi. Doub. Tact. Doub. Audio. Doub.
0.288 0.391 0.209 0.230 0.125
p.010 2*10
.002 .006 .051
These relate the variability of the vertical distance between left and right
consecutive throws (DBTz) and the differences between the frequency of hands
movement and the frequency of metronomes (FSI).
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juggling coordination, namely individual hand movement, can be
interpreted as arising from the well known gating effect that results
in tactile suppression, which was also shown in juggling [39].
Alternatively, it can be due to the mismatch between in-phase
tactile events and the anti-phase movements of the hands. Please
note that the former interpretation calls for a non specific sensory-
motor mechanism while the latter emphasize on specific properties
of the information specified by the tactile stimuli and its relation to
the coordination pattern of the movement of the hand. Further
work is required to disentangle, or relate, these two lines of
Advantage of multi-modal over uni-modal conditions
We found that the detrimental effect of the tactile metronome
alone could be reduced when presented together with a sound. In
particular, we found that the variability of this ball’s velocity at
throws and its flight duration was lower in the antiphase audio-
tactile condition than in the Tact Doub condition (Figure 3 and 4).
As the minimization of the variability of the flight duration in
skilled jugglers was interpreted as the signature of a global variable
of coordination [52], this result suggests that the multimodal
stimulation was better integrated within the juggling coordination.
In the present case, each one of the two metronomes brings a
distinct tempo, and each tempo is sustained by distinct sensory
pathways, allowing for an easier segregation of the two basic
rhythms. Deciphering whether such segregation takes place at
perceptual, attentional, or more integrated sensori-motor level,
requires further work. Taken as an ensemble, these two distinct
tempos also define a specific relative frequency and relative
phasing between them, and this relative information is the most
meaningful to the ongoing coordination. Hence, it seems logical
that these properties have collectively contributed to strengthen, or
stabilize, the perception-action coordination underlying the
relation between the hands and the balls.
As a consequence, the improvement observed when combining
audio-tactile stimulations in a multi-frequency multi-modal
metronome cannot be exclusively explained by the added
contribution of the sound only. Similarly, we cannot argue that
the benefit obtained with the audio-tactile conditions was precisely
multimodal, because these conditions also specified non negligible
relative frequency and a specific relative phasing. We will discuss
further the latter below.
We suggest that the audio-tactile stimulations may overcome the
tactile detrimental effect, not by acting locally at the level of the
throwing movements, but by acting globally onto the ordering the
overall pattern of coordination, which requires a tight coupling
between the movement of the hands and visual information pick
up about the motion of the balls [40,44,45].
Another line of thinking is to consider asynchronies in the
encoding of visual, auditory and somatosensory cues in the brain.
Schroeder and Foxe [82] found evidences in the onset of neural
activity in the superior temporal polysensory area for shorter
delays following somatosensory stimuli than auditory or visual
ones. In the multimodal case, it was suggested that ‘‘early-
arriving’’ somatosensory inputs could modulate the local cellular
excitability and thus enhance the ‘‘later-arriving’’ auditory input.
Such potentiation may explain the improvement observed when
combining audio-tactile stimulations in the present experiment,
even if only one third of the multimodal stimuli are synchronous
because of the 3:2 coordination involved. Anyway, such suggested
multisensory processing is not yet sufficient to explain the
improvement found specifically in the case of the multimodal
antiphase metronome.
Parametric coupling of movement to multimodal
external events
We examined to what extent the stabilization properties of a
double periodic forcing, interpreted formally as a parametric
function [59,65,83], could generalize to the coordination encoun-
tered in a multimodal and multifrequency context. We found a
reduction of variability by the double metronome when compared
to the simple metronome close to the significance level (Figure 5,
p = .051). However when compared to the baseline level of
variability taken with respect to the control condition, this
stabilization effect did not reach significance (Figure 5). Thus,
our results provide only partial support to the idea that the
stabilization effect of double periodic forcing extends to a
multimodal and multifrequency context. This generalization
requires further validation, which would confirm the assumption
that the underlying parametric coupling is acting at an abstract
level and is amodal [83].
Phasing of the metronomes matters
We found that, for ball flight duration and vertical distance
between throws, variability in the Multi Simp condition was higher
than in the Multi Anti condition (Figure 5). Let us recall that these
two metronomes differed only by the relative phasing between the
tactile events. This specific phasing of the tactile metronome
matched the antiphase pattern of hands movement required to
perform the 3 balls cascade trick, and is likely to be one important
contribution to a more regular behavior. This is a first indication
that the phasing of the stimulation (whether multimodal or not) is
of high importance for the juggler. A second indication is that the
antiphase metronome was the only one that effectively helped the
juggler to be more stable. More precisely, matching the phasing of
the tactile stimulations with the actual phasing of the movement of
the hands reduced the variation of distance between successive
projection points of left and right hands (i.e., Multi Anti is lower
than zero in Figure 5), presumably by favoring a specific instance
of the so-called anchoring phenomena [55–58].
Taken together, these two indications denote the key role of the
relative phasing in the effective integration of external stimuli
within an ongoing coordination pattern: the degree to which
information can be useful is the degree to which it can be
integrated within the intrinsic behavioral dynamics [54]. Further-
more, a multimodal improvement of movement coordination may
be conditioned by a matching of the structure of the coordination,
as suggested by the advantage of providing non coincident tactile
stimulation corresponding to the anti- phase movement of the
The mediating role of synchronization to the stimuli
The variability of the juggling coordination covaried with the
difference of frequency between hands movement and the
metronomes. These frequency gaps varied because some partic-
ipants accelerated or slowed down during the course of the
experiments. This suggests that synchronization favors the
integration of the parameters specified by the metronomes to
enhance spatial and temporal coordination. Participants were only
at an intermediate level in juggling skills, and it was difficult for
them to match their movement to the stimuli, hence only weak
frequency locking was established. This explained why we didn’t
find systematic phase synchronization epochs during a trial, only a
loose frequency concordance between metronome and hand
indicative of weak entrainment, which however was sufficient to
pass on the information about the periodic parameters to affect the
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Much work has gone toward identifying robust rules for
multisensory combination and integration [3,5,6]. Firstly, when
compared to uni-sensory events, two or more sensory cues from
distinct modalities with spatial or temporal congruency can elicit a
better spatial detection, orientation behavior, or shorter reaction
time. Secondly, departure of multimodal environments from
spatial contiguity and/or synchrony fails to improve such
elementary behaviors when compared to unimodal performances,
but can facilitate the execution of other type of tasks, for instance
the identification of a temporal gap between events [15]. These
two cross- modal phenomena can be tentatively classified
respectively as integration, to express a degree of fusion between
functional units (e.g., percepts, actions), and as segregation, to
indicate a degree of separation between units [84,85]. One may
assume that, depending on the coordination pattern required by
the task, integration or segregation may be sought using
multimodal stimuli. The multimodal and multifrequency metro-
nomes specified also a timing relation between the two main
components of the coordination problem of juggling, because it
associated tactile events matching the tempo of the hands and
sound events matching the tempo of the balls. Therefore, the
present study may be seen as an attempt to use cross-modal stimuli
to segregate two frequencies putatively relevant for two compo-
nents of the coordination, but ultimately to enhance the overall
juggling coordination. The latter was presumably determined also
by the phasing between the two stimuli in a multimodal pair,
associated to antiphase tactile stimuli, despite the weak entrain-
ment of movement to the stimuli.
One specific combination of auditory and tactile metronome
decreased of the spatiotemporal variability of the juggler’s
performance: a sound associated to left and right tactile cues
presented antiphase to each other, the latter which corresponded
to the temporal pattern of hands movement in the juggling task.
Differently we found that tactile cues presented alone increased the
behavioral variability. Because audio-tactile events efficiently
complemented vision in the regulation of movements in a
challenging task and under severe physical constraints, we argue
that this class of bimodal combination could, if properly scaled, be
used in a wide class of applications to guide and stabilize behavior
in the case of efficient or deficient behavior, to accelerate skill
acquisition or rehabilitation, and to improve prosthesis. Whether
such applications are sought within a limb or between limbs, the
coordination has to be carefully analyzed to identify which
information, spatial and temporal, should be specified to benefit
from a multimodal synergy. Clearly such direction of research
could widen the set of laws already established for multisensory
integration, namely the laws of inverse effectiveness and
coincidence in time and space.
Supporting Information
Appendix S1 Within participant statistical test for phase
Author Contributions
Conceived and designed the experiments: GZ JL DM. Performed the
experiments: GZ. Analyzed the data: GZ JL DM. Contributed reagents/
materials/analysis tools: GZ JL DM. Wrote the paper: GZ JL DM.
1. Bushara KO, Hanakawa T, Immisch I, Toma K, Kansa ku K, et al. (2003)
Neural correlates of cross-modal binding. Nat Neurosci 6(2): 190–195.
2. Calvert GA, Thesen T (2004) Multisensory integration: methodological
approaches and emerging principles in the human brain. J Physiol Paris 98:
3. Driver J, Spence C (2000) Multisensory perception: beyond modularity and
convergence. Curr Biol 10(20): 731–735.
4. Foxe JJ, Molholm S (2009) Ten years at the multisensory forum: Musings on the
evolution of a field. Brain topogr 21(3): 149–154.
5. Meredith MA (2002) On the neuronal basis for multisensory convergence: a
brief overview. Brain Res Cogn Brain Res 14(1): 31–40.
6. Meredith MA, Stein BE (1983) Interactions among converging sensory inputs in
the superior colliculus. Science 221: 389–391.
7. Sperdin HF, Cappe C, Murray MM (2010) The behavioral relevance of
multisensory neural response interactions. Front Neurosci 4: 9.
8. Wallace MT, Meredith MA, Stein BE (1998) Multisensory integration in the
superior colliculus of the alert cat. J Neurophysiol 80(2): 1006–1010.
9. Bernstein IH, Rose R, Ashe VM (1970) Energy integration in intersensory
facilitation. J Exp Psychol 86(2): 196–203.
10. Dunlap K (1910) Reaction to rhythmic stimuli wit h attempt to synchronize.
Psychological Rev 17(6): 399–416.
11. Hershenson M (1962) Reaction time as a measure of intersensory facilitation.
J Exp Psychol 63(3): 289–293.
12. Nickerson RS, Pew RW (1973) Visual pattern matching: an investigation of
some effects of decision task, auditory codability, and spatial correspondence.
J Exp Psychol 98(1): 36–43.
13. Raab DH (1962) Magn itude Estimation of the Brightness of Brief Foveal Stimuli.
Science 135: 42–44.
14. Todd JW (1912) Reaction to multi ple stimuli The Science Press.
15. Vroomen J, Keetels M (2010) Perception of intersensory synchrony: a tutorial
review. Atten Percept Psychophys 72(4): 871–84.
16. Sinnett S, Kingstone A (2010) A preliminary investigation regarding the effect of
tennis grunting: does white noise during a tennis shot have a negative impact on
shot perception? PLoS ONE 5(10): e13148.
17. Jeka JJ, Schoner G, Dijkstra T, Ribeiro P, Lackner JR (1997) Coupling of
fingertip somatosensory information to head and body sway. Exp Brain Res
113(3): 475–483.
18. Kelso JA, Fink PW, DeLaplain CR, Carson RG (2001) Haptic information
stabilizes and destabilizes coordination dynamics. Proc Biol Sci 268(1472):
19. Lagarde J, Kelso JA (2006) Binding of movement, sound and touch: multimodal
coordination dynamics. Exp Brain Res 173(4): 673–88.
20. Bernstein NA (1967) The co-ordination and regulation of movements.
21. Von Holst E (1939/1973) Relative coordin ation as a phenomenon and as a
method of analysis of central nervous function. In: Martin R, ed. The collected
papers of Erich von Holst, University of Miami Press: Coral Gables, FL.
22. Kelso JAS (1995) Dynamic patterns: The self-organization of brain and behavior
The MIT Press.
23. Turvey MT (1990) Coordination. Am Psychol 45(8): 938–953.
24. Howard IS, Ingram JN, Ko¨rding KP, Wolpert DM (2009) The statistics of
natural movements are reflected in motor errors. J Neurophysiol 102:
25. Savelsbergh GJP, Davids K, Van der Kamp J, Bennett SJ (2003) Development
of Movement Co-ordination in Children: Applications in the fields of
Ergonomics. Health Sciences and Sport. LondonRoutledge: Taylor & Francis.
26. Swinnen SP, Duysens J (2004) Neuro-behavioral determinants of interlimb
coordination: a multidisciplinary approach Kluwer Academic Publishers.
27. Lagarde J, Kelso JA, Peham C, Licka T (2005) Coordination dynamics of the
horse-rider system. J Mot Behav 37(6): 418–24.
28. Todorov E, Jordan MI (2002) Optimal feedback control as a theory of motor
coordination. Nat Neurosci 5(11): 1226–35.
29. Tognoli E, Lagarde J, DeGuzman GC, Kelso JA (2007) The phi complex as a
neuromarker of human social coordination. Proc Natl Acad Sci U S A 104(19):
30. Sporns O, Edelman GM (1993) Solving Bernstein’s problem: a proposal for the
development of coordinated movement by selection. Child Dev 64(4): 960–81.
31. Warren WH (2006) The dynamics of perception and action. Psychological Rev
113(2): 358.
32. Sperdin HF, Cappe C, Murray MM (2010) Auditory-somatosensory multisen-
sory interactions in humans: dissociating detection and spatial discrimination.
Neuropsychologia 48(13): 3696–705.
33. Williams SR, Shenasa J, Chapman CE (1998) Time course and magnitude of
movement-related gating of tactile detection in humans. Importance of stimulus
location. J Neurophysiol 79(2): 947–63.
34. Chapman CE, Tremblay F, Jiang W, Belingard L, Meftah el M (2002) Central
neural mechanisms contributing to the perception of tactile roughness. Behav
Brain Res 135(1–2): 225–33.
35. Voss M, Ingram JN, Haggard P, Wolpert DM (2006) Sensorimotor attenuation
by central motor command signals in the absence of movement. Nat Neurosci
9(1): 26–7.
Sound-Touch Facilitation of Movement Coordination
PLoS ONE | 10 February 2012 | Volume 7 | Issue 2 | e32308
36. Voss M, Ingram JN, Wolpert DM, Haggard P (2008) Mere expectation to move
causes attenuation of sensory signals. PLoS ONE 3(8): e2866.
37. Juravle G, Deubel H, Tan HZ, Spence C (2010) Changes in tactile sensitivity
over the time-course of a goal-directed movement. Behav Brain Res 208(2):
38. Ho C, Tan HZ, Spence C (2005) Using spatial vibrotactile cues to direct visual
attention in driving scenes. Transport Research Part F 8: 397–412.
39. Juravle G, Spence C (2011) Juggling reveals a decisional component to tactile
suppression. Exp Brain Res 213(1): 87–97.
40. Huys R, B eek PJ (2002) The coupling between po int-of-gaze and ball
movements in three-ball cascade juggling: the effects of expertise, pattern and
tempo. J Sports Sci 20(3): 171–86.
41. Huys R, Daffertshofer A, Beek PJ (2004) Multiple time scales and subsystem
embedding in the learning of juggling. Hum Mov Sci 23(3–4): 315–36.
42. Post AA, Daffertshofer A, Beek PJ (2000) Principal components in three-ball
cascade juggling. Biol Cybern 82(2): 143–52.
43. Beek PJ, Turvey MT (1992) Temporal patterning in cascade juggling. J Exp
Psychol Hum Percept Perform 18(4): 934–47.
44. Amazeen EL, Amazeen PG, Post AA, Beek PJ (1999) Timing the Selection of
Information During Rhythmic Catching. J Mot Behav 31(3): 279–289.
45. Amazeen EL, Amazeen PG, Beek PJ (2001) Eye movements and the selection of
optical information for catching. Ecol Psychol 13(2): 71–85.
46. Draganski B, Gaser C, Busch V, Schuierer G, Bogdahn U, et al. (2004)
Neuroplasticity: changes in grey matter induced by training. Nature 427(6972):
47. Driemeyer J, Boyke J, Gaser C, Buchel C, May A (2008) Changes in gray matter
induced by learning–revisited. PLoS ONE 3(7): e2669.
48. Huys R, Daffertshofer A, Beek PJ (2004) Multiple time scales and multiform
dynamics in learning to juggle. Motor Control 8(2): 188–212.
49. Austin HA (1976) A computational theory of physical skill. In:
Unpublished Ph.D, ed. thesis, Department of Electrical Engineering and
Computer Science, MIT: Boston, MA.
50. Van Santvoord AAM, Beek PJ (1994) Phasing and the Pickup of Optical
Information in Cascade Juggling. Ecol Psychol 6(4): 239–263.
51. Haibach PS, Daniels GL, Newell KM (2004) Coordination changes in the early
stages of learning to cascade juggle. Hum Mov Sci 23(2): 185–206.
52. Van Santvoord AAM, Beek PJ (1996) Spatiotemporal variability in cascade
juggling. Acta Psychol 91(2): 131–151.
53. Tuller B, Kelso JA (1989) Environmentally-specified patterns of movement
coordination in normal and split-brain subjects. Exp Brain Res 75(2): 306–316.
54. Zanone PG, Kelso JA (1992) Evolution of behavioral attractors with learning:
nonequilibrium phase transitions. J Exp Psychol Hum Percept Perform 18(2):
55. Beek PJ (1989) Timing and phase locking in cascade juggling. Ecol Psychol 1(1):
56. Byblow WD, Carson RG, Goodman D (1994) Expressions of asymmetries and
anchoring in bimanual coordination. Hum Mov Sci 13(1): 3–28.
57. Carson RG (1995) The dynamics of isometric bimanual coordination. Exp Brain
Res 105(3): 465–76.
58. Kelso JAS, DeGuzman GC, Holroyd T (1991) Synergetic dynamics of biological
coordination with special reference to phase attraction and intermittency. In:
Haken H, Koepchen HP, eds. Rhythms in physiological systems. Springer:
Heidelberg. pp 195–213.
59. Fink PW, Foo P, Jirsa VK, Kelso JA (2000) Local and global stabilization of
coordination by sensory information. Exp Brain Res 134(1): 9–20.
60. Kelso JAS, DelColle JD, Scho¨ner G (1990) Action-perception as a pattern
formation process. In: Jeannerod M, ed. Attention and performance. Erlbaum:
Hillsdale, NJ. pp 139–169.
61. Beek PJ, van Santvoord AA (1992) Learning the cascade juggle: a dynamical
systems analysis. J Mot Behav 24(1): 85–94.
62. Ernst MO, Banks MS (2002) Humans integrate visual and haptic information in
a statistically optimal fashion. Nature 415: 429–433.
63. Peper CE, Beek PJ, van Wieringen PC (1995) Coupling strength in tapping a 2:3
polyrhythm. Hum Movt Sci 14(2): 217–245.
64. Assisi CG, Jirsa VK, Kelso JA (2005) Dynamics of multifrequency coordination
using parametric driving: theory and experiment. Biol Cybern 93(1): 6–21.
65. Kay BA, Warren WH (2001) Coupling of posture and gait: mode locking and
parametric excitation. Biol Cybern 85(2): 89–106.
66. Lagarde J, Zelic G, Avizzano CA, Lippi V, Ruffaldi E, et al. (2009) The Light
Weight Juggling training system for juggling, in SKILLS09, International
Conference on Skills: Bilbao, Spain.
67. Dessing JC, Daffertshofer A, Peper CE, Beek PJ (2007) Pattern stability and
error correction during in-phase and antiphase four-ball juggling. J Mot Behav
39(5): 433–46.
68. Mardia KV (1972) Statistics of directional data. Academic Press (London and
New York).
69. Pikovsky A, Rosenblum M, Kurths J (2001) Synchronization: a universal concept
in nonlinear sciences Cambridge University Press.
70. Bendat JS, Piersol AG (2000) Random data: Analysis and measurement
procedures. John Wiley & Sons, Inc., New York, NY.
71. Fuchs A, Jirsa VK, Haken H Kelso JA (1996) Extending the HKB model of
coordinated movement to oscillators with different eigenfrequencies. Biol
Cybern 74(1): 21–30.
72. Fuchs A, Kelso JA (1994) A theoretical note on models of interlimb
coordination. J Exp Psychol Hum Percept Perform 20(5): 1088–97.
73. Kralemann B, Cimponeriu L, Rosenbl um M, Pikovsky A, Mrowka R (2007)
Uncovering interaction of coupled oscillators from data. Phys Rev E Stat Nonlin
Soft Matter Phys 76(5 Pt 2): 055201-1 - 055201-4.
74. Scho¨ner G, Haken H, Kelso JA (1986) A stochastic theory of phase transitions in
human hand movement. Biol Cybern 53(4): 247–57.
75. Tass P, Rosenblum MG, Weule MG, Kurths J, Pikovsky, et al. (1998) Detection
of n:m Phase Locking from Noisy Data: Application to Magnetoencephalogra-
phy. Phys. Rev. Lett 81(15): 3291–3294.
76. Kelso JAS, de Guzman GC, Reveley C, Tognoli E (2009) Virtual partner
interaction (VPI): exploring novel behaviors via coordination dynamics. PLoS
ONE 4(6): 1–11.
77. Feise RJ (2002) Do multip le outcome measures require p-value adjustment?
BMC Med Res Method 2(1): 2–8.
78. Rothman KJ (1990) No adjustments are needed for multiple comparisons.
Epidemiology 1(1): 43–46.
79. Tass PA (2004) Transmission of stimulu s-locked responses in two coupled phase
oscillators. Phys Rev E 69: 051909-1- 051909-24.
80. Lakatos P, Chen CM, O’Connell MN, Mills A, Schroeder CE (2007) Neuronal
oscillations and multisensory interaction in primary auditory cortex. Neuron
53(2): 279–92.
81. Miller J (1982) Divided attention: Evidence for coactivation with redundant
signals. Cog Psychol 14(2): 247–279.
82. Schroeder CE, Foxe JJ (2002) The timing and laminar profile of converging
inputs to multisensory areas of the macaque neocortex. Cognit Brain Res 14:
83. Jirsa VK, Fink P, Foo P, Kelso JAS (2000) Parametric stabilization of biological
coordination: a theoretical model. J Biol Physics 26(2): 85–112.
84. Dhamala M, Assisi CG, Jirsa VK, Steinberg FL, Kelso JA (2007) Multisensory
integration for timing engages different brain networks. Neuroimage 34(2):
85. Jirsa VK, Kelso JAS (2004) Integration and segregation of perceptual and motor
behavior. In: Jirsa VK, Kelso JAS, eds. Coordination dynamics: issues and
trends, vol 1, Springer series in understanding complex systems. Springer, Berlin
Heidelberg NY. pp 243–259.
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Supplementary resource (1)

... Kelso et al.., 1990 ;Schöner, 1991 ;Wimmers et al., 1992 ;Stins & Michaels, 1999 ;Peper et al.., 1995 ;Beek, 1989 ;Assissi et al. 2005 ;Kay & Warren, 2001 ;Huys et al.., 2008 ;Tuller & Kelso, 1984 ;Zanone & Kelso, 1992) et multi-modal (e.g. Lagarde et al.., 2006 ;Zelic et al.. (2012) ; Zelic et al.., in prep.), ont permis de mieux comprendre la motricité et la cognition humaine. ...
... La perte de stabilité d'un patron de coordination indique que les tendances à la désunion, au désordre, l'emporte sur la coopération reposant sur les couplages. En comparant différentes conditions de coordination multimodale on peut ainsi trouver dans quelles conditions la formation des patrons multisensoriels est facilitée ou au contraire difficile Lagarde, Zelic, Mottet, (en révision) ;Zelic, Mottet, Lagarde, 2012). Nous étudions aussi la coordination multimodale au moyen de paradigmes stationnaires (Zelic et al., 2012). ...
... En comparant différentes conditions de coordination multimodale on peut ainsi trouver dans quelles conditions la formation des patrons multisensoriels est facilitée ou au contraire difficile Lagarde, Zelic, Mottet, (en révision) ;Zelic, Mottet, Lagarde, 2012). Nous étudions aussi la coordination multimodale au moyen de paradigmes stationnaires (Zelic et al., 2012). Cependant les études paramétriques permettent de façon unique de rendre observable par des changements qualitatifs, aux échelles spatiales et temporelles qui caractérisent le comportement dirigé vers des buts, l'influence d'une variable indépendante sur l'équilibre entre l'ordre et désordre. ...
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Habilitation dissertation
... The finding that VMS stability is increased when the pacer and synchronization movement patterns match is in line with previous research showing a facilitation of sensorimotor performances for compatible perceptive and motor activities [46,47]. Different accounts have been proposed to explain such an advantage. ...
... These results highlight the importance of the pacer type used in sensorimotor synchronisation tasks and whether its characteristics of continuity and pattern match those of the movement produced. Future research is needed to investigate whether these findings can be extended to other sensory modalities (e.g., auditory, tactile) and whether they persist when modalities are combined in bimodal sensorimotor synchronisation tasks [17,20,46,47,62,63]. Such research would be a first step in optimising the cueing techniques currently used in various clinical protocols for the rehabilitation of patients with motor disorders [64][65][66]. ...
There is growing evidence that movement synchronisation to an external rhythm is affected by the type of pacers involved. Specifically, visuomotor synchronisation (VMS) is facilitated when the pacer is continuous (continuity condition) and moves in the same direction as the movement produced (pattern matching condition). However, the extent to which the continuity and pattern matching conditions each contribute to facilitation of VMS remains unclear. The present study aimed to disentangle the potential dual influence of pacer continuity and pacer pattern on VMS. Twenty participants were asked to synchronise continuous left-right forearm movements of tracking (continuous VMS - Experiment 1) or discrete up-down finger movements of tapping (discontinuous VMS - Experiment 2) with four visual pacers. The pacers consisted of a red dot target that either oscillated (continuous pacers) or flashed (discrete pacers) periodically. The target also exhibited a left-right (left-right pacers) or a centred (centred pacers) movement pattern. Results showed lower variability in synchrony with the continuous visual pacer that respectively matched the left-right and the centred movement pattern of forearm and finger tapping. Both the continuity condition and the pattern matching condition facilitated VMS when synchronising continuous forearm tracking movements (Experiment 1) whereas both conditions were required to facilitate VMS when synchronising discrete finger tapping movements (Experiment 2). These results provide new insights into the mechanisms underlying VMS and how they are modulated by variations in pacer pattern and pacer continuity.
... To date, however, it is largely unknown whether multisensory integration can facilitate the continuous coordination of movements, and whether the same three principles apply. Only a few studies have investigated the advantage of multimodal cues when synchronizing a single joint movement with an external pacing (Lagarde and Kelso 2006;Elliott et al. 2010) or when coordinating limb movements (Ronsse et al. 2009;Lagarde et al. 2012;Zelic et al. 2012). The present experiment addressed for the first time the conditions of the stabilization of coordination patterns by multisensory integration. ...
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Uncertainty, spatial or temporal errors, variability, are classic themes in the study of human and animal behaviors. Several theoretical approaches1 and concepts have been adopted to tackle those issues, often considering the CNS as an observer, using Shannon information and entropy, signal to noise ratio, and recently a Bayesian approach, and free energy minimization. In the coordination dynamics framework, addressing pattern formation processes underlying cognitive functions, and goal directed human movement among others, the tools employed originate from the statistical physics of Brownian motion and stochastic processes. The relations between those theories/ concepts have been drawn for some cases in their original fields, for example between free energy minimization and diffusion model in a force field (Jordan et al., 1998). Here an introductory presentation of the approach of noise in coordination dynamics is proposed, aimed at the experimentalist.
... These findings are in line with studies by Jansen and Heil (2010) who found a relation between MR performance and motor tasks involving coordinative aspects of 5 and 6 year old children and Pietsch and Jansen (2012), who report a correlation between MR and motor-coordinative abilities in young adults. As juggling might also be considered an intervention with high motor-coordinative requirements (Zelic et al., 2012), results from the study by Jansen et al. (2011a) could be viewed from this point of view as well. Since these authors, did not find notable improvements in MR performance, one might consider that the study population were gymnasts. ...
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Background: Regular physical exercise plays an integral part in the psychomotor and psychosocial development of children and adolescents, with complex motor and cognitive processes closely linked. Spatial abilities, one aspect of cognitive functioning start to evolve from earliest childhood and reach adult-like levels by early adolescence. As they have been associated with good spatial orientation, wayfinding, map-reading skills, problem solving or analyzing spatial information, these skills facilitate independence and autonomy while growing up. Despite promising results, only few studies investigate this relation between physical exercise and spatial abilities. To use this benefit and develop purposive physical exercise interventions, it is essential to summarize the current evidence. Objectives: This literature review aims to systematically summarize findings regarding the impact of physical exercise interventions on spatial abilities in healthy children and adolescents and identify knowledge gaps. Methods: A systematic search of the literature according to the PRISMA guidelines was conducted on the databases Pubmed, Web of Science, Cochrane Library, SportDiscus, and PsycInfo from their inception date till March 2021. Additionally, Google Scholar and refence lists of relevant publications were searched. A descriptive analysis of results was conducted. Results: The literature search identified a total of N = 1,215 records, 11 of which met the inclusion criteria and were analyzed in this review. A total of 621 participants aged 4 to 15 years participated in the studies. Exercise interventions included sport-specific activities, motor-coordinative exercises, high-intensity functional training or spatial orientation/navigation training. Five studies evaluated training effects on mental rotation performance (i.e., Mental Rotation Test), four studies investigated visuo-spatial working memory function/spatial memory (i.e., Corsi Block Test, Virtual Reality Morris Water Maze) and two studies tested spatial orientation capacity (i.e., Orientation-Running Test). Overall, results show a potential for improvement of spatial abilities through physical exercise interventions. However, keeping the diversity of study designs, populations and outcomes in mind, findings need to be interpreted with care. Conclusions: Despite growing interest on the effects of physical exercise interventions on spatial abilities and promising findings of available studies, evidence to date remains limited. Future research is needed to establish how spatial ability development of healthy children and adolescents can be positively supported.
... Hashizume & Matsuo, 2004). Moreover, Zelic et al. (2012) showed that the number of consecutive catches in intermediate jugglers, defined as people "who can juggle for more than 20 s and less than 60 s in a circle with a diameter of 2 m," varied between 50 and 150. The learning session consisted of one set for 15 min and up to four sets a day. ...
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The learning process of ball juggling is characterized by considerable individual differences in acquired coordination patterns. Previous research has shown that the coordination patterns observed in novice jugglers can be roughly divided into two classes: the high ratio pattern, in which the ball is held for a relatively long time, and the low ratio pattern, in which the ball is held for a relatively short time. To account for these differences in coordination patterns, we examined the anchoring strategies employed by novice jugglers for controlling the juggling movements. Analyses of the correlation between coordination patterns and selected spatiotemporal variabilities revealed that the coordination patterns with a high dwell ratio had lower temporal variability than patterns with a low dwell ratio, which in turn had lower variability of spatial variables than patterns with a high dwell ratio. These findings indicate that individual differences in the coordination patterns adopted by novice jugglers, and hence their learning paths, result from differences in the control strategies employed.
... Multisensory encoding is thought to minimize variance in the perceptual estimate of a stimulus, and accordingly can improve performance in a variety of tasks (Elliott, Wing, & Welchman, 2010;Ernst & Bülthoff, 2004). Auditory-tactile multisensory stimulation (compared with unimodal stimulation) can improve movement timing in gait (Roy et al., 2017), spatiotemporal variability in arm movements (Zelic, Mottet, & Lagarde, 2012), and quality judgments of music (Merchel & Altinsoy, 2014). Auditory and tactile rhythmic information are integrated into a coherent multisensory percept (Huang et al., 2012) and are coded in a common brain network (Araneda et al., 2017). ...
Music is both heard and felt-tactile sensation is especially pronounced for bass frequencies. Although bass frequencies have been associated with enhanced bodily movement, time perception, and groove (the musical quality that compels movement), the underlying mechanism remains unclear. In 2 experiments, we presented high-groove music to auditory and tactile senses and examined whether tactile sensation affected body movement and ratings of enjoyment and groove. In Experiment 1, participants (N = 22) sat in a parked car and listened to music clips over sound-isolating earphones (auditory-only condition), and over earphones plus a subwoofer that stimulated the body (auditory-tactile condition). Experiment 2 (N = 18) also presented music in auditory-only and auditory-tactile conditions, but used a vibrotactile backpack to stimulate the body and included 2 loudness levels. Participants tapped their finger with each clip, rated each clip, and, in Experiment 1, we additionally video recorded spontaneous body movement. Results showed that the auditory-tactile condition yielded more forceful tapping, more spontaneous body movement, and higher ratings of groove and enjoyment. Loudness had a small, but significant, effect on ratings. In sum, findings suggest that bass felt in the body produces a multimodal auditory-tactile percept that promotes movement through the close connection between tactile and motor systems. We discuss links to embodied aesthetics and applications of tactile stimulation to boost rhythmic movement and reduce hearing damage. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
... For instance, a decrease in reaction time has been shown when the spatial location of the stimulus matches with the spatial location of the motor response; a benefit likely due to a simplification of the processes binding the sensory processing of the perception of the external event and the motor implementation (Hommel 1996;Hommel and Prinz 1997;Iacoboni et al. 1998;Prinz 1997;Umiltá and Nicoletti 1990). Compatible perceptual-motor interactions have also been shown to facilitate the stabilisation (decreased variability) of bimanual coordination by an external pacer and enhance multisensory integration in such coordinated behaviours (Zelic et al. 2012(Zelic et al. , 2016a. ...
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People commonly move along with auditory rhythms in the environment. Although the processes underlying such sensorimotor synchronisation have been extensively investigated in the previous research, the properties of auditory rhythms that facilitate the synchronisation remain largely unclear. This study explored the possible benefits of a continuity matching between auditory pacers and the movement produced as well as of a spatial pattern matching that has been previously demonstrated with visual pacers. Participants synchronised either finger tapping or forearm oscillations with either discrete or continuous pacers. The pacers had either a spatial pattern (left–right panning) that matched the movement pattern produced or no spatial pattern. The accuracy and variability of synchronisation were assessed by the mean and standard deviation of the asynchronies, respectively, between participant’s movement and the pacers. Results indicated that synchronisation was more accurate and less variable for discrete pacers and continuous movement (i.e., forearm oscillations). The interaction between those two factors involved a more complex relationship than a simple continuity match benefit. Although synchronisation variability increased with continuous pacers for both types of movement, this increase was smaller for continuous movement than discrete movement, suggesting that continuous movement is more beneficial only for continuous pacers. Moreover, the results revealed limited benefits of spatial pattern matching on auditory-motor synchronisation variability, which might be due to lower spatial resolution of the auditory sensory modality. Together, these findings confirm that sensorimotor synchronisation is modulated by complex relations between pacer and movement properties.
... Movement with external stimuli is called sensorimotor synchronization (Repp, 2005;Miura et al., 2011;Repp and Su, 2013). Also, in ball juggling tasks, experts juggle in synchrony with other jugglers or music; thus, sensorimotor synchronization is an important process to increase expertise ( Zelic et al., 2012). During juggling with others or music, the timing of throw or catch should be adjusted to the timing of the external stimuli such as a music, and the juggler should change the movement timing or amplitude. ...
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In this study, we examined the degree of adaptability to new constraints after learning of a fundamental skill in juggling. Adaptation of sensorimotor synchronization with the various constraints is important for expertise. However, this adaptability may not be equivalent between coordination patterns which learners acquired in the previous learning process. In other words, there may be “asymmetric” adaptability among intrinsic patterns. Then, we examined the influence of intrinsic patterns on the adaptation of sensorimotor synchronization according to various temporal constraints. To set the adaptation task, experiment 1 was designed to examine the relationship between tempo and coordination pattern for expert jugglers. Based on experiment 1, juggling in accordance with the tempo change was performed as adaption task in experiment 2, and we compared the performances of the jugglers from the viewpoint of the intrinsic pattern. In experiment 1, participants performed juggling by adjusting catch timing to beep timing in ten conditions with the interval from 260 to 620 ms in steps of 40 ms. Results of experiment 1 presented that when the juggling tempo is fast, the coordination pattern with “rhythmic” frequency characteristics appeared. By contrast, when the tempo is slow, the coordination pattern with “discrete” frequency characteristics appeared. That is, jugglers should switch their coordination patterns when performing under various tempo conditions. In experiment 2, we compared the adaptability to perform juggling under temporal constraints among intermediate jugglers who have different intrinsic coordination patterns acquired through a previous learning process. The adaptation task required participants to adjust their catch timing to a gradually changing tempo. Participants performed juggling under two conditions: gradually ascending and descending tempo ranging from 300 to 600 ms. The results of experiment. 2 showed that participants who had a discrete pattern showed a significantly better adaptation than participants who had a rhythmic pattern. Furthermore, this result of adaptation was not related to juggling experience. This suggests that an intrinsic pattern characterized by different frequency characteristics has the different adaptability to sensorimotor synchronization tasks. Collectively, the degree of adaptability was dependent on the pattern acquired in the early stages of learning.
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Les mouvements, même pour le jonglage le plus élémentaire, évoquent une structure qui se répète de façon cyclique, de balle en balle. Cette structure apparente est la marque d’une co-ordination , propre à l’être vivant, animal ou humain. Elle repose sur une mise en jeu spatiale et temporelle, mesurée en millisecondes, de multiples composants : les doigts, les mains, leurs muscles (au nombre de 29), les avant-bras et bras, le regard, le centre des masses, la tête, les appuis au sol. Les relations entre ces composants et la structure globale qui caractérise la performance du jonglage, sa forme ou gestalt, ont été étudiées dans les champs des mathématiques, des sciences du mouvement humain et des neurosciences du “contrôle” des mouvements.
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Information coming from multiple senses, as compared to a single one, typically enhances our performance. The multisensory improvement has been extensively examined in perception studies, as well as in tasks involving a motor response like a simple reaction time. However, how this effect extends to more complex behavior, typically involving the coordination of movements, such as bimanual coordination or walking, is still unclear. A critical element in achieving motor coordination in complex behavior is its stability. Reaching a stable state in the coordination pattern allows to sustain complex behavior over time (e.g., without interruption or negative consequences, like falling). This study focuses on the relation between stability in the coordination of movement patterns, like walking, and multisensory improvement. Participants walk with unimodal and audio-tactile metronomes presented either at their preferred rate or at a slower walking rate, the instruction being to synchronize their steps to the metronomes. Walking at a slower rate makes gait more variable than walking at the preferred rate. Interestingly however, the multimodal stimuli enhance the stability of motor coordination but only in the slower condition. Thus, the reduced stability of the coordination pattern (at a slower gait rate) prompts the sensorimotor system to capitalize on multimodal stimulation. These findings provide evidence of a new link between multisensory improvement and behavioral stability, in the context of ecological sensorimotor task.
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Does the structure of an adult human brain alter in response to environmental demands? Here we use whole-brain magnetic-resonance imaging to visualize learning-induced plasticity in the brains of volunteers who have learned to juggle. We find that these individuals show a transient and selective structural change in brain areas that are associated with the processing and storage of complex visual motion. This discovery of a stimulus-dependent alteration in the brain's macroscopic structure contradicts the traditionally held view that cortical plasticity is associated with functional rather than anatomical changes.
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This paper presents the training of juggling skills, a highly complex problem of coordination, under tight time and space constraints. This training is achieved with a simple training platform, a light weight juggling platform (LWJ), and is compared to training with real balls. The principle directing the design of the platform is to obtain a simple tool. The simplification, in comparison to real world juggling, is based on the identification of invariant properties in the spatiotemporal coordination of intermediate and expert jugglers. Two classes training solutions were added to the LWJ: An audio-tactile pacing or augmented multimodal environment, and the manipulation of cognitive components of the juggling skills. The transfer to juggling with real balls was evaluated in four different experiments.
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Three expert jugglers and three intermediate jugglers performed a three-ball cascade pattern under spatially and temporally constrained conditions. In the spatially constrained conditions the balls were thrown to a specific height, whereas in the temporally constrained conditions the balls were thrown to the beeps of a metronome. The experiment was conducted to examine the hypothesis that juggling represents a spatial clock in that jugglers attempt to set up an invariant time base for the hand movements by throwing the balls consistently to a fixed height. Specifically, two expectations following from this hypothesis were examined: (1) that the spatiotemporal variability of the produced patterns would be less when juggling to an externally specified height than to an externally specified beat, because throwing to a height would be more in line with what jugglers actually do, and (2) that in both conditions the space-time trajectories of the balls would be less variable than the space-time trajectories of the hands. Examination of the observed patterns in terms of a set of theoretically motivated variables confirmed the second expectation. At the level of the individual variables the first expectation was not confirmed by the data: the spatiotemporal variability of the patterns was very similar under the two conditions. However, at the level of ensemble variables, the variability of the ball loop time (defined as the time that the ball was carried by the hand plus the subsequent flight time) was smaller when juggling to a height than when juggling to a beat, while the variability of the hand loop time (defined as the time that the hand carried a ball plus the time that it moved empty) was the same. These results were largely independent of skill level; only a few differences between expert and intermediate jugglers were found. The implications of the findings with regard to the development of a theory of perceptual-motor control in which spatial and temporal variables are linked in a task-specific manner are discussed.
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A natural-physical approach is pursued in uncovering basic timing and phase relations in human rhythmic movement. The approach is based on the theory of nonlinear oscillatory motion, entrained by continuously and discretely distrib- uted forcing. In the context of juggling three balls in a figure-eight pattern, a preliminary modeling attempt of the cyclical hand motion suggested that the dynamics underwriting juggling are captured best by a discretely kicked, highly nonlinear, self-sustained oscillator. Discretely kicked, nonlinear oscillators may be characterized by regime diagrams that depict the periodic (phase-locked) and quasiperiodic (not phase-locked) regimes in which the system can operate depending on the magnitude of the kicks. This article provides evidence for 2-quasiperiodicity and near, but not perfect, phase locking between tl/tf and tu/tf (where tl is the mean time that the hands move loaded with a ball, tu is the mean time that the hands move empty, and tf is the mean flight time of the b...
First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is outlined. The remainder of the book presents the main effects of synchronization in a rigorous and systematic manner, describing classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering and natural sciences.
S ummary Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet the needs of scientific workers dealing with directional data. The paper first introduces the two basic models for the multi‐dimensional case known as the von Mises–Fisher distribution and the Bingham distribution. Their sampling distribution theory depends heavily on the isotropic case and some developments are discussed. An optimum property of an important test for the von Mises–Fisher case is established. A non‐parametric test is proposed for the hypothesis of independence for observations on a torus. In addition to some numerical examples on the preceding topics, five case studies are given which illuminate the power of this new methodology. The case studies are concerned with cancer research, origins of comets, arrival times of patients, navigational problems and biological rhythms. Some unsolved problems are also indicated.
Neuro-Behavioral Determinants of Interlimb Coordination: A multidisciplinary approach focuses on bimanual coordination against the broader context of the coordination between the upper and lower limbs. However, it is also broad in scope in that it reviews recent developments in the study of coordination by means of the latest technologies for the study of brain function, such as functional magnetic resonance imaging, near-infrared spectroscopy, magneto-encephalography, and transcranial magnetic stimulation. In addition, new developments in recovery of interlimb coordination following spinal cord injury and other insults of the central nervous system, such as stroke, are reviewed.
Under conditions in which absolute phase and frequency synchronization are neither essential nor attainable for biological functioning, some form of relative coordination is still possible. Attraction toward certain phase and frequency relations remains, but phase slippage as well as occasional skips and jumps occur as the component units adjust spatially and temporally. We establish the connection between this less rigid form of coordination and intermittency, a generic feature of dynamical systems near tangent bifurcations. Intermittency provides a mechanism for entering and exiting mode-locked states, endowing the system with a vital mix of flexibility and coherence. In the intermittent régime close to critical points, the system possesses a ‘predictive’ or ‘anticipatory’ property. The identified dynamics are level-independent and may be essential to a number of different biological functions.