Journal of Experimental Psychology: Human Perception and Performance 2014, Vol. 40, No. 5, 1849-1860

© 2014 American Psychological Association 0096-1523/14/$ 12.00 http://dx.doi.org/! 0.1037/a0037417

Influence of Stimulus Velocity Profile on Rhythmic Visuomotor Coordination Manuel Varlet

Charles A. Coey

University of Western Sydney, University of Cincinnati, and Montpellier-1 University

University of Cincinnati

R. C. Schmidt

Ludovic Marin

College of the Holy Cross

Montpellier-1 University

Benoit G. Bardy

Michael J. Richardson

Montpellier-1 University and Institut Universitaire de France

University of Cincinnati

Every day, we visually coordinate our movements with environmental rhythms. Despite its ubiquity, it largely remains unclear why certain visual rhythms or stimuli facilitate such visuomotor coordination. The goal of the current study was to investigate whether the velocity profile of a rhythmic stimulus modulated the emergence and stability of this coordination. We examined both intended (Experiment 1) and unintended or spontaneous coordination (Experiment 2) between the rhythmic limb movements of participants and stimuli exhibiting different velocity profiles. Specifically, the stimuli oscillated with either a sinusoidal (harmonic), nonlinear Rayleigh, or nonlinear Van der Pol velocity profile, all of which are typical of human or biological rhythmic movement. The results demonstrated that the dynamics of both intended and unintended visuomotor coordination were modulated by the stimulus velocity profile, and that the Rayleigh velocity profile facilitated the coordination, suggesting a crucial role of the slowness to the endpoints or turning points of the stimulus trajectory for stable coordination. More generally, these findings open promising research directions to better understand and improve coordi­ nation with artificial agents and people with social deficits. Keywords: visuomotor coordination, motor entrainment, external visual rhythms, velocity profile, kine­ matics

We often visually coordinate our movements with rhythms in our environment, particularly those produced by our coactors. This coordination can happen intentionally, as when we work or dance

with someone else, but also occurs unintentionally, as when we talk, walk, or applaud with one another (Neda, Ravasz, Brechet, Vicsek, & Barabasi, 2000; Ramenzoni, Davis, Riley, Shockley, & Baker, 2011; Schmidt, O’Brien, & Sysko, 1999; Shockley, San­ tana, & Fowler, 2003; van Ulzen, Lamoth, Daffertshofer, Semin, & Beek, 2008). Understanding the processes underlying such intended and unintended visuomotor coordination has received an increasing amount of attention over the last decade (Roerdink, Bank, Peper, & Beek, 2013; Roerdink, Ophoff, Peper, & Beek, 2008; Schmidt, Fitzpatrick, Caron, & Mergeche, 2011; Schmidt & Richardson, 2008), and a number of different factors have been found to influence the occurrence and stability of such coordina­ tion. For instance, changes in the frequency, amplitude, or conti­ nuity of the movements involved are all known to influence the form and stability of visuomotor coordination (Amazeen, Schmidt, & Turvey, 1995; Hove, Spivey, & Krumhansl, 2010; LoprestiGoodman, Richardson, Silva, & Schmidt, 2008; Peper & Beek, 1998; Varlet, Coey, Schmidt, & Richardson, 2012a; Varlet, Marin, Issartel, Schmidt, & Bardy, 2012b; Wimmers, Beek, & van Wieringen, 1992). There is also some evidence to suggest that the social nature of an environmental rhythm (i.e., agency) also influ­ ences the occurrence of visuomotor coordination (Kilner, Hamil­ ton, & Blakemore, 2007; Kilner, Paulignan, & Blakemore, 2003;

This article was published Online First July 14, 2014. Manuel Varlet, The MARCS Institute, University of Western Sydney, Perceptual-Motor Dynamics Laboratory, CAP Center for Cognition, Ac­ tion, and Perception, Department of Psychology, University of Cincinnati, and Movement to Health Laboratory, EuroMov, Montpellier-1 University; Charles A. Coey, Perceptual-Motor Dynamics Laboratory, CAP Center for Cognition, Action, and Perception, Department of Psychology, University of Cincinnati; R. C. Schmidt, Department of Psychology, College of the Holy Cross; Ludovic Marin, Movement to Health Laboratory, EuroMov, Montpellier-1 University; Benoit G. Bardy, Movement to Health Labora­ tory, EuroMov, Montpellier-1 University, and Institut Universitaire de France; Michael J. Richardson, Perceptual-Motor Dynamics Laboratory, CAP Center for Cognition, Action, and Perception, Department of Psy­ chology, University of Cincinnati. This research was supported by the National Science Foundation (BCS Awards: 0750190, 0750187, 0926662). Correspondence concerning this article should be addressed to Manuel Varlet, University of Western Sydney, Marcs Institute, Bullecourt Avenue, Milperra NSW 2214, Australia. E-mail: [email protected] 1849

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Stanley, Gowen, & Miall, 2007). It remains unclear, however, why such agency manipulations influence the strength of visuomotor coordination. More generally, it remains unclear why certain forms or types of external visual rhythms result in more robust coordi­ nation. As we detail below, the velocity profiles of external envi­ ronmental stimuli (i.e., visual rhythms) may provide a coherent explanation for these differences.

Rhythmic Visuomotor Coordination Previous research has shown that the coordination between the movements of an actor and a visual environmental rhythm can be understood as constrained by the dynamical entrainment processes of coupled oscillators (Byblow, Chua, & Goodman, 1995; Coey, Varlet, Schmidt, & Richardson, 2011b; Peper & Beek, 1998; Richardson, Marsh, Isenhower, Goodman, & Schmidt, 2007; Schmidt & O’Brien, 1997; Schmidt, Carello, & Turvey, 1990; Tognoli, Lagarde, DeGuzman, & Kelso, 2007; Wimmers et al., 1992). In line with the predictions of the Haken-Kelso-Bunz model of bimanual coordination (Haken, Kelso, & Bunz, 1985; Kelso, 1984, 1995; Schoner, Haken, & Kelso, 1986), it has been demon­ strated that intended and unintended visuomotor coordination are preferentially attracted toward in-phase and antiphase patterns. These two patterns of coordination have been observed across a wide variety of laboratory and ecological situations (Schmidt & Richardson, 2008). They correspond to movements that oscillate at the same time in the same direction or in opposite directions, and correspond to relative phase values of 0° or 180°, respectively (Richardson et al., 2007; Schmidt et al., 1990; Wimmers et al., 1992). Of particular note is that in-phase (0°) coordination is more stable than antiphase (180°) coordination, as indicated by lower levels of relative phase variability for in-phase compared to anti­ phase coordination.

Visuomotor Coordination and Stimulus Kinematics Numerous studies have demonstrated that the emergence and stability of such rhythmic visuomotor coordination depends on the movement kinematics of the stimulus. The period or frequency of visual rhythms plays a crucial role in the coordination dynamics (Schmidt & Richardson, 2008). In agreement with Haken-KelsoBunz model predictions (Fuchs, Jirsa, Haken, & Kelso, 1996; Haken et al., 1985), the most stable coordination occurs when the stimulus period is equal to the preferred movement period of the actor, and that faster and slower stimulus periods result in a decrease in coordination stability (Amazeen et al., 1995; LoprestiGoodman et al., 2008; Richardson et al., 2007; Richardson, Marsh, & Schmidt, 2005; Schmidt, Bienvenu, Fitzpatrick, & Amazeen, 1998). In addition, the antiphase pattern can only be maintained for slow to moderate stimulus frequencies. The stability of the anti­ phase pattern decreases with faster stimulus periods, which often results in a spontaneous breakdown or transition to the in-phase pattern of coordination (Peper & Beek, 1998; Schmidt et al., 1990; Wimmers et al., 1992). Bingham and his colleagues proposed that this effect reflects the increasing difficulty for participants to detect the movement information that serves stable coordination at faster stimulus periods (Bingham, Schmidt, & Zaal, 1999; Bing­ ham, Zaal, Shull, & Collins, 2001; Bingham, 2004a; Wilson, Collins, & Bingham, 2005a; Zaal, Bingham, & Schmidt, 2000).

With more mixed results, previous research has also demon­ strated an influence of the movement amplitude of visual rhythms (de Rugy, Oullier, & Temprado, 2008; Peper & Beek, 1998; Varlet et al., 2012a). In line with results observed in bimanual coordina­ tion (Peper, de Boer, de Poel, & Beek, 2008), larger stimulus amplitudes strengthen the coupling underlying unintended visuo­ motor coordination resulting in stronger spontaneous in-phase and antiphase entrainment (Varlet et al., 2012a). This effect of stimulus amplitude, however, has not been found when the visuomotor coordination was intentional (de Rugy et al., 2008; Peper & Beek, 1998).

Stimulus Velocity Profile In contrast to the extensive knowledge that we have about the influence of the period or frequency of visual rhythms, only little is known about whether the stimulus velocity profile modulates visuomotor coordination. The different studies cited above inves­ tigated visuomotor coordination with computer-generated stimuli that oscillated with a perfectly sinusoidal trajectory or in interper­ sonal coordination tasks in which the velocity profile of partici­ pants’ movement was not manipulated or controlled. Despite the lack of research directly examining this factor, a variety of results in the literature do support the hypothesis that the stimulus velocity profile can modulate the emergence and stability of visuomotor coordination. Of particular relevance is the previous research that has shown that certain locations in the trajectory of a visual rhythm appear to be especially important for stable coordination. Hajnal, Richard­ son, Harrison, and Schmidt (2009) manipulated the occlusion of different locations of the trajectory of an oscillating (sinusoidal) stimulus when participants performed intended in-phase and anti­ phase coordination. They found that the least stable coordination occurred when occluding the endpoints or turn-around points of the trajectory, indicating that they are the privileged parts of the trajectory providing access to movement information that supports stable coordination. Similarly, Roerdink and collaborators demon­ strated that participants in intended visuomotor coordination pref­ erentially pick up information about stimulus displacements by gazing at the endpoints of the trajectory, an effect that increases with faster stimulus periods (Roerdink, Peper, & Beek, 2005). Such fixations on the endpoints of the stimulus trajectory result in participants’ movements being locally more anchored in time and space, and such anchoring facilitates stable coordination (Beek, 1989; Fink, Foo, Jirsa, & Kelso, 2000; Roerdink et al., 2008). The importance of the endpoints of visual (sinusoidal) rhythms could be explained by the slowness of this part of the trajectory, which might facilitate the detection of critical movement information (Bingham et al., 2001; Hajnal et al., 2009; Wilson et al., 2005a; Zaal et al., 2000). Another particularly interesting finding is that the velocity pro­ file of visual rhythms modulates the occurrence of movement interference during action observation tasks (Chaminade, Franklin, Oztop, & Cheng, 2005; Kilner et al., 2007, 2003; Kupferberg et al., 2011). Working from the common-coding approach to perception and action (Hommel, Miisseler, Aschersleben, & Prinz, 2001; Prinz, 1997; Sebanz, Rnoblich, & Prinz, 2003), researchers have examined how the rhythmic horizontal and vertical arm move­ ments of participants are influenced by the observation of visual

STIMULUS KINEMATIC AND VISUOMOTOR COORDINATION

rhythmic movements in compatible and incompatible directions. These studies have suggested that observed movements “inter­ fered” with the movement of participants when the participants observed a visual rhythm oscillating in incompatible direction, as indicated by larger spatial variability in the uninstructed movement plane (Kilner et al., 2007, 2003; Stanley et al., 2007). This effect, however, only occurred when the stimulus velocity profile was similar to that of a human. The observation of a computer­ generated stimulus with a harmonic (sinusoidal), or close to har­ monic, velocity profile characteristic of human movement kine­ matics produced a similar form of movement interference, whereas stimuli with a nonhuman, constant velocity profile had no effect (Chaminade et al., 2005; Kilner et al., 2007, 2003; Kupferberg et al., 2011). Interestingly, recent studies working from a dynamical system perspective have demonstrated that this additional move­ ment in the uninstructed plane actually results from actors becom­ ing unintentionally coordinated with the observed movement (Fine, Gibbons, & Amazeen, 2013; Richardson, Campbell, & Schmidt, 2009; Romero, Coey, Schmidt, & Richardson, 2012). This suggests that the same control processes underlie both the occurrence of rhythmic movement interference and rhythmic movement coordination and, hence, that the dynamics of visuomotor coordination is likely to be modulated by the velocity profile of the observed rhythms. It remains largely unclear, however, how the velocity profile of visual rhythms could modulate the processes underlying the oc­ currence and stability of visuomotor coordination. Why would a human (harmonic) velocity profile facilitate visuomotor coordina­ tion? So far, this effect has been interpreted as a consequence of an increased affinity for the human or biological nature of the visual rhythm (Chaminade et al., 2005; Kilner et al., 2007, 2003). Alter­ natively, questions can be raised about whether this effect could be due to the properties of the stimulus velocity profile that would moderate the strength of the visual coupling. Supporting this possibility is previous research by Jansson and collaborators that has shown that the same effects can occur with both human and nonhuman stimuli when their movement kinematics are controlled to be identical (Jansson, Wilson, Williams, & Mon-Williams, 2007). Specifically, it is possible that the damping or slowness at the endpoints of the trajectory of human (harmonic) oscillations facilitates the detection of movement information serving stable coordination (Bingham et al., 2001; Hajnal et al., 2009; Roerdink et al., 2005). Important to this alternative account is the fact that human rhythmic movements are not always perfectly harmonic but often display nonlinear velocity profiles that might influence visuomotor coordination if it is not only the biological nature of the stimulus velocity profile that matters. When an actor performs an oscillatory movement of his index finger, arm, or leg, for example, subtle to moderate deviations from a perfectly harmonic motion can be observed, which depend on the task and movements constraints. (Beek, Rikkert, & van Wieringen, 1996; Beek, Schmidt, Morris, Sim, & Turvey, 1995; Kay, Kelso, Saltzman, & Schoner, 1987; Mottet & Bootsma, 1999; Roerdink et al., 2008). For example, Mottet and Bootsma (1999) have shown that continuous deviations from ideal (harmonic) motion occur in the kinematics of goal-directed aiming movements in a reciprocal Fitts’ task and that these nonlinearities change as a function of the distance and precision constraints of the task. Such nonlinearities have been demonstrated for several other move­

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ments and tasks, including the simple swinging of handheld pen­ dulums in which the form and magnitude of nonlinear deviations occurring depend on the movement frequency and mechanical properties of the pendulum used (Beek et al., 1995; Varlet et al., 2012b). In accordance with these observations, the kinematics of human rhythmic movement have been captured with the HakenKelso-Bunz model by using “hybrid,” nonlinear limit cycle oscil­ lators (Haken et al., 1985; Kay et al., 1987). Specifically, this model employs the nonlinear terms of Rayleigh and Van der Pol oscillators to account for general properties of human rhythmic movement (Kay et al., 1987). The nonlinear Van der Pol and Rayleigh terms, producing respectively earlier and later velocity peaks in the movement cycle, allow the model to capture most of the kinematic deviations of human rhythmic movement from a purely harmonic motion. Despite the numerous studies that have demonstrated that hu­ man movements are rarely perfectly harmonic and often have nonlinearities, no connection has been made between this literature and research on movement coordination or interference during the observation of visual (human) rhythmic movements. More partic­ ularly, no study has yet investigated whether such nonlinearities in the velocity profiles of visual (human) rhythmic movements mod­ ulate the occurrence and stability of visuomotor coordination. Making this connection is important, however. As discussed be­ fore, an individual’s movements are known to be more influenced by the observation of human than nonhuman movements and this effect has been assumed to originate from an increased affinity for biological movements (i.e., movements produced by other hu­ mans; Chaminade et al., 2005; Kilner et al., 2007, 2003; Stanley et al., 2007). In line with the assumption that only the biological nature of the velocity profile of visual rhythms matters, one would not expect any difference between sinusoidal (harmonic), Rayleigh and Van der Pol velocity profiles on the emergence and stability of visuomotor coordination, because they are all typical of biological rhythmic movements. Indeed, as explained above, sinusoidal (har­ monic), Rayleigh and Van der Pol velocity profiles are all ob­ served in the rhythmic movements produced by humans, with their occurrence depending on the movement and task constraints. In contrast, if it is not only the biological nature of the rhythms that matters, but also the properties of the movement kinematics as suggested for example by Jansson Wilson, Williams, and MonWilliams (2007), these different velocities profiles could be ex­ pected to yield differences in coordination in specific ways. Ray­ leigh oscillations start faster and finish slower than harmonic motion, and Van der Pol oscillations start slower and finish faster (Kay et al., 1987). It is possible that the movement information available in the part of the trajectory going toward the endpoints is more important to the stability of coordination than that available in the part going away from the endpoints. Supporting this as­ sumption are numerous studies showing, in a variety of goal directed tasks, that control is greatest at the endpoint of the trajectory (e.g., Desmurget & Grafton, 2000; Mottet & Bootsma, 1999). We thus hypothesized that Rayleigh oscillations, which “finish” slower than harmonic oscillations, would facilitate coor­ dination, and Van der Pol oscillations, which “finish” faster, would degrade coordination. The following two experiments were aimed at investigating these hypotheses.

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Experiment 1 The goal of Experiment 1 was to investigate the influence of the velocity profile of visual rhythms on intended visuomotor coordi­ nation. We examined the in-phase coordination between forearm movements of participants and computer-generated stimuli oscil­ lating with sinusoidal (sinus), Rayleigh or Van der Pol velocity profiles. The Rayleigh and Van der Pol stimuli were expected to result in more and less stable coordination (respectively) compared with the sinus stimulus because their velocities to the trajectory endpoints are slower and faster (respectively) than the sinus stim­ ulus. In contrast, no difference was expected between these three stimulus velocity profiles if it is only the human or biological nature of visual rhythms that modulates the form and stability of coordination.

Method Participants. Twenty-two undergraduates from the Univer­ sity of Cincinnati participated in the experiment for partial course credit. All of them had normal or corrected-to-normal vision and provided written informed consent prior the experiment. This experiment was approved by the University of Cincinnati Institu­ tional Review Board. Apparatus. The participants sat in chair in front of a projec­ tion screen (1.25 m X 1.70 m; see Figure 1). An Epson Powerlite 53c projector (Epson America, Long Beach, CA) was used to display on the screen a dot that oscillated horizontally at the height of the participant’s forearm. A 1 cm X 1 cm X 1.5 cm FASTRAK motion-tracking sensor (Polhemus Ltd., Colchester, VT) was fixed to the tip of participants’ right index finger to record their forearm movement (with index finger extended) in the horizontal plane at a sampling rate of 60 Hz with a 0.01 mm spatial resolution. The participants wore safety goggles adapted to prevent them from seeing their own movements. Depending on their posture and forearm position, some participants might have had access to visual information about the rhythmic movements they performed in addition to somatosensory information. Having access to such visual information could modulate the control processes underly­ ing the coordination, and thus, safety goggles were used to avoid such an issue.

Figure 1.

Illustration of the experimental setup used in the current study.

Task and stimuli. The stimulus was a red dot with a diameter of 5.75 cm and movement amplitude of 80 cm (i.e., visual angle of approximately 60°). Stimulus periods of 1.5 s and 0.75 s were used. The stimulus displacements were either perfectly harmonic (i.e., sinus stimulus), or were generated using a nonlinear Rayleigh oscillator equation (i.e., Rayleigh stimulus), or a nonlinear Van der Pol oscillator equation (i.e., Van der Pol stimulus; see Figure 2). The time series of the Rayleigh and Van der Pol stimuli were obtained prior the experiment with numerical simulations in which the parameters were chosen in order to have Rayleigh and Van der Pol stimuli kinematics with moderate deviations from the sinus kinematics and from each other (see Appendix). Procedure. On their arrival, the experimenter informed the participants that the experiment was investigating their perfor­ mance in rhythmic manual tracking task, and that they would be required to do their best to track the displacements of an oscillating dot with the movement of their right-forearm (index finger ex­ tended) in the horizontal plane without moving their wrist and their finger. Although stimulus movements were comfortably tracked using only eye movements due to moderate amplitude (i.e., visual angle of approximately 60°), participants were asked to not move their head when tracking the stimulus and the experimenter made sure that participants complied with this instruction throughout the experiment. Participants first completed practice trials in which they had to coordinate with the different stimuli (sinus, Rayleigh and Van der Pol stimuli). Following this practice period, the participants performed 12 randomized trials (three stimulus kine­ matics [sinus, Rayleigh, and Van der Pol] X 2 stimulus periods [1.5 s and 0.75 s] X 2 trials per condition) of 40 s each with a 5-min break halfway through the trials. Design and analysis. The forearm movement of participants in the horizontal plane was extracted, centered around zero, and low-pass filtered using a 10 Hz Butterworth filter. We then dis­ carded the first five cycles of each trial to eliminate transient behavior. To examine the coordination of participants, we com­ puted discrete (point-estimate) relative phase because of the ex­ perimental manipulations of the current study. Although continu­ ous and discrete relative phase are often equivalent, the use and interpretation of the continuous relative phase is limited in some circumstances, specifically when the movement is not perfectly sinusoidal (Fuchs et al., 1996; Fuchs & Kelso, 1994; Peters, Haddad, Heiderscheit, Van Emmerik, & Hamill, 2003; Varlet & Richardson, 2011). We computed discrete relative phase between 0° and 360° at both minimum and maximal inflection points of the time series (Kelso, 1984). We then used circular statistics to compute two variables (Batschelet, 1981). We calculated the mean phase shift from the intended in-phase coordination (Richardson et al., 2007; Schmidt et al., 1998). Negative and positive phase shift values indicated that the movement of participants led or lagged behind the stimulus, respectively. We also computed the standard deviation of the relative phase in order to examine the variability of the coordination (Richardson et al., 2007; Schmidt et al., 1998). Perfect performance in the manual-tracking task would be charac­ terized by mean phase shift and standard deviation values of zero. We also computed the standard deviation of the movement positions at both minimum and maximum inflection points in order to examine the spatial anchoring of participants’ movements (Fink et al., 2000; Roerdink et al., 2008). Finally, to quantify the non­ linearity of the movement kinematics of participants in the differ-

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Van d e r P ol

Figure 2. Representations of the position over time and of the limit-cycles (velocity vs. position) of the sinus, Rayleigh, and Van der Pol stimuli. The black dots represent the endpoints of the oscillations of the stimuli.

ent experimental conditions, we calculated the deviation from a straight line in the average normalized Hooke’s portraits (Mottet & Bootsma, 1999; Roerdink et al., 2008). This represents the contri­ bution of nonlinear components and can be quantified by NL = 1 —r2, where r2 is the amount of variance explained by the linear regression of position onto acceleration and attributed to a har­ monic oscillation. To obtain the average normalized Hooke’s portraits, we computed the velocity and acceleration of participants from their positions normalized between - 1 and 1 (Mottet & Bootsma, 1999). Velocity and acceleration were then time normal­ ized to 30 points using a spline interpolation procedure and all half-cycles were then averaged point by point. Higher values of NL indicate stronger nonlinearity in participants’ movement kine­ matics. Statistical analysis. We used 2 X 3 repeated-measures ANOVAs with variables of Stimulus Period (1.5 s and 0.75 s) and Stimulus Kinematics (sinus, Rayleigh, and Van der Pol) for statistical anal­ ysis of mean phase shift, standard deviation of the relative phase, spatial anchoring, and nonlinearity of the movement kinematics (NL) of participants. We used Bonferroni post hoc comparisons to determine the nature of the effect when necessary.

Results Phase shift from intended coordination. The ANOVA per­ formed on the mean phase shift yielded significant main effects for Stimulus Period, F (l, 21) = 279.48, p < .05, rip = 0.93, and for Stimulus Kinematics, F(2, 42) = 45.98, p < .05, tip = 0.69. These results indicated lower phase shift values when coordinating with the slowest stimulus, with the Rayleigh stimulus compared to the sinus and Van der Pol stimuli (p < .05), and with the sinus stimulus compared with the Van der Pol stimulus (p < .05; see

Figure 3A). There was no significant interaction between the Stimulus Period and Stimulus Kinematics, F(2, 42) = 1.61, p > .05, ti2 = 0.07. Variability of coordination. The ANOVA performed on the standard deviation of the relative phase revealed a significant main effect for Stimulus Period, F (l, 21) = 92.26, p < .05, tip = 0.81, showing more variable coordination with the fastest stimulus (see Figure 3B). There were no significant main effect for Stimulus Kinematics, F(2, 42) = 1.29, p > .05, r\l = 0.06, and significant interaction between the two factors, F(2,42) = 2.69, p > •05, r)p = 0.07. Spatial anchoring. The ANOVA performed on the spatial anchoring yielded significant main effects for Stimulus Period, F (l, 21) = 25.53, p < .05, T|p = 0.55, and for Stimulus Kinemat­ ics, F(2, 42) = 4.07, p < .05, rip = 0.16. These results indicated lower variability of the movement position of participants at in­ flection points when coordinating with the slowest stimulus and with the Rayleigh stimulus compared with the sinus stimulus (p < .05); an effect that tended to also occur when compared with the Van der Pol stimulus (p = .11; see Figure 3C). There was no significant interaction between the Stimulus Period and Stimulus Kinematics, F(2, 42) = 0.30, p > .05, r)p = 0.01. Nonlinearity of the movement kinematics (NL). The mean of NL values was 0.05 (SD = 0.05) indicating that participants exhibited harmonic or very close to harmonic motion. Although the nonlinearity of participants’ movement obviously tended to increase when coordinating with nonlinear stimuli as indicated by a marginally significant main effect of Stimulus Kinematics, F(2, 42) = 2.80, p = .07, rip = 0.07, the movement produced remained very harmonic as indicated by NL values very close to 0 (all values below 0.06). Note, these values were quite lower than those of the

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VARLET ET AL.

c

S tim ulus Period

Figure 3. Mean phase shift from the instructed in-phase coordination (A), standard deviation of the relative phase (B), and spatial anchoring (C) for the sinus, Rayleigh, and Van der Pol stimuli as a function of the movement period. Error bars represent the standard error of the mean.

Rayleigh and Van der Pol stimuli (i.e., 0.2). The analysis also revealed a significant main effect for Stimulus Period, F(l, 21) = 88.58, p < .05, T)p = 0.81, indicating an increase of the nonlin­ earity of the movement kinematics of participants when coordi­ nating with the slowest stimulus (M = 0.07; SD = 0.05) as compared with the fastest stimulus (M = 0.02; SD = 0.02). There was no significant interaction between Stimulus Kinematics and Stimulus Period, F(2, 42) = 2.48, p > .05, tip = 0.09.

Discussion Experiment 1 tested whether the velocity profile of visual rhythms influenced intended visuomotor coordination by compar­ ing the synchronization of participants with visual stimuli that oscillated with a sinusoidal, Rayleigh, or Van der Pol kinematics. Again, if the availability of critical movement information is increased for the actor with slower approach toward the endpoints of the movement trajectory, the Rayleigh stimulus should have produced more stable coordination and the Van der Pol stimulus

less stable coordination with respect to the sinus stimulus. How­ ever, if it is only the human or biological nature of visual rhythms that is important, there should have been no differences in the stability of coordination between the three velocity profiles. Although adequate synchronization was evident in the different conditions, the results did, in fact, demonstrate differences be­ tween the three stimulus velocity profiles. Specifically, the Ray­ leigh stimulus yielded lower mean phase shifts from the instructed in-phase coordination pattern than did the sinus stimulus, and the Van der Pol stimulus yielded greater phase shifts. The results also showed stronger spatial anchoring when coordinating with the Rayleigh stimulus, as indicated by lower positional variability at inflection points of participants’ movement. These modifications, however, were not accompanied by changes at the level of coor­ dination variability. Nonetheless, these results do support that it is not only the human or biological nature of the stimulus that modulates the dynamics of coordination, but also the properties of the stimulus velocity profile, and suggest the slowness toward the endpoints of the Rayleigh stimulus facilitated the coordination. It is possible that effects on the variability of coordination might be more likely to occur for weaker states of coordination, as it is the case for unintended rhythmic visuomotor coordination (Rich­ ardson et al., 2007; Schmidt & O’Brien, 1997). Contrary to in­ tended coordination that is often absolute with a stable phase relation, unintended coordination is relative and characterized by intermittent attractions toward in-phase and antiphase patterns of coordination (von Holst, 1973). Accordingly, unintended coordi­ nation is more likely to be affected by certain experimental ma­ nipulations, such as stimulus period and visual attention, than is intended coordination (Richardson et al., 2007; Schmidt, Richard­ son, Arsenault, & Galantucci, 2007). Of particular note, previous research has also shown that manipulations of stimulus amplitude only influences the stability of unintended coordination (de Rugy et al., 2008; Peper & Beek, 1998; Varlet et al., 2012a). Therefore, we designed Experiment 2 to examine the influence of the velocity profile of visual rhythms on unintended visuomotor coordination.

Experiment 2 In Experiment 2, participants performed rhythmic forearm movement at a self-selected tempo while simultaneously calling out the changing color of an oscillating stimulus. Participants believed the experiment was designed to test color perception, and the movements of the stimulus were a “distraction” from this primary task. This method ensured participants visually tracked the stimulus movements and also preserved the unintended character of any resulting coordination (Lopresti-Goodman et al., 2008; Schmidt et al., 2007; Varlet et al., 2012a). In view of Experiment 1, stronger entrainment was expected when participants visually tracked a stimulus oscillating with a Rayleigh kinematics as com­ pared to stimuli oscillating with either sinusoidal or Van der Pol kinematics.

Method Participants. Twenty-two undergraduates from the Univer­ sity of Cincinnati participated in the experiment for partial course credit. All participants had normal or corrected-to-normal vision. All of them participated in Experiment 1. However, in order to

STIMULUS KINEMATIC AND VISUOMOTOR COORDINATION

conserve the unintended nature of the coordination, Experiment 2 was performed before Experiment 1. This experiment was ap­ proved by the University of Cincinnati Institutional Review Board. Apparatus. The apparatus was the same as in Experiment 1 with the exception that the stimulus display was different. Task and stimuli. The experimenter instructed participants to name the color changes of a stimulus as quickly as possible while they performed rhythmic forearm movement in the horizontal plane at a self-chosen tempo in two different conditions: tracking and control (Lopresti-Goodman et al., 2008; Schmidt et al., 2007; Varlet et al., 2012a). In the tracking condition, the color changes appeared on a horizontally oscillating dot that participants visually tracked. Even if stimulus movements were comfortably tracked using only eye movements due to moderate amplitude (i.e., visual angle of approximately 60°), participants were instructed to not move their head. The experimenter checked throughout the exper­ iment that participants complied with this instruction. In the con­ trol condition, the color changes appeared on a stationary dot in the middle of the screen (i.e., Figure 1). Although the stimulus did not oscillate during these trials, the computer program generated os­ cillating stimulus time series. The coordination between these control trial stimulus time series and the movement of participants could then be used to assess chance level coordination. Both the oscillating and stationary dots had a diameter of 5.75 cm and were displayed at the forearm height of participants. The dots changed color randomly from red to either yellow, blue, green, or white for 200 ms every 2 s plus a random offset between 0 and 0.999 ms. As in Experiment 1, the oscillating dot had a movement amplitude of 80 cm (i.e., visual angle 60°) and either sinusoidal, Rayleigh, or Van der Pol movement kinematics. The moving dots oscillated with a period of 1.5 s, which corresponded to the average preferred period of 10 participants obtained in a pilot study. Procedure. On arrival, the experimenter informed partici­ pants that the experiment was investigating color processing dur­ ing multitask performance, and that they would be required to call out color changes that appeared on stimuli on the screen as quickly as possible while simultaneously performing rhythmic forearm movements. The participants first completed a practice period to explore different movement periods and find what was the most comfortable for them. They then performed eight randomized trials (two trials for each stimulus [sinus, Rayleigh, and Van der Pol] in the tracking condition and two trials in the control condition) of 40 s each with a 5-min break halfway through the trials. Design and analysis. As in Experiment 1, we computed the relative phase and the nonlinearity of the movement kinematics (NL) of participants. However, because unintended visuomotor coordination is relative instead of absolute, we normalized the relative phase angles between 0° and 180°, and then computed the distribution of relative phase to examine entrainment toward inphase and antiphase patterns (see Lopresti-Goodman et al., 2008; Richardson et al., 2007). Statistical analysis. We used a 2 X 3 X 9 repeated-measures ANOVA with variables of Visual Condition (control and tracking), Stimulus Kinematics (sinus, Rayleigh, and Van der Pol) and Phase Region (0°-20°, 20°-40°, . . . , 160°-180°) for the statistical analysis of the relative phase distributions. In view of previous research that demonstrated that unintended visuomotor phase en­ trainment occurs around 0° and 180°, we focused only on the interactions involving the factor phase region, and only on the

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phase region 0-20° and 160-180° for the Bonferroni post hoc comparisons (Issartel, Marin, & Cadopi, 2007; Lopresti-Goodman et al., 2008; Schmidt et al., 2007). We used a 2 X 3 repeatedmeasures ANOVA with variables of Visual Condition (control and tracking) and Stimulus Kinematics (sinus, Rayleigh, and Van der Pol) for the statistical analysis of the nonlinearity (NL) of the movement kinematics of participants. In both of these analyses, the control data corresponded to the averages of the chance level coordination between the participant’s movements during the two control trials and the (nonpresented) stimulus time series, for each of the three different stimulus types.

Results Relative phase distributions. The ANOVA performed on relative phase distributions showed a significant interaction be­ tween visual condition, phase region, and stimulus kinematics, F(16, 336) = 2.43, p < .05, rip = 0.11 (see Figure 4). Post hoc comparisons for the phase region 0°-20° showed that in-phase entrainment occurred for all the stimuli in the tracking condition, as indicated by a greater percentage of occurrence than in the control condition (no stimulus displayed; p < .05), and that inphase entrainment was stronger for the Rayleigh stimulus com­ pared with the sinus and Van der Pol stimuli (p < .05). Post hoc comparisons for the phase region 160°-180° revealed that anti­ phase entrainment occurred only for the Van der Pol stimulus, as indicated by greater percentage of occurrence compared to the control condition (p < .05), and that this entrainment was stronger compared with the Rayleigh Stimulus (p < .05) but not signifi­ cantly different from the sinus stimulus (p > .05). Nonlinearity of the movement kinematics (NL). The ANOVA performed on NL did not show any significant main effects of visual condition, F (l, 21) = 0.12, p > .05, tip = 0.01, and stimulus kinematics, F(2, 42) = 0.59, p > .05, rip = 0.03, or significant interaction between these two factors, F(2, 42) = 0.59, p > .05, rip = 0.03. As indicated by NL values very close to 0 (M = 0.05; SD = 0.05), participants exhibited harmonic or very close to harmonic movements irrespective of stimulus movements displayed on the projection screen.

0

30

50

70

90

110

130

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180

R e la tiv e P h a s e R e g io n (°)

Figure 4. Mean relative phase distributions obtained in the control and tracking conditions with the sinus, Rayleigh, and Van der Pol stimuli. The distribution of the control condition represented on the figure corresponds to the average one of the three stimuli (no statistically significant differ­ ences).

VARLET ET AL.

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Discussion The goal of Experiment 2 was to determine the influence of the velocity profile of visual rhythms on unintended visuomotor co­ ordination. We examined the spontaneous movement entrainment of participants with visual stimuli oscillating with sinusoidal, Ray­ leigh, or Van der Pol velocity profiles. We expected that partici­ pants’ movements would become spontaneously synchronized with the stimulus movements during visually tracking, and that synchronization would be strongest for the Rayleigh stimulus, as in Experiment 1. As a replication of previous research, the results showed that participants did spontaneously synchronize their movements with the stimulus while visually tracking its displacements, and that this synchronization occurred toward the preferred in-phase and anti­ phase patterns of coordination (Issartel et al., 2007; Oullier, De Guzman, Jantzen, Lagarde, & Scott Kelso, 2008; Richardson et al., 2007; Schmidt et al., 2007; Tognoli et al., 2007). These results extend previous research in showing that spontaneous movement entrainment of participants is modulated by the velocity profile of the observed visual rhythms. In line with Experiment 1, the results of Experiment 2 showed that the coordination of participants was strengthened when the stimulus oscillated with a Rayleigh move­ ment kinematics. Again, this facilitative effect of the Rayleigh velocity profile might be attributed to its slower approach to the end of its trajectory, which might aid the detection of movement infor­ mation underlying entrainment (Bingham et al., 2001; Hajnal et al., 2009; Wilson et al., 2005a; Zaal et al., 2000). This account is consistent with previous research which proposed the most important information for stabilizing coordination with an os­ cillating stimulus is available for the actor around the endpoints of its trajectory (Elajnal et al., 2009; Roerdink et al., 2008, 2005), and extends them by suggesting the part of the trajectory going toward the endpoints is more important than the part going away from the endpoints. Nevertheless, it should be noted that there was no difference in the strength of coordination with the sinus and Van der Pol stimuli. The Van der Pol stimulus did not degrade spontaneous synchronization compared to the sinus stimulus despite its speediness to the endpoints of the trajectory that theoretically might have affected the detection of important movement in­ formation (Bingham et al., 2001; Hajnal et al., 2009; Wilson et al., 2005a; Zaal et al., 2000). This suggests that other properties of the rhythms’ trajectory might modulate the dynamics of unintended visuomotor coordination in addition to its slowness to the endpoints. It is possible for example that certain forms of nonlinearity such as Van der Pol kinematics increase the visual attention of participants, and thus, the emergence of spontane­ ous synchronization (Richardson et al., 2007; Schmidt et al., 2007; Varlet et al., 2012a). This encourages therefore further explorations using other kinds and magnitudes of stimulus nonlinearity in order to better understand the role played by the stimulus velocity profile in the stability of visuomotor coordi­ nation.

General Discussion Across two experiments the current study investigated whether the velocity profile of environmental or external rhythms influ­

ences the dynamics of visuomotor coordination. We hypothesized that the velocity profile of visual rhythms would modulate the emergence and stability of intended and unintended visuomotor coordination and, more specifically, that the coordination would depend on the damping or slowness around the endpoints of the observed rhythms’ trajectory. Generally, these results corroborate previous research which showed that intended and unintended rhythmic visuomotor coor­ dination can be understood as constrained by the dynamical en­ trainment processes of coupled oscillators, and further demonstrate the necessity to focus on the components’ properties to better understand coordination dynamics (Lopresti-Goodman et al., 2008; Peper & Beek, 1998; Roerdink et al., 2008; Schmidt et al., 2011; Schmidt & Richardson, 2008; Varlet et al., 2012a; Wimmers et al., 1992). Consistent with our expectations, the results of these two experiments demonstrated that the dynamics of both intended and unintended visuomotor coordination are modulated by the velocity profile of the observed environmental rhythms. More specifically, our study connects for the first time previous studies showing nonlinearities in human movement kinematics with re­ search on visuomotor (interpersonal) coordination. Our results extend previous findings by showing that an actor looking at an external or environmental movement is sensitive to nonlinearities in its kinematics, resulting in greater or poorer coordinated behav­ ior. In short, the movement of an actor is more easily coordinated to visual stimuli oscillating with Rayleigh kinematics compared with sinusoidal or Van der Pol kinematics, suggesting a construc­ tive effect of the slowness of the rhythm to its endpoints for the coordination. In view of the previous research by Bingham and his colleagues, and more specifically, the visually mediated model of rhythmic coordination they have proposed (Bingham, 2004a, 2004b; SnappChilds, Wilson, & Bingham, 2011), an alternative explanation for such effects could be that there is greater similarity between the velocity profiles of the stimulus movements and participants’ movements. Indeed, they have shown that the information that can be used to control rhythmic visuomotor coordination is the relative direction between the observed and produced movements and that the detection of this information depends on the relative speed between these two movements that acts as noise (Bingham, 2004a, 2004b; Snapp-Childs et al., 2011; Wilson et al, 2005a; Wilson, Collins, & Bingham, 2005b). When performing an in-phase or antiphase coordination, the relative direction does not change (always the same and always different at 0° and 180°, respec­ tively), but antiphase coordination is less stable because the rela­ tive speed ranges from zero to maximally different, which de­ grades the detection of the relative direction information. Numerous studies that investigated the perception of visual coor­ dination between two oscillating visual dots support the model and it predictions, including studies with perturbed kinematics (Bing­ ham, 2004b; Bingham et al., 1999, 2001; Wilson & Bingham, 2008; Zaal et al., 2000). Bingham and colleagues have also dem­ onstrated the validity of the model for rhythmic visuomotor coor­ dination (Snapp-Childs et al., 2011; Wilson et al., 2005a, 2005b). The relative speed between participant and stimulus movements has been manipulated for example by changing the difference of amplitude between the two movements (Snapp-Childs et al., 2011) or by asking participants to coordinate a circular movement with a

STIMULUS KINEMATIC AND VISUOMOTOR COORDINATION

stimulus oscillating horizontally either with a constant or harmonic velocity profile (Wilson et al., 2005b). Although it was not the primary aim of our experiments, the manipulation of the stimulus velocity profiles was found to affect the relative speed between participants’ and stimulus movements and raises questions about whether it might have affected the coordination and contributed to our results. In particular, did greater coordination with the Rayleigh stimulus occur because of minimal relative speed in this condition as predicted by the model? In other words, is the coordination facilitation observed with the Rayleigh stimulus is due to the fact that the natural or preferred movement kinematics of participants was close to a Rayleigh kinematics? The analyses of the movement kinematics of partici­ pants showed that they exhibited harmonic or very close to har­ monic motion, and even tend to keep this movement trajectory when coordinating with nonlinear stimuli. Therefore, greater co­ ordination should have occurred with the sinus (harmonic) stimu­ lus according to the visually mediated model. In contrast, the results demonstrated greater coordination with the Rayleigh stim­ ulus, and thus, support a constructive effect of the slowness of the rhythm to its endpoints, independently of the movement kinemat­ ics produced by participants. Nevertheless, it remains possible that differences in the nonlin­ earities of observed and produced movements influence the emer­ gence and stability of the coordination as predicted by the model. The rhythmic limb movements of an individual might be more likely to become coordinated with a visual rhythm, not only because of its velocity profile as demonstrated in the current study, but also because they share similar movement profiles. Therefore, it would be particularly interesting to manipulate in future research the (dis)similarity between participants’ and stimulus preferred velocity profiles to directly test the predictions of Bingham’s model as initiated by Wilson, Collins, and Bingham (2005b) using circular movements. Moreover, to further understand how move­ ment kinematics modulate rhythmic visuomotor coordination, fu­ ture research ought to investigate more forms and magnitudes of stimulus nonlinearity as explained above. Indeed, the understand­ ing of the role played by the stimulus velocity profiles remains limited in the current study due to the small number of kinematic patterns tested. We examined two forms of nonlinearity (i.e., Rayleigh and Van der Pol) and only one (low/moderate) magni­ tude for each of them whereas it is possible that some effects would only occur for certain ranges of nonlinearity. In particular, Muchisky and Bingham (2002) have investigated the discrimina­ tion of different stimulus trajectories and have shown the existence threshold effects, suggesting that stronger and/or additional effects might be observed when coordinating with stimuli oscillating with greater nonlinearity. The results of the current study have important implications to better understand the influence of the social nature (i.e., agency) of external visual rhythms and the dynamics of interpersonal coordi­ nation in general (Chaminade et al., 2005; Coey, Varlet, Schmidt, & Richardson, 2011a; Kilner et al., 2003; Stanley et al., 2007). The movement of an actor is known to be more influenced or attracted to the movement of a social stimulus than a nonsocial stimulus (Chaminade et al., 2005; Kilner et al., 2007, 2003; Stanley et al., 2007). However, a number of studies have failed to show such agency effects when human and nonhuman stimuli were rigorously controlled to have identical movement kinematics (Coey et al.,

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2011a; Jansson et al., 2007). Together with these results, our findings support the proposal that such agency effects in visuo­ motor coordination may mainly originate from differences at the level of the stimulus velocity profiles, and more specifically from the damping of human or biological rhythmic movement that might facilitate synchronization. These results are also of particular interest for the numerous researchers that investigate the efficiency and deficiency of inter­ personal coordination. They can help to better understand and improve the synchronization performance in activities requiring very efficient interpersonal coordination such as team rowing, dance or music situations (de Brouwer, de Poel, & Hofmijster, 2013; Phillips-Silver & Keller, 2012; Sevdalis & Keller, 2011; Varlet et al., 2013). They also have implication for understanding the impaired interpersonal coordination of patients suffering from mental and social disorders. A growing interest in understanding the role that movement coordination plays in interpersonal respon­ siveness has occurred due to findings that indicate that motor coordination of interacting people modulates the success of their interaction or exchange (Marsh, Richardson, & Schmidt, 2009). Indeed, naturally occurring movement coordination can influence feelings of group cohesion, connectedness, or even facilitate in­ terpersonal communication (Bemieri, 1988; Chartrand & Bargh, 1999; Hove & Risen, 2009; Richardson, Dale, & Kirkham, 2007; Shockley, Richardson, & Dale, 2009; Wiltermuth & Heath, 2009). Impairments of interpersonal coordination have been recently demonstrated in autism and schizophrenia, but their origin remains largely unclear (Fitzpatrick, Diorio, Richardson, & Schmidt, 2013; Kupper, Ramseyer, Hoffmann, Kalbermatten, & Tschacher, 2010; Marsh et al., 2013; Varlet et al., 2012c). The results of this study encourages further investigations of the movement kinematics of patients to determine whether changes in their velocity profiles might explain their impaired coordination dynamics, and develop if necessary rehabilitations protocols aiming at recovering more biological or healthy movement kinematics and successful social interactions. Finally, the present findings can be also of importance to im­ prove our interactions with virtual agents and humanoid robots (Chaminade et al., 2005; Hasnain, Mostafaoui, & Gaussier, 2013; Kopp, 2010; Kupferberg et al., 2011). Several previous studies have tried to improve the interaction of these agents by enhancing the human nature of their appearance despite there is no demon­ strated influence at our knowledge of such manipulations on our movement coordination (Coey et al., 2011a). This study therefore supports that improving the human or biological nature of the movement kinematics of these agents might represent an alterna­ tive promising research direction to enhance the interaction.

References Amazeen, P. G., Schmidt, R. C., & Turvey, M. T. (1995). Frequency detuning of the phase entrainment dynamics of visually coupled rhyth­ mic movements. Biological Cybernetics, 72, 511-518. doi:10.1007/ BF00199893 Batschelet, E. (1981). Circular statistics in biology (Vol. 371). London, UK: Academic Press. Beek, P. J. (1989). Juggling dynamics. Amsterdam, The Netherlands: Free University Press. Beek, P. J., Rikkert, W. E., & van Wieringen, P. C. (1996). Limit cycle properties of rhythmic forearm movements. Journal of Experimental

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VARLET ET AL.

Psychology: Human Perception and Performance, 22, 1077-1093. doi: 10.1037/0096-1523.22.5.1077 Beek, P. J., Schmidt, R. C., Morris, A. W„ Sim, M.-Y., & Turvey, M. T. (1995). Linear and nonlinear stiffness and friction in biological rhythmic movements. Biological Cybernetics, 73, 499-507. doi:10.1007/ BF00199542 Bernieri, F. J. (1988). Coordinated movement and rapport in teacherstudent interactions. Journal o f Nonverbal behavior, 12, 120-138. doi: 10.1007/BF00986930 Bingham, G. P. (2004a). A perceptually driven dynamical model of bi­ manual rhythmic movement (and phase perception). Ecological Psy­ chology, 16, 45-53. doi: 10.1207/s 15326969eco 1601_6 Bingham, G. P. (2004b). Another timing variable composed of state variables: Phase perception and phase driven oscillators. Advances in psychology, 135, 421-442. doi: 10.1016/SO166-4115(04)80020-7 Bingham, G. P., Schmidt, R. C., & Zaal, F. T. (1999). Visual perception of the relative phasing of human limb movements. Perception & Psycho­ physics, 61, 246-258. doi:10.3758/BF03206886 Bingham, G. P., Zaal, F. T., Shull, J. A., & Collins, D. R. (2001). The effect of frequency on the visual perception of relative phase and phase variability of two oscillating objects. Experimental Brain Research, 136, 543-552. doi:10.1007/s002210000610 Byblow, W. D., Chua, R., & Goodman, D. (1995). Asymmetries in cou­ pling dynamics of perception and action. Journal o f Motor Behavior, 27, 123-137. doi:10.1080/00222895.1995.9941705 Chaminade, T., Franklin, D. W., Oztop, E., & Cheng, G. (2005). Motor interference between humans and humanoid robots: Effect of biological and artificial motion. In Development and Learning, 2005. Proceedings. The 4th International Conference on (pp. 96-101). Chartrand, T. L., & Bargh, J. A. (1999). The chameleon effect: The perception-behavior link and social interaction. Journal o f Personality and Social Psychology, 76, 893-910. doi:10.1037/0022-3514.76.6.893 Coey, C. A., Varlet, M., Schmidt, R. C., & Richardson, M. J. (2011a). Agency and rhythmic coordination: Are we naught but moving dots. In Proceedings o f the 33rd Annual Conference o f the Cognitive Science Society (pp. 172-177). Coey, C., Varlet, M., Schmidt, R. C., & Richardson, M. J. (201 lb). Effects of movement stability and congruency on the emergence of spontaneous interpersonal coordination. Experimental Brain Research, 211, 483493. doi: 10.1007/s00221-011 -2689-9 de Brouwer, A. J., de Poel, H. J., & Hofmijster, M. J. (2013). Don’t rock the boat: How antiphase crew coordination affects rowing. PloS One, 8, e54996. doi: 10.137 l/joumal.pone.0054996 de Rugy, A., Oullier, O., & Temprado, J.-J. (2008). Stability of rhythmic visuo-motor tracking does not depend on relative velocity. Experimental Brain Research, 184, 269-273. doi:10.1007/s00221-007-1180-0 Desmurget, M., & Grafton, S. (2000). Forward modeling allows feedback control for fast reaching movements. Trends in Cognitive Sciences, 4, 423-431. doi: 10.1016/S1364-6613(00)01537-0 Fine, J. M., Gibbons, C. T., & Amazeen, E. L. (2013). Congruency effects in interpersonal coordination. Journal o f Experimental Psychology: Hu­ man Perception and Performance, 39, 1541-1556. doi:10.1037/ a0031953 Fink, P. W„ Foo, P„ Jirsa, V. K„ & Kelso, J. S. (2000). Local and global stabilization of coordination by sensory information. Experimental Brain Research, 134, 9-20. doi:10.1007/s002210000439 Fitzpatrick, P., Diorio, R., Richardson, M. J., & Schmidt, R. C. (2013). Dynamical methods for evaluating the time-dependent unfolding of social coordination in children with autism. Frontiers in Integrative Neuroscience, 7, 21. doi:10.3389/fnint.2013.00021 Fuchs, A., Jirsa, V. K., Haken, H., & Kelso, J. S. (1996). Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies. Biological Cybernetics, 74, 21-30. doi:10.1007/ BF00199134

Fuchs, A., & Kelso, J. A. (1994). A theoretical note on models of interlimb coordination. Journal o f Experimental Psychology: Human Perception and Performance, 20, 1088-1097. doi:10.1037/0096-1523.20.5.1088 Hajnal, A., Richardson, M. J., Harrison, S. J., & Schmidt, R. C. (2009). Location but not amount of stimulus occlusion influences the stability of visuo-motor coordination. Experimental Brain Research, 199, 89-93. doi: 10.1007/s00221-009-1958-3 Haken, H., Kelso, J. S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51, 347356. doi: 10.1007/BF00336922 Hasnain, S. K., Mostafaoui, G., & Gaussier, P. (2013). A synchrony-based perspective for partner selection and attentional mechanism in humanrobot interaction. Paladyn, 1-16. Hommel, B., Miisseler, J., Aschersleben, G., & Prinz, W. (2001). The theory of event coding (TEC): A framework for perception and action planning. Behavioral and Brain Sciences, 24, 849-878. doi: 10.1017/ S0140525X01000103 Hove, M. J., & Risen, J. L. (2009). It’s all in the timing: Interpersonal synchrony increases affiliation. Social Cognition, 27, 949-960. doi: 10.1521/soco.2009.27.6.949 Hove, M. J., Spivey, M. J., & Krumhansl, C. L. (2010). Compatibility of motion facilitates visuomotor synchronization. Journal o f Experimental Psychology: Human Perception and Performance, 36, 1525-1534. doi: 10.1037/a0019059 Issartel, J., Marin, L., & Cadopi, M. (2007). Unintended interpersonal co-ordination:“can we march to the beat of our own drum?” Neurosci­ ence Letters, 411, 174-179. doi:10.1016/j.neulet.2006.09.086 Jansson, E., Wilson, A. D., Williams, J. H., & Mon-Williams, M. (2007). Methodological problems undermine tests of the ideo-motor conjecture. Experimental Brain Research, 182, 549-558. doi:10.1007/s00221-0071013-1 Kay, B. A., Kelso, J. A., Saltzman, E. L., & Schoner, G. (1987). Spacetime behavior of single and bimanual rhythmical movements: Data and limit cycle model. Journal o f Experimental Psychology: Human Per­ ception and Performance, 13, 178-192. doi:10.1037/0096-1523.13.2 .178 Kelso, J. A. (1984). Phase transitions and critical behavior in human bimanual coordination. American Journal o f Physiology-Regulatory, Integrative and Comparative Physiology, 246, R1000-R1004. Kelso, J. A. (1995). Dynamic patterns: The self organization o f brain and behaviour. Cambridge, MA: The MIT Press. Kilner, J., de, C. Hamilton, A. F., & Blakemore, S.-J. (2007). Interference effect of observed human movement on action is due to velocity profile of biological motion. Social Neuroscience, 2, 158-166. doi:10.1080/ 17470910701428190 Kilner, J. M., Paulignan, Y., & Blakemore, S. J. (2003). An interference effect of observed biological movement on action. Current Biology, 13, 522-525. doi: 10.1016/S0960-9822(03)00165-9 Kopp, S. (2010). Social resonance and embodied coordination in face-toface conversation with artificial interlocutors. Speech Communication, 52, 587-597. doi:10.1016/j.specom.2010.02.007 Kupferberg, A., Glasauer, S., Huber, M., Rickert, M., Knoll, A., & Brandt, T. (2011). Biological movement increases acceptance of humanoid robots as human partners in motor interaction. A l & Society, 26, 3 3 9 345. doi: 10.1007/s00146-010-0314-2 Kupper, Z., Ramseyer, F., Hoffmann, H., Kalbermatten, S., & Tschacher, W. (2010). Video-based quantification of body movement during social interaction indicates the severity of negative symptoms in patients with schizophrenia. Schizophrenia Research, 121, 90-100. doi: 10.1016/j .schres.2010.03.032 Lopresti-Goodman, S. M., Richardson, M. J., Silva, P. L., & Schmidt, R. C. (2008). Period basin of entrainment for unintentional visual coordina­ tion. Journal o f Motor Behavior, 40, 3-10. doi:10.3200/JMBR.40.1.3-10

STIMULUS KINEMATIC AND VISUOMOTOR COORDINATION Marsh, K. L., Isenhower, R. W., Richardson, M. J., Helt, M., Verbalis, A. D., Schmidt, R. C., & Fein, D. (2013). Autism and social disconnec­ tion in interpersonal rocking. Frontiers in Integrative Neuroscience, 7, 4. doi:10.3389/fnint.2013.00004 Marsh, K. L., Richardson, M. J., & Schmidt, R. C. (2009). Social connec­ tion through joint action and interpersonal coordination. Topics in Cog­ nitive Science, I, 320-339. doi:10.1111/j.l756-8765.2009.01022.x Mottet, D., & Bootsma, R. J. (1999). The dynamics of goal-directed rhythmical aiming. Biological Cybernetics, 80, 235-245. doi:10.1007/ S004220050521 Muchisky, M. M., & Bingham, G. P. (2002). Trajectory forms as a source of information about events. Perception & Psychophysics, 64, 15-31. doi: 10.3758/BF03194554 Neda, Z., Ravasz, E., Brechet, Y., Vicsek, T., & Barabasi, A.-L. (2000). Self-organizing processes: The sound of many hands clapping. Nature, 403, 849 - 850. doi: 10.1038/35002660 Oullier, O., De Guzman, G. C., Jantzen, K. J., Lagarde, J., & Scott Kelso, J. A. (2008). Social coordination dynamics: Measuring human bonding. Social Neuroscience, 3, 178-192. doi:10.1080/17470910701563392 Peper, C. L. E., & Beek, P. J. (1998). Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude? Biological Cybernetics, 79, 291-300. doi:10.1007/s004220050479 Peper, C. E., de Boer, B. J., de Poel, H. J., & Beek, P. J. (2008). Interlimb coupling strength scales with movement amplitude. Neuroscience Let­ ters, 437(1), 10-14. doi:10.1016/j.neulet.2008.03.066 Peters, B. T., Haddad, J. M., Heiderscheit, B. C., Van Emmerik, R. E., & Hamill, J. (2003). Limitations in the use and interpretation of continuous relative phase. Journal o f Biomechanics, 36, 271-274. doi:10.1016/ S0021-9290(02)00341-X Phillips-Silver, J., & Keller, P. E. (2012). Searching for roots of entrain­ ment and joint action in early musical interactions. Frontiers in Human Neuroscience, 6, 26. doi:10.3389/fnhum.2012.00026 Prinz, W. (1997). Perception and action planning. European Journal o f Cognitive Psychology, 9, 129-154. doi:10.1080/713752551 Ramenzoni, V. C., Davis, T. J., Riley, M. A., Shockley, K., & Baker, A. A. (2011). Joint action in a cooperative precision task: Nested processes of intrapersonal and interpersonal coordination. Experimental Brain Re­ search, 211, 447-457. doi:10.1007/s00221-011-2653-8 Richardson, D. C., Dale, R., & Kirkham, N. Z. (2007). The art of conver­ sation is coordination common ground and the coupling of eye move­ ments during dialogue. Psychological Science, 18, 407-413. doi: 10.1111/j. 1467-9280.2007,01914.x Richardson, M. J., Campbell, W. L., & Schmidt, R. C. (2009). Movement interference during action observation as emergent coordination. Neu­ roscience Letters, 449, 117-122. doi:10.1016/j.neulet.2008.10.092 Richardson, M. J., Marsh, K. L., Isenhower, R. W., Goodman, J. R., & Schmidt, R. C. (2007). Rocking together: Dynamics of intentional and unintentional interpersonal coordination. Human Movement Science, 26, 867-891. doi:10.1016/j.humov.2007.07.002 Richardson, M. J., Marsh, K. L., & Schmidt, R. C. (2005). Effects of visual and verbal interaction on unintentional interpersonal coordination. Jour­ nal o f Experimental Psychology: Human Perception and Performance, 31, 62-79. doi: 10.1037/0096-1523.31.1.62 Roerdink, M., Bank, P. J., Peper, C. E., & Beek, P. J. (2013). Anchoring in rhythmic in-phase and antiphase visuomotor tracking. Motor Control, 17, 176-189. Roerdink, M., Ophoff, E. D., Peper, C. E„ & Beek, P. J. (2008). Visual and musculoskeletal underpinnings of anchoring in rhythmic visuo-motor tracking. Experimental Brain Research, 184, 143-156. doi:10.1007/ s00221-007-1085-y Roerdink, M., Peper, C. E., & Beek, P. J. (2005). Effects of correct and transformed visual feedback on rhythmic visuo-motor tracking: Track­ ing performance and visual search behavior. Human Movement Science, 24, 379-402. doi:10.1016/j.humov.2005.06.007

1859

Romero, V., Coey, C., Schmidt, R. C., & Richardson, M. J. (2012). Movement coordination or movement interference: Visual tracking and spontaneous coordination modulate rhythmic movement interference. PloS One, 7, e44761. doi:10.1371/joumal.pone.0044761 Schmidt, R. C., Bienvenu, M., Fitzpatrick, P. A., & Amazeen, P. G. (1998). A comparison of intra-and interpersonal interlimb coordination: Coor­ dination breakdowns and coupling strength. Journal o f Experimental Psychology: Human Perception and Performance, 24, 884-900. doi: 10.1037/0096-1523.24.3.884 Schmidt, R. C., Carello, C., & Turvey, M. T. (1990). Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. Journal o f Experimental Psychology: Human Percep­ tion and Performance, 16, 227-247. doi:10.1037/0096-1523.16.2.227 Schmidt, R. C., Fitzpatrick, P., Caron, R., & Mergeche, J. (2011). Under­ standing social motor coordination. Human Movement Science, 30, 834-845. doi:10.1016/j.humov.2010,05.014 Schmidt, R. C., & O’Brien, B. (1997). Evaluating the dynamics of unin­ tended interpersonal coordination. Ecological Psychology, 9, 189-206. doi: 10.1207/sl5326969eco0903_2 Schmidt, R. C., O’Brien, B., & Sysko, R. (1999). Self-organization of between-persons cooperative tasks and possible application to sport. International Journal o f Sport Psychology, 30, 558-579. Schmidt, R. C., & Richardson, M. J. (2008). Dynamics of interpersonal coordi­ nation. In A. Fuchs & V. K. Jirsa (Eds.), Coordination: Neural, behav­ ioral and social dynamics (pp. 281-308). New York, NY: Springer. Schmidt, R. C., Richardson, M. J., Arsenault, C., & Galantucci, B. (2007). Visual tracking and entrainment to an environmental rhythm. Journal o f Experimental Psychology: Human Perception and Performance, 33, 860-870. doi: 10.1037/0096-1523.33.4.860 Schoner, G., Haken, H., & Kelso, J. A. S. (1986). A stochastic theory of phase transitions in human hand movement. Biological Cybernetics, 53, 247-257. doi:10.1007/BF00336995 Sebanz, N., Knoblich, G., & Prinz, W. (2003). Representing others’ ac­ tions: Just like one’s own? Cognition, 88, B11-B21. doi:10.1016/S00100277(03)00043-X Sevdalis, V., & Keller, P. E. (2011). Captured by motion: Dance, action understanding, and social cognition. Brain and Cognition, 77, 231-236. doi: 10.1016/j.bandc.2011.08.005 Shockley, K., Richardson, D. C., & Dale, R. (2009). Conversation and coordinative structures. Topics in Cognitive Science, I, 305-319. doi: 10.1 lll/j.1756-8765.2009.01021.x Shockley, K., Santana, M.-V., & Fowler, C. A. (2003). Mutual interper­ sonal postural constraints are involved in cooperative conversation. Journal o f Experimental Psychology: Human Perception and Perfor­ mance, 29, 326-332. doi:10.1037/0096-1523.29.2.326 Snapp-Childs, W., Wilson, A. D., & Bingham, G. P. (2011). The stability of rhythmic movement coordination depends on relative speed: The Bingham model supported. Experimental Brain Research, 215, 89-100. doi:10.1007/s00221-011-2874-x Stanley, J., Gowen, E., & Miall, R. C. (2007). Effects of agency on movement interference during observation of a moving dot stimulus. Journal o f Experimental Psychology: Human Perception and Perfor­ mance, 33, 915-926. doi:10.1037/0096-1523.33.4.915 Tognoli, E., Lagarde, J., DeGuzman, G. C., & Kelso, J. S. (2007). The phi complex as a neuromarker of human social coordination. Proceedings o f the National Academy o f Sciences o f the United States o f America, 104, 8190-8195. doi:10.1073/pnas.0611453104 van Ulzen, N. R., Lamoth, C. J., Daffertshofer, A., Semin, G. R„ & Beek, P. J. (2008). Characteristics of instructed and uninstructed interpersonal coordination while walking side-by-side. Neuroscience Letters, 432, 88-93. doi: 10.1016/j.neulet.2007.11.070 Varlet, M., Coey, C. A., Schmidt, R. C., & Richardson, M. J. (2012a). Influence of stimulus amplitude on unintended visuomotor entrainment.

VARLET ET AL.

1860

Human Movement Science, 31, 541-552. doi:10.1016/j.humov.2011.08 .002

Varlet, M., Filippeschi, A., Ben-sadoun, G., Ratio, M., Marin, L., Ruffaldi, E., & Bardy, B. G. (2013). Virtual reality as a tool to learn interpersonal coordination: Example of team rowing. Presence: Teleoperators and Virtual Environments, 22, 202-215. doi:10.1162/PRES_a_00151 Varlet, M., Marin, L., Issartel, J., Schmidt, R. C., & Bardy, B. G. (2012b). Continuity of visual and auditory rhythms influences sensorimotor co­ ordination. PloS One, 7, e44082. doi:10.1371/journal.pone.0044082 Varlet, M., Marin, L., Raffard, S., Schmidt, R. C., Capdevielle, D., Boulenger, J.-P., . . . Bardy, B. G. (2012c). Impairments of social motor coordination in schizophrenia. PloS One, 7, e29772. doi:10.1371/joumal .pone.0029772 Varlet, M., & Richardson, M. J. (2011). Computation of continuous rela­ tive phase and modulation of frequency of human movement. Journal of Biomechanics, 44, 1200-1204. doi:10.1016/j.jbiomech.2011.02.001 von Holst, E. (1973). Relative coordination as a phenomenon and as a method of analysis of central nervous system function. In R. Martin (Ed. and Trans.), The collected papers o f Erich von Holst: Vol. 1. The behavioral physiology o f animal and man (pp. 33-135). Coral Gables, FL: University of Miami Press. (Original work published 1939)

Wilson, A. D., & Bingham, G. P. (2008). Identifying the information for the visual perception of relative phase. Perception & psychophysics, 70, 465-476. doi: 10.3758/PP.70.3.465 Wilson, A. D., Collins, D. R., & Bingham, G. P. (2005a). Perceptual coupling in rhythmic movement coordination: Stable perception leads to stable action. Experimental Brain Research, 164, 517-528. doi: 10.1007/ s00221-005-2272-3 Wilson, A. D., Collins, D. R., & Bingham, G. P. (2005b). Human move­ ment coordination implicates relative direction as the information for relative phase. Experimental Brain Research, 165, 351-361. doi: 10.1007/s00221-005-2301 -2 Wiltermuth, S. S., & Heath, C. (2009). Synchrony and cooperation. Psy­ chological Science, 20(1), 1-5. doi: 10.1111/j. 1467-9280.2008.02253.X Wimmers, R. H., Beek, P. J., & van Wieringen, P. C. (1992). Phase transitions in rhythmic tracking movements: A case of unilateral cou­ pling. Human Movement Science, 11, 217-226. doi: 10.1016/01679457(92)90062-G Zaal, F. T., Bingham, G. P., & Schmidt, R. C. (2000). Visual perception of mean relative phase and phase variability. Journal o f Experimental Psychology: Human Perception and Performance, 26(3), 1209-1220. doi: 10.1037/0096-1523.26.3.1209

Appendix Nonlinear Stimuli To obtain the time series of the Rayleigh and Van der Pol stimuli, we respectively simulated the following Rayleigh (1) Van der Pol (2) oscillator equations: X

—e(l —x 2) * + x

x -

0

(1)

|x(l —jc2)* + x = 0

(2)

=

where x represents the position of the oscillator and the dot notation represents derivative with respect to time. In order to have kinematics of the Rayleigh and Van der Pol stimuli that have

moderates deviations from perfect sinusoidal motion and are the opposite of each other, numerical integrations of the Rayleigh Van der Pol oscillator equations were performed with e = 8.2 and p. = 1.7, respectively. The time series were then normalized to obtain the stimulus period needed and to have the same movement amplitude for all stimuli (i.e., 80 cm). Received January 7, 2014 Revision received May 9, 2014 Accepted May 27, 2014 ■

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