Journal of Motor Behavior, Vol. 0, No. 0, 2015 Copyright Taylor & Francis Group, LLC

Journal of Motor Behavior, Vol. 0, No. 0, 2015 Copyright Taylor & Francis Group, LLC RESEARCH ARTICLE Influence of Internal and External Noise on Spontaneous Visuomotor Synchronization Manuel Varlet 1,2,3, R. C. Schmidt 4, Michael J. Richardson 2 1 The MARCS Institute, University of Western Sydney, Australia. 2 Perceptual-Motor Dynamics Laboratory, CAP Center for Cognition, Action, and Perception, University of Cincinnati, Ohio. 3 Movement to Health Laboratory, EuroMov, Montpellier-1 University, France. 4 Department of Psychology, College of the Holy Cross, Worcester, Massachusetts. ABSTRACT. Historically, movement noise or variability is considered to be an undesirable property of biological motor systems. In particular, noise is typically assumed to degrade the emergence and stability of rhythmic motor synchronization. Recently, however, it has been suggested that small levels of noise might actually improve the functioning of motor systems and facilitate their adaptation to environmental events. Here, the authors investigated whether noise can facilitate spontaneous rhythmic visuomotor synchronization. They examined the influence of internal noise in the rhythmic limb movements of participants and external noise in the movement of an oscillating visual stimulus on the occurrence of spontaneous synchronization. By indexing the natural frequency variability of participants and manipulating the frequency variability of the visual stimulus, the authors demonstrated that both internal and external noise degrade synchronization when the participants and stimulus movement frequencies are similar, but can actually facilitate synchronization when the frequencies are different. Furthermore, the two kinds of noise interact with each other. Internal noise facilitates synchronization only when external noise is minimal and vice versa. Too much internal and external noise together degrades synchronization. These findings open new perspectives for better understanding the role of noise in human rhythmic coordination. Keywords: sensorimotor synchronization, unintentional coordination, entrainment, movement variability, noise, frequency fluctuations Human rhythmic movements often become spontaneously synchronized with environmental events and rhythms, including the rhythmic movements of other individuals (Dijkstra, Sch oner, Giese, & Gielen, 1994; Lopresti-Goodman, Richardson, Silva, & Schmidt, 2008; Repp, 2006; Richardson, Marsh, Isenhower, Goodman, & Schmidt, 2007; Schmidt, Richardson, Arsenault, & Galantucci, 2007; Schmidt & O Brien, 1997; Tognoli, Lagarde, DeGuzman, & Kelso, 2007; van Ulzen, Lamoth, Daffertshofer, Semin, & Beek, 2008). Synchrony can simply occur by chance, especially when the movements of the actor and the external rhythm have similar intrinsic temporal dynamics. Nevertheless, synchrony will have a greater tendency to occur spontaneously or unintentionally if information about the external rhythm is pickedup by the actor (Richardson, Marsh et al., 2007; Schmidt et al., 2007; van Ulzen et al., 2008). Apparently, just seeing or hearing an external rhythm creates an active process of synchronization and leads to a state of synchrony. It remains unclear, however, why such spontaneous synchronization emerges, is maintained, and sometimes vanishes. In the current study, we investigate the role that the movement noise or variability (two terms considered as identical throughout this article) plays in spontaneous visuomotor synchronization. More specifically, we examine whether internal noise in the actor s movement and external noise in an observed environmental stimulus movement modulate the occurrence and stability of spontaneous synchronization. Of particular relevance to the current study is that the dynamical entrainment processes of coupled oscillators have been argued to be the organizing principle behind such spontaneous visuomotor synchronization and human rhythmic coordination more generally (Beek, Peper, & Daffertshofer, 2002; Haken, Kelso, & Bunz, 1985; Sch oner, Haken, & Kelso, 1986). Consistent with this understanding, the movements of an actor become spontaneously entrained or attracted to observed movements in an in-phase or antiphase pattern of coordination, which correspond to movements that oscillate at the same time in the same or opposite direction, and to relative phase values of 0 or 180, respectively (Kelso, 1995; Peper & Beek, 1998; Richardson, Marsh et al. 2007; Schmidt & O Brien, 1997; Wimmers, Beek, & van Wieringen, 1992). Furthermore, the dynamic stabilities of the synchronization are known to be moderated by (a) the strength of the informational couplings that connect the actor and the external rhythmic movements and (b) the magnitude of the differences between their intrinsic or natural frequencies (Fuchs, Jirsa, Haken, & Kelso, 1996; Jeka & Kelso, 1995; Richardson, Marsh et al., 2007; Schmidt, Bienvenu, Fitzpatrick, & Amazeen, 1998; Sternad, Collins, & Turvey, 1995). Accordingly, the greater the coupling strength between the movements involved and the more similar their intrinsic frequencies the stronger the resultant synchronization. Due to the unintended or unintentional nature of such spontaneous synchronization, the strength of the coupling between the movements of the actor and an external rhythm is often insufficient for the occurrence of stable in-phase and antiphase coordination for long periods of time (Richardson, Marsh et al., 2007; Schmidt et al., 2007; Schmidt & O Brien, 1997). In-phase and antiphase coordination usually occur only intermittently. The coupling is even Correspondence address: Manuel Varlet, The MARCS Institute, University of Western Sydney, Locked Bag 1797, Penrith NSW 2751, Australia. e-mail: M.Varlet@uws.edu.au 1

M. Varlet, R. C. Schmidt, & M. J. Richardson sometimes insufficient to result in any synchronization, and thus, the synchrony occurring in such a situation is not greater than the one that can simply occur incidentally or by chance despite the movements of the environmental rhythm being observed by the actor (Richardson, Marsh et al., 2007; Schmidt et al., 2007; Schmidt & O Brien, 1997). Researchers have argued that the emergence and stability of movement synchronization are also driven by the magnitude of the noise in the system (Kay, 1988; Richardson, Lopresti-Goodman, Mancini, Kay, & Schmidt, 2008; Richardson, Schmidt, & Kay, 2007; Sch oner et al., 1986). Coming from the neural and metabolic microstructure of the motor system, as well as more macroscopic environmental noise, there are continuous slight perturbations to the rhythmic movements which result in small fluctuations around individuals intrinsic frequency and amplitude (Fuchs & Kelso, 1994; Rosenblum & Turvey, 1988). Such fluctuations have been observed experimentallyatthelevels of the kinematics and neuromuscular activities of individuals producing coordinated rhythmic movements (Kelso & Scholz, 1985) and modeled by Sch oner et al. (1986) by adapting the Haken-Kelso-Bunz coupled oscillator model using stochastic equations. Components oscillating with greater magnitudes of noise or under conditions that entail greater environmental noise are understood to result in weaker states of synchronization (Sch oner et al., 1986). Greater magnitudes of noise in the system shall continuously perturb and push the movements away from in-phase and antiphase synchrony. Changes at the level of the magnitude of noise in motor systems have been often investigated as potential origins of the weaker synchronization occurring with pathologies, aging, or additional degrees of freedom for example (Richardson et al., 2008; Temprado, Vercruysse, Salesse, &Berton,2010;Varoqui,Froger,Lagarde,Pelissier,& Bardy, 2010). Accordingly, it would be assumed that greater magnitude of noise in the movements of an actor and an environmental stimulus should be detrimental to the occurrence and stability of spontaneous visuomotor synchronization. In contrast to this traditional view, recent research has shown that noise in biological systems is not necessarily detrimental and can actually in some circumstances improve their functioning (McDonnell & Ward, 2011; Moss, Ward, & Sannita, 2004, Riley & Turvey, 2002; Stergiou & Decker, 2011). Evidence comes from research that investigated stochastic resonance phenomenon occurring in nonlinear threshold systems and how the addition of noise can facilitate the detection and transmission of weak signals (for reviews, see Gammaitoni, H anggi, Jung, & Marchesoni, 1998; Moss et al., 2004). It has been found for example that detection of an environmental stimulus can be enhanced by internal noise in the brain and external noise in the stimulus (Moss et al., 2004). Enhanced detection actually depends on the interplay between the magnitudes of these two kinds of noise (Aihara, Kitajo, Nozaki, & Yamamoto, 2010). There is also growing evidence of constructive effects of noise or variability on the functioning of the human motor systems (Latash, Scholz, & Sch oner, 2002; Riley & Turvey, 2002; Stergiou & Decker, 2011). These constructive effects of noise, however, differ from the phenomenon of stochastic resonance, in that movement noise or variability appears to improve the efficiency of motor systems by increasing their flexibility and adaptability to changing external constraints (Riley & Turvey, 2002; Stergiou & Decker, 2011). Movement variability within the human perceptuomotor system can also facilitate the exploration of environmental constraints (Riccio, 1993). These different results support the possibility that internal noise in the movement of an actor and external noise in the movement of an environmental stimulus could actually be beneficial to the occurrence and stability of spontaneous visuomotor synchronization and that these two kinds of noise may interact with each other. The hypothesis that small magnitudes of noise or movement variability might enhance visuomotor synchronization is also supported in the mathematical literature, which has demonstrated how noise can facilitate the synchronization of weakly coupled oscillators (Kiss, Zhai, Hudson, Zhou, & Kurths, 2003; Zhou, Kurths, Kiss, & Hudson, 2002), similar to the intermittent spontaneous or unintentional synchronization that can occur between the movement of an actor and an external visual rhythm (Lopresti-Goodman et al., 2008; Richardson, Marsh et al., 2007; Schmidt et al., 2007; Tognoli et al., 2007; van Ulzen et al., 2008). The current study thus investigated this possibility using an unintentional or spontaneous visuomotor synchronization task that manipulated the magnitude of external noise in stimulus movement and indexed the magnitude of internal noise in participants movement (Lopresti-Goodman et al., 2008; Schmidt et al., 2007; Varlet, Coey, Schmidt, & Richardson, 2012). More specifically, we examined the degree to which the preferred handheld pendulum swinging of participants with low and high magnitudes of frequency variations became spontaneously synchronized with a visual stimulus that oscillated horizontally with different magnitudes of frequency fluctuations. We also manipulated the average or intrinsic frequency of the stimulus. The frequency was either equal to the participant s preferred movement frequency, slightly faster or slightly slower (Lopresti-Goodman et al., 2008). The difference between participants preferred and stimulus frequency was manipulated because it may mediate the influence of internal or external noise on the synchronization. Indeed, the synchronization process might benefit from greater magnitudes of noise when participants preferred and stimulus frequencies are different by facilitating exploration and adaptability to in-phase and antiphase synchrony. In contrast, noise was expected to be detrimental when the participant and stimulus movement frequencies are similar by 2 Journal of Motor Behavior

Movement Noise and Entrainment perturbing the system away from a state of inphase or antiphase synchrony. Method Participants Twenty-eight undergraduates from the University of Cincinnati participated in the experiment for partial course credit. All participants had normal or corrected-to-normal vision. The experiment was approved by the University of Cincinnati s Institutional Review Board and informed consent was obtained from each participant. Apparatus Participants sat in a chair positioned parallel to the sagittal plane and a 140 180 cm projection screen. The chair had a forearm support parallel to the ground on the righthand side, on which the forearm of participants was positioned to swing a handheld pendulum in the sagittal plane using ulnar-radial deviation of the wrist joint (see Figure 1A). The pendulum was constructed from a wooden dowel measuring 45 cm in length and had a 75 g plastic weight attached to its base, resulting in a gravitational eigenfrequency of 0.9 Hz. A 1 cm 1 cm 1.5 cm FAS- TRAK motion-tracking sensor (Polhemus Ltd., Colchester, VT) was fixed to the pendulum. It recorded the oscillations performed by participants at a sampling rate of 60 Hz with a 0.01 mm spatial resolution. A PC computer (Dell Inc., Round Rock, TX) both recorded the pendulum oscillation time series and controlled the stimulus displays. The stimulus displays were projected on the screen using an Epson Powerlite 53 c projector (Epson America, Long Beach, CA). The stimulus was a red dot (diameter of 8 cm) in which letters that participants had to read appeared for 200 ms every 2 s plus a random offset between zero and 0.999 ms. Participants wore modified safety glasses that prevented them from seeing the pendulum or their wrist movements, but ensured that they could see everything displayed on the screen. Design and Task The study was divided in two sessions. In the first session, participants were instructed to swing the pendulum while reading letters that appeared on a stationary stimulus displayed in the middle of the screen. This preliminary session allowed the determination of the participant s preferred movement frequency as well as their natural frequency variability (Schmidt et al., 2007). In the second session, participants performed the pendulum-swinging task under two different conditions: a tracking and a control condition (Lopresti-Goodman et al., 2008; Schmidt et al., 2007; Varlet, Coey et al., 2012; see Figure 1A). During the tracking condition, a moving stimulus with letters appearing on it oscillated horizontally across the projection screen. In order to read the letters, participants had to track the oscillation of the stimulus with their eye movements. During the control condition, as in the preliminary session, participants read letters that appeared on a stationary stimulus in the middle of the screen. Note that no moving stimulus was displayed on the screen in the control condition, but participants movements were still recorded in order to assess the synchrony that could occur incidentally or by chance (i.e., without coupling) between participant s movement and the movement of the different stimuli presented in the tracking conditions. The participant s movement time series recorded in the control condition and the movement time series of the different stimuli presented in the tracking conditions were combined a posteriori to compute an incidental or chance participant-stimulus synchrony (see data reduction and analysis section for further details about the computation). This control synchrony was computed separately for all the different FIGURE 1. Experimental setup and example of collected time series. (A) The handheld pendulum coordination task used in the study. (B) Movement time series of a participant (grey line) and of the stimulus (black line) typically obtained in visual tracking condition with spontaneous and intermittent synchronization over time. (C) The corresponding computed continuous relative phase. 2015, Vol. 0, No. 0 3

M. Varlet, R. C. Schmidt, & M. J. Richardson stimulus frequency and noise conditions because manipulating the properties (frequency and noise) of the stimulus time series can influence not only the occurrence of synchronization but also the occurrence of simple chance or incidental synchrony. Indeed, independent of the presence of any visual coupling and active process of synchronization, a participant might be more likely to move incidentally with a stimulus that oscillates at a frequency equal to her or his preferred tempo, for example. The frequency of the horizontally oscillating stimulus was manipulated. The stimulus oscillated either with a frequency equal to the preferred frequency of the participant (determined in the first session) or with a frequency offset of 12.5% (for similar manipulations, see Lopresti-Goodman et al., 2008). Additionally, the magnitude of the stochastic noise or frequency fluctuations of the stimulus oscillation was also manipulated. Three magnitudes of noise were added to the stimulus that equaled standard deviations of 0%, 3%, or 6% of the mean frequency. The frequency fluctuations were added by slightly lengthening or shortening each stimulus period, such that the stimulus frequency changed between cycles but remained constant within each cycle. These changes of frequency occurred at each right turning points of the oscillating stimulus trajectory. As in Richardson, Schmidt, and Kay (2007), the noise added or subtracted to each stimulus period was generated a priori in the form of random number time series that were normally distributed with a mean of 0 and standard deviation of 1. In addition, no value in these time series was greater or less than two standard deviations from zero and the absolute deviation from one value to the next one was always less than two standard deviations apart. The stimulus period of each cycle was then determined by adding these random number time series (randomly selected) multiplied by the stimulus period (preferred period of participants or 12.5%) to the stimulus period. Such an implementation of the noise in the stimulus time series assured that the stimulus frequencies were never greater than 6% or 12% of its average value in the 3% or 6% stimulus noise conditions, respectively. It also assured that cycleto-cycle frequency variations of the stimulus in the 3% or 6% stimulus noise conditions were respectively never greater than 6% or 12% of its average value. Cycle-to-cycle stimulus frequency series generated for the different stimulus frequency and stimulus noise conditions of a representative participant are displayed in Figure 2. For all these conditions, the stimulus oscillated with an amplitude of 80 cm, which corresponded for participants to a visual angle of approximately 60. Procedure On arrival, the participants were informed that the experiment was investigating multitask performance. FIGURE 2. Cycle-to-cycle stimulus frequency series generated for the different stimulus frequency and stimulus noise conditions of a representative participant. 4 Journal of Motor Behavior

Movement Noise and Entrainment They were told they would be required to swing a handheld pendulum while reading out loud letters that appeared on the screen. They were instructed to keep their forearm on the support, to grasp the pendulum firmly in the hand and swing it using the wrist joint in a back and forward motion. A practice period was given to the participants to experience the dual task of swinging the pendulum while reading letters flashing on the screen as well as time to explore their preferred movement frequency. The participants were also told to call out the letters appearing on the screen as fast as possible and to keep swinging the pendulum at their comfort tempo; the tempo that you could swing all day if you have to. Following this practice period, participants performed two trials in a preliminary session to determine their preferred movement frequency and natural frequency variability. They then performed 18 trials two trials for each of the three stimulus frequencies by three stimulus noise combinations for the tracking condition and then two trials for the control condition (again, the control trials were included to provide a measure of chance level synchrony for the different stimulus frequency and stimulus noise conditions). The duration of the trials was 45 s. The order of the trials was randomized. Finally, to ensure that the synchronization of the participants was spontaneous a funnel debriefing procedure was performed to determine if they guessed the true purpose of the study and if they were aware or noticed if their movements became synchronized with the stimulus. Some participants noticed that their movement was sometimes in synchrony with the stimulus but none of them guessed that the study was investigating spontaneous movement synchronization. All participants reported that they did their best to perform the letter detection task whilekeepingoscillating the pendulum at their preferred tempo. Data Reduction and Analysis The collected movement time series were centered around zero and low-pass filtered using a 10 Hz Butterworth filter. The first 5 s of each trial was discarded to eliminate transient behavior. The time between the points of maximum angular extension as defined by the maxima of the movement time series was then computed to determine the average preferred movement frequency of participants and their corresponding coefficient of variation (COV; COV D SD/Mean 100), which indexed the magnitude of the frequency variability inherent in the preferred swinging movement of participants. Two different measures were used to determine the degree of the pendulum-stimulus synchrony. They both evaluated the synchrony on a scale from 0 to 1, with 1 reflecting a perfect synchrony and 0 reflecting an absence of synchrony. The first measure was the circular variance of relative phase angles between the stimulus and participant time series (Batschelet, 1981; Tognoli et al., 2007; Varlet, Marin et al., 2012). The relative phase was calculated as f.t/ D u 1.t/ u 2.t/ where u 1.t/ and u 2.t/ were respectively the phase angles of the stimulus and the participant computed as uðþd t arctan. _xðþ=x t ðþ/; t where _xðþ t was the velocity (normalized in terms of the mean angular frequency of each half-cycle (for details, see Varlet & Richardson, 2011) and xt ðþ was the position (Kelso, 1995). The circular variance was then calculated as V D 1 jrj; where R was computed for N relative phase points as R D 1 N X N t D 1 e i.f.t// The second measure was the average cross-spectral coherence corresponding to the correlation between the stimulus and participant movements in the frequency domain (Richardson, Marsh et al., 2007; Schmidt & O Brien, 1997). Given time series x and y (i.e., participant and stimulus movement time series), the coherence K xy at a given frequency f i was computed as the ratio of the square of the cross-spectrum F xy divided by the product of the spectra of the individual series (F xx and F yy ): K xy.f i / D jf xy.f i /j 2 = F xx.f i /F yy.f i / For the statistical analysis, being bounded by 0 and 1, the values of the indexes of synchrony were p standardized ffiffi using an arcsine transformation (y D arcsin x where x and y correspond to the initial and transformed values, respectively) to promote the homogeneity of the variance and the normality of the distributions (Winer, Brown, & Michels, 1991). In order to examine whether the magnitude of natural variability in participants preferred swinging influenced their entrainment with the stimulus, participants were divided for the statistical analysis into low and high variability groups as a function of their COV using a median split. Arcsine standardized values were then submitted to a 2 2 3 3 repeated measures analysis of variance (ANOVA) with the factors group (low, high), visual condition (tracking, control), stimulus frequency (preferred, preferred C 12.5%, preferred 12.5%) and stimulus noise (0%, 3%, and 6%). The values for the control condition (in the factor visual condition) corresponded to the indexes of synchrony 2015, Vol. 0, No. 0 5

M. Varlet, R. C. Schmidt, & M. J. Richardson obtained for the two control trials with the different stimulus frequency and noise time series presented to the participant in the tracking condition. In other words, we associated a posteriori the stimulus time series presented to participants in their tracking condition (e.g., stimulus frequency C12.5% and noise 3%), with the movement time series of participants recorded in their control trials (no moving stimulus) and the indexes of synchrony between these two time series were computed to obtain chance level synchrony values of the control condition in this specific condition (i.e., stimulus frequency C12.5% and noise 3%). The stimulus time series (and thus the stimulus frequency and noise) used to compute the indexes of synchrony were thus identical in the control and tracking conditions, which allowed distinguishing the effects of stimulus properties on the occurrence of incidental or chance synchrony and on the occurrence of synchronization. Indeed, synchrony can increase in a tracking condition without being different from the corresponding control condition indicating that frequency and noise properties of the stimulus in this condition only increased the chance that a participant and a stimulus move incidentally together. Inversely, synchrony can increase in a tracking condition and not in the corresponding control condition revealing that this condition strengthened the process of synchronization. Newman-Keuls post hoc comparisons were used to determine the nature of the effect when necessary. Results Corroborating previous research (Kugler & Turvey, 1987; Schmidt et al., 2007), the analysis of the preferred movement of participants in control pretrials (without oscillating stimulus) determined an average preferred frequency of 0.85 Hz (SD D 0.07), close to the pendulum s gravitational eigenfrequency, and normalized coefficient of COV values from 1.98% to 5.93% (M D 3.53; SD D 0.95). The low and high variability groups had a mean COV of 2.79 (SD D 0.39; n D 14) and 4.27 (SD D 0.72; n D 14), respectively. As expected, the values of synchrony (all below 0.6; see Figure 3 presenting circular variance values) indicate that participants movement became synchronized with the stimulus only intermittently. The ANOVAs on relative phase circular variance and coherence values yielded significant four-way interactions between the factors group (low, high), visual condition (tracking, control), stimulus frequency (preferred, preferred C 12.5%, preferred 12.5%), and stimulus noise (0, 3 and 6%), F(4, 104) D 3.46, p <.05, h 2 p D 0.12; and F(4, 104) D 3.56, p <.05, h 2 p D 0.12, respectively. Significant main effects and significant lower order interactions (not reported here) were identical for the two variables. When the stimulus oscillated at the preferred movement frequency of participants, Newman-Keuls post hoc tests revealed that for both relative phase circular variance and coherence values only the low-cov group exhibited greater than chance (control) level synchrony in the visual tracking condition and that this synchronization appears only when the stimulus noise equaled 0% (all ps <.05; see Figure 3). These results demonstrate that when there was no difference between the stimulus movement frequency and the preferred frequency of participants, spontaneous synchronization only occurred when internal noise in participants movement and external noise in stimulus movement were minimal. When the stimulus oscillated faster than the preferred movement frequency of participants (i.e., C12.5%), however, post hoc analyses showed an entirely different pattern. Post hoc analyses revealed for the two measures of synchrony that only high-cov participants exhibited greater than control level synchrony in the visual tracking condition and that this was the case for both the 0% and 3% stimulus frequency variation conditions (all ps <.05; see Figure 3). These results therefore demonstrate that greater magnitude of internal noise in participant s movement can facilitate the emergence of spontaneous visuomotor synchronization when the frequency of the stimulus is faster than participants preferred movement frequency. When the stimulus oscillated slower than the preferred movement frequency of participants, post hoc tests also revealed that only the high-cov group exhibited significantly greater than chance level synchrony for the 0% stimulus noise condition (all ps <.05). This result provides further evidence that greater magnitude of internal noise in participant s movement can facilitate the emergence of spontaneous visuomotor synchronization when there is a difference between her or his preferred frequency and the stimulus frequency. Interestingly, when the stimulus oscillated slower than the preferred movement frequency of participants, post hoc tests also revealed that although no difference occurred for the low-cov group between the tracking and control (chance) conditions for frequency variations of 0% and 3% (all ps >.05), a significant difference appeared for 6% stimulus noise condition (p <.05 and p D.09 for relative phase circular variance and coherence values, respectively). Accordingly, this result indicates that when there is a difference between participants preferred and stimulus frequency, synchronization can also be facilitated by external noise in stimulus movement. However, why larger variance (i.e., 6%) was needed for the facilitating effects of external movement noise to be observed for the low-cov group remains to be determined. One possibility is that the movements of the low-cov group were inherently more stable, and thus a greater overlap between the participants and stimulus movements was needed in order to induce intermittent synchronization. However, it is important to note that external noise facilitated synchronization for the low-cov group, but degraded synchronization of the high-cov group, showing that synchronization depends on interplay between internal and external noises. 6% stimulus noise in the slower stimulus 6 Journal of Motor Behavior

Movement Noise and Entrainment FIGURE 3. Synchronization between the participant and stimulus movements (circular variance of the relative phase) as a function of the visual condition and stimulus frequency for the low and high coefficient of variation groups and stimulus noise of 0%, 3%, and 6%. The error bars represent standard error of the mean. The asterisks represent significant differences between tracking and control conditions. The patterning of results for the cross-spectral coherence dependent variable (not presented here) was similar. condition facilitated synchronization for the low-cov group, but degraded synchronization of the high-cov group compared to the 0% stimulus noise condition. Facilitative effects observed for the high-cov group in slower and faster stimulus conditions did not occur when stimulus noise respectively equaled 3% or 6% (i.e., no difference between the tracking and control conditions; all ps >.05). Internal noise facilitated synchronization when there was no or low external noise and external noise facilitated synchronization when internal noise was minimal. In summary, the magnitude of internal and external noises together has to be moderate in order to strengthen synchronization when participants preferred and stimulus frequencies are different. Discussion The current study investigated the constructive effects of internal noise in the movement of an actor and external noise in the movement of an environmental stimulus on the occurrence of spontaneous visuomotor synchronization. More specifically, we examined the influence of internal and external frequency noises on the spontaneous or unintentional synchronization that occurred between the pendulum swinging of participants and an oscillating visual stimulus. By manipulating the magnitude of frequency noise in stimulus movement and indexing the internal noise in participants movement, the results demonstrate that synchronization depends on a complex interplay between internal noise in participants movement, external noise in stimulus movement and the difference between participants preferred and stimulus frequency. Results showed that both internal and external noises degrade the synchronization when participants preferred and stimulus frequencies are similar, but that internal and external noises can facilitate synchronization when these frequencies are different. We now discuss these results in turn. Corroborating previous research, the results showed that participants movements became spontaneously and intermittently synchronized with the oscillating stimulus when visually tracking its displacements and that the synchronization was mediated by the difference between the participant s preferred and the observed stimulus frequency (Lopresti-Goodman et al., 2008; Schmidt et al., 2007; Varlet, Coey et al., 2012). The results of the current study extend these previous findings by showing that the synchronization was also mediated by the magnitude of the internal and external noises, an effect that depended on the difference between the frequencies of the participant s preferred movements and the stimulus movements. Synchronization depends on a complex interplay between participants internal noise, stimulus external noise and the difference between participants preferred and stimulus frequency. When there was no difference between the two frequencies, the results were consistent with the traditional proposal that movement noise is detrimental to movement synchronization (Kay, 1988; Richardson, Schmidt, & Kay, 2007, 2008; Sch oner et al., 1986): Greater synchronization than chance 2015, Vol. 0, No. 0 7

M. Varlet, R. C. Schmidt, & M. J. Richardson (control) level synchrony only occurred for participants with the lowest internal or intrinsic movement variability and when the magnitude of the external stimulus noise equaled zero. In other words, movement synchronization only occurred for the lowest magnitude of noise possible in the system (i.e., when internal and external noises together were minimal). The results, however, contrast with this traditional view when the frequencies of the participants preferred movements and the stimulus movements were different. In fact, we found that both internal noise in participants movement and external noise in the movement of the stimulus being observed, can facilitate synchronization and that these two kinds of noise interact with each other. The results demonstrate that participants with greater magnitudes of internal movement noise or variability (high-cov group) exhibited stronger movement synchronization when observing stimuli oscillating faster or slower than their preferred frequency. This facilitation is likely due to the fact that internal movement (in this case, frequency) noise or variability is a signature of movement flexibility participants that were not tightly locked to one specific movement frequency were more likely to become synchronized across a greater range of stimulus frequencies. This assumption is in line with the results reported for other biological systems, such as the heart for example, for which it has been shown that a natural degree of variability of beat-to-beat intervals is a signature of a healthy, flexible and robust cardiovascular system (Edelman & Gally, 2001; Goldberger et al., 2002). Interestingly, the results also demonstrated that when the frequencies of the participant s preferred movements and the stimulus movements are different, the synchronization is also facilitated by external noise or fluctuations. Such external, stimulus noise, may have played a constructive role in the current study by inducing a variable exploration of different synchronization states (Kelso, de Guzman, Reveley, & Tognoli, 2009; Riccio, 1993), or by perturbing the participants movements away from their preferred natural frequencies and toward frequencies more conducive to the emergence of synchronization. Such external stimulus noise was, however, only beneficial for participants that had a low level of internal movement noise (low-cov group). Alternatively, the external noise became detrimental for participants that had high level of internal movement variability (high-cov group), showing that the effects of internal and external noises interact with each other and are magnitude dependent. External noise facilitates spontaneous synchronization of an actor with low magnitude of internal noise whereas external noise degrades synchronization of an actor with high magnitude of internal noise. Only small to moderate magnitudes of total noise in the system (i.e., internal and external noises together) facilitated the synchronization when participants preferred and stimulus frequency are different. While small or modest magnitudes of noise might facilitate the exploration of, and thus, the entrainment to preferred patterns of coordination, greater magnitude of noise seems to produce too many fluctuations that continuously perturb the movement system away from a synchronized state. Too little variability or noise and the system can become too rigid, with a decreased basin of frequency entrainment (Lopresti-Goodman et al., 2008). In other words, too low or too high variability results in too much order or disorder, respectively, both impeding the adaptive and flexible functioning of coordinated movement systems (Edelman & Gally, 2001; Goldberger et al., 2002; Riley & Turvey, 2002; Stergiou & Decker, 2011). However, a number of questions remain. For example, why did the low variability group unintentionally synchronized to the stimulus in the 6% noise condition when the stimulus was slower than the preferred frequency but not when the stimulus was faster? Moreover, why did they not synchronize in the 3% noise condition if this is a moderate level of noise? Furthermore why did the high variability group unintentionally synchronize to the stimulus in the 3% noise condition when the stimulus moved faster than the preferred frequency but not slower? These questions raise the necessity of further explorations to better determine the optimum level of internal and external noises in the system and how it could depend on the intrinsic or preferred frequency of the movements. The present results also raise the possibility that the kind of noise in the movements may have mediated the synchronization. In fact, period-to-period changes in participants movements were more correlated than in stimulus movements, 1 which might have resulted in different effects of noise despite similar magnitudes. Previous research has shown that the structure of the noise or variability in biological systems, and human movement systems in particular, could better reflect the flexibility, adaptability and functional behavior of the systems (Hausdorff et al., 1997; Lipsitz & Goldberger, 1992;Vaillancourt & Newell, 2002). For example, pathologies can affect the structure of the noise or variability without affecting its magnitude (Lipsitz & Goldberger, 1992). Accordingly, optimal structures of frequency variability in participants and/or stimulus movements might also facilitate spontaneous visuomotor synchronization. Future research may well benefit from controlling the variability structure in participants movement and employing both correlated and uncorrelated noise structures for stimulus movements (Hunt, McGrath, & Stergiou, 2014; Rhea, Kiefer, D Andrea, Warren, & Aaron, 2014; Torre, Varlet, & Marmelat, 2013). The facilitating effects of external stimulus noise may be strengthened with more correlated structures. In conclusion, this study demonstrates that the occurrence of spontaneous visuomotor synchronization depends on a complex interplay between internal noise in the actor s movement, external noise in the stimulus movement and the difference between the actor s preferred and stimulus frequency. Internal and external noises in spontaneous visuomotor synchronization can play both a facilitating as 8 Journal of Motor Behavior

Movement Noise and Entrainment well as a detrimental role (Riley & Turvey, 2002; Stergiou & Decker, 2011). While it is true that internal and external movement noises can both degrade synchronization, this only appears to be the case when the movements of the actor and the stimulus have the same intrinsic frequencies or when the magnitude of the total noise in the system (internal and external together) becomes too high. When the components have different intrinsic frequencies, which is more often the case during everyday situations, small to moderate magnitudes of internal and external noises can facilitate synchronization. Before extending these conclusions to human rhythmic coordination in general, however, future research will have to confirm that the features of the synchronization task used in the present study were not responsible of the constructive effects of noise observed. Indeed, the visual coupling, its unidirectionality (nonadaptive stimulus), and weak strength (resulting in intermittent synchronization), are properties that may have facilitated the positive effects of noise observed in the present study. Our findings thus encourage further explorations to determine the processes underlying the constructive effects of movement noise, including the degree to which the presence or absence of movement variability might underlie the movement synchronization deficits known to occur with aging and for several pathologies (e.g., poststroke, Parkinson s disease, schizophrenia). NOTE 1. Lag 1 to lag 5 of the autocorrelation function were significantly positive for participants movements (tested in pretrials) whereas only the lag 1 was significantly positive for stimulus movements (p <.05). FUNDING This research was supported by the National Science Foundation (BCS Awards: 0750190, 0750187, 0926662). 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