Timing and Phase Locking in Cascade Juggling

A natural-physical approach is pursued in uncovering basic timing and phase relations in human rhythmic movement. The approach is based on the theory of nonlinear oscillatory motion, entrained by continuously and discretely distrib- uted forcing. In the context of juggling three balls in a figure-eight pattern, a preliminary modeling attempt of the cyclical hand motion suggested that the dynamics underwriting juggling are captured best by a discretely kicked, highly nonlinear, self-sustained oscillator. Discretely kicked, nonlinear oscillators may be characterized by regime diagrams that depict the periodic (phase-locked) and quasiperiodic (not phase-locked) regimes in which the system can operate depending on the magnitude of the kicks. This article provides evidence for 2-quasiperiodicity and near, but not perfect, phase locking between tl/tf and tu/tf (where tl is the mean time that the hands move loaded with a ball, tu is the mean time that the hands move empty, and tf is the mean flight time of the balls). Jugglers perform along the boundaries of Arnol'd tongues (representing complete phase locking) in a regime diagram without actually entering into them. With the help of Denjoy's decomposition of phase modulation into a fast and a slow mode, the deviation from the potential minimum defined by complete phase locking can be understood. The frequency ratios within the continuous relative phase between the two juggling hands reveal a Farey type of phase-locking structure, allowing a qualitative insight into which regimes jugglers position themselves when asked to speed up or slow down their act. Modulation of the hand movements increases when timing constraints become more severe (e.g., when the number of balls in the air increases). The modified standard map promises to he an adequate tool in analyzing the phase progression in juggling. All in all, the results favor an understanding of rhythmic movement in terms of discretely forced, nonlinear dynamics, rather than fully autonomous, self-sustaining oscillators.     

One-Handed Juggling: A Dynamical Approach to a Rhythmic Movement Task

The skill of rhythmically juggling a ball on a racket was investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system were analyzed by means of local and nonlocal stability analyses. These analyses showed that the task dynamics offer an economical juggling pattern that is stable even for open-loop actuator motion. For this pattern, two types of predictions were extracted: (a) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball, and (b) a nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment in which subjects (N = 6) performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The following predictions were confirmed: (a) For stable rhythmic performance, the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; and (b) for each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results permit one to conclude that humans reliably exploit the stable solutions inherent to the dynamics of the given task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle for generating different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.     

Pattern Stability and Error Correction During In-Phase and Antiphase Four-Ball Juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Pattern stability and error correction during in-phase and antiphase four-ball juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Constrained paths based on the Farey sequence in learning to juggle

In this article we report the results of a study conducted to investigate the learning dynamics of three-ball juggling from the perspective of frequency locking. Based on the Farey sequence, we predicted that four stable coordination patterns, corresponding to dwell ratios of 0.83, 0.75, 0.67, and 0.50, would appear in the learning process. We examined the learning process in terms of task performance, taking into account individual differences in the amount of learning. We observed that the participants acquired individual-specific coordination patterns in a relatively early stage of learning, and that those coordination patterns were preserved in subsequent learning, even though performance in terms of number of successful consecutive throws increased substantially. This increase appeared to be related to a reduction in spatial variability of the juggling movements. Finally, the observed coordination patterns were in agreement with the predicted patterns, with the proviso that the pattern corresponding to a dwell ratio of 0.50 was not realized and only a hint of evidence was found for the dwell ratio of 0.67. This implies that the dwell ratios of 0.83 and 0.75 in particular exhibited a stable coordination structure due to strong frequency locking between the temporal variables of juggling.     

Effects of attentional-focus instructions on movement kinematics

BackgroundRecent research has shown that internal (body-related) attention-focus instructions disrupt motor learning and performance, whereas paying attention to the environmental effects of movements (external focus) leads to better performance than an internal focus [see, for reviews, Wulf, G. (2007). Attentional focus and motor learning: a review of 10 years of research. E-Journal Bewegung und Training, 1, 4–14.; Wulf, G., &; Prinz, W. (2001). Directing attention to movement effects enhances learning: a review. Psychonomic Bulletin &; Review, 8, 648–660.]. However, Beilock's studies [Beilock, S. L., Bertenthal, B. I., McCoy, A. M., &; Carr, T. H. (2004). Haste does not always make waste: expertise, direction of attention, and speed versus accuracy in performing sensorimotor skills. Psychonomic Bulletin &; Review, 11, 373–379.] suggest that an internal focus is detrimental in experts but not in novices. Because detrimental effects of consciously attending to movements have generally been measured by performance scores such as accuracy scores or reaction times, it remains unclear how internal and external attentional-focus instructions influence movement kinematics when learning a new skill. To fill this gap, the present study investigated attentional-focus effects on a biomechanical level.MethodsA video of an expert juggler demonstrating a two-ball juggling task was presented to juggling novices. Experimental groups were given either body-related (internal group) or ball-related (external group) verbal instructions or no attention-guiding instructions (control group). In the retention phase without attention-guiding instructions, the body-movement and ball-flight aspects of performance focused on in the verbal instruction were subjected to biomechanical analyses.Results and ConclusionsJuggling performance improved equally in all three groups. However, internally vs. externally instructed acquisition phases had differential effects on the kinematics of the upper body as well as ball trajectories when performing the juggling task. Remarkably, ball trajectories in the control group who received no specific attentional cueing were similar to those in the externally instructed group. This suggests that task-relevant information is picked up independently of instructions, and that external instructions provide redundant information. Internal instructions for object-related tasks, however, may confront novice learners with the need to process additional information. As a result, task difficulty might be unnecessarily enhanced in an observational learning setting.     

Temporal patterning in cascade juggling.

A key variable in cascade juggling is the proportion of time that a juggler holds onto a juggled object during a hand cycle, that is, the time from catch to throw in relation to the time from catch to catch. Space-time constraints and principles of frequency locking suggest 3/4 as the primary ratio and 2/3 and 5/8 as the most accessible options. In 5 experiments, object number, mass, and type (ball or scarf) were manipulated together with the frequency at which the objects were juggled. With 5 or 7 balls, the ratio was 3/4, independent of frequency. With 3 balls, the ratio decreased with frequency, with 3/4, 2/3, and 5/8 tending to predominate independently of the force variations induced by variation in object mass. With 3 scarves, ratios varied inversely with frequency and often exceeded 3/4. Implications for a dynamical theory of juggling were discussed with the issue of relative timing in coordination and the manipulation of task constraints as an experimental strategy.     

Phasing and the Pickup of Optical Information in Cascade Juggling

Four experiments were conducted to examine the relationship between the phasing of hand movements and the pickup of optical information in cascade juggling. Three jugglers of intermediate skill juggled three balls while wearing liquid crystal (LC) glasses that opened and closed at preset intervals. The first experiment, in which the duration of the viewing window was gradually reduced to zero, revealed a preference for seeing the segment of the ball flight following the zenith in one subject; such a preference was hinted at in the other two subjects. The second experiment, in which the tachistoscopic rhythm of the glasses was perturbed, showed that, in the case of a stable phase lock, the phasing of the hand movements was adjusted to restore the visibility of the segment following the zenith when it was lost. The third experiment, however, revealed that, after practice, the jugglers did not become better attuned to the optical information contained in this segment. The fourth experiment, in which two jugglers per- formed a cascade together while viewing the ball flights intermittently, suggested that haptic information about the trajectories of the balls to be caught is not necessary for subsequent catching: Optical information picked up during brief intervals of viewing was sufficient to perform the task equally well as when they juggled alone (i.e., when haptic information about the throws was available). Although, admittedly, the results raised only a tip of the veil covering the perceptual basis of juggling, they testify to the potential power of the new technique that was used to let subjects themselves reveal what optical information is relevant for performance.     

Goal-directed imitation: the means to an end

The effects of goal-directed imitation and observational learning were examined whilst learning a goal-directed motor skill (three-ball cascade juggling). An observational learning (OL) group observed a model and a control (CON) group received minimal verbal instructions regarding how to hold and release the juggling balls. The OL group performed more juggling cycles across practice and retention than the CON group. In addition, the OL group's upper limb coordination and ball flight trajectory pattern were more similar to the model's movements than the CON group. These data show that when the to-be-learnt movement pattern and end-goal are not specified by the task's mechanical constraints, or can be achieved by modifying a pre-existing motor skill, individuals have difficulty learning on the basis of discovery processes alone. Under these circumstances, observational learning is effective because it conveys to the individual the specific means by which the end-goal can be achieved. These findings lead us to suggest that when the end-goal and the means to achieve the end-goal are directly linked, the means are given sufficient weight in the goal hierarchy such that the model's movement is imitated.     

Learning the cascade juggle: a dynamical systems analysis

How beginning jugglers discover the temporal constraints governing the juggling workspace while learning to juggle three balls in a cascade pattern was the subject of this investigation. On the basis of previous theoretical and experimental work on expert jugglers, we proposed a three-stage model of the learning process, for which objective evidence was sought. The first stage consists of learning to accommodate the real-time requirements of juggling, as expressed in Shannon's equation of juggling, which states that, averaged over time, the cycle time of the hands should be a fixed proportion of the cycle time of the balls. The second stage of learning consists of discovering the primary frequency lock of.75 between the shorter term dynamical regime underlying the repetitive subtask of transporting a ball and the longer term dynamical regime underlying the total hand loop cycle. The third and last stage of learning consists of discovering the principles of frequency modulation from.75 to lower (averaged) values of the proportion of time that a hand carries a ball during the total hand cycle time. Twenty subjects were taught to juggle three balls in a cascade pattern. Ten subjects were trained with the aid of an instructor and a metronome, and 10 with the instructor only. The metronome proved to be of no particular additional help, but the timing results obtained were in agreement with the proposed three stages of learning. The picture that emerged from this study was that learning a new motor skill involves the discovery of invariance's or fixed points in the perceptual-motor workspace associated with that skill, from which excursions can be made and the skill further refined. Because these fixed points afford stability of operation, discovering them logically and factually precedes the acquisition of the functional adaptability and flexibility of operation ("flair") inherent to frequency modulation.     

Changes in smoking behaviors from late childhood to adolescence: insights from the Canadian National Longitudinal Survey of Children and Youth.

OBJECTIVE: To examine smoking behaviors in Canadian youth from late childhood to adolescence. By following participants from as young as 10 and 11 years, the authors proposed to identify distinct developmental pathways of smoking acquisition. DESIGN: Growth mixture modeling was used to identify developmental trajectories of smoking among 10- to 17-year-old participants of the Canadian National Longitudinal Survey of Children and Youth. MAIN OUTCOME MEASURES: Developmental trajectories of trying smoking, smoking frequency, and smoking intensity. Results: Five developmental trajectories related to smoking frequency were identified, of which 2 were acquisition patterns that led to daily smoking at age 16-17, and 3 were experimentation patterns that led to nonsmoking at age 16-17. The largest variability in changes in smoking behavior over time was the reported level of smoking frequency. CONCLUSION: Analysis showed that there is more than 1 way in which Canadian children and adolescents acquire smoking behaviors over time. The authors were able to differentiate patterns of experimentation from patterns of acquisition. Whereas experimentation has been generally considered as 1 of the stages in the smoking acquisition process leading to regular smoking, these results indicate that experimentation can be described as a distinct process in itself.     

Dynamical aspects of learning an interlimb rhythmic movement pattern

Learning a bimanual rhythmic task is explored from the perspective that motor skill acquisition involves the successive reparameterization of a dynamical control structure in the direction of increasing stability, where the intentional process of reparameterization is itself dynamical. Subjects learned to oscillate pendulums held in the right and left hands such that the right hand frequency was twice that of the left (2:1 frequency lock). Over 12 learning sessions of 20 trials each, we interpreted the decreasing fluctuations in the frequency locking to be an index of the increasing concavity of the underlying potential, a measure of stability; the time required to achieve the 2: 1 pattern was interpreted as indexing the relaxation time of an intentional dynamic. Power spectral analyses of the phase velocity ratio exhibited two strategies for acquiring the interlimb movement pattern: (a) adding spectral peaks at integer multiples of the left hand frequency or (b) distributing power across many frequencies in a l/f-like manner. Results are discussed in terms of the promise of a dynamical approach to learning coordinated movements.     

Quiet Eye Training Improves Small Arms Maritime Marksmanship

Quiet eye training—teaching task-specific gaze control—has been consistently shown to optimize the acquisition of motor skills. The present study aimed to examine the potential benefits of a quiet eye training intervention in a simulated maritime marksmanship task that involved shooting fast approaching moving targets with a decommissioned general-purpose machine gun. Twenty participants were randomly assigned to a quiet eye trained (QET) or technical trained (TT) group and completed 2 baseline, 20 training, and 2 retention trials on the moving-target task. Compared to their TT counterparts, the QET group displayed more effective gaze control (longer quiet eye durations and greater target locking) and more accurate performance (smaller radial error of both the initial shot and average of all shots) at retention. These findings highlight the potential for quiet eye training to be used to support the training of marksmanship skills in military settings.     

Practice effects on intra-team synergies in football teams

Developing synchronised player movements for fluent competitive match play is a common goal for coaches of team games. An ecological dynamics approach advocates that intra-team synchronization is governed by locally created information, which specifies shared affordances responsible for synergy formation. To verify this claim we evaluated coordination tendencies in two newly-formed teams of recreational players during association football practice games, weekly, for fifteen weeks (thirteen matches). We investigated practice effects on two central features of synergies in sports teams – dimensional compression and reciprocal compensation here captured through near in-phase modes of coordination and time delays between coupled players during forward and backwards movements on field while attacking and defending. Results verified that synergies were formed and dissolved rapidly as a result of the dynamic creation of informational properties, perceived as shared affordances among performers. Practising once a week led to small improvements in the readjustment delays between co-positioning team members, enabling faster regulation of coordinated team actions. Mean values of the number of player and team synergies displayed only limited improvements, possibly due to the timescales of practice. No relationship between improvements in dimensional compression and reciprocal compensation were found for number of shots, amount of ball possession and number of ball recoveries made. Findings open up new perspectives for monitoring team coordination processes in sport.     

Importance of head movements in gaze tracking during table tennis forehand stroke

The purpose of this study was to clarify the properties of gaze and head movements during forehand stroke in table tennis. Collegiate table tennis players (n = 12) conducted forehand strokes toward a ball launched by a skilled experimenter. A total of ten trials were conducted for the experimental task. Horizontal and vertical movements of the ball, gaze, head and eye were analyzed from the image recorded by an eye tracking device. The results showed that participants did not always keep their gaze and head position on the ball throughout the entire ball path. Our results indicate that table tennis players tend to gaze at the ball in the initial ball-tracking phase. Furthermore, there was a significant negative correlation between eye and head position especially in the vertical direction. This result suggests that horizontal VOR is suppressed more than vertical VOR in ball-tracking during table tennis forehand stroke. Finally, multiple regression analysis showed that the effect of head position to gaze position was significantly higher than that of eye position. This result indicates that gaze position during forehand stroke could be associated with head position rather than eye position. Taken together, head movements may play an important role in maintaining the ball in a constant egocentric direction in table tennis forehand stroke.     

Territorial gain dynamics regulates success in attacking sub-phases of team sports

Background and objective

Field invasion games, such as rugby union, can be conceptualised as dynamic social systems in which the agents continuously interact to contest ball possession and territorial gain. Accordingly, this study aimed to identify the collective system dynamics of rugby union phases-of-play near the try line by investigating whether ball displacement trajectory on the playing field provides insights on successful team performance.

Methods

Five rugby union matches were videotaped involving teams at a national league performance level. From these matches, 22 second phases-of-play were selected and digitized for analysis. The variable “distance gained” was investigated as a potential coordination variable describing functional coordination between players and teams. This variable concerned the distance between ball initial position and ball current position over time and was used to define the degree of territory gained by an attacking team.

Results

Analysis of distance gained dynamics in attacking sub-phases demonstrated the intermittent character of rugby union performers displacement trajectories on the playing field. Amplitude of ball movements was revealed as a distinguishing feature related to attacking effectiveness. Successful attacking phases displayed lower distances of positional retreat, with the maximum retreat distance achieved sooner in successful compared to unsuccessful phases-of-play. Autocorrelation and ApEn analyses suggested low system variability within time series data concerning both performance outcomes. However, evidence of less regularity and more complexity was found in unsuccessful phases-of-play.

Conclusion

Results suggested that distance gained dynamics manifests a characteristic collective behaviour pattern that captures the macroscopic functional order of multi-player attack–defence systems in team sports like rugby union.     

Eye-Hand Coordination in Rhythmical Pointing

The authors investigated the relation between hand kinematics and eye movements in 2 variants of a rhythmical Fitts's task in which eye movements were necessary or not necessary. P. M. Fitts's (1954) law held in both conditions with similar slope and marginal differences in hand-kinematic patterns and movement continuity. Movement continuity and eye—hand synchronization were more directly related to movement time than to task index of difficulty. When movement time was decreased to fewer than 350 ms, eye—hand synchronization switched from continuous monitoring to intermittent control. The 1:1 frequency ratio with stable π/6 relative phase changed for 1:3 and 1:5 frequency ratios with less stable phase relations. The authors conclude that eye and hand movements in a rhythmical Fitts's task are dynamically synchronized to produce the best behavioral performance.     

Eye movements in drawing simple lines

As part of an investigation into real-world drawing, eye movements and eye-hand interactions have been recorded for twenty subjects of varying drawing experience drawing simple straight and curved lines and a square. Two modes of eye-hand behaviour were observed. In the first, named 'close pursuit', fixations closely followed the pencil with a sequence of small saccades. In the second, named 'target locking', a stable fixation was made on the end-point of the line throughout the entire drawing action. Depending on subject and type of line, close pursuit, target locking, or a combination of these modes was used regardless of previous drawing experience. The results are discussed in terms of the role of the eye in the control of the movement trajectory of the hand.     

Freezing degrees of freedom under stress: kinematic evidence of constrained movement strategies

The present study investigated the effect of psychological stress imposed on movement kinematics in a computer-simulated batting task involving a backward and forward swing of the forearm. The psychological stress was imposed by a mild electric stimulus following poor performance. Fourteen participants hit a moving ball with a horizontal lever and aimed at a distant target with as much accuracy as possible. The kinematic characteristics appearing under stress were delay of movement initiation, small amplitude of movement and low variability of spatial kinematic events between trials. These features were also found in previous studies in which the experimental task required high accuracy. The characteristic kinematics evident in the present study suggested that the movement strategies adopted by the stressed participants were similar to those that appear under high accuracy demand. Moreover, a correlation analysis between the onset times of kinematic events revealed that temporally consistent movements were reproduced under stress. Taken together, the present findings demonstrated that, under psychological stress, movement strategies tend to shift toward the production of more constrained trajectories, as is seen under conditions of high accuracy demand, even though the difficulty of the task itself does not change.