Rhythmic performance during a whole body movement: dynamic analysis of force-time curves

The purpose of this study was to investigate rhythmic performance during two-legged hopping in place. In particular, it was tested whether (a) timing control is independent of force control, (b) a dynamic timer model explains rhythmic performance, and (c) it is a force related parameter that carries the timing information. Eleven participants performed two-legged hopping at their preferred hopping frequency (PHF) and at two hopping frequencies set by an external rhythmic stimulus as lower (LHF) and higher (HHF) than their PHF, respectively. A force plate was used to record the ground reaction force (GRF) time curves during two-legged hopping. The primary temporal and force related parameters determined from the GRF-time curves were the durations of the cycle of movement (t(cycle)), of the contact phase (t(contact)), of the flight phase (t(flight)), the magnitude of peak force (Fz(peak)) and the rate of peak force development (RFD). Control of t(cycle) was independent of force control as shown by the non-significant correlations between t(cycle) and the force parameters of the GRF-time curve. Lag 1 autocorrelations of t(cycle) were not significant in any of the HF, thereby a dynamic timer model is considered to explain the timing of t(cycle) during two-legged hopping. RFD varied more than any other GRF-time curve parameter, exhibited consistent significant strong correlations with the GRF-time curve parameters and significant negative lag 1 autocorrelations in PHF, thus, it was highlighted as the potent timing control parameter. Finally, we provide a practical application for the optimization of rhythmic performance.     

Hitting a moving target: perception and action in the timing of rapid interceptions

Different interceptive tasks and modes of interception (hitting or capturing) do not necessarily involve similar control processes. Control based on preprogramming of movement parameters is possible for actions with brief movement times but is now widely rejected; continuous perceptuomotor control models are preferred for all types of interception. The rejection of preprogrammed control and acceptance of continuous control is evaluated for the timing of rapidly executed, manual hitting actions. It is shown that a preprogrammed control model is capable of providing a convincing account of observed behavior patterns that avoids many of the arguments that have been raised against it. Prominent continuous perceptual control models are analyzed within a common framework and are shown to be interpretable as feedback control strategies. Although these models can explain observations of on-line adjustments to movement, they offer only post hoc explanations for observed behavior patterns in hitting tasks and are not directly supported by data. It is proposed that rapid manual hitting tasks make up a class of interceptions for which a preprogrammed strategy is adopted--a strategy that minimizes the role of visual feedback. Such a strategy is effective when the task demands a high degree of temporal accuracy.     

Intraday reliability of ground reaction force data

Based upon independent parameter reliability and minimum sample size evaluations, a sample size of 25 trials was identified as necessary to provide accurate ground reaction force (GRF) data describing a subject's running performance. Intraday parameter reliability based on this sample size was approximately 75% indicating that subject variability must be acknowledged when comparing the effects of different running shoes. The minimum differences in GRF parameter values that are biomechanically significant have been estimated at 1 N/kg and 2% for force and relative temporal measures, respectively.     

Acceptable timing error at ball-bat impact for different pitches and its implications for baseball skills

In baseball hitting, batters need high precision timing control to hit the ball with bat’s sweet spot. Knowing the acceptable range of timing error for hitting the ball in the aimed direction for various pitch types is helpful to understand whether the cause of the batter's mis-hit is a spatial or temporal error and highlight the motor skills required by the batter. The purpose of this study was to determine the acceptable timing error in different baseball pitches and the impact characteristics of mis-hits. Twenty-six high school baseball players hit a ball launched from a pitching machine with three types of pitches: fastballs, curveballs, and slowballs. We recorded the three-dimensional behavior of the ball, bat, and human body (pelvis) using an optical motion capture system. We then defined the optimal impact location based on timing accuracy, and determined the acceptable range of timing error by the interactive relationship between the horizontal orientation of the bat’s long axis at the time of ball impact and the horizontal direction of the batted ball. The ±30° width in the horizontal direction of the batted ball was set as the precondition for the tolerance of timing. The acceptable timing error was ±7.9 ms for fastballs, ±10.7 ms for curveballs, and ±10.7 ms for slowballs, and the optimal timing for outside pitches was approximately 10 ms later than that for inside pitches. The timing error was also explained 38.1% by variation in the impact location along the long axis of the bat (R² = 0.381, P < 0.001) and was minimized at a position close to the bat’s sweet spot. These results suggest that the optimal impact location and acceptable range of timing error depend on the pitching course and speed and that timing accuracy is essential to achieve the spatial accuracy required to hit the ball at the bat’s sweet spot.     

The relative efficacy of different forms of knowledge of results for the learning of a new relative timing pattern

The goal of the present study was to determine the relative efficacy of verbal and auditory knowledge of results for promoting learning of a new constrained relative timing pattern. In a series of four experiments we compared the efficiency of verbal knowledge of results to that of auditory knowledge of results. The results of all four experiments revealed that verbal knowledge of result is a very effective source of information to promote learning of a new imposed relative timing pattern. Auditory knowledge of results favoured learning of a new relative timing pattern in a very limited set of circumstances. In the present study, this was only the case when movement velocity remained constant from one segment of the task to the next and if it resulted in an unfamiliar temporal pattern. The results of all four experiments also provided evidence that movement parameterization and relative timing are independent processes that can be developed in parallel.     

Against Relative Timing Invariance in Movement Kinematics

The kinematics of stair climbing were examined to test the assertion that relative timing is an invariant feature of human gait. Six male and four female subjects were video-recorded (at 60 Hz) while they climbed a flight of stairs 10 times at each of three speeds. Each gait cycle was divided into three segments by the maximum and minimum angular displacement of the left knee and left foot contact. Gentner's (1987) analysis methods were applied to the individual subject data to determine whether the duration of the segments remained a fixed proportion of gait cycle duration across changes in stair-climbing speed. A similar analysis was performed using knee velocity maxima to partition the gait cycle. Regardless of how the gait cycle was divided, relative timing was not found to remain strictly invariant across changes in speed. This conclusion is contrary to previous studies of relative timing that involved less conservative analysis but is consistent with the wider gait literature. Strict invariant relative timing may not be a fundamental feature of movement kinematics.     

Adjustment and readjustment of the relative timing of a motor pattern

Summary The hypothesis of a generalized motor program with relative timing as an invariant characteristic is contrasted with a continuity hypothesis. According to this hypothesis, temporal characteristics are determined by the same parameters of a generalized motor program as spatial characteristics are; different temporal patterns are assumed to be associated with different costs. In two experiments uniarticular arm movements with different relative timing were studied. Three results were obtained that support the continuity hypothesis. (1) Reproductions exhibited asymmetric biases, that is, reproductions of one target pattern were biased toward the other, but not vice versa. (2) Readjustment to a new target pattern that had a correlation of almost zero with the practice pattern was not immediate, as found by Heuer and Schmidt (1988), who used more similar patterns. This suggests that readjustment of a temporal pattern depends on the similarity between the old and the new patterns. (3) Readjustment to another target pattern that had been practiced before was immediate for similar patterns, but not immediate for dissimilar patterns. The effects of the similarity of different temporal patterns on readjustment are not consistent with the view that each temporal pattern is governed by its own generalized motor program.     

"Markov at the bat": a model of cognitive processing in baseball batters

Anecdotal evidence from players and coaches indicates that cognitive processing (e.g., expectations about the upcoming pitch) plays an important role in successful baseball batting, yet this aspect of hitting has not been investigated in detail. The present study provides experimental evidence that prior expectations significantly influence the timing of a baseball swing. A two–state Markov model was used to predict the effects of pitch sequence and pitch count on batting performance. The model is a hitting strategy of switching between expectancy states using a simple set of transition rules. In a simulated batting experiment, the model provided a good fit to the hitting performance of 6 experienced college baseball players, and the estimated model parameters were highly correlated with playing level.     

The effect of alcohol administration on human timing: a comparison of prospective timing, retrospective timing and passage of time judgements

Previous research suggests that human timing may be affected by alcohol administration. The current study aimed to expand on previous research by examining the effect of alcohol on prospective timing, retrospective timing and passage of time judgements. A blind between-subjects design was employed in which participants were either administered 0 g of alcohol per kilogramme of body weight (placebo), 0.4 g/kg (low dose) or 0.6 g/kg (high dose). Participants completed four types of temporal task; verbal estimation and temporal generalisation, a retrospective timing task and a passage of time judgement task. A high dose of alcohol resulted in overestimations of duration relative to the low dose and placebo group in the verbal estimation task. A high dose of alcohol was also associated with time passing more quickly than normal. Alcohol had no effect on retrospective judgements. The results suggest that a high dose of alcohol increases internal clock speed leading to over-estimations of duration on prospective timing tasks, and the sensation of time passing more quickly than normal. The absence of an effect of alcohol on retrospective timing supports the suggestion that retrospective judgements are not based on the output of an internal clock.     

Offline improvement occurs for temporal stability but not accuracy following practice of integer and non-integer rhythms

Procedural learning benefits from memory processes occurring outside practice resulting in offline learning. Offline gains have been demonstrated almost exclusively for the ordinal structure of sequential motor tasks. Many skills also demand that the correct serial order of events be appropriately timed. Evidence indicates that the temporal aspect of a procedural skill can be encoded independent of serial order knowledge and governed by at least two distinct neural circuits. The present experiment determined if (a) offline gains emerge for temporal learning, and (b) if such gains occur for timing supervised by distinct timing systems. Participants experienced 216 practice trials of a 7-key press sequence that involved integer- or non-integer timing rhythms. Twenty-four hours after training 30 test trials were administered. Results revealed robust offline enhancement for timing performance of the non-integer based temporal sequences. This improvement was localized to stabilization of the required relative but not absolute time profiles. The neural circuitry central to supporting the performance of non-integer timing sequences is also a principal constituent of what is described as the "cognitive" timing system. Timing governed by this system appears most susceptible to offline gains via consolidation.     

Correlations for timing consistency among tapping and drawing tasks: evidence against a single timing process for motor control.

Three experiments were conducted to examine whether timing processes can be shared by continuous tapping and drawing tasks. In all 3 experiments, temporal precision in tapping was not related to temporal precision in continuous drawing. There were modest correlations among the tapping tasks, and there were significant correlations among the drawing tasks. In Experiment 3, the function relating timing variance to the square of the observed movement duration for tapping was different from that for drawing. The conclusions drawn were that timing is not an ability to be shared by a variety of tasks but instead that the temporal qualities of skilled movement are the result of the specific processes necessary to produce a trajectory. These results are consistent with the idea that timing is an emergent property of movement.     

Two asymmetries governing neural and mental timing

Mental timing studies may be influenced by powerful cognitive illusions that can produce an asymmetry in their rate of progress relative to neuronal timing studies. Both types of timing research are also governed by a temporal asymmetry, expressed by the fact that the direction of causation must follow time's arrow. Here we refresh our earlier suggestion that the temporal asymmetry offers promise as a means of timing mental activities. We update our earlier analysis of Libet's data within this framework. Then we consider the surprises which often occur on those rare occasions when neural timing experiments parallel mental timing work exactly. Together, these surprises and asymmetries prescribe a relentlessly meticulous and fully transparent exposition of timing methods, terms, and concepts which shuns plausible narratives, even when buttressed by rigorous formal models, unless guided by opposite empirical evidence.     

Animal timing: a synthetic approach

Inspired by Spence’s seminal work on transposition, we propose a synthetic approach to understanding the temporal control of operant behavior. The approach takes as primitives the temporal generalization gradients obtained in prototypical concurrent and retrospective timing tasks and then combines them to synthetize more complex temporal performances. The approach is instantiated by the learning-to-time (LeT) model. The article is divided into three parts. In the first part, we review the basic findings concerning the generalization gradients observed in fixed-interval schedules, the peak procedure, and the temporal generalization procedure and then describe how LeT explains them. In the second part, we use LeT to derive by gradient combination the typical performances observed in mixed fixed-interval schedules, the free-operant psychophysical procedure, the temporal bisection task, and the double temporal bisection task. We also show how the model plays the role of a useful null hypothesis to examine whether temporal control in the bisection task is relative or absolute. In the third part, we identify a set of issues that must be solved to advance our understanding of temporal control, including the shape of the generalization gradients outside the range of trained stimulus durations, the nature of temporal memories, the influence of context on temporal learning, whether temporal control can be inhibitory, and whether temporal control is also relational. These issues attest to the heuristic value of a Spencean approach to temporal control.     

Serial Organization and Timing in a Motor Skill

The temporal and serial organization (or timing) of responses in motor skill was investigated in a repetitive motor task, resisted hand cranking. Both positional timing and serial timing were analyzed using strain-gauge techniques and were related to the performance of the preferred and non-preferred hands. The results demonstrated the superiority of the preferred hand on the serial timing criteria and supported the hypothesis that skilled performance is characterized by more effective temporal structuring of the components of the response.     

Evidence against the relative invariance of timing in handwriting

Gentner (1987) has called into question the role of timing information in a number of motor behaviours. The status of an invariant relative timing model for handwriting, however, is still unclear, due to lack of previous studies that have applied appropriate tests to a suitable database.

This study employs a direct application of the tests proposed by Gentner (1987) to handwriting samples collected from adult subjects, to ascertain whether an invariant temporal pattern was retained across changes in size and speed of writing.

In line with Gentner's (1987) study of typing, the findings are strongly against the invariant relative timing model and bring into question motor program models that posit timing as an independent parameter.     

How the propagation of error through stochastic counters affects time discrimination and other psychophysical judgments

The performance of fallible counters is investigated in the context of pacemaker-counter models of interval timing. Failure to reliably transmit signals from one stage of a counter to the next generates periodicity in mean and variance of counts registered, with means power functions of input and standard deviations approximately proportional to the means (Weber's law). The transition diagrams and matrices of the counter are self-similar: Their eigenvalues have a fractal form and closely approximate Julia sets. The distributions of counts registered and of hitting times approximate Weibull densities, which provide the foundation for a signal-detection model of discrimination. Different schemes for weighting the values of each stage may be established by conditioning. As higher order stages of a cascade come on-line the veridicality of lower order stages degrades, leading to scale-invariance in error. The capacity of a counter is more likely to be limited by fallible transmission between stages than by a paucity of stages. Probabilities of successful transmission between stages of a binary counter around 0.98 yield predictions consistent with performance in temporal discrimination and production and with channel capacities for identification of unidimensional stimuli.     

Contextual relative temporal duration judgment: an investigation of sequence interruptions

How do listeners judge relative duration? There currently are three primary classes of proposed timing mechanisms: interval based (judgments of discrete events), beat based (judgments of beat synchrony), and oscillator based (judgments of relative phase or synchrony). In the present research, these mechanisms were examined in terms of predictions both about how an induction sequence of preceding intervals affects relative temporal duration comparison in a simple, two-interval task and about how a pause (e.g., an interstimulus interval) within the presented sequence affects relative temporal duration judgment. Results indicated that a relative temporal judgment was best when all intervals preceding the to-be-judged interval were equal in duration to the to-be-judged interval. Results also indicated that whereas short pauses significantly impair a relative temporal duration judgment, long pauses generally do not reduce the effectiveness of the induction sequence. The results are not entirely consistent with current conceptualizations of any of the proposed mechanisms but can be fully accommodated with simple modifications to the oscillator-based mechanism.     

Timing and executive function: Bidirectional interference between concurrent temporal production and randomization tasks

A review of interference effects in concurrent temporal/nontemporal dual-task studies suggests that prospective timing may be related to executive cognitive functions. Executive processes play a supervisory role in behavior by controlling attention, coordinating information, and scheduling actions. In the present research, a timing task was paired with an established executive task in a dual-task paradigm. The timing task required subjects t o generate a series o f 5-sec temporal productions,and the executive task was random number generation. These tasks were performed both separately and concurrently. Comparisons of single-task and dual-task conditions showed that (1) the randomization task interfered with timing by making temporal productions more variable and longer and (2) concurrent timing disrupted randomization performance by making responses less random. This pattern of bidirectional interference supports the idea that timing relies on the same attentional resources used by other executive-level tasks.     

Temporal ventriloquism in a purely temporal context

This study examines how audiovisual signals are combined in time for a temporal analogue of the ventriloquist effect in a purely temporal context, that is, no spatial grounding of signals or other spatial facilitation. Observers were presented with two successive intervals, each defined by a 1250-ms tone, and indicated in which interval a brief audiovisual stimulus (visual flash + noise burst) occurred later. In "test" intervals, the audiovisual stimulus was presented with a small asynchrony, while in "probe" intervals it was synchronous and presented at various times guided by an adaptive staircase to find the perceived temporal location of the asynchronous stimulus. As in spatial ventriloquism, and consistent with maximum likelihood estimation (MLE), the asynchronous audiovisual signal was shifted toward the more reliably localized component (audition, for all observers). Moreover, these temporal shifts could be forward or backward in time, depending on the asynchrony order, suggesting perceived timing is not entirely determined by physical timing. However, the critical signature of MLE combination--better bimodal than unimodal precision--was not found. Regardless of the underlying model, these results demonstrate temporal ventriloquism in a paradigm that is defined in a purely temporal context.     

Learning the invariants of a perceptual motor skill

The concept of invariant relative timing has typically been associated with the concept of a generalized motor programme. The present study approaches the phenomenon of invariant relative timing from the perspective of learning. The underlying question of concern for this study was, "What is learned." The specific question was whether relative timing is one of the essential properties of movement that is learned during skill acquisition. In the present experiment, subjects were given extensive practice in learning to track and reproduce a criterion waveform using a joystick control for their response. In order to test whether subjects learn the relative timing of a movement, they were transferred to tracking waveforms that were identical to the criterion in terms of relative timing, but different in terms of absolute timing. Measurements were taken on all waveforms in two conditions: (a) in a pursuit tracking condition where subjects were temporally constrained by the stimulus, and (b) in a reproduction condition where subjects' timing was not constrained. The outcome from both conditions gives support to the idea that humans learn invariant relative timing during the acquisition of a motor skill.