Statistical Analysis of Timing Errors (original) (raw)
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Deterministic and stochastic features of rhythmic human movement
Biological Cybernetics, 2006
The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method's merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.
Nature of variability in rhythmical movement
Human Movement Science, 1995
If you look back at your footprints on a snowy road, you will notice that you never move in the same way. Learning theory (Hebb, 1949) can explain the decrease of variability in human movement, but cannot explain the nature of the variability. Feedfoward motor control by the cerebellum (Shidara et al., 1993) can explain the precise movement of the limbs to objects, but cannot explain error in movement from objects. In past studies (e.g., Schijner et al., 1986; Kelso et al., 1987; Kay, 19881, the cause of errors was assumed to be noise originating in the movement system. In other words, human movement has been considered to be the result of a combination of deterministic and stochastic mechanisms. Hurst (1965) proposed an empirical law of variability for natural phenomena from observation of the rise and fall of water in rivers. Variability in stereotyped movements such as walking and running, that have been considered as repetition of the same movement, was analyzed using Hurst's empirical law. The result suggests that variation in stereotyped human movement can not be modeled as Brownian motion or noise separated from a deterministic movement system.
1/f structure of temporal fluctuation in rhythm performance and rhythmic coordination
This dissertation investigated the nature of pulse in the tempo fluctuation of music performance and how people entrain with these performed musical rhythms. In Experiment 1, one skilled pianist performed four compositions with natural tempo fluctuation. The changes in tempo showed long-range correlation and fractal (1/f) scaling for all four performances. To determine whether the finding of 1/f structure would generalize to other pianists, musical styles, and performance practices, fractal analyses were conducted on a large database of piano performances in Experiment 3. Analyses revealed signicant long-range serial correlations in 96% of the performances. Analysis showed that the degree of fractal structure depended on piece, suggesting that there is something in the composition's musical structure which causes pianists' tempo fluctuations to have a similar degree of fractal structure. Thus, musical tempo fluctuations exhibit long-range correlations and fractal scaling. To examine how people entrain to these temporal fluctuations, a series of behavioral experiments were conducted where subjects were asked to tap the pulse (beat) to temporally fluctuating stimuli. The stimuli for Experiment 2 were musical performances from Experiment 1, with mechanical versions serving as controls. Subjects entrained to all stimuli at two metrical levels, and predicted the tempo fluctuations observed in Experiment 1. Fractal analyses showed that the fractal structure of the stimuli was reected in the inter-tap intervals, suggesting a possible relationship between fractal tempo scaling, pulse perception, and entrainment. Experiments 4-7 investigated the extent to which people use long-range correlation and fractal scaling to predict tempo fluctuations in fluctuating rhythmic sequences.
Fluctuations and phase symmetry in coordinated rhythmic movements
Journal of Experimental Psychology: Human Perception and Performance, 1986
Pendular, clocking movements typify mammalian terrestrial locomotion. They can be investigated with a procedure in which people swing hand-held pendulums at the wrists, comfortably and rhythmically. Pendular, clocking behavior was examined for in-phase and out-of-phase coordinations. The periodic timing and powering of rhythmic movements in the comfort state follow from different laws (Kugler & Turvey, 1986). One law guides the assembling of the reference frame for "clocking." Another law guides the assembling of the muscular, escapement processes determining the cycle energy. Wing and Kristofferson's(1973) method for parsing periodic-timing variance into independent "clock" and "motor" sources was applied. Mean periodicity was unaffected by phase. "Clock" fluctuations, however, were larger out of phase than in phase. "Motor" fluctuations were indifferent to phase but reflected the departures of individual wrist-pendulum systems from their preferred periods. It appears that an intended phase relation is realized as a constraint on "clock" states. These states are more stable under the in-phase constraint than under the out-of-phase constraint.
The Quarterly Journal of Experimental Psychology, 2009
The aim of this study was to test different methods for distinguishing between two known timing processes involved in human rhythmic behaviours. We examined the implementation of two approaches used in the literature: the high-frequency slope of the power spectrum and the lag one value of the autocorrelation function, ACF(1). We developed another method based on the Wing and Kristofferson (1973a) model and the predicted negative ACF(1) for event-based series: the detrended windowed (lag one) autocorrelation (DWA). We compared the reliability and performance of these three methods on simulation and experimental series. DWA gave the best results, and guidelines are given for its appropriate use for identifying underlying timing processes.
Interaction of discrete and rhythmic movements over a wide range of periods
Experimental Brain Research, 2002
This study investigates a complex task in which rhythmic and discrete components have to be combined in single-joint elbow rotations. While previous studies of similar tasks already reported that the initiation of the discrete movement is constrained to a particular phase window of the ongoing rhythmic movement, interpretations have remained contradictory due to differences in paradigms, oscillation frequencies, and data analysis techniques. The present study aims to clarify these findings and further elucidate the bidirectional nature of the interaction between discrete and rhythmic components. Participants performed single-degree-of-freedom elbow oscillatory movements at five prescribed periods (400, 500, 600, 800, 1000 ms). They rapidly switched the midpoint of oscillation to a second target after an auditory signal that occurred at a random phase of the oscillation, without stopping the oscillation. Results confirmed that the phase of the discrete movement initiation is highly constrained with respect to the oscillation period. Further, the duration, peak velocity, and the overshoot of the discrete movement varied systematically with the period of the rhythmic movement. Effects of the discrete-ontorhythmic component were seen in a phase resetting of the oscillation and a systematic acceleration after the discrete movement, which also varied as a function of the oscillation period. These results are interpreted in terms of an inhibitory bidirectional coupling between discrete and rhythmic movement. The interaction between discrete and rhythmic movement elements is discussed in comparison to sequential and gating processes suggested previously.
Variability, Symmetry, and Dynamics in Human Rhythmic Motor Control
2015
How humans and other animals control rhythmic behaviors, and locomotion in particular, is one of the grand challenges of neuroscience and biomechanics. And yet remarkably few studies address the fundamental control-systems modeling of locomotor control. This thesis attempts to address several pieces of this grand challenge through the development of experimental, theoretical, and computational tools. Specifically, we focus our attention on three key features of human rhythmic motor control, namely variability, symmetry, and dynamics. Variability: Little is known about how haptic sensing of discrete events, such as heel-strike in walking, in rhythmic dynamic tasks enhances behavior and performance. In order to discover the role of discrete haptic cues on rhythmic motor control performance, we study a virtual paddle juggling behavior. We show that haptic sensing of a force impulse to the hand at the moment of ball-paddle collision categorically improves performance over visual feedbac...