Theories and models for 1/f(beta) noise in human movement science

Long-range correlation in synchronization and syncopation tapping: a linear phase correction model

We propose in this paper a model for accounting for the increase in long-range correlations observed in asynchrony series in syncopation tapping, as compared with synchronization tapping. Our model is an extension of the linear phase correction model for synchronization tapping. We suppose that the timekeeper represents a fractal source in the system, and that a process of estimation of the half-period of the metronome, obeying a random-walk dynamics, combines with the linear phase correction process. Comparing experimental and simulated series, we show that our model allows accounting for the experimentally observed pattern of serial dependence. This model complete previous modeling solutions proposed for self-paced and synchronization tapping, for a unifying framework of event-based timing.

Unraveling the finding of 1/f beta noise in self-paced and synchronized tapping: a unifying mechanistic model

1/f (beta) noise has been revealed in both self-paced and synchronized tapping sequences, without being consistently taken into consideration for the modeling of underlying timing mechanisms. In this study we characterize variability, short-range, and long-range correlation properties of asynchronies and inter-tap intervals collected in a synchronization tapping experiment, attesting statistically the presence of 1/f (beta) noise in asynchronies. We verify that the linear phase correction model of synchronization tapping in its original formulation cannot account for the empirical long-range correlation properties. On the basis of previous accounts of 1/f (beta) noise in the literature on self-paced tapping, we propose an extension of the original synchronization model by modeling the timekeeping process as a source of 1/f (beta) fluctuations. Simulations show that this '1/f-AR synchronization model' accounts for the statistical properties of empirical series, including long-range correlations, and provides an unifying mechanistic account of 1/f (beta) noise in self-paced and synchronization tapping. This account opens the original synchronization framework to further investigations of timing mechanisms with regard to the serial correlation properties in performed time intervals.