Fractal modeling of human isochronous serial interval production

Abstract

The Hurst exponent (H) was estimated for series of 256 time intervals produced by human participants, collected in 5 sessions performed on different days. Each series was obtained during the continuation phase following synchronization with 25 isochronous intervals generated by a computer and presented through headphones. Dispersional analysis yielded estimates of H > 0.5. These were sufficiently stable to yield statistically significant differences between participants and between each target interval duration (0.5, 0.8, 1.1, and 1.5 s). The results indicate that variability in isochronous serial interval production (ISIP) can be modeled as fractional Gaussian noise, which corroborates and qualifies previous research indicating positive serial dependency or long memory in ISIP data in terms of drift and 1/ f noise characteristics. It is concluded that ISIP is a more complex process than is assumed by influential timing models and theories, and that realistic modeling of human timing must account for nonlinear variability patterns.

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

“…Analyzing the variability of rhythms generated by diverse functions in the human organism has revealed the presence of persistent long-range correlation, or 1/ f β noise. This recurrent result was evidenced notably in heart rate (e.g., Peng et al 1995Peng et al , 1999West et al 1999), respiratory cycles (Fadel et al 2004;Peng et al 2002), stride intervals in gait (Hausdorff et al 1995(Hausdorff et al , 1996West and Scafetta 2003), brain activity (e.g., Bédard et al 2006;Novikov et al 1997), or in the production of rhythmic movements (Gilden et al 1995;Gilden 2001;Delignières et al 2004;Delignières et al 2008;Madison 2004;Pressing and Jolley-Rogers 1997;Yamada 1995). 1/ f β noise denotes a very specific kind of variability defined by two main features: First, series of successive measures present persistent longrange correlation.…”

“…Self-paced tapping requires an internal regulation of timing, which has been supposed to involve a central timekeeping process (Wing and Kristofferson 1973). Numerous studies have shown that series of inter-tap intervals (ITI) in self-paced tapping contained 1/ f β noise Delignières et al 2004;Gilden et al 1995;Gilden 2001;Madison 2004;Yamada 1995), which was assumed to represent the variability inherent to the internal timekeeping process (Gilden et al 1995;Gilden 2001;Delignières et al 2004;Delignières et al 2008). In this view, Delignières et al (2008) proposed to provide the timekeeper with 1/ f properties using the socalled shifting strategy model, and showed that a combination of this fractal timekeeper and the original Wing and Kristofferson (1973)'s model allowed to account for the statistical properties typically observed in self-paced tapping.…”

On the limits of anisochrony in pulse attribution

“…154-155), as in ensemble music and other group activities. Since naturally produced sequences, including human serial time production, contain a range of deviations from strict isochrony (for a review see Madison, 2000), a margin of tolerance for such deviations is necessary for synchronisation to occur. We assume that the experience of pulse is closely related to the ability to synchronise, and that it should, therefore, not be rigidly dependent on physical isochrony.…”

Force-feedback interaction with a neural oscillator model: for shared human-robot control of a virtual percussion instrument

“…Humans can even track rhythms despite changes in tempo, perturbations, and complex syncopation, and humans can maintain a pulse even after the external stimulus ceases [14]. Brain imaging studies reveal neural correlates of rhythm perception in the brain.…”