Long Memory Processes ( 1 / f α Type) in Human Coordination

The wide occurrence of 1yf a type of long memory (long range correlated) processes in electrical systems and in solid state devices has long posed a challenging problem for physics [1]. A number of mechanisms, ranging from the superposition of many independent relaxation processes [2] to self-organized criticality [3], are proffered to explain this phenomenon. In this Letter we report the manifestation of long memory processes in a human sensorimotor coordination experiment in which a subject synchronizes his finger tapping with an external periodic stimulus. Using an array of diagnostic tools including rescaled range analysis and the spectral maximum likelihood estimator, we show that the error time series, defined as the time between a predetermined point in the tapping cycle and the onset of the stimulus, exhibits long memory of 1yf a type, and can be modeled as fractional Gaussian noise [4]. The average value of a is found to be about 0.5. This result adds the present human sensorimotor coordination system to a growing list of biological examples in which one observes long range correlated random fluctuations [5‐ 7]. In addition, we report our attempt at modeling the experimental findings using stochastic delay differential equations. Our motivation is to present a unifying mechanism for a diverse set of long memory processes, observed under a variety of sensorimotor conditions [7], by incorporating both the inevitable occurrence of noise (white) in the nervous system and delay feedback networks involved in controlling the motor output. Experiment and data collection.—Five right-handed male subjects ranging in age from 25 to 35 took part in the synchronization experiment. Seated in a sound attenuated chamber, each subject was instructed to cyclically press his index finger against a computer key in synchrony with a periodic series of auditory beeps, delivered through a headphone. Two frequency conditions, F1 › 2 Hz (T1 › 500 ms) and F2 › 1.25 Hz (T2 › 800 ms), were studied. These frequencies were chosen such that the subject was able to perform the required tapping motion continuously

[1]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[2]  Bruce J. West,et al.  Fractal physiology , 1994, IEEE Engineering in Medicine and Biology Magazine.