Long Memory Processes (1/fαType) in Human Coordination

Abstract

Consider the task of synchronizing the movement of one's limb to a periodic environmental signal. Using rescaled range analysis and the spectral maximum likelihood estimator, we establish that the experimental errors of human synchronization exhibit 1͞f a type long memory where a is about 0.5, and that the underlying stochastic process can be modeled by fractional Gaussian noise. In addition, we provide a preliminary model of this phenomenon using stochastic delayed differential equations. [S0031-9007(97)04698-X] PACS numbers: 87.22.Jb, 05.40. + j, The wide occurrence of 1͞f 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 1͞f 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][6][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, F 1 2 Hz (T 1 500 ms) and F 2 1.25 Hz (T 2 800 ms), were studied. These frequencies were chosen such that the subject was able to perform the required tapping motion continuously [8,9].Each experimental session consisted of the subject performing 1200 continuous taps for a given frequency.A computer program was used to register the time of a specific point in the tapping cycle in millisecond resolution. The data collected were the interresponse intervals (IRIs) I i , and the synchronization or tapping errors e i . As defined in Fig. 1, e i is the time between th...

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