A Feedback Information-Theoretic Transmission Scheme (FITTS) for Modelling Aimed Movements
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We build on the variability of human movements by focusing on how the stochastic variance of the limb position varies over time. This implies analyzing a whole set of trajectories at once rather than a single trajectory. We show, using real data previously acquired by two independent studies, that in a tapping task, the positional variance profiles are unimodal. The first phase, where positional variance increases steadily, is followed by a second phase where positional variance decreases until it reaches some small level. We show consistency of this two-phase description with two-component models of movement of the literature. During the second phase, the problem of aiming can be reduced to a Shannon-like communication problem where information is transmitted from a "source" (determined by the distance between current and target position), to a "destination" (the movement's endpoint) over a "channel" perturbed by Gaussian noise, with the presence of a feedback information from the current position. We obtain an optimal solution to this problem, re-derive the so-called Elias scheme, and determine that the fastest rate of decrease of variance during the second component is exponential. This leads to a new, "local" Fitts' law, from which the classical "global" Fitts' law is also re-derived. The validity of the model is assessed on real data; the rate at which variance is decreased, i.e., at which information is transmitted over the channel, is about 5 bit/s on average.
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