Simulating the Fast Prediction Strategy of the Sensorimotor System

The values of a physiological parameter and its time derivatives, detected at different times by different sensory receptors, are processed by the sensorimotor system to predict the time evolution of the parameter and convey appropriate control commands acting with minimum latency (few milliseconds) from the sensory stimulus. We have derived a power-series expansion (U-expansion) to simulate the fast prediction strategy of the sensorimotor system. Given a time-function f, a time-instant t(0), and a time-increment tau, the U-expansion enables the calculation of f (t(0) + tau) from f (t(0)) and the values f((n)) (t(n)) of the derivatives f((n)) of f at arbitrarily different times t(0) (n = 1, 2, ...), instead of time t o as in the Taylor series. For increments T significantly greater than the maximum t among the differences vertical bar t(n) -t(n-1)vertical bar, the error associated with truncation of the U-expansion at a given order closely equalizes the error of the corresponding Taylor series (t = 0) truncated at the same order. Small values of t and higher values of tau correspond to the high-frequency discharge of sensory neurons and the need for longer-term prediction, respectively. Taking inspiration from the sensorimotor system, the U-expansion can potentially provide an analytical background for the development of algorithms designed for the fast and accurate feedback control of nonlinear systems.

Automated summary

This passage discusses the processing of physiological parameters and their derivatives by the sensorimotor system, showcasing the use of U-expansion for fast prediction strategies. By employing this expansion method, it may offer an analytical background for the development of algorithms designed for the fast and accurate feedback control of nonlinear systems.