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2000 Macmillan Magazines Ltd letters to nature

Summary: © 2000 Macmillan Magazines Ltd
letters to nature
NATURE |VOL 403 |3 FEBRUARY 2000 |www.nature.com 549
velocity in cartesian coordinates with accuracy greater than 0.1 mm and 1.3 mm s-1
Jerk was estimated by applying a fourth-order Savitsky±Golay ®lter on a 250-ms
window of velocity data. This ®lter is equivalent to taking the second derivative at the
window's centre of the continuous least-squares best-®t fourth-order polynomial. This
fourth-order polynomial ®t is a low-pass ®lter with a cutoff frequency of 6.83 Hz. Power
spectra of mean subtracted velocity pro®les of very fast 10-cm reaching movements show
that 99.9% of the power is below 6 Hz.
We assessed motion state transition ef®ciency using cumulative squared jerk to
characterize the ef®ciency of recovery after perturbation offset. To accomplish this, we
compared the amount of jerk that occurred between two different motion states within the
same movement, with the jerk that would occur for a maximally smooth transition
between those two states in the elapsed time. The minimum jerk trajectory between two
motion states (state = [position, velocity, acceleration]) is given by a ®fth-order
polynomial in time:
xt C5t=tf 5


Source: Ahissar, Ehud - Department of Neurobiology, Weizmann Institute of Science
Shulz, Daniel - Unité de Neurosciences Information et Complexité


Collections: Biology and Medicine