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Summary: This article outlines a methodology for investigating the coordinate
systems by which movement variables are encoded in the firing
rates of individual motor cortical neurons. Recent neurophysiological
experiments have probed the issue of underlying coordinates by
examining how cellular preferred directions (as determined by the
center-out task) change with posture. Several key experimental
findings have resulted that constrain hypotheses about how motor
cortical cells encode movement information. But while the sig-
nificance of shifts in preferred direction is well known and widely
accepted, posture-dependent changes in the depth of modulation of
a cell's tuning curve -- that is, gain changes -- have not been
similarly identified as a means of coordinate inference. This article
develops a vector field framework in which the preferred direction
and the gain of a cell's tuning curve are viewed as dual components
of a unitary response vector. The formalism can be used to compute
how each aspect of cell response covaries with posture as a func-
tion of the coordinate system in which a given cell is hypothesized to
encode its movement information. Such an integrated approach
leads to a model of motor cortical cell activity that codifies the
following four observations: (i) cell activity correlates with hand
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