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01-07-2007 | Research Article

On rhythmic and discrete movements: reflections, definitions and implications for motor control

Authors: Neville Hogan, Dagmar Sternad

Published in: Experimental Brain Research | Issue 1/2007

Abstract

At present, rhythmic and discrete movements are investigated by largely distinct research communities using different experimental paradigms and theoretical constructs. As these two classes of movements are tightly interlinked in everyday behavior, a common theoretical foundation spanning across these two types of movements would be valuable. Furthermore, it has been argued that these two movement types may constitute primitives for more complex behavior. The goal of this paper is to develop a rigorous taxonomic foundation that not only permits better communication between different research communities, but also helps in defining movement types in experimental design and thereby clarifies fundamental questions about primitives in motor control. We propose formal definitions for discrete and rhythmic movements, analyze some of their variants, and discuss the application of a smoothness measure to both types that enables quantification of discreteness and rhythmicity. Central to the definition of discrete movement is their separation by postures. Based on this intuitive definition, certain variants of rhythmic movement are indistinguishable from a sequence of discrete movements, reflecting an ongoing debate in the motor neuroscience literature. Conversely, there exist rhythmic movements that cannot be composed of a sequence of discrete movements. As such, this taxonomy may provide a language for studying more complex behaviors in a principled fashion.

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This notation means that both t _i and t _j are contained within the interval between t _p − δ_p and t _p.

A familiar example is the tangent to a curve, a line which touches the curve at a single point with the same slope as the curve at that point. Of course, the slope of a point is meaningless but the slope of a curve at a point may be defined by considering a line through two suitably close points and noting the limiting value to which its slope converges as the separation of the points diminishes. This avoids the “divide-by-zero” problem which would otherwise confound attempts at precision.

Subjects gave informed consent as approved by the Institutional Review Boards of the Massachusetts Institute of Technology and the Pennsylvania State University.

It should be noted that because a strictly periodic function has infinite duration, periodicity can never be proven conclusively from experimental observation, and certainly in biology deviations from strict periodicity should be anticipated.

A function y(t) is continuous if at every point a in its domain, there exists a constant δ > 0 corresponding to every constant ɛ > 0 such that |y(t) − y(a)| < ɛ for all t in the neighborhood |t − a| < δ. To be continuous at a specific point a the function must be defined at t = a and \({{\mathop {\lim}\limits_{t \to a}}\;y{\left(t \right)} = y{\left(a \right)};}\) a continuous function is continuous at all points in its domain.

This is similar to the definition of familiar concepts such as the shortest line. The shortest line has zero length (a trivial answer), so we need boundary conditions, i.e., two points. The shortest line between two points may be found by defining a measure of length, which assigns a scalar to each possible path. This scalar is defined by adding all of the infinitesimal displacements along the path. Variational calculus may then be applied to find the path with minimal length (a straight line in Euclidean space, a Great Circle on the surface of a sphere and so on). Note that length, like smoothness, is not a categorical distinction but a matter of degree.

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Title: On rhythmic and discrete movements: reflections, definitions and implications for motor control
Authors: Neville Hogan
Dagmar Sternad
Publication date: 01-07-2007
Publisher: Springer-Verlag
Published in: Experimental Brain Research / Issue 1/2007
Print ISSN: 0014-4819
Electronic ISSN: 1432-1106
DOI: https://doi.org/10.1007/s00221-007-0899-y

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On rhythmic and discrete movements: reflections, definitions and implications for motor control

Abstract

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Abstract

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