TY - JOUR

T1 - The speed-curvature power law of movements

T2 - a reappraisal

AU - Zago, Myrka

AU - Matic, Adam

AU - Flash, Tamar

AU - Gomez-Marin, Alex

AU - Lacquaniti, Francesco

PY - 2017/10/25

Y1 - 2017/10/25

N2 - Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685–690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

AB - Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685–690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

KW - Drawing

KW - Motor control

KW - Statistical analysis

KW - Two-thirds power law

UR - http://www.scopus.com/inward/record.url?scp=85032186247&partnerID=8YFLogxK

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U2 - 10.1007/s00221-017-5108-z

DO - 10.1007/s00221-017-5108-z

M3 - Article

AN - SCOPUS:85032186247

VL - 236

SP - 69

EP - 82

JO - Experimental Brain Research

JF - Experimental Brain Research

SN - 0014-4819

IS - 1

ER -