English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Neuroscientific studies of drawing-like movements usually analyze neuralrepresentation of either geometric (eg. direction, shape) or temporal (eg.speed) features of trajectories rather than trajectory's representation as awhole. This work is about empirically supported mathematical ideas behindsplitting and merging geometric and temporal features which characterizebiological movements. Movement primitives supposedly facilitate the efficiencyof movements' representation in the brain and comply with different criteriafor biological movements, among them kinematic smoothness and geometricconstraint. Criterion for trajectories' maximal smoothness of arbitrary order$n$ is employed, $n = 3$ is the case of the minimum-jerk model. I derive aclass of differential equations obeyed by movement paths for which $n$-th ordermaximally smooth trajectories have constant rate of accumulating geometricmeasurement along the drawn path. Constant rate of accumulating equi-affine arccorresponds to compliance with the two-thirds power-law model. Geometricmeasurement is invariant under a class of geometric transformations and may bechosen to be an arc in certain geometry. Equations' solutions presumably serveas candidates for geometric movement primitives. The derived class ofdifferential equations consists of two parts. The first part is identical forall geometric parameterizations of the path. The second part enforcesconsistency with desired (geometric) parametrization of curves on solutions ofthe first part. Equations in different geometries in plane and in space andtheir known solutions are presented. Connection between geometric invariance,motion smoothness, compositionality and performance of the compromised motorcontrol system is discussed. The derived class of differential equations is anovel tool for discovering candidates for geometric movement primitives.

Affine differential geometry and smoothness maximization as tools for identifying geometric movement primitives