A Compact Representation of Drawing Movements with Sequences of Parabolic Primitives

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2–4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences (“words”) of a small number of elementary parabolic primitives (“letters”). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry)

Qualitative identification of copper bearing minerals using near infrared sensors

Application of sensors for on-site fast identification and discrimination of dominant ore bearing particles from associated gangues in a complex ore is an important route in minerals exploration and extraction industries. This paper considers identification and discrimination of copper bearing minerals from associated gangues using near infrared sensors. Different copper bearing minerals in the Akiri copper ore are differentiated on the basis of their near infrared spectra behaviour. The near infrared spectra of individual samples are correlated with their mineralogy and chemistry as analysed by X-Ray diffraction and X-Ray fluorescence equipment, respectively. The obtained results indicated that the detection limit of the near infrared sensor is better than that of both X-ray diffraction and X-ray fluorescence equipment used. Hence, in addition to the minerals identified by the X-ray diffraction equipment, other near infrared active minerals with concentration below the X-ray diffraction detection limit were also detected by the near infrared sensors