This dissertation demonstrates a new method for inferring a representation of the motor command, generated by the central nervous system for interactive point-to-point movements. This new tool, the input inference neural network or IINN, allows estimation of the complexity of the motor command. The IINN was applied to experimental data gathered from 7 volunteer subjects who performed point-to-point tasks while interacting with a specially constructed haptic robot. The motor plan inference demonstrates that, for the point-to-point movement tasks executed during experiments, the motor command can be projected onto a low-dimensional manifold. This dimension is estimated to be 4 or 5 and far less than the degrees of freedom available in the arm. It is hypothesized that subjects simplify the problem of adapting to changing environments by projecting the motor control problem onto a motor manifold of low dimension. Reducing the dimension of the movement optimization problem through the development of a motor manifold can explain rapid adaptation to new motor tasks.

This dissertation demonstrates a new method for inferring a representation of the motor command, generated by the central nervous system for interactive point-to-point movements. This new tool, the input inference neural network or IINN, allows estimation of the complexity of the motor command. The IINN was applied to experimental data gathered from 7 volunteer subjects who performed point-to-point tasks while interacting with a specially constructed haptic robot. The motor plan inference demonstrates that, for the point-to-point movement tasks executed during experiments, the motor command can be projected onto a low-dimensional manifold. This dimension is estimated to be 4 or 5 and far less than the degrees of freedom available in the arm. It is hypothesized that subjects simplify the problem of adapting to changing environments by projecting the motor control problem onto a motor manifold of low dimension. Reducing the dimension of the movement optimization problem through the development of a motor manifold can explain rapid adaptation to new motor tasks.

We study the empirical quantization error in case the number of prototypes increases with the size of the sample. We present a proof of the consistency of the empirical quantization error and of corresponding estimators of the quantization dimensions of distributions. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

<p>This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which are embedded in a <italic>D</italic>>><italic>k</italic> dimensional Euclidean space are considered. Assuming one has samples from such a set, possibly corrupted by high-dimensional noise, if the data is linear the dimension can be recovered using PCA. However, when the data is non-linear, PCA fails, overestimating the intrinsic dimension. A multiscale version of PCA is thus introduced which is robust to small sample size, noise, and non-linearities in the data.</p> / Dissertation