In order to enhance dexterity in execution of robot tasks, a redundant number of degrees-of-freedom (DOF) is adopted for design of robotic mechanisms like robot arms and multi-fingered robot hands. Associated with such redundancy in DOFs relative to the number of physical variables necessary and sufficient for description of a given task, an extra performance index is introduced for controlling such a redundant robot in order to avoid arising of ill-posedness of inverse kinematics from the task space to the joint space. This paper shows that such an ill-posedness problem of DOF redundancy can be resolved in a natural way on the basis of construction of sensory feedback signals from the task space and a novel concept named "stability on a manifold". To show this, two illustrative robot tasks are analyzed in details, which are 1) posture control of an object via rolling contact by a redundant multi-DOF finger and 2) stable pinching and object manipulation by a pair of multi-DOF robot fingers.

The object of this paper is to introduce the new family of cracked sets which yields a compactness result in the W ^1,p-topology associated with the oriented distance function and to give an original application to the celebrated image segmentation problem formulated by Mumford and Shah [21]. The originality of the approach is that it does not require a penalization term on the length of the segmentation and that, within the set of solutions, there exists one with minimum density perimeter as defined by Bucur and Zolesio in [3]. This theory can also handle N-dimensional images. The paper is completed with several variations of the problem with or without a penalization term on the length of the segmentation. In particular, it revisits and recasts the earlier existence theorem of Bucur and Zolesio [3] for sets with a uniform bound or a penalization term on the density perimeter in the W^1,p-framework.

In this paper we consider practical stabilization strategies of scalar linear systems by means of quantized feedback maps which use a minimal number of quantization levels. These stabilization schemes are based on the chaotic properties of piecewise affine maps and their performance can be analyzed in terms of the mean time needed to shrink the system from an initial interval into a fixed target interval. We show here that this entrance time grows linearly with respect to the contraction rate defined as the quotient of the length of the initial and target interval respectively. Estimations are obtained using denumerable Markov chains arguments.

Cryo electron microscopy is a measurement modality which provides images from which 3-D reconstructions of biological particles such as viruses can be estimated. When the specimen is composed of mixtures of particles of different types, the 3-D reconstruction problem must be solved jointly with a pattern classification problem. The performance of the estimators is not well understood because the computations are not suitable for analytical results and are too large for extensive Monte Carlo results. The problem formulation typically has nuisance parameters and different treatments of the nuisance parameters lead to different estimators. In this paper two types of estimators and two model problems are studied with the conclusion that it is difficult to improve upon maximum likelihood estimators based on integrating out the nuisance parameters.

In this paper a relationship between the Birkhoff interpolation problem and the problem of control theoretic splines is established. It is shown that the Birkhoff interpolation problem has a solution if and only if a certain cost function remains bounded under perturbation of a suitably chosen variable.

Density evolution is a dynamic system in a space of probability distributions representing the progress of iterative decoders in the infinite block length limit. In this paper we establish some basic results concering this process. In particular we show that the decoding threshold is equivalent to to appearance of non-trivial fixed point solutions to the density evolution equations. In the case of LDPC codes we prove the sufficiency of the previously published stability condition for stability of the DELTA_INFINITY fixed point and slightly strengthen the necessity result.