The unique ergodic measure of the symmetric piecewise toral isometry of rotation angle θ=kπ/5 is the Hausdorff measure of its singular set

It is known that the symmetric piecewise toral isometry of rotation angle θ = k π /5, k=1, 2, 3, 4 is uniquely ergodic in 'a certain subset' of its singular set (aka exceptional set). The purpose of this paper is to identify the unique ergodic measure explicitly. In fact, we prove that the unique ergodic measure is none other than the normalized Hausdorff measure of the singular set, consequently proving that the unique ergodicity holds in the entire singular set. We use the 'phantom dynamics' given by a number of symmetry identifications as our main tool.     

Cooperative Mobile Robotics: Antecedents and Directions

There has been increased research interest in systems composed of multiple autonomous mobile robots exhibiting cooperative behavior. Groups of mobile robots are constructed, with an aim to studying such issues as group architecture, resource conflict, origin of cooperation, learning, and geometric problems. As yet, few applications of cooperative robotics have been reported, and supporting theory is still in its formative stages. In this paper, we give a critical survey of existing works and discuss open problems in this field, emphasizing the various theoretical issues that arise in the study of cooperative robotics. We describe the intellectual heritages that have guided early research, as well as possible additions to the set of existing motivations.     

Quantifying Error in Dynamic Power Estimation of CMOS Circuits

Conventional power estimation techniques are prone to many sources of error. With increasing dominance of coupling capacitances, capacitive coupling potentially contributes significantly to power consumption in the deep sub-micron regimes. We analyze potential sources of inaccuracy in power estimation, focusing on those due to coupling. Our results suggest that traditional power estimates can be off by as much as 50%.This research was supported in part by the MARCO Gi- gascale Silicon Research Center and Cadence Design Systems, Inc.     

Epitaxial Mn(5)Ge(3) nano-islands on a Ge(001) surface

The growth behavior and atomic structure of Mn germanide, grown on Ge(001), is studied with x-ray diffraction and scanning probe microscopy. The amorphous clusters of as-deposited Mn are crystallized into Mn(5)Ge(3) nano-islands with a size of ～100?nm by solid phase epitaxy. At low coverage, the shape of the nano-islands is plateau-like, while at increased coverage it becomes mound-like. At the flat top of the plateau-like nano-islands, the hexagonal atomic structure is resolved. It is interpreted, with the help of first-principles study, as a Mn-terminated Mn(5)Ge(3)(0001) structure.