We study the relation between transitivity and strong transitivity, introduced by W. Parry, for graph self-maps. We establish that if a graph self-map f is transitive and the set of fixed points of fk is finite for each k ≥ 1, then f is strongly transitive. As a corollary, if a piecewise monotone graph self-map is transitive, then it is strongly transitive.
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This article discusses the basic capabilities needed to enable robots to operate in human-populated environments for accomplishing both autonomous tasks and human-guided tasks. These capabilities are key to many new emerging robotic applications in service, construction, field, underwater, and space. An important characteristic of these robots is the "assistance" ability they can bring to humans in performing various physical tasks. To interact with humans and operate in their environments, these robots must be provided with the functionality of mobility and manipulation. The article presents developments of models, strategies, and algorithms concerned with a number of autonomous capabilities that are essential for robot operations in human environments. These capabilities include: integrated mobility and manipulation, cooperative skills between multiple robots, interaction ability with humans, and efficient techniques for real-time modification of collision-free path. These capabilities are demonstrated on two holonomic mobile platforms designed and built at Stanford University in collaboration with Oak Ridge National Laboratories and Nomadic Technologies.
Single charge manipulation for useful electronic functionalities has become an exciting and fast-paced direction of research in recent years. In structures with dimensions below about 100 nm, the physics governing the device operation turn out to be strikingly different than in the case of larger devices. The presence of even a single charge may completely suppress current flow due to the basic electronelectron repulsion (so called Coulomb blockade effect) [1]. It is even more exciting to control this effect at the level of single-electron/single-atom interaction. The atomic entity can be one donor present in silicon lattice with a Coulombic potential well. In principle, it can accommodate basically a single electron. We study the electrical behavior of nanoscale-channel silicon-on-insulator field-effect transistors (SOI-FETs) that contain a discrete arrangement of donors. The donors can be utilized as "stepping stones" for the transfer of single charges. This ability opens the doors to a rich world of applications based on the simple interplay of single charges and single atoms, while still utilizing mostly conventional and well established fabrication techniques. In this work, we distinguish the effects of single-electron transport mediated by one or few dopants only. Furthermore, we show how the single-electron/single-donor interaction can be tuned by using the external biases. We demonstrate then by simulation and experiment the feasibility of single-electron/bit transfer operation (single-electron turnstile).
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