In 1973 Dijkstra introduced to computer science the notion of self-stabilization in the context of distributed systems. He defined a system as self-stabilizing when “regardless of its initial state, it is guaranteed to arrive at a legitimate state in a finite number of steps.” A system which is not self-stabilizing may stay in an illegitimate state forever. Dijkstra's notion of self-stabilization, which originally had a very narrow scope of application, is proving to encompass a formal and unified approach to fault tolerance under a model of transient failures for distributed systems. In this paper we define self-stabilization, examine its significance in the context of fault tolerance, define the important research themes that have arisen from it, and discuss the relevant results. In addition to the issues arising from Dijkstra's original presentation as well as several related issues, we discuss methodologies for designing self-stabilizing systems, the role of compilers with respect to self-stabilization, and some of the factors that prevent self-stabilization.

Abstract.A stabilizing algorithm is silent if starting from an arbitrary state it converges to a global state after which the values stored in the communication registers are fixed. Many silent stabilizing algorithms have appeared in the literature. In this paper we show that there cannot exist constant memory silent stabilizing algorithms for finding the centers of a graph, electing a leader, and constructing a spanning tree. We demonstrate a lower bound of Ω(log n) bits per communication register for each of the above tasks.

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Characterizing the morphology of the carpometacarpal (CMC) joint bones and how they vary across the population is important for understanding the functional anatomy and pathology of the thumb. The purpose of this paper was to develop a statistical shape model of the trapezium and first metacarpal bones to characterize the size and shape of the whole bones across a cohort of 50. We used this shape model to investigate the effects of sex and age on the size and shape of the CMC joint bones and the articulating surface area of the CMC joint. We hypothesized that women have similar shape trapezium and first metacarpal bones compared to men, following scaling for overall size. We also hypothesized that age would be a significant predictor variable for CMC joint bone changes. CT image data and segmented point clouds of 50 CMC bones from healthy adult men and women were obtained from an ongoing study and used to generate two statistical shape models. Statistical analysis of the principal component weights of both models was performed to investigate morphological sex and age differences. We observed sex differences, but were unable to detect any age differences. Between men and women the only difference in morphology of the trapezia and first metacarpal bones was size. These findings confirm our first hypothesis, and suggest that the women have similarly shaped trapezium and first metacarpal bones compared to men. Furthermore, our results reject our second hypothesis, indicating that age is a poor predictor of CMC joint morphology.

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