Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Matching search in fractal video compression and its parallel implementation in distributed computing environments

Fractal video compression is a relatively new video compression method. Its attraction is due to the high compression ratio and the simple decompression algorithm. But its computational complexity is high and as a result parallel algorithms on high performance machines become one way out. In this study we partition the matching search, which occupies the majority of the work in a fractal video compression process, into small tasks and implement them in two distributed computing environments, one using DCOM and the other using .NET Remoting technology, based on a local area network consists of loosely coupled PCs. Experimental results show that the parallel algorithm is able to achieve a high speedup in these distributed environments.

Using historical data to detect temporal changes in the abundances of intertidal species on Irish shores

An historical data set, collected in 1958 by Southward and Crisp, was used as a baseline for detecting change in the abundances of species in the rocky intertidal of Ireland. In 2003, the abundances of each of 27 species was assessed using the same methodologies (ACFOR [which stands for the categories: abundant, common, frequent, occasional and rare] abundance scales) at 63 shores examined in the historical study. Comparison of the ACFOR data over a 45-year period, between the historical survey and re-survey, showed statistically significant changes in the abundances of 12 of the 27 species examined. Two species (one classed as northern and one introduced) increased significantly in abundance while ten species (five classed as northern, one classed as southern and four broadly distributed) decreased in abundance. The possible reasons for the changes in species abundances were assessed not only in the context of anthropogenic effects, such as climate change and commercial exploitation, but also of operator error. The error or differences recorded among operators (i.e. research scientists) when assessing species abundance using ACFOR categories was quantified on four shores. Significant change detected in three of the 12 species fell within the margin of operator error. This effect of operator may have also contributed to the results of no change in the other 15 species between the two census periods. It was not possible to determine the effect of operator on our results, which can increase the occurrence of a false positive (Type 1) or of a false negative (Type 2) outcome