Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Assessing the extent to which temporal changes in waterbird community composition are driven by either local, regional or global factors.

1. Lough Neagh and Lough Beg Special Protection Area (SPA, hereafter Lough Neagh) is an important non-estuarine site in Britain and Ireland for overwintering wildfowl. Multivariate analysis of the winter counts showed a state-shift in the waterbird community following winter 2000/2001, mostly due to rapid declines in abundance (46–57% declines in the mean mid-winter January counts between 1993–2000 and 2002–2009) of members of the diving duck guild (pochard Aythya ferina, tufted duck Aythya fuligula and goldeneye Bucephala clangula) and coot (Fulica atra), a submerged macrophyte feeder.
2. Only pochard showed correlations between declines at Lough Neagh and those of overall species flyway population indices to suggest that global changes could contribute to declines at the site. However, indices from the Republic of Ireland showed no overall decline in the rest of Ireland. Tufted duck indices at the site were inversely related to indices in Great Britain. Lough Neagh goldeneye indices were positively correlated with indices in the Republic of Ireland and Great Britain, suggesting that short-stopping could contribute to declines at the site. Coot declines at Lough Neagh did not correlate with trends elsewhere, suggesting local factors involved in the decline.
3. These analyses indicate that although there are potentially different explanations for the dramatic declines in these four waterbird species at this site, the simultaneous nature of the declines across two feeding guilds strongly
suggest that local factors (such as loss of submerged macrophytes and benthic invertebrates) were involved. An assessment of the food supply, local disturbance and other factors at Lough Neagh is required to find an explanation for the observed adverse trends in wintering numbers of the affected species.
4. This study highlights the potential of waterbird community structure to reflect the status of aquatic systems, but confirms the need to establish site-specific factors responsible for the observed changes in abundance of key waterbird species at a site.