Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accordingly, we have also changed the manuscript titl

A multi-criteria decision approach to decommissioning of offshore oil and gas infrastructure

Thousands of the world's offshore oil and gas structures are approaching obsolescence and will require decommissioning within the next decade. Many nations have blanket regulations requiring obsolete structures to be removed, yet this option is unlikely to yield optimal environmental, societal and economic outcomes in all situations. We propose that nations adopt a flexible approach that allows decommissioning options to be selected from the full range of alternatives (including ‘rigs-to-reefs’ options) on a case-by-case basis. We outline a method of multi-criteria decision analysis (Multi-criteria Approval, MA) for evaluating and comparing alternative decommissioning options across key selection criteria, including environmental, financial, socioeconomic, and health and safety considerations. The MA approach structures the decision problem, forces explicit consideration of trade-offs and directly involves stakeholder groups in the decision process. We identify major decommissioning options and provide a generic list of selection criteria for inclusion in the MA decision process. To deal with knowledge gaps concerning environmental impacts of decommissioning, we suggest that expert opinion feed into the MA approach until sufficient data become available. We conducted a limited trial of the MA decision approach to demonstrate its application to a complex and controversial decommissioning scenario; Platform Grace in southern California. The approach indicated, for this example, that the option ‘leave in place intact’ would likely provide best environmental outcomes in the event of future decommissioning. In summary, the MA approach will allow the environmental, social, and economic impacts of decommissioning decisions to be assessed simultaneously in a transparent manner

Multiple sclerosis genomic map implicates peripheral immune cells and microglia in susceptibility

We analyzed genetic data of 47,429 multiple sclerosis (MS) and 68,374 control subjects and established a reference map of the genetic architecture of MS that includes 200 autosomal susceptibility variants outside the major histocompatibility complex (MHC), one chromosome X variant, and 32 variants within the extended MHC. We used an ensemble of methods to prioritize 551 putative susceptibility genes that implicate multiple innate and adaptive pathways distributed across the cellular components of the immune system. Using expression profiles from purified human microglia, we observed enrichment for MS genes in these brain-resident immune cells, suggesting that these may have a role in targeting an autoimmune process to the central nervous system, although MS is most likely initially triggered by perturbation of peripheral immune responses