Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson’s space.

Evolutionary agglomeration theory: increasing returns, diminishing returns, and the industry life cycle

According to Marshall’s agglomeration theory, Krugman’s New Economic Geography models, and Porter’s cluster policies, firms should receive increasing returns from a trinity of agglomeration economies: a local pool of skilled labour, local supplier linkages, and local knowledge spillovers. Recent evolutionary theories suggest that whether agglomeration economies generate increasing returns or diminishing returns depends on time, and especially the evolution of the industry life cycle. At the start of the twenty-first century, we re-examine Marshall’s trinity of agglomeration economies in the city-region where he discovered them. The econometric results from our multivariate regression models are the polar opposite of Marshall’s. During the later stages of the industry life cycle, Marshall’s agglomeration economies decrease the economic performance of firms and create widespread diminishing returns for the economic development of the city-region, which has evolved to become one of the poorest city-regions in Europe.

High incidence of cryptic repeated elements in microsatellite flanking regions of galatheid genomes and its evolutionary implications

During the development of PCR primer sets for icrosatellite marker loci from enriched genomic libraries for three squat lobster species from Galatheidae (Decapoda: Anomura); Munida rugosa (Fabricius, 1775), M. sarsi (Huus, 1935), and Galathea strigosa (Linnaeus, 1761) (collectively known as squat lobsters), a number of unforeseen problems were encountered. These included PCR amplification failure, lack of amplification consistency, and the amplification of multiple fragments. Careful examination of microsatellite containing sequences revealed the existence of cryptic repeated elements on presumed unique flanking regions. BLAST analysis of these and other VNTR containing sequences (N 5 252) indicates that these cryptic elements can be grouped into families based upon sequence similarities. The unique features characterising these families suggest that different molecular mechanisms are involved. Of particular relevance is the association of microsatellites with mobile elements. This is the first reported observation of this phenomenon in crustaceans, and it also helps to explain why microsatellite primer development in galatheids has been relatively unsuccessful to date. We suggest a number of steps that can be used to identify similar problems in microsatellite marker development for other species, and also alternative approaches for both marker development and for the study of molecular evolution of species characterised by complex genome organisation. More specifically, we argue that new generation sequencing methodologies, which capitalise on parallel and multiplexed sequencing may pave the way forward for future crustacean research.