The Riesz space structure of an Abelian W*-algebra

Let M be an Abelian W*-algebra of operators on a Hilbert space H. Let M₀ be the set of all linear, closed, densely defined transformations in H which commute with every unitary operator in the commutant M’ of M. A well known result of R. Pallu de Barriere states that if ɸ is a normal positive linear functional on M, then ɸ is of the form T → (Tx, x) for some x in H, where T is in M. An elementary proof of this result is given, using only those properties which are consequences of the fact that ReM is a Dedekind complete Riesz space with plenty of normal integrals. The techniques used lead to a natural construction of the class M₀, and an elementary proof is given of the fact that a positive self-adjoint transformation in M₀ has a unique positive square root in M₀. It is then shown that when the algebraic operations are suitably defined, then M₀ becomes a commutative algebra. If ReM₀ denotes the set of all self-adjoint elements of M₀, then it is proved that ReM₀ is Dedekind complete, universally complete Riesz spaces which contains ReM as an order dense ideal. A generalization of the result of R. Pallu de la Barriere is obtained for the Riesz space ReM₀ which characterizes the normal integrals on the order dense ideals of ReM₀. It is then shown that ReM₀ may be identified with the extended order dual of ReM, and that ReM₀ is perfect in the extended sense.

Some secondary questions related to the Riesz space ReM are also studied. In particular it is shown that ReM is a perfect Riesz space, and that every integral is normal under the assumption that every decomposition of the identity operator has non-measurable cardinal. The presence of atoms in ReM is examined briefly, and it is shown that ReM is finite dimensional if and only if every order bounded linear functional on ReM is a normal integral.

Permanent Genetic Resources added to Molecular Ecology Resources Database 1 May 2009-31 July 2009

This article documents the addition of 512 microsatellite marker loci and nine pairs of Single Nucleotide Polymorphism (SNP) sequencing primers to the Molecular Ecology Resources Database. Loci were developed for the following species: Alcippe morrisonia morrisonia, Bashania fangiana, Bashania fargesii, Chaetodon vagabundus, Colletes floralis, Coluber constrictor flaviventris, Coptotermes gestroi, Crotophaga major, Cyprinella lutrensis, Danaus plexippus, Fagus grandifolia, Falco tinnunculus, Fletcherimyia fletcheri, Hydrilla verticillata, Laterallus jamaicensis coturniculus, Leavenworthia alabamica, Marmosops incanus, Miichthys miiuy, Nasua nasua, Noturus exilis, Odontesthes bonariensis, Quadrula fragosa, Pinctada maxima, Pseudaletia separata, Pseudoperonospora cubensis, Podocarpus elatus, Portunus trituberculatus, Rhagoletis cerasi, Rhinella schneideri, Sarracenia alata, Skeletonema marinoi, Sminthurus viridis, Syngnathus abaster, Uroteuthis (Photololigo) chinensis, Verticillium dahliae, Wasmannia auropunctata, and Zygochlamys patagonica. These loci were cross-tested on the following species: Chaetodon baronessa, Falco columbarius, Falco eleonorae, Falco naumanni, Falco peregrinus, Falco subbuteo, Didelphis aurita, Gracilinanus microtarsus, Marmosops paulensis, Monodelphis Americana, Odontesthes hatcheri, Podocarpus grayi, Podocarpus lawrencei, Podocarpus smithii, Portunus pelagicus, Syngnathus acus, Syngnathus typhle,Uroteuthis (Photololigo) edulis, Uroteuthis (Photololigo) duvauceli and Verticillium albo-atrum. This article also documents the addition of nine sequencing primer pairs and sixteen allele specific primers or probes for Oncorhynchus mykiss and Oncorhynchus tshawytscha; these primers and assays were cross-tested in both species.

G.W.F.Hegel (1770-1831) : Cyfundrefn, Ysbryd a Hanes

Williams, Howard, G.W.F.Hegel (1770-1831): Cyfundrefn, Ysbryd a Hanes (University of Wales Press, 2005), pp.30-48

Waldo Williams:? 'Holi'n Hir yn y Tir Tywyll'

Bryant-Quinn, M. (2006). Waldo Williams: 'Holi'n Hir yn y Tir Tywyll'. In D. Walford Davies and J. Walford Davies(Eds.), Cof ac Arwydd: Ysgrifau Newydd ar Waldo Williams (pp.143-162). Abertawe: Cyhoeddiadau Barddas.

Neurobiological model of visuo-spatial cognition in young Williams Syndrome children: measures of dorsal-stream and frontal function

We examine hypotheses for the neural basis of the profile of visual cognition in young children with Williams syndrome (WS). These are: (a) that it is a consequence of anomalies in sensory visual processing; (b) that it is a deficit of the dorsal relative to the ventral cortical stream; (c) that it reflects deficit of frontal function, in particular of fronto-parietal interaction; (d) that it is related to impaired function in the right hemisphere relative to the left. The tests reported here are particularly relevant to (b) and (c). They form part of a more extensive programme of investigating visual, visuospatial, and cognitive function in large group of children with WS children, aged 8 months to 15 years. To compare performance across tests, avoiding floor and ceiling effects, we have measured performance in children with WS in terms of the ‘age equivalence’ for typically developing children. In this paper the relation between dorsal and ventral function was tested by motion and form coherence thresholds respectively. We confirm the presence of a subgroup of children with WS who perform particularly poorly on the motion (dorsal) task. However, such performance is also characteristic of normally developingchildren up to 5 years: thus the WS performance may reflect an overall persisting immaturity of visuospatial processing which is particularly evident in the dorsal stream. Looking at the performance on the global coherence tasks of the entire WS group, we find that there is also a subgroup who have both high form and motion coherence thresholds, relative to the performance of children of the same chronological age and verbal age on the BPVS, suggesting a more general global processing deficit. Frontal function was tested by a counterpointing task, ability to retrieve a ball from a ‘detour box’, and the Stroop-like ‘day-night’ task, all of which require inhibition of a familiar response. When considered in relation to overall development as indexed by vocabulary, the day-night task shows little specific impairment, the detour box shows a significant delay relative to controls, and the counterpointing task shows a marked and persistent deficit in many children. We conclude that frontal control processes show most impairment in WS when they are associated with spatially directed responses, reflecting a deficit of fronto-parietal processing. However, children with WS may successfully reduce the effect of this impairment by verbally mediated strategies. On all these tasks we find a range of difficulties across individual children and a small subset of WS who show very good performance, equivalent to chronological age norms of typically developing children. Neurobiological models of visuo-spatial cognition in children with WS p.4 Overall, we conclude that children with WS have specific processing difficulties with tasks involving frontoparietal circuits within the spatial domain. However, some children with WS can achieve similar performance to typically developing children on some tasks involving the dorsal stream, although the strategies and processing may be different in the two groups.

The persistence of the HgCl2 molecule in five new compounds in the system (NH4)(w)HgxCly(H2O)(z) with w : x : y : z=1 : 5 : 11 : 0, 2 : 3 : 8 : 1, 4 : 3 : 10 : 2, 2 : 1 : 4 : 1, and 10 : 3 : 16 : 0

Five new compounds in the system (NH4)Cl/HgCl2/H2O have been obtained as colourless single crystals, (NH4)Hg5Cl11, (NH4)(2)Hg3Cl8(H2O), (NH4)(4)Hg3Cl10(H2O)(2), (NH4)(2)HgCl4(H2O), and (NH4)(10)Hg3Cl16. In all of these, as in HgCl2 itself, (almost) linear HgCl2 molecules persist with Hg-Cl distances varying from 229 to 236 pm. In (NH4)(10)Hg3Cl16 there are also tetrahedra [HgCl4] with d(Hg-Cl) = 247 pm present. If larger Hg-Cl distances (of up to 340 pm) are considered as belonging to the coordination sphere of Hg-II, the structures may be described as consisting of isolated octahedra and tetrahedra as in (NH4)(10)Hg3Cl16, edge-connected chains as in (NH4)(2)HgCl4(H2O), edge-connected chains and layers of octahedra as in (NH4)(4)Hg3Cl10(H2O)(2), corrugated layers of edge-connected octahedra as in (NH4)(2)Hg3Cl8(H2O), and, finally, a three-dimensional network of connected six- and seven-coordinate Hg-Cl polyhedra as in (NH4)Hg5Cl11. The water molecules are never attached to Hg-II. The (NH4)(+) cations, and sometimes Cl- anions, play a role for electroneutrality only.

Genome-wide association study identifies variants at CLU and PICALM associated with Alzheimer's disease

We undertook a two-stage genome-wide association study (GWAS) of Alzheimer's disease (AD) involving over 16,000 individuals, the most powerful AD GWAS to date. In stage 1 (3,941 cases and 7,848 controls), we replicated the established association with the apolipoprotein E (APOE) locus (most significant SNP, rs2075650, P = 1.8 x 10(-157)) and observed genome-wide significant association with SNPs at two loci not previously associated with the disease: at the CLU (also known as APOJ) gene (rs11136000, P = 1.4 x 10(-9)) and 5. to the PICALM gene (rs3851179, P = 1.9 x 10(-8)). These associations were replicated in stage 2 (2,023 cases and 2,340 controls), producing compelling evidence for association with Alzheimer's disease in the combined dataset (rs11136000, P = 8.5 x 10(-10), odds ratio = 0.86; rs3851179, P = 1.3 x 10(-9), odds ratio = 0.86).

The Cambridge Companion to Vaughan Williams

An icon of British national identity and one of the most widely performed twentieth-century composers, Ralph Vaughan Williams has been as much misunderstood as revered; his international impact, and enduring influence on areas as diverse as church music, film scores, and popular music, has been insufficiently appreciated. This volume brings together a team of leading scholars, examining all areas of the composer’s output from new perspectives, and re-evaluating the cultural politics of his lifelong advocacy for the music-making of ordinary people. Surveys of major genres are complemented by chapters exploring such topics as the composer’s relationship with the BBC, and his studies with Ravel; uniquely, the book also includes specially commissioned interviews with major living composers Peter Maxwell Davies, Piers Hellawell, Nicola Lefanu, and Anthony Payne.

Genetic Evidence Implicates the Immune System and Cholesterol Metabolism in the Aetiology of Alzheimer's Disease

Background: Late Onset Alzheimer's disease (LOAD) is the leading cause of dementia. Recent large genome-wide association studies (GWAS) identified the first strongly supported LOAD susceptibility genes since the discovery of the involvement of APOE in the early 1990s. We have now exploited these GWAS datasets to uncover key LOAD pathophysiological processes. Methodology: We applied a recently developed tool for mining GWAS data for biologically meaningful information to a LOAD GWAS dataset. The principal findings were then tested in an independent GWAS dataset.

Common variants at ABCA7, MS4A6A/MS4A4E, EPHA1, CD33 and CD2AP are associated with Alzheimer's disease

We sought to identify new susceptibility loci for Alzheimer's disease through a staged association study (GERAD+) and by testing suggestive loci reported by the Alzheimer's Disease Genetic Consortium (ADGC) in a companion paper. We undertook a combined analysis of four genome-wide association datasets (stage 1) and identified ten newly associated variants with P = 1 × 10(-5). We tested these variants for association in an independent sample (stage 2). Three SNPs at two loci replicated and showed evidence for association in a further sample (stage 3). Meta-analyses of all data provided compelling evidence that ABCA7 (rs3764650, meta P = 4.5 × 10(-17); including ADGC data, meta P = 5.0 × 10(-21)) and the MS4A gene cluster (rs610932, meta P = 1.8 × 10(-14); including ADGC data, meta P = 1.2 × 10(-16)) are new Alzheimer's disease susceptibility loci. We also found independent evidence for association for three loci reported by the ADGC, which, when combined, showed genome-wide significance: CD2AP (GERAD+, P = 8.0 × 10(-4); including ADGC data, meta P = 8.6 × 10(-9)), CD33 (GERAD+, P = 2.2 × 10(-4); including ADGC data, meta P = 1.6 × 10(-9)) and EPHA1 (GERAD+, P = 3.4 × 10(-4); including ADGC data, meta P = 6.0 × 10(-10)).

Vaughan Williams and contemporary music: composers' forum

Like many long-lived composers, Vaughan Williams suffered a decline in his reputation immediately following his death, as the emergence in the 1960s of a younger generation of composers rendered much of his work outmoded in the eyes of many critics. In recent years, however, the reception of Vaughan Williams's music among composers has improved markedly, a combination of the ebbing of the tide of high modernism and greater pluralism in contemporary music, and a growing awareness that Vaughan Williams was perhaps more modernist (or at least progressive) than had previously been thought. In interviews with four leading British composers (two of whom were part of the 1960s generation mentioned above), I investigate the nature and extent of Vaughan Williams's legacy to his successors, both musical and social. What emerges is a near consensus on Vaughan Williams's greatest works, but a diversity of views on his compositional techniques and on his place among his European contemporaries.