The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

Correlation between carbon isotope discrimination and transpiration efficiency in lines of the C-4 species Sorghum bicolor in the glasshouse and the field

Transpiration efficiency, W, the ratio of plant carbon produced to water transpired and carbon isotope discrimination of leaf dry matter, Delta(d)' were measured together on 30 lines of the C-4 species, Sorghum bicolor in the glasshouse and on eight lines grown in the field. In the glasshouse, the mean W observed was 4.9 mmol C mol(-1) H2O and the range was 0.8 mmol C mol(-1) H2O The mean Delta(d) was 3.0 parts per thousand and the observed range was 0.4 parts per thousand. In the field, the mean W was lower at 2.8 mmol C mol H2O and the mean Delta(d) was 4.6 parts per thousand. Significant positive correlations between W and Delta(d) were observed for plants grown in the glasshouse and in the field. The observed correlations were consistent with theory, opposite to those for C-4 species, and showed that variation in Delta(d) was an integrated measure of long-term variation in the ratio of intercellular to ambient CO2 partial pressure, p(i)/p(a). Detailed gas exchange measurements of carbon isotope discrimination during CO2 uptake, Delta(A) and p(i)/p(a) were made on leaves of eight S. bicolor lines. The observed relationship between Delta(A) and p(i)/p(a) was linear with a negative slope of 3.7 parts per thousand in Delta(A) for a unit change in p(i)/p(a). The slope of this linear relationship between Delta(A) and p(i)/p(a) in C-4 species is dependent on the leakiness of the CO2 concentrating mechanism of the C pathway, We estimated the leakiness (defined as the fraction of CO2 released in the bundle sheath by C-4 acid decarboxylations, which is lost by leakage) to be 0.2. We conclude that, although variation in Delta(d) observed in the 30 lines of S. bicolor is smaller than that commonly observed in C-4 species, it also reflects variation in transpiration efficiency, W. Among the eight lines examined in detail and in the environments used, there was considerable genotype x environment interaction.

New stereoselective routes to macrocyclic ligands

Reaction of bis(ethane-1,2-diamine)copper(II) with acetaldehyde and nitromethane in methanol leads, stereoselectively, to the new macrocyclic complex (trans-5(R),7(R),12(S),14(S))-tetramethyl-6,13-dinitro-1,4,8,11-tetraazacyclotetradecane)copper(II) perchlorate alpha-[CuL1](ClO4)(2) in good yield. Reduction of the nitro groups affords the hexaamine (L-2), which was crystallized as [H4L2](ClO4)(4) . 2H(2)O and characterized by an X-ray crystal structure study (monoclinic P2(1)/n, a = 9.763(2) Angstrom, b = 12.1988(7) Angstrom, c = 13.036(2) Angstrom, beta = 105.668(7)degrees, Z = 2) and complexed with Cu-II to produce the complex beta-[Cu(H2L2)](ClO4)(4) . 2H(2)O, which has also been characterized by X-ray crystallography (monoclinic P2(1)/n, a = 9.717(4) Angstrom, b = 12.174(2) Angstrom, c = 13.036(5) Angstrom, beta = 106.51(2)degrees, Z = 2). Reaction of alpha-[CuL1](2+) with either basic hydrogen peroxide or dilute nitrous acid leads to mild reduction of the nitro groups to afford the ketoxime L-3 as its N-based isomeric Cu-II complexes, trans-I [CuL3](ClO4)(2) and trans-II [Cu(L-3)Cl]Cl . 7H(2)O, the latter of which has been characterized structurally: triclinic, <P(1)over bar> a = 10.8441(5) Angstrom, b = 11.6632(9) Angstrom, c = 11.8723(9) Angstrom, alpha = 113.634(7)degrees, beta = 95.744(5), gamma = 94.851(5)degrees Z = 2. Variations in the configurations of the coordinated amines in [CuL1](2+), [CuL2](2+), and [CuL3](2+) have a profound effect on the spectroscopy and electrochemistry of their complexes.

A role for protein kinase B beta/Akt2 in insulin-stimulated GLUT4 translocation in adipocytes

Insulin stimulates glucose uptake into muscle and fat cells by promoting the translocation of glucose transporter 4 (GLUT4) to the cell surface. Phosphatidylinositide 3-kinase (PI3K) has been implicated in this process. However, the involvement of protein kinase B (PKB)/Akt, a downstream target of PI3K in regulation of GLUT4 translocation, has been controversial. Here we report that microinjection of a PKB substrate peptide or an antibody to PKB inhibited insulin-stimulated GLUT4 translocation to the plasma membrane by 66 or 56%, respectively. We further examined the activation of PKB isoforms following treatment of cells with insulin or platelet-derived growth factor (PDGF) and found that PKB beta is preferentially expressed in both rat and 3T3-L1 adipocytes, whereas PKB alpha expression is down-regulated in 3T3-L1 adipocytes. A switch in growth factor response was also observed when 3T3-L1 fibroblasts were differentiated into adipocytes. While PDGF was more efficacious than insulin in stimulating PKB phosphorylation in fibroblasts, PDGF did not stimulate PKB beta phosphorylation to any significant extent in adipocytes, as assessed by several methods. Moreover, insulin, but not PDGF, stimulated the translocation of PKB beta to the plasma membrane and high-density microsome fractions of 3T3-L1 adipocytes. These results support a role for PKB beta in insulin-stimulated glucose transport in adipocytes.

Estimating HIV incidence rates from age prevalence data in epidemic situations

We present a method of estimating HIV incidence rates in epidemic situations from data on age-specific prevalence and changes in the overall prevalence over time. The method is applied to women attending antenatal clinics in Hlabisa, a rural district of KwaZulu/Natal, South Africa, where transmission of HIV is overwhelmingly through heterosexual contact. A model which gives age-specific prevalence rates in the presence of a progressing epidemic is fitted to prevalence data for 1998 using maximum likelihood methods and used to derive the age-specific incidence. Error estimates are obtained using a Monte Carlo procedure. Although the method is quite general some simplifying assumptions are made concerning the form of the risk function and sensitivity analyses are performed to explore the importance of these assumptions. The analysis shows that in 1998 the annual incidence of infection per susceptible woman increased from 5.4 per cent (3.3-8.5 per cent; here and elsewhere ranges give 95 per cent confidence limits) at age 15 years to 24.5 per cent (20.6-29.1 per cent) at age 22 years and declined to 1.3 per cent (0.5-2.9 per cent) at age 50 years; standardized to a uniform age distribution, the overall incidence per susceptible woman aged 15 to 59 was 11.4 per cent (10.0-13.1 per cent); per women in the population it was 8.4 per cent (7.3-9.5 per cent). Standardized to the age distribution of the female population the average incidence per woman was 9.6 per cent (8.4-11.0 per cent); standardized to the age distribution of women attending antenatal clinics, it was 11.3 per cent (9.8-13.3 per cent). The estimated incidence depends on the values used for the epidemic growth rate and the AIDS related mortality. To ensure that, for this population, errors in these two parameters change the age specific estimates of the annual incidence by less than the standard deviation of the estimates of the age specific incidence, the AIDS related mortality should be known to within +/-50 per cent and the epidemic growth rate to within +/-25 per cent, both of which conditions are met. In the absence of cohort studies to measure the incidence of HIV infection directly, useful estimates of the age-specific incidence can be obtained from cross-sectional, age-specific prevalence data and repeat cross-sectional data on the overall prevalence of HIV infection. Several assumptions were made because of the lack of data but sensitivity analyses show that they are unlikely to affect the overall estimates significantly. These estimates are important in assessing the magnitude of the public health problem, for designing vaccine trials and for evaluating the impact of interventions. Copyright (C) 2001 John Wiley & Sons, Ltd.

A Randomized Trial of Sodium Fluoride (60 mg) ± Estrogen in Postmenopausal Osteoporotic Vertebral Fractures

Postmenopausal Caucasian women aged less than 80 years (n = 99) with one or more atraumatic vertebral fracture and no hip fractures, were treated by cyclical administration of enteric coated sodium fluoride (NaF) or no NaF for 27 months, with precautions to prevent excessive stimulation of bone turnover. In the first study 65 women, unexposed to estrogen (-E study), age 70.8 +/- 0.8 years (mean SEM) were all treated with calcium (Ca) 1.0-1.2 g daily and ergocalciferol (D) 0.25 mg per 25 kg once weekly and were randomly assigned to cyclical NaF (6 months on. 3 months off, initial dose 60 mg/day; group F CaD, n = 34) or no NaF (group CaD, n = 3 1). In the second study 34 patients. age 65.5 +/- 1.2 years, on hormone replacement therapy (E) at baseline, had this standardized, and were all treated with Ca and D and similarly randomized (FE CaD, n = 17, E CaD, n = 17) (+E study). The patients were stratified according to E status and subsequently assigned randomly to NaF. Seventy-five patients completed the trial. Both groups treated with NaF showed an increase in lumbar spinal density (by DXA) above baseline by 27 months: FE CaD + 16.2% and F CaD +9.3% (both p = 0.0001). In neither group CaD nor E CaD did lumbar spinal density increase. Peripheral bone loss occurred at most sites in the F CaD group at 27 months: tibia/fibula shaft -7.3% (p = 0.005); femoral shaft -7.1% (p = 0.004); distal forearm -4.0% (p = 0.004); total hip -4.1% (p = 0. 003); and femoral neck -3.5% (p = 0.006). No significant loss occurred in group FE CaD. Differences between the two NaF groups were greatest at the total hip at 27 months but were not significant [p < 0.05; in view of the multiple bone mineral density (BMD) sites, an alpha of 0.01 was employed to denote significance in BMD changes throughout this paper]. Using Cox's proportional hazards model, in the -E study there were significantly more patients with first fresh vertebral fractures in those treated with NaF than in those not so treated (RR = 24.2, p = 0.008, 95% CI 2.3-255). Patients developing first fresh fractures in the first 9 months were markedly different between groups: -23% of F CaD, 0 of CaD, 29% of FE CaD and 0 of E CaD. The incidence of incomplete (stress) fractures was similar in the two NaF-treated groups. Complete nonvertebral fractures did not occur in the two +E groups, there were no differences between groups F CaD and CaD. Baseline BMD (spine and femoral neck) was related to incident vertebral fractures in the control groups (no NaF), but not in the two NaF groups. Our results and a literature review indicate that fluoride salts. if used, should be at low dosage, with pretreatment and co-treatment with a bone resorption inhibitor.

The interaction of metal ions and Marimastat with matrix metalloproteinase 9

The effect of a range of metal ions on the ability of Marimastat to inhibit matrix metalloproteinase 9 (MMP-9) was examined in a fluorescence based proteolytic assay. Whilst none of the metals examined significantly affected the inhibitory ability of Marimastat, several metal ions did have a significant effect on MMP-9 activity itself. In the absence of Marimastat, Zn(II) and Fe(II) significantly inhibited MMP-9 activity at metal ion concentrations of 10 and 100 muM, respectively. In both the absence and presence of Marimastat, Cd(II) significantly inhibited MMP-9 at 100 muM. In contrast, 1 mM Co(II) significantly upregulated MMP-9 proteolytic activity. (C) 2003 Elsevier Science Inc. All rights reserved.

Aspects of adaptive management of coastal wetlands: Case studies of processes, conservation, restoration, impacts and assessment

Coastal wetlands are dynamic and include the freshwater-intertidal interface. In many parts of the world such wetlands are under pressure from increasing human populations and from predicted sea-level rise. Their complexity and the limited knowledge of processes operating in these systems combine to make them a management challenge.Adaptive management is advocated for complex ecosystem management (Hackney 2000; Meretsky et al. 2000; Thom 2000;National Research Council 2003).Adaptive management identifies management aims,makes an inventory/environmental assessment,plans management actions, implements these, assesses outcomes, and provides feedback to iterate the process (Holling 1978;Walters and Holling 1990). This allows for a dynamic management system that is responsive to change. In the area of wetland management recent adaptive approaches are exemplified by Natuhara et al. (2004) for wild bird management, Bunch and Dudycha (2004) for a river system, Thom (2000) for restoration, and Quinn and Hanna (2003) for seasonal wetlands in California. There are many wetland habitats for which we currently have only rudimentary knowledge (Hackney 2000), emphasizing the need for good information as a prerequisite for effective management. The management framework must also provide a way to incorporate the best available science into management decisions and to use management outcomes as opportunities to improve scientific understanding and provide feedback to the decision system. Figure 9.1 shows a model developed by Anorov (2004) based on the process-response model of Maltby et al. (1994) that forms a framework for the science that underlies an adaptive management system in the wetland context.

Spontaneous and stimulus-evoked intrinsic optical signals in primary auditory cortex of the cat

Spontaneous and tone-evoked changes in light reflectance were recorded from primary auditory cortex (A1) of anesthetized cats (barbiturate induction, ketamine maintenance). Spontaneous 0.1-Hz oscillations of reflectance of 540- and 690-nm light were recorded in quiet. Stimulation with tone pips evoked localized reflectance decreases at 540 nm in 3/10 cats. The distribution of patches activated by tones of different frequencies reflected the known tonotopic organization of auditory cortex. Stimulus-evoked reflectance changes at 690 nm were observed in 9/10 cats but lacked stimulus-dependent topography. In two experiments, stimulus-evoked optical signals at 540 nm were compared with multiunit responses to the same stimuli recorded at multiple sites. A significant correlation (P < 0.05) between magnitude of reflectance decrease and multiunit response strength was evident in only one of five stimulus conditions in each experiment. There was no significant correlation when data were pooled across all stimulus conditions in either experiment. In one experiment, the spatial distribution of activated patches, evident in records of spontaneous activity at 540 nm, was similar to that of patches activated by tonal stimuli. These results suggest that local cerebral blood volume changes reflect the gross tonotopic organization of A1 but are not restricted to the sites of spiking neurons.