SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Unitary SK1 of unitary and graded division algebras

The reduced unitary Whitehead group $\SK$ of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary $\SK$ of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary $\SK$ of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary $\SK$ for much wider classes of division algebras over henselian fields.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Effect of providing free glasses on children's educational outcomes in China: cluster randomized controlled trial

Objective: To assess the effect of provision of free glasses on academic performance in rural Chinese children with myopia. Design: Cluster randomized, investigator masked, controlled trial.Setting 252 primary schools in two prefectures in western China, 2012-13. Participants: 3177 of 19 934 children in fourth and fifth grades (mean age 10.5 years) with visual acuity <6/12 in either eye without glasses correctable to >6/12 with glasses. 3052 (96.0%) completed the study.Interventions Children were randomized by school (84 schools per arm) to one of three interventions at the beginning of the school year: prescription for glasses only (control group), vouchers for free glasses at a local facility, or free glasses provided in class. Main outcome measures: Spectacle wear at endline examination and end of year score on a specially designed mathematics test, adjusted for baseline score and expressed in standard deviations. Results: Among 3177 eligible children, 1036 (32.6%) were randomized to control, 988 (31.1%) to vouchers, and 1153 (36.3%) to free glasses in class. All eligible children would benefit from glasses, but only 15% wore them at baseline. At closeout glasses wear was 41% (observed) and 68% (self reported) in the free glasses group, and 26% (observed) and 37% (self reported) in the controls. Effect on test score was 0.11 SD (95% confidence interval 0.01 to 0.21) when the free glasses group was compared with the control group. The adjusted effect of providing free glasses (0.10, 0.002 to 0.19) was greater than parental education (0.03, −0.04 to 0.09) or family wealth (0.01, −0.06 to 0.08). This difference between groups was significant, but was smaller than the prespecified 0.20 SD difference that the study was powered to detect. Conclusions: The provision of free glasses to Chinese children with myopia improves children’s performance on mathematics testing to a statistically significant degree, despite imperfect compliance, although the observed difference between groups was smaller than the study was originally designed to detect. Myopia is common and rarely corrected in this setting. Trial Registration: Current Controlled Trials ISRCTN03252665.

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

Association Between Results of a Gene Expression Signature Assay and Recurrence-Free Interval in Patients With Stage II Colon Cancer in Cancer and Leukemia Group B 9581 (Alliance)

PURPOSE: Conventional staging methods are inadequate to identify patients with stage II colon cancer (CC) who are at high risk of recurrence after surgery with curative intent. ColDx is a gene expression, microarray-based assay shown to be independently prognostic for recurrence-free interval (RFI) and overall survival in CC. The objective of this study was to further validate ColDx using formalin-fixed, paraffin-embedded specimens collected as part of the Alliance phase III trial, C9581.

PATIENTS AND METHODS: C9581 evaluated edrecolomab versus observation in patients with stage II CC and reported no survival benefit. Under an initial case-cohort sampling design, a randomly selected subcohort (RS) comprised 514 patients from 901 eligible patients with available tissue. Forty-nine additional patients with recurrence events were included in the analysis. Final analysis comprised 393 patients: 360 RS (58 events) and 33 non-RS events. Risk status was determined for each patient by ColDx. The Self-Prentice method was used to test the association between the resulting ColDx risk score and RFI adjusting for standard prognostic variables.

RESULTS: Fifty-five percent of patients (216 of 393) were classified as high risk. After adjustment for prognostic variables that included mismatch repair (MMR) deficiency, ColDx high-risk patients exhibited significantly worse RFI (multivariable hazard ratio, 2.13; 95% CI, 1.3 to 3.5; P < .01). Age and MMR status were marginally significant. RFI at 5 years for patients classified as high risk was 82% (95% CI, 79% to 85%), compared with 91% (95% CI, 89% to 93%) for patients classified as low risk.

CONCLUSION: ColDx is associated with RFI in the C9581 subsample in the presence of other prognostic factors, including MMR deficiency. ColDx could be incorporated with the traditional clinical markers of risk to refine patient prognosis.

Neighboring Group-Controlled Hydrolysis: Towards “Designer” Drug Release Biomaterials

To give the first demonstration of neighboring group-controlled drug delivery rates, a series of novel, polymerizable ester drug conjugates was synthesized and fully characterized. The monomers are suitable for copolymerization in biomaterials where control of drug release rate is critical to prophylaxis or obviation of infection. The incorporation of neighboring group moieties differing in nucleophilicity, geometry, and steric bulk in the conjugates allowed the rate of ester hydrolysis, and hence drug liberation, to be rationally and widely controlled. Solutions (2.5 x 10-5 mol dm-3) of ester conjugates of nalidixic acid incorporating pyridyl, amino, and phenyl neighboring groups hydrolyzed according to first-order kinetics, with rate constants between 3.00 ( 0.12 10-5 s -1 (fastest) and 4.50 ( 0.31 10- 6 s-1 (slowest). The hydrolysis was characterized using UV-visible spectroscopy. When copolymerized with poly(methyl methacrylate), free drug was shown to elute from the resulting materials, with the rate of release being controlled by the nature of the conjugate, as in solution. The controlled molecular architecture demonstrated by this system offers an attractive class of drug conjugate for the delivery of drugs from polymeric biomaterials such as bone cements in terms of both sustained, prolonged drug release and minimization of mechanical compromise as a result of release. We consider these results to be the rationale for the development of 'designer' drug release biomaterials, where the rate of required release can be controlled by predetermined molecular architecture.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

Electroreduction of oxygen in a series of room temperature ionic liquids composed of group 15-centered cations and anions

The electrochemical reduction of oxygen is reported in four room temperature ionic liquids (RTILs) based on quaternary alkyl -onium cations and heavily fluorinated anions in which the central atom is either nitrogen or phosphorus. Data were collected using cyclic voltammetry and potential step chronoamperometry at gold, platinum, and glassy carbon disk electrodes of micrometer dimension under water-free conditions at a controlled temperature. Analysis via fitting, to appropriate theoretical equations was then carried out to obtain kinetic and thermodynamic information pertaining to the electrochemical processes observed. In the quaternary ammonium electrolytes, reduction of oxygen was found to occur reversibly to give stable superoxide, in an analogous manner to that seen in conventional aprotic solvents such as dimethyl sufoxide and acetonitrile. The most significant difference is in the relative rate of diffusion; the diffusion coefficients of oxygen in the RTILs are an order of magnitude lower than in common organic solvents, and for superoxide these values are reduced by a further factor of 10. In the quaternary phosphonium ionic liquids, however, more complex voltammetry is observed, akin to that expected for the reduction of oxygen in acidified organic media. This is shown to be consistent with the occurrence of a proton abstraction reaction between the electrogenerated superoxide and quaternary alkyl phosphonium cations following the initial electron transfer.

Sedentary aging increases resting and exercise-induced intramuscular free radical formation

Mitochondrial free radical formation has been implicated as a potential mechanism underlying degenerative senescence, although human data are lacking. Therefore, the present study was designed to examine if resting and exercise-induced intramuscular free radical-mediated lipid peroxidation is indeed increased across the spectrum of sedentary aging. Biopsies were obtained from the vastus lateralis in six young (26 ± 6 yr) and six aged (71 ± 6 yr) sedentary males at rest and after maximal knee extensor exercise. Aged tissue exhibited greater (P < 0.05 vs. the young group) electron paramagnetic resonance signal intensity of the mitochondrial ubisemiquinone radical both at rest (+138 ± 62%) and during exercise (+143 ± 40%), and this was further complemented by a greater increase in a-phenyl-tert-butylnitrone adducts identified as a combination of lipid-derived alkoxyl-alkyl radicals (+295 ± 96% and +298 ± 120%). Lipid hydroperoxides were also elevated at rest (0.190 ± 0.169 vs. 0.148 ± 0.071 nmol/mg total protein) and during exercise (0.567 ± 0.259 vs. 0.320 ± 0.263 nmol/mg total protein) despite a more marked depletion of ascorbate and uptake of a/ß-carotene, retinol, and lycopene (P < 0.05 vs. the young group). The impact of senescence was especially apparent when oxidative stress biomarkers were expressed relative to the age-related decline in mitochondrial volume density and absolute power output at maximal exercise. In conclusion, these findings confirm that intramuscular free radical-mediated lipid peroxidation is elevated at rest and during acute exercise in aged humans.

RESONANCE RAMAN-SPECTRA OF THE TRIPLET-STATE OF FREE-BASE TETRAPHENYLPORPHYRIN AND 6 OF ITS ISOTOPOMERS

The resonance Raman spectra of the ground state and the lowest excited tripler state of free-base tetraphenylporphyrin and six of its isotopomers have been obtained using two-color time-resolved techniques. Ground-state spectra were recorded using low-energy 447 nm probe laser pulses, and triplet-state spectra were probed, with similar pulses, 30 ns after high-energy excitation with 532 nm pump pulses. Polarization data on both the ground and triplet states are also reported. The resonance Raman spectrum of the triplet is very different from that of the ground state but the combination of extensive isotope substitution with polarization data allows bands in the ground state to be assigned and corresponding bands in the tripler state to be located. Isotope shifts of the same bands in the S-0 and T-1 states are similar, implying that the compositions of the vibrational modes do not change significantly on excitation. Two of the strongest bands in the T-1 spectra are associated with phenyl ring substituents; these are shifted less than 5 cm(-1) between the S-0 and T-1 states so that bonding in the phenyl substituents is barely affected by excitation to the T-1 state. The changes in position of the porphyrin ring bands are larger, but still only tens of cm(-1) or less, the main changes in the spectra being due to differences in relative band intensities in the two states. The relatively small shifts in the porphyrin ring band positions which are observed show that the excitation energy is not localized on a single small region of the molecule but is delocalized over the entire porphyrin skeleton. This picture of an excited species with high chemical reactivity, but with individual bonds only slightly perturbed from the ground state, is contrasted with molecules, such as benzophenone, where excitation causes a large perturbation in the bonding within a single functional group.

Killer immunoglobulin-like Receptors (KIR) haplogroups A and B track with Natural Killer Cells and Cytokine Profile in Aged Subjects: Observations from Octo/Nonagenarians in the Belfast Elderly Longitudinal Free-living Aging STudy (BELFAST)

Background: Natural Killer Cells (NK) play an important role in detection and elimination of virus-infected, damaged or cancer cells. NK cell function is guided by expression of Killer Immunoglobulin-like Receptors (KIRs) and contributed to by the cytokine milieu. KIR molecules are grouped on NK cells into stimulatory and inhibitory KIR haplotypes A and B, through which NKs sense and tolerate HLA self-antigens or up-regulate the NK-cytotoxic response to cells with altered HLA self-antigens, damaged by viruses or tumours. We have previously described increased numbers of NK and NK-related subsets in association with sIL-2R cytokine serum levels in BELFAST octo/nonagenarians. We hypothesised that changes in KIR A and B haplotype gene frequencies could explain the increased cytokine profiles and NK compartments previously described in Belfast Elderly Longitudinal Free-living Aging STudy (BELFAST) octo/nonagenarians, who show evidence of ageing well.

Results: In the BELFAST study, 24% of octo/nonagenarians carried the KIR A haplotype and 76% KIR B haplotype with no differences for KIR A haplogroup frequency between male or female subjects (23% v 24%; p=0.88) or for KIR B haplogroup (77% v 76%; p=0.99). Octo/nonagenarian KIR A haplotype carriers showed increased NK numbers and percentage compared to Group B KIR subjects (p=0.003; p=0.016 respectively). There were no KIR A/ B haplogroup-associated changes for related CD57+CD8 (high or low) subsets. Using logistic regression, KIR B carriers were predicted to have higher IL-12 cytokine levels compared to KIR A carriers by about 3% (OR 1.03, confidence limits CI 0.99–1.09; p=0.027) and 14% higher levels for TGF-ß (active), a cytokine with an anti-inflammatory role, (OR 1.14, confidence limits CI 0.99–1.09; p=0.002).

Conclusion: In this observational study, BELFAST octo/nonagenarians carrying KIR A haplotype showed higher NK cell numbers and percentage compared to KIR B carriers. Conversely, KIR B haplotype carriers, with genes encoding for activating KIRs, showed a tendency for higher serum pro-inflammatory cytokines compared to KIR A carriers. While the findings in this study should be considered exploratory they may serve to stimulate debate about the immune signatures of those who appear to age slowly and who represent a model for good quality survivor-hood.© 2013 Rea et al.; licensee BioMed Central Ltd.

Three different types of quasi-model networks: synthesis by group transfer polymerization and characterization

Group transfer polymerization (GTP) chemistry was employed for the preparation of polymethacrylate networks of controlled structure (quasi-model networks) of three different types: (a) regular quasi-model networks, in which all polymer chains were linked at their ends, leaving, in principle, no free chain ends, (b) crosslinked star polymer quasi-model networks, in which star polymers were interlinked via half of their chains, letting the other half free (dangling), and (c) shell-crosslinked polymer quasi-model networks, in which the outer part of the network contained polymer arms (dangling chains). Combination of hydrophilic and hydrophobic monomers led to amphiphilic networks whose aqueous swelling behavior was characterized gravimetrically.

Does social deprivation influence inter-group contact outcomes for pupils in Northern Ireland?

The education system in Northern Ireland is characterized by division, with
around 95% of the pupil population attending predominantly co-religionist
schools. In a society that is transitioning from a thirty year conflict that has been
framed by hostilities between the main Catholic and Protestant communities, reconciliation
interventions in education have sought to promote the value of intergroup
contact between pupils attending separate schools. Some qualitative research
suggests that such initiatives are more likely to have positive outcomes for
pupils from more middle class backgrounds than those from more disadvantaged
communitiesand areas that experienced high levels of conflict related incidents and deaths during the pre-ceasefire years. Drawing on contact theory and empirical evidence from a large scale quantitative study, we seek to examine this theory. Using free school meals as a proxy for social class, our findings are consistent in finding that there is a differential impact of contact for those from less affluent backgrounds, and we conclude by arguing that this should be reflected in policy responses.

Impact of Free Glasses and a Teacher Incentive on Children's Use of Eyeglasses: A Cluster-Randomized Controlled Trial.

Purpose: To study the effect of free glasses combined with teacher incentives on in-school glasses wear among Chinese urban migrant children. Design: Cluster-randomized controlled trial. Methods: Children with VA <= 6/12 in either eye due to refractive error in 94 randomly-chosen primary schools underwent randomization by school to receive free glasses, education on their use and a teacher incentive (Intervention), or glasses prescriptions only (Control). Intervention group teachers received a tablet computer if >= 80% of children given glasses wore them during un-announced visits 6 weeks and 6 months (main outcome) after intervention. Results: Among 4376 children, 728 (16.7%, mean age 10.9 years, 51.0% boys) met enrollment criteria and were randomly allocated, 358 (49.2%, 47 schools) to Intervention and 370 (50.8%, 47 schools) to Control. Among these, 693 children (95.2%) completed the study and underwent analysis. Spectacle wear was significantly higher at 6 months among Intervention children (Observed [main outcome]: 68.3% versus 23.9%, Adjusted Odds Ratio [OR]=11.5, 95% Confidence Interval [CI] 5.91-22.5, P<0.001; Self-reported: 90.6% versus 32.1%, OR = 43.7, 95% CI = 21.7-88.5, P < 0.001). Other predictors of observed wear at 6 months included baseline spectacle wear (P<0.001), uncorrected VA<6/18 (P=0.01) and parental spectacle wear (P=0.02). The 6-month observed wear rate was only 41% among similar-aged children provided free glasses in our previous trial without teacher incentives. Conclusions: Free spectacles and teacher incentives maintain classroom wear in the large majority of children needing glasses over a school year. Low wear among Control children demonstrates the need for interventions.