Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Phonon renormalization in doped bilayer graphene

We report phonon renormalization in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping as a result of the nonadiabatic Kohn anomaly at the Gamma point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This gives a change of slope in the variation of G peak position with doping which allows a direct measurement of the interlayer coupling strength.

The use of F-specific coliphages to assess effluent treatment and reuse schemes

This study reports on the use of naturally occurring F-specific coliphages, as well as spiked MS-2 phage, to evaluate a land-based effluent treatment/reuse system and an effluent irrigation scheme. Both the natural phages and the spiked MS-2 phage indicated that the effluent treatment/reuse system (FILTER - Filtration and Irrigated cropping for Land Treatment and Effluent Reuse) achieved a reduction in phage levels over the treatment system by one to two log10. FILTER reduced natural F-specific phage numbers from around 103 to below 102 100-ml-1 and the spiked phage from 105 to around 104 100-ml-1 (incoming compared with outgoing water). In the effluent irrigation scheme, phage spiked into the holding ponds dropped from 106 to 102 100-ml-1 after 168 h (with no detectable levels of natural F-specific phage being found prior to spiking). Only low levels of the spiked phage (102 gm-1) could be recovered from soil irrigated with phage-spiked effluent (at 106 phage 100 ml-1) or from fruits (around 102 phage per fruit) that had direct contact with soil which had been freshly irrigated with the same phage-spiked effluent.

Influence of validation schemes in a laser Doppler anemometer period timing device for frequency measurement

The short duration of the Doppler signal and noise content in it necessitate a validation scheme to be incorporated in the electronic processor used for frequency measurement, There are several different validation schemes that can be employed in period timing devices. A detailed study of the influence of these validation schemes on the measured frequency has been reported here. These studies were carried out by using a combination of a fast A/D converter and computer. Doppler bursts obtained from an air flow were digitised and stored on magnetic discs. Suitable computer programs were then used to simulate the performance of period timing devices with different validation schemes and the frequency of the stored bursts were evaluated. It is found that best results are obtained when the validation scheme enables frequency measurement to be made over a large number of cycles within the burst.

Renormalization of the phonon spectrum in semiconducting single-walled carbon nanotubes studied by Raman spectroscopy

In situ Raman experiments together with transport measurements have been carried out in single-walled carbon nanotubes as a function of electrochemical top gate voltage (Vg). We have used the green laser (EL=2.41 eV), where the semiconducting nanotubes of diameter ~1.4 nm are in resonance condition. In semiconducting nanotubes, the G−- and G+-mode frequencies increase by ~10 cm−1 for hole doping, the frequency shift of the G− mode is larger compared to the G+ mode at the same gate voltage. However, for electron doping the shifts are much smaller: G− upshifts by only ~2 cm−1 whereas the G+ does not shift. The transport measurements are used to quantify the Fermi-energy shift (EF) as a function of the gate voltage. The electron-hole asymmetry in G− and G+ modes is quantitatively explained using nonadiabatic effects together with lattice relaxation contribution. The electron-phonon coupling matrix elements of transverse-optic (G−) and longitudinal-optic (G+) modes explain why the G− mode is more blueshifted compared to the G+ mode at the same Vg. The D and 2D bands have different doping dependence compared to the G+ and G− bands. There is a large downshift in the frequency of the 2D band (~18 cm−1) and D (~10 cm−1) band for electron doping, whereas the 2D band remains constant for the hole doping but D upshifts by ~8 cm−1. The doping dependence of the overtone of the G bands (2G bands) shows behavior similar to the dependence of the G+ and G− bands.

Binary decompositions and acyclic schemes

It is well known that the notions of normal forms and acyclicity capture many practical desirable properties for database schemes. The basic schema design problem is to develop design methodologies that strive toward these ideals. The usual approach is to first normalize the database scheme as far as possible. If the resulting scheme is cyclic, then one tries to transform it into an acyclic scheme. In this paper, we argue in favor of carrying out these two phases of design concurrently. In order to do this efficiently, we need to be able to incrementally analyze the acyclicity status of a database scheme as it is being designed. To this end, we propose the formalism of "binary decompositions". Using this, we characterize design sequences that exactly generate theta-acyclic schemes, for theta = agr,beta. We then show how our results can be put to use in database design. Finally, we also show that our formalism above can be effectively used as a proof tool in dependency theory. We demonstrate its power by showing that it leads to a significant simplification of the proofs of some previous results connecting sets of multivalued dependencies and acyclic join dependencies.

Recognition And Top-Down Generation Of Beta-Acyclic Database Schemes

Database schemes can be viewed as hypergraphs with individual relation schemes corresponding to the edges of a hypergraph. Under this setting, a new class of "acyclic" database schemes was recently introduced and was shown to have a claim to a number of desirable properties. However, unlike the case of ordinary undirected graphs, there are several unequivalent notions of acyclicity of hypergraphs. Of special interest among these are agr-, beta-, and gamma-, degrees of acyclicity, each characterizing an equivalence class of desirable properties for database schemes, represented as hypergraphs. In this paper, two complementary approaches to designing beta-acyclic database schemes have been presented. For the first part, a new notion called "independent cycle" is introduced. Based on this, a criterion for beta-acyclicity is developed and is shown equivalent to the existing definitions of beta-acyclicity. From this and the concept of the dual of a hypergraph, an efficient algorithm for testing beta-acyclicity is developed. As for the second part, a procedure is evolved for top-down generation of beta-acyclic schemes and its correctness is established. Finally, extensions and applications of ideas are described.

Effect of exercise referral schemes in primary care on physical activity and improving health outcomes: Systematic review and meta-analysis

Objective To assess the impact of exercise referral schemes on physical activity and health outcomes. Design Systematic review and meta-analysis. Data sources Medline, Embase, PsycINFO, Cochrane Library, ISI Web of Science, SPORTDiscus, and ongoing trial registries up to October 2009. We also checked study references. Study selection - Design: randomised controlled trials or non-randomised controlled (cluster or individual) studies published in peer review journals. - Population: sedentary individuals with or without medical diagnosis. - Exercise referral schemes defined as: clear referrals by primary care professionals to third party service providers to increase physical activity or exercise, physical activity or exercise programmes tailored to individuals, and initial assessment and monitoring throughout programmes. - Comparators: usual care, no intervention, or alternative exercise referral schemes. Results Eight randomised controlled trials met the inclusion criteria, comparing exercise referral schemes with usual care (six trials), alternative physical activity intervention (two), and an exercise referral scheme plus a self determination theory intervention (one). Compared with usual care, follow-up data for exercise referral schemes showed an increased number of participants who achieved 90-150 minutes of physical activity of at least moderate intensity per week (pooled relative risk 1.16, 95% confidence intervals 1.03 to 1.30) and a reduced level of depression (pooled standardised mean difference −0.82, −1.28 to −0.35). Evidence of a between group difference in physical activity of moderate or vigorous intensity or in other health outcomes was inconsistent at follow-up. We did not find any difference in outcomes between exercise referral schemes and the other two comparator groups. None of the included trials separately reported outcomes in individuals with specific medical diagnoses. Substantial heterogeneity in the quality and nature of the exercise referral schemes across studies might have contributed to the inconsistency in outcome findings. Conclusions Considerable uncertainty remains as to the effectiveness of exercise referral schemes for increasing physical activity, fitness, or health indicators, or whether they are an efficient use of resources for sedentary people with or without a medical diagnosis.

The clinical effectiveness and cost-effectiveness of exercise referral schemes: A systematic review and economic evaluation

- Background Exercise referral schemes (ERS) aim to identify inactive adults in the primary-care setting. The GP or health-care professional then refers the patient to a third-party service, with this service taking responsibility for prescribing and monitoring an exercise programme tailored to the needs of the individual. - Objective To assess the clinical effectiveness and cost-effectiveness of ERS for people with a diagnosed medical condition known to benefit from physical activity (PA). The scope of this report was broadened to consider individuals without a diagnosed condition who are sedentary. - Data sources MEDLINE; EMBASE; PsycINFO; The Cochrane Library, ISI Web of Science; SPORTDiscus and ongoing trial registries were searched (from 1990 to October 2009) and included study references were checked. - Methods Systematic reviews: the effectiveness of ERS, predictors of ERS uptake and adherence, and the cost-effectiveness of ERS; and the development of a decision-analytic economic model to assess cost-effectiveness of ERS. - Results Seven randomised controlled trials (UK, n = 5; non-UK, n = 2) met the effectiveness inclusion criteria, five comparing ERS with usual care, two compared ERS with an alternative PA intervention, and one to an ERS plus a self-determination theory (SDT) intervention. In intention-to-treat analysis, compared with usual care, there was weak evidence of an increase in the number of ERS participants who achieved a self-reported 90-150 minutes of at least moderate-intensity PA per week at 6-12 months' follow-up [pooled relative risk (RR) 1.11, 95% confidence interval 0.99 to 1.25]. There was no consistent evidence of a difference between ERS and usual care in the duration of moderate/vigorous intensity and total PA or other outcomes, for example physical fitness, serum lipids, health-related quality of life (HRQoL). There was no between-group difference in outcomes between ERS and alternative PA interventions or ERS plus a SDT intervention. None of the included trials separately reported outcomes in individuals with medical diagnoses. Fourteen observational studies and five randomised controlled trials provided a numerical assessment of ERS uptake and adherence (UK, n = 16; non-UK, n = 3). Women and older people were more likely to take up ERS but women, when compared with men, were less likely to adhere. The four previous economic evaluations identified suggest ERS to be a cost-effective intervention. Indicative incremental cost per quality-adjusted life-year (QALY) estimates for ERS for various scenarios were based on a de novo model-based economic evaluation. Compared with usual care, the mean incremental cost for ERS was £169 and the mean incremental QALY was 0.008, with the base-case incremental cost-effectiveness ratio at £20,876 per QALY in sedentary people without a medical condition and a cost per QALY of £14,618 in sedentary obese individuals, £12,834 in sedentary hypertensive patients, and £8414 for sedentary individuals with depression. Estimates of cost-effectiveness were highly sensitive to plausible variations in the RR for change in PA and cost of ERS. - Limitations We found very limited evidence of the effectiveness of ERS. The estimates of the cost-effectiveness of ERS are based on a simple analytical framework. The economic evaluation reports small differences in costs and effects, and findings highlight the wide range of uncertainty associated with the estimates of effectiveness and the impact of effectiveness on HRQoL. No data were identified as part of the effectiveness review to allow for adjustment of the effect of ERS in different populations. - Conclusions There remains considerable uncertainty as to the effectiveness of ERS for increasing activity, fitness or health indicators or whether they are an efficient use of resources in sedentary people without a medical diagnosis. We failed to identify any trial-based evidence of the effectiveness of ERS in those with a medical diagnosis. Future work should include randomised controlled trials assessing the cinical effectiveness and cost-effectivenesss of ERS in disease groups that may benefit from PA. - Funding The National Institute for Health Research Health Technology Assessment programme.

The cost-effectiveness of exercise referral schemes

Background Exercise referral schemes (ERS) aim to identify inactive adults in the primary care setting. The primary care professional refers the patient to a third party service, with this service taking responsibility for prescribing and monitoring an exercise programme tailored to the needs of the patient. This paper examines the cost-effectiveness of ERS in promoting physical activity compared with usual care in primary care setting. Methods A decision analytic model was developed to estimate the cost-effectiveness of ERS from a UK NHS perspective. The costs and outcomes of ERS were modelled over the patient's lifetime. Data were derived from a systematic review of the literature on the clinical and cost-effectiveness of ERS, and on parameter inputs in the modelling framework. Outcomes were expressed as incremental cost per quality-adjusted life-year (QALY). Deterministic and probabilistic sensitivity analyses investigated the impact of varying ERS cost and effectiveness assumptions. Sub-group analyses explored the cost-effectiveness of ERS in sedentary people with an underlying condition. Results Compared with usual care, the mean incremental lifetime cost per patient for ERS was £169 and the mean incremental QALY was 0.008, generating a base-case incremental cost-effectiveness ratio (ICER) for ERS at £20,876 per QALY in sedentary individuals without a diagnosed medical condition. There was a 51% probability that ERS was cost-effective at £20,000 per QALY and 88% probability that ERS was cost-effective at £30,000 per QALY. In sub-group analyses, cost per QALY for ERS in sedentary obese individuals was £14,618, and in sedentary hypertensives and sedentary individuals with depression the estimated cost per QALY was £12,834 and £8,414 respectively. Incremental lifetime costs and benefits associated with ERS were small, reflecting the preventative public health context of the intervention, with this resulting in estimates of cost-effectiveness that are sensitive to variations in the relative risk of becoming physically active and cost of ERS. Conclusions ERS is associated with modest increase in lifetime costs and benefits. The cost-effectiveness of ERS is highly sensitive to small changes in the effectiveness and cost of ERS and is subject to some significant uncertainty mainly due to limitations in the clinical effectiveness evidence base.

Republished research: Effect of exercise referral schemes in primary care on physical activity and improving health outcomes: systematic review and meta-analysis

Study question Can exercise referral schemes improve health outcomes in individuals with or without pre-existing conditions? Summary answer We found weak evidence of a short term increase in physical activity and reduction in levels of depression in sedentary individuals after participation in exercise referral schemes, compared with after usual care. What is known and what this paper adds Exercise referral schemes are commonly used in primary care to promote physical activity. Evidence indicating a health benefit of these schemes is limited, so their value in primary care remains to be ascertained.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.