Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2) orbifolds remains an ever-haunting conundrum. Motivated by techniques in some works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic outlook, a method which we call stepwise projection, that may shed some light on this puzzle. We exemplify this method, consisting of transformation rules for obtaining complex quivers and brane setups from more elementary ones, to the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we demonstrate the generality of the stepwise procedure by appealing to Frobenius' theory of Induced Representations. Our algorithm suggests the existence of generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure

Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

From nodal liquid to nodal Mottness in a frustrated Hubbard model

We investigate the physics of frustrated 3-leg Hubbard ladders in the band limit, when hopping across the ladder's rungs (t$_{\perp}$) is of the same order as hopping along them (t) much greater than the onsite Coulomb repulsion (U). We show that this model exhibits a striking electron-hole asymmetry close to half-filling: the hole-doped system at low temperatures develops a Resonating Valence Bond (RVB)-like d-wave gap (pseudogap close to ($\pi$,0)) coinciding with gapless nodal excitations (nodal liquid); in contrast, the electron-doped system is seen to develop a Mott gap at the nodes, whilst retaining a metallic character of its majority Fermi surface. At lower temperatures in the electron-doped case, d-wave superconducting correlations -- here, coexisting with gapped nodal excitations -- are already seen to arise. Upon further doping the hole-doped case, the RVB-like state yields to d-wave superconductivity. Such physics is reminiscent of that exhibited by the high temperature cuprate superconductors--notably electron-hole asymmetry as noted by Angle Resolved PhotoEmission Spectroscopy (ARPES) and the resistivity exponents observed. This toy model also reinforces the importance of a more thorough experimental investigation of the known 3-leg ladder cuprate systems, and may have some bearing on low dimensional organic superconductors.Comment: 26 pages, 16 figure

Interaction-induced Fermi surface deformations in quasi one-dimensional electronic systems

We consider serious conceptual problems with the application of standard perturbation theory, in its zero temperature version, to the computation of the dressed Fermi surface for an interacting electronic system. In order to overcome these difficulties, we set up a variational approach which is shown to be equivalent to the renormalized perturbation theory where the dressed Fermi surface is fixed by recursively computed counterterms. The physical picture that emerges is that couplings that are irrelevant tend to deform the Fermi surface in order to become more relevant (irrelevant couplings being those that do not exist at vanishing excitation energy because of kinematical constraints attached to the Fermi surface). These insights are incorporated in a renormalization group approach, which allows for a simple approximate computation of Fermi surface deformation in quasi one-dimensional electronic conductors. We also analyze flow equations for the effective couplings and quasiparticle weights. For systems away from half-filling, the flows show three regimes corresponding to a Luttinger liquid at high energies, a Fermi liquid, and a low-energy incommensurate spin-density wave. At half-filling Umklapp processes allow for a Mott insulator regime where the dressed Fermi surface is flat, implying a confined phase with vanishing effective transverse single-particle coherence. The boundary between the confined and Fermi liquid phases is found to occur for a bare transverse hopping amplitude of the order of the Mott charge gap of a single chain.Comment: 38 pages, 39 figures. Accepted for publication in Phys. Rev.

Hypervitaminosis A is prevalent in children with CKD and contributes to hypercalcemia.

Vitamin A accumulates in renal failure, but the prevalence of hypervitaminosis A in children with predialysis chronic kidney disease (CKD) is not known. Hypervitaminosis A has been associated with hypercalcemia. In this study we compared dietary vitamin A intake with serum retinoid levels and their associations with hypercalcemia

Can programme theory be used as a 'translational tool’ to optimise health service delivery in a national early years’ initiative in Scotland: a case study

Background Theory-based evaluation (TBE) approaches are heralded as supporting formative evaluation by facilitating increased use of evaluative findings to guide programme improvement. It is essential that learning from programme implementation is better used to improve delivery and to inform other initiatives, if interventions are to be as effective as they have the potential to be. Nonetheless, few studies describe formative feedback methods, or report direct instrumental use of findings resulting from TBE. This paper uses the case of Scotland’s, National Health Service, early years’, oral health improvement initiative (Childsmile) to describe the use of TBE as a framework for providing feedback on delivery to programme staff and to assess its impact on programmatic action.<p></p> Methods In-depth, semi-structured interviews and focus groups with key stakeholders explored perceived deviations between the Childsmile programme 'as delivered’ and its Programme Theory (PT). The data was thematically analysed using constant comparative methods. Findings were shared with key programme stakeholders and discussions around likely impact and necessary actions were facilitated by the authors. Documentary review and ongoing observations of programme meetings were undertaken to assess the extent to which learning was acted upon.<p></p> Results On the whole, the activities documented in Childsmile’s PT were implemented as intended. This paper purposefully focuses on those activities where variation in delivery was evident. Differences resulted from the stage of roll-out reached and the flexibility given to individual NHS boards to tailor local implementation. Some adaptations were thought to have diverged from the central features of Childsmile’s PT, to the extent that there was a risk to achieving outcomes. The methods employed prompted national service improvement action, and proposals for local action by individual NHS boards to address this.<p></p> Conclusions The TBE approach provided a platform, to direct attention to areas of risk within a national health initiative, and to agree which intervention components were 'core’ to its hypothesised success. The study demonstrates that PT can be used as a 'translational tool’ to facilitate instrumental use of evaluative findings to optimise implementation within a complex health improvement programme.<p></p&gt

Patient-centric trials for therapeutic development in precision oncology

An enhanced understanding of the molecular pathology of disease gained from genomic studies is facilitating the development of treatments that target discrete molecular subclasses of tumours. Considerable associated challenges include how to advance and implement targeted drug-development strategies. Precision medicine centres on delivering the most appropriate therapy to a patient on the basis of clinical and molecular features of their disease. The development of therapeutic agents that target molecular mechanisms is driving innovation in clinical-trial strategies. Although progress has been made, modifications to existing core paradigms in oncology drug development will be required to realize fully the promise of precision medicine

Can screening and brief intervention lead to population-level reductions in alcohol-related harm?

A distinction is made between the clinical and public health justifications for screening and brief intervention (SBI) against hazardous and harmful alcohol consumption. Early claims for a public health benefit of SBI derived from research on general medical practitioners' (GPs') advice on smoking cessation, but these claims have not been realized, mainly because GPs have not incorporated SBI into their routine practice. A recent modeling exercise estimated that, if all GPs in England screened every patient at their next consultation, 96% of the general population would be screened over 10 years, with 70-79% of excessive drinkers receiving brief interventions (BI); assuming a 10% success rate, this would probably amount to a population-level effect of SBI. Thus, a public health benefit for SBI presupposes widespread screening; but recent government policy in England favors targeted versus universal screening, and in Scotland screening is based on new registrations and clinical presentation. A recent proposal for a national screening program was rejected by the UK National Health Service's National Screening Committee because 1) there was no good evidence that SBI led to reductions in mortality or morbidity, and 2) a safe, simple, precise, and validated screening test was not available. Even in countries like Sweden and Finland, where expensive national programs to disseminate SBI have been implemented, only a minority of the population has been asked about drinking during health-care visits, and a minority of excessive drinkers has been advised to cut down. Although there has been research on the relationship between treatment for alcohol problems and population-level effects, there has been no such research for SBI, nor have there been experimental investigations of its relationship with population-level measures of alcohol-related harm. These are strongly recommended. In this article, conditions that would allow a population-level effect of SBI to occur are reviewed, including their political acceptability. It is tentatively concluded that widespread dissemination of SBI, without the implementation of alcohol control measures, might have indirect influences on levels of consumption and harm but would be unlikely on its own to result in public health benefits. However, if and when alcohol control measures were introduced, SBI would still have an important role in the battle against alcohol-related harm