On the variational interpretation of the discrete KP equation

We study the variational structure of the discrete Kadomtsev-Petviashvili (dKP) equation by means of its pluri-Lagrangian formulation. We consider the dKP equation and its variational formulation on the cubic lattice ${\mathbb Z}^{N}$ as well as on the root lattice $Q(A_{N})$. We prove that, on a lattice of dimension at least four, the corresponding Euler-Lagrange equations are equivalent to the dKP equation.Comment: 24 page

Glucocorticoid-induced hyperglycaemia in respiratory disease: a systematic review and meta-analysis.

The relative risk of glucocorticoid-induced hyperglycaemia is poorly quantified. We undertook a meta-analysis to estimate the association between glucocorticoid treatment and hyperglycaemia, overall and separately in individuals with and without diabetes and underlying respiratory disease. We searched electronic databases for clinical trials of adults randomized to either glucocorticoid treatment or placebo. Eight articles comprising 2121 participants were identified. We performed a random effects meta-analysis to determine relative risks for the associations between glucocorticoid use and both hyperglycaemia and starting hypoglycaemic therapy. In all individuals, the relative risk of hyperglycaemia comparing glucocorticoid treatment with placebo was 1.72 [95% confidence interval (CI) 1.50-2.04; p < .001]. The relative risks in individuals with and those without diabetes were 2.10 (95% CI 0.92-5.02; p = .079) and 1.50 (95% CI 0.79-2.86; p = .22), respectively. In all individuals, the relative risk of hyperglycaemia requiring initiation of hypoglycaemic therapy, comparing glucocorticoid treatment with placebo, was 1.73 (95% CI 1.40-2.14; p < .001). In conclusion, glucocorticoid therapy increases the risk of hyperglycaemia in all individuals with underlying respiratory disease but not when diabetic status is analysed separately.Medical Research Council (Grant ID: MC_UU_12015/1)This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1111/dom.1273

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained

On the Relationship Between Ultrasonic and Micro-Structural Properties of Imperfect Interfaces in Layered Solids

The interaction of ultrasonic waves with interfaces formed by two non-conforming, rough surfaces in contact has been the subject of numerous investigations [1–10]. The motivations behind these studies have been various: from the assessment of the real area of contact between two rough surfaces [1], to the modeling of crack closure near the tip of a fatigue crack [4]; from the identification of the nature of interfacial imperfections in kissing and partial bonds [6], to the generation of ultrasonic waves [8]. In most of these studies, the characterization of the interfacial properties has been attempted by studying the reflection of longitudinal and shears waves at normal incidence. Only recently, the problem concerning the interaction of ultrasonic waves with realistic complex systems such as that formed by two neighboring imperfect interfaces has been addressed. Lavrentyev and Rokhlin [9, 10] used ultrasonic spectroscopy to evaluate the interfacial conditions from the spectra of longitudinal and shear waves reflected normally from the interfaces

Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

Protocol for an observational cohort study investigating personalised medicine for intensification of treatment in people with type 2 diabetes mellitus: the PERMIT study

INTRODUCTION: For people with type 2 diabetes mellitus (T2DM) who require an antidiabetic drug as an add-on to metformin, there is controversy about whether newer drug classes such as dipeptidyl peptidase-4 inhibitors (DPP4i) or sodium-glucose co-transporter-2 inhibitors (SGLT2i) reduce the risk of long-term complications compared with sulfonylureas (SU). There is widespread variation across National Health Service Clinical Commissioning Groups (CCGs) in drug choice for second-line treatment in part because National Institute for Health and Care Excellence guidelines do not specify a single preferred drug class, either overall or within specific patient subgroups. This study will evaluate the relative effectiveness of the three most common second-line treatments in the UK (SU, DPP4i and SGLT2i as add-ons to metformin) and help target treatments according to individual risk profiles. METHODS AND ANALYSIS: The study includes people with T2DM prescribed one of the second-line treatments-of-interest between 2014 and 2020 within the UK Clinical Practice Research Datalink linked with Hospital Episode Statistics and Office of National Statistics. We will use an instrumental variable (IV) method to estimate short-term and long-term relative effectiveness of second-line treatments according to individuals' risk profiles. This method minimises bias from unmeasured confounders by exploiting the natural variation in second-line prescribing across CCGs as an IV for the choice of prescribed treatment. The primary outcome to assess short-term effectiveness will be change in haemoglobin A1c (%) 12 months after treatment initiation. Outcome measures to assess longer-term effectiveness (maximum ~6 years) will include microvascular and macrovascular complications, all-cause mortality and hospital admissions during follow-up. ETHICS AND DISSEMINATION: This study was approved by the Independent Scientific Advisory Committee (20-064) and the London School of Hygiene & Tropical Medicine Research Ethics Committee (21395). Results, codelists and other analysis code will be made available to patients, clinicians, policy-makers and researchers

Using psychological theory to understand the clinical management of type 2 diabetes in Primary Care : a comparison across two European countries

Peer reviewedPublisher PD

The Perfect Family: Decision Making in Biparental Care

Background Previous theoretical work on parental decisions in biparental care has emphasized the role of the conflict between evolutionary interests of parents in these decisions. A prominent prediction from this work is that parents should compensate for decreases in each other\u27s effort, but only partially so. However, experimental tests that manipulate parents and measure their responses fail to confirm this prediction. At the same time, the process of parental decision making has remained unexplored theoretically. We develop a model to address the discrepancy between experiments and the theoretical prediction, and explore how assuming different decision making processes changes the prediction from the theory. Model Description We assume that parents make decisions in behavioral time. They have a fixed time budget, and allocate it between two parental tasks: provisioning the offspring and defending the nest. The proximate determinant of the allocation decisions are parents\u27 behavioral objectives. We assume both parents aim to maximize the offspring production from the nest. Experimental manipulations change the shape of the nest production function. We consider two different scenarios for how parents make decisions: one where parents communicate with each other and act together (the perfect family), and one where they do not communicate, and act independently (the almost perfect family). Conclusions/Significance The perfect family model is able to generate all the types of responses seen in experimental studies. The kind of response predicted depends on the nest production function, i.e. how parents\u27 allocations affect offspring production, and the type of experimental manipulation. In particular, we find that complementarity of parents\u27 allocations promotes matching responses. In contrast, the relative responses do not depend on the type of manipulation in the almost perfect family model. These results highlight the importance of the interaction between nest production function and how parents make decisions, factors that have largely been overlooked in previous models

What two models may teach us about duality violations in QCD

Though the operator product expansion is applicable in the calculation of current correlation functions in the Euclidean region, when approaching the Minkowskian domain, violations of quark-hadron duality are expected to occur, due to the presence of bound-state or resonance poles. In QCD finite-energy sum rules, contour integrals in the complex energy plane down to the Minkowskian axis have to be performed, and thus the question arises what the impact of duality violations may be. The structure and possible relevance of duality violations is investigated on the basis of two models: the Coulomb system and a model for light-quark correlators which has already been studied previously. As might yet be naively expected, duality violations are in some sense "maximal" for zero-width bound states and they become weaker for broader resonances whose poles lie further away from the physical axis. Furthermore, to a certain extent, they can be suppressed by choosing appropriate weight functions in the finite-energy sum rules. A simplified Ansatz for including effects of duality violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE