Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure

Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure

Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

Finite-size corrections for logarithmic representations in critical dense polymers

We study (analytic) finite-size corrections in the dense polymer model on the strip by perturbing the critical Hamiltonian with irrelevant operators belonging to the tower of the identity. We generalize the perturbation expansion to include Jordan cells, and examine whether the finite-size corrections are sensitive to the properties of indecomposable representations appearing in the conformal spectrum, in particular their indecomposability parameters. We find, at first order, that the corrections do not depend on these parameters nor even on the presence of Jordan cells. Though the corrections themselves are not universal, the ratios are universal and correctly reproduced by the conformal perturbative approach, to first order.Comment: 5 pages, published versio

A ‘quiet revolution’? The impact of Training Schools on initial teacher training partnerships

This paper discusses the impact on initial teacher training of a new policy initiative in England: the introduction of Training Schools. First, the Training School project is set in context by exploring the evolution of a partnership approach to initial teacher training in England. Ways in which Training Schools represent a break with established practice are considered together with their implications for the dominant mode of partnership led by higher education institutions (HEIs). The capacity of Training Schools to achieve their own policy objectives is examined, especially their efficacy as a strategy for managing innovation and the dissemination of innovation. The paper ends by focusing on a particular Training School project which has adopted an unusual approach to its work and enquires whether this alternative approach could offer a more profitable way forward. During the course of the paper, five different models of partnership are considered: collaborative, complementary, HEI-led, school-led and partnership within a partnership

Use of liothyronine (T3) in hypothyroidism: Joint British Thyroid Association/Society for endocrinology consensus statement

\ua9 2023 The Authors. Clinical Endocrinology published by John Wiley & Sons Ltd.Persistent symptoms in patients treated for hypothyroidism are common. Despite more than 20 years of debate, the use of liothyronine for this indication remains controversial, as numerous randomised trials have failed to show a benefit of treatment regimens that combine liothyronine (T3) with levothyroxine over levothyroxine monotherapy. This consensus statement attempts to provide practical guidance to clinicians faced with patients who have persistent symptoms during thyroid hormone replacement therapy. It applies to non-pregnant adults and is focussed on care delivered within the UK National Health Service, although it may be relevant in other healthcare environments. The statement emphasises several key clinical practice points for patients dissatisfied with treatment for hypothyroidism. Firstly, it is important to establish a diagnosis of overt hypothyroidism; patients with persistent symptoms during thyroid hormone replacement but with no clear biochemical evidence of overt hypothyroidism should first have a trial without thyroid hormone replacement. In those with established overt hypothyroidism, levothyroxine doses should be optimised aiming for a TSH in the 0.3–2.0 mU/L range for 3 to 6 months before a therapeutic response can be assessed. In some patients, it may be acceptable to have serum TSH below reference range (e.g. 0.1–0.3 mU/L), but not fully suppressed in the long term. We suggest that for some patients with confirmed overt hypothyroidism and persistent symptoms who have had adequate treatment with levothyroxine and in whom other comorbidities have been excluded, a trial of liothyronine/levothyroxine combined therapy may be warranted. The decision to start treatment with liothyronine should be a shared decision between patient and clinician. However, individual clinicians should not feel obliged to start liothyronine or to continue liothyronine medication provided by other health care practitioners or accessed without medical advice, if they judge this not to be in the patient\u27s best interest

Prevalence and Predictors of Vitamin D Insufficiency in Children: A Great Britain Population Based Study

Objectives To evaluate the prevalence and predictors of vitamin D insufficiency (VDI) in children In Great Britain. Design A nationally representative cross-sectional study survey of children (1102) aged 4–18 years (999 white, 570 male) living in private households (January 1997–1998). Interventions provided information about dietary habits, physical activity, socio-demographics, and blood sample. Outcome measures were vitamin D insufficiency (<50 nmol/L). Results Vitamin D levels (mean = 62.1 nmol/L, 95%CI 60.4–63.7) were insufficient in 35%, and decreased with age in both sexes (p<0.001). Young People living between 53–59 degrees latitude had lower levels (compared with 50–53 degrees, p = 0.045). Dietary intake and gender had no effect on vitamin D status. A logistic regression model showed increased risk of VDI in the following: adolescents (14–18 years old), odds ratio (OR) = 3.6 (95%CI 1.8–7.2) compared with younger children (4–8 years); non white children (OR = 37 [95%CI 15–90]); blood levels taken December-May (OR = 6.5 [95%CI 4.3–10.1]); on income support (OR = 2.2 [95%CI 1.3–3.9]); not taking vitamin D supplementation (OR = 3.7 [95%CI 1.4–9.8]); being overweight (OR 1.6 [95%CI 1.0–2.5]); <1/2 hour outdoor exercise/day/week (OR = 1.5 [95%CI 1.0–2.3]); watched >2.5 hours of TV/day/week (OR = 1.6[95%CI 1.0–2.4]). Conclusion We confirm a previously under-recognised risk of VDI in adolescents. The marked higher risk for VDI in non-white children suggests they should be targeted in any preventative strategies. The association of higher risk of VDI among children who exercised less outdoors, watched more TV and were overweight highlights potentially modifiable risk factors. Clearer guidelines and an increased awareness especially in adolescents are needed, as there are no recommendations for vitamin D supplementation in older children

Prenatal Vitamin D Supplementation and Child Respiratory Health: A Randomised Controlled Trial

PMCID: PMC3691177This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Anti-Allergic Cromones Inhibit Histamine and Eicosanoid Release from Activated Human and Murine Mast Cells by Releasing Annexin A1

PMCID: PMC3601088This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The actin-myosin regulatory MRCK kinases: regulation, biological functions and associations with human cancer

The contractile actin-myosin cytoskeleton provides much of the force required for numerous cellular activities such as motility, adhesion, cytokinesis and changes in morphology. Key elements that respond to various signal pathways are the myosin II regulatory light chains (MLC), which participate in actin-myosin contraction by modulating the ATPase activity and consequent contractile force generation mediated by myosin heavy chain heads. Considerable effort has focussed on the role of MLC kinases, and yet the contributions of the myotonic dystrophy-related Cdc42-binding kinases (MRCK) proteins in MLC phosphorylation and cytoskeleton regulation have not been well characterized. In contrast to the closely related ROCK1 and ROCK2 kinases that are regulated by the RhoA and RhoC GTPases, there is relatively little information about the CDC42-regulated MRCKα, MRCKβ and MRCKγ members of the AGC (PKA, PKG and PKC) kinase family. As well as differences in upstream activation pathways, MRCK and ROCK kinases apparently differ in the way that they spatially regulate MLC phosphorylation, which ultimately affects their influence on the organization and dynamics of the actin-myosin cytoskeleton. In this review, we will summarize the MRCK protein structures, expression patterns, small molecule inhibitors, biological functions and associations with human diseases such as cancer