Selmer Groups in Twist Families of Elliptic Curves

The aim of this article is to give some numerical data related to the order of the Selmer groups in twist families of elliptic curves. To do this we assume the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated theorem of Waldspurger to get a fast algorithm to compute $$. Having an extensive amount of data we compare the distribution of the order of the Selmer groups by functions of type $\alpha \frac{(\log \log (X))^{1+\varepsilon}}{\log (X)}$ with $\varepsilon$ small. We discuss how the "best choice" of $\alpha$ is depending on the conductor of the chosen elliptic curves and the congruence classes of twist factors.Comment: to appear in Quaestiones Mathematicae. 16 page

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Numerical properties of isotrivial fibrations

In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations \varphi \colon X \lr C, where $X$ is a smooth, projective surface and $C$ is a curve. In particular we prove that, if $g(C) \geq 1$ and $X$ is neither ruled nor isomorphic to a quasi-bundle, then K_X^2 \leq 8 \chi(\mO_X)-2; this inequality is sharp and if equality holds then $X$ is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that $K_X$ is ample, we obtain K_X^2 \leq 8 \chi(\mO_X)-5 and the inequality is also sharp. This improves previous results of Serrano and Tan.Comment: 30 pages. Final version, to appear in Geometriae Dedicat

Efficacy and safety of ciclosporin versus methotrexate in the treatment of severe atopic dermatitis in children and young people (TREAT): a multicentre parallel group assessor-blinded clinical trial

Background Conventional systemic drugs are used to treat children and young people (CYP) with severe atopic dermatitis (AD) worldwide, but no robust randomized controlled trial (RCT) evidence exists regarding their efficacy and safety in this population. While novel therapies have expanded therapeutic options, their high cost means traditional agents remain important, especially in lower-resource settings. Objectives To compare the safety and efficacy of ciclosporin (CyA) with methotrexate (MTX) in CYP with severe AD in the TREatment of severe Atopic Eczema Trial (TREAT) trial. Methods We conducted a parallel group assessor-blinded RCT in 13 UK and Irish centres. Eligible participants aged 2–16 years and unresponsive to potent topical treatment were randomized to either oral CyA (4 mg kg–1 daily) or MTX (0.4 mg kg–1 weekly) for 36 weeks and followed-up for 24 weeks. Co-primary outcomes were change from baseline to 12 weeks in Objective Severity Scoring of Atopic Dermatitis (o-SCORAD) and time to first significant flare (relapse) after treatment cessation. Secondary outcomes included change in quality of life (QoL) from baseline to 60 weeks; number of participant-reported flares following treatment cessation; proportion of participants achieving ≥ 50% improvement in Eczema Area and Severity Index (EASI 50) and ≥ 75% improvement in EASI (EASI 75); and stratification of outcomes by filaggrin status. Results In total, 103 participants were randomized (May 2016–February 2019): 52 to CyA and 51 to MTX. CyA showed greater improvement in disease severity by 12 weeks [mean difference in o-SCORAD –5.69, 97.5% confidence interval (CI) –10.81 to –0.57 (P = 0.01)]. More participants achieved ≥ 50% improvement in o-SCORAD (o-SCORAD 50) at 12 weeks in the CyA arm vs. the MTX arm [odds ratio (OR) 2.60, 95% CI 1.23–5.49; P = 0.01]. By 60 weeks MTX was superior (OR 0.33, 95% CI 0.13–0.85; P = 0.02), a trend also seen for ≥ 75% improvement in o-SCORAD (o-SCORAD 75), EASI 50 and EASI 75. Participant-reported flares post-treatment were higher in the CyA arm (OR 3.22, 95% CI 0.42–6.01; P = 0.02). QoL improved with both treatments and was sustained after treatment cessation. Filaggrin status did not affect outcomes. The frequency of adverse events (AEs) was comparable between both treatments. Five (10%) participants on CyA and seven (14%) on MTX experienced a serious AE. Conclusions Both CyA and MTX proved effective in CYP with severe AD over 36 weeks. Participants who received CyA showed a more rapid response to treatment, while MTX induced more sustained disease control after discontinuation

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease