Bistable travelling waves for nonlocal reaction diffusion equations

We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium $u\equiv 1$ is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is "above and away", from the intermediate equilibrium. For focusing kernels we prove that, as expected, the wave connects 0 to 1. Our results also apply readily to the nonlocal ignition case

Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration

Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term.Comment: 7 page

Dynamics of sexual populations structured by a space variable and a phenotypical trait

International audienc

Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems

International audienceWe study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium

Integrator complex regulates NELF-mediated RNA polymerase II pause/release and processivity at coding genes

International audienc

Glyburide versus insulin for the prevention of perinatal complications of Gestational Diabetes Mellitus: a pragmatic, non-inferiority, randomized trial

38th Annual Meeting and Pregnancy Meeting of the Society-for-Maternal-Fetal-Medicine, Dallas, TX, JAN 29-FEB 03, 2018International audienc

Cervical ripening in prolonged pregnancies by silicone double balloon catheter versus vaginal dinoprostone slow release system: The MAGPOP randomised controlled trial

International audienceBackground Prolonged pregnancies are a frequent indication for induction of labour. When the cervix is unfavourable, cervical ripening before oxytocin administration is recommended to increase the likelihood of vaginal delivery, but no particular method is currently recommended for cervical ripening of prolonged pregnancies. This trial evaluates whether the use of mechanical cervical ripening with a silicone double balloon catheter for induction of labour in prolonged pregnancies reduces the cesarean section rate for nonreassuring fetal status compared with pharmacological cervical ripening by a vaginal pessary for the slow release of dinoprostone (prostaglandin E2). Methods and findings This is a multicentre, superiority, open-label, parallel-group, randomised controlled trial conducted in 15 French maternity units. Women with singleton pregnancies, a vertex presentation, ≥41+0 and ≤42+0 weeks’ gestation, a Bishop score <6, intact membranes, and no history of cesarean delivery for whom induction of labour was decided were randomised to either mechanical cervical ripening with a Cook Cervical Ripening Balloon or pharmacological cervical ripening by a Propess vaginal pessary serving as a prostaglandin E2 slow-release system. The primary outcome was the rate of cesarean for nonreassuring fetal status, with an independent endpoint adjudication committee determining whether the fetal heart rate was nonreassuring. Secondary outcomes included delivery (time from cervical ripening to delivery, number of patients requiring analgesics), maternal and neonatal outcomes. Between January 2017 and December 2018, 1,220 women were randomised in a 1:1 ratio, 610 allocated to a silicone double balloon catheter, and 610 to the Propess vaginal pessary for the slow release of dinoprostone. The mean age of women was 31 years old, and 80% of them were of white ethnicity. The cesarean rates for nonreassuring fetal status were 5.8% (35/607) in the mechanical ripening group and 5.3% (32/609) in the pharmacological ripening group (proportion difference: 0.5%; 95% confidence interval (CI) −2.1% to 3.1%, p = 0.70). Time from cervical ripening to delivery was shorter in the pharmacological ripening group (23 hours versus 32 hours, median difference 6.5 95% CI 5.0 to 7.9, p < 0.001), and fewer women required analgesics in the mechanical ripening group (27.5% versus 35.4%, difference in proportion −7.9%, 95% CI −13.2% to −2.7%, p = 0.003). There were no statistically significant differences between the 2 groups for other delivery, maternal, and neonatal outcomes. A limitation was a low observed rate of cesarean section. Conclusions In this study, we observed no difference in the rates of cesarean deliveries for nonreassuring fetal status between mechanical ripening with a silicone double balloon catheter and pharmacological cervical ripening with a pessary for the slow release of dinoprostone. Trial registration ClinicalTrials.gov NCT02907060

Effect of Glyburide vs Subcutaneous Insulin on Perinatal Complications Among Women With Gestational Diabetes: A Randomized Clinical Trial.

Randomized trials have not focused on neonatal complications of glyburide for women with gestational diabetes. To compare oral glyburide vs subcutaneous insulin in prevention of perinatal complications in newborns of women with gestational diabetes. The Insulin Daonil trial (INDAO), a multicenter noninferiority randomized trial conducted between May 2012 and November 2016 (end of participant follow-up) in 13 tertiary care university hospitals in France including 914 women with singleton pregnancies and gestational diabetes diagnosed between 24 and 34 weeks of gestation. Women who required pharmacologic treatment after 10 days of dietary intervention were randomly assigned to receive glyburide (n=460) or insulin (n=454). The starting dosage for glyburide was 2.5 mg orally once per day and could be increased if necessary 4 days later by 2.5 mg and thereafter by 5 mg every 4 days in 2 morning and evening doses, up to a maximum of 20 mg/d. The starting dosage for insulin was 4 IU to 20 IU given subcutaneously 1 to 4 times per day as necessary and increased according to self-measured blood glucose concentrations. The primary outcome was a composite criterion including macrosomia, neonatal hypoglycemia, and hyperbilirubinemia. The noninferiority margin was set at 7% based on a 1-sided 97.5% confidence interval. Among the 914 patients who were randomized (mean age, 32.8 [SD, 5.2] years), 98% completed the trial. In a per-protocol analysis, 367 and 442 women and their neonates were analyzed in the glyburide and insulin groups, respectively. The frequency of the primary outcome was 27.6% in the glyburide group and 23.4% in the insulin group, a difference of 4.2% (1-sided 97.5% CI, -∞ to 10.5%; P=.19). This study of women with gestational diabetes failed to show that use of glyburide compared with subcutaneous insulin does not result in a greater frequency of perinatal complications. These findings do not justify the use of glyburide as a first-line treatment. clinicaltrials.gov Identifier: NCT01731431