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

Evolutionary outcomes arising from bistability in ecosystem dynamics

While it is known that shallow lakes ecosystems may experience abrupt shifts (ie tippingpoints) from one state to a contrasting degraded alternative state as a result of gradual envi-ronmental changes, the role of evolutionary processes and the impact of trait variation in thiscontext remain largely unexplored. It is crucial to elucidate how eco-evolutionary feedbacksaffect abrupt ecological transitions in shallow lakes. These feedbacks can significantly alterthe dynamics of aquatic plants competition, community structure, and species diversity, po-tentially affecting the existence of alternative states or either delay or expedite the thresholdsat which these ecological shifts occur. In this paper, we explore the eco-evolutionary dyna-mics of submerged and floating macrophytes in a shallow lake ecosystem under asymmetriccompetition for nutrients and light. We use adaptive dynamics and a structured populationmodel to analyze the evolution of the growth depth of the submerged and floating macro-phytes population, which influences their competitive ability for the two resources. We showhow rapid trait evolution can result in complex dynamics including evolutionary oscillations,extensive diversification and evolutionary suicide. Furthermore, we find that the co-evolutionof the two competitive species can play a stabilizing role, while not significantly affectingthe overall evolutionary dynamics. Overall, this study shows that evolution can have strongeffects in the ecological dynamics of bistable ecosystems

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