Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain

Rotation of an immersed cylinder sliding near a thin elastic coating

It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [Saintyves et al. PNAS 113(21), 2016]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observations, namely that a softer elastic layer results in a greater angular speed of the cylinder.Comment: 16 pages, 4 figure

Budget constraint and vaccine dosing: A mathematical modelling exercise

BACKGROUND: Increasing the number of vaccine doses may potentially improve overall efficacy. Decision-makers need information about choosing the most efficient dose schedule to maximise the total health gain of a population when operating under a constrained budget. The objective of this study is to identify the most efficient vaccine dosing schedule within a fixed vaccination budget from a healthcare payer perspective. METHODS: An optimisation model is developed in which maximizing the disease reduction is the functional objective and the constraint is the vaccination budget. The model allows variation in vaccination dosing numbers, in cost difference per dose, in vaccine coverage rate, and in vaccine efficacy. We apply the model using the monovalent rotavirus vaccine as an example. RESULTS: With a fixed budget, a 2-dose schedule for vaccination against rotavirus infection with the monovalent vaccine results in a larger reduction in disease episodes than a 3-dose scheme with the same vaccine under most circumstances. A 3-dose schedule would only be better under certain conditions: a cost reduction of >26% per dose, combined with vaccine efficacy improvement of ≥5% and a target coverage rate of 75%. Substantial interaction is observed between cost reduction per dose, vaccine coverage rate, and increased vaccine efficacy. Sensitivity analysis shows that the conditions required for a 3-dose strategy to be better than a 2-dose strategy may seldom occur when the budget is fixed. The model does not consider vaccine herd effect, precise timing for additional doses, or the effect of natural immunity development. CONCLUSIONS: Under budget constraint, optimisation modelling is a helpful tool for a decision-maker selecting the most efficient vaccination dosing schedule. The low dosing scheme could be the optimal option to consider under the many scenarios tested. The model can be applied under many different circumstances of changing dosing schemes with single or multiple vaccines

Diverse Cis-Regulatory Mechanisms Contribute to Expression Evolution of Tandem Gene Duplicates

The deposited article is a post-print version and has peer review. The deposited article version contains attached the supplementary materials within the pdf.Pairs of duplicated genes generally display a combination of conserved expression patterns inherited from their unduplicated ancestor and newly acquired domains. However, how the cis-regulatory architecture of duplicated loci evolves to produce these expression patterns is poorly understood. We have directly examined the gene-regulatory evolution of two tandem duplicates, the Drosophila Ly6 genes CG9336 and CG9338, which arose at the base of the drosophilids between 40 and 60 million years ago. Comparing the expression patterns of the two paralogs in four Drosophila species with that of the unduplicated ortholog in the tephritid Ceratitis capitata, we show that they diverged from each other as well as from the unduplicated ortholog. Moreover, the expression divergence appears to have occurred close to the duplication event and also more recently in a lineage-specific manner. The comparison of the tissue-specific cis-regulatory modules (CRMs) controlling the paralog expression in the four Drosophila species indicates that diverse cis-regulatory mechanisms, including the novel tissue-specific enhancers, differential inactivation, and enhancer sharing, contributed to the expression evolution. Our analysis also reveals a surprisingly variable cis-regulatory architecture, in which the CRMs driving conserved expression domains change in number, location, and specificity. Altogether, this study provides a detailed historical account that uncovers a highly dynamic picture of how the paralog expression patterns and their underlying cis-regulatory landscape evolve. We argue that our findings will encourage studying cis-regulatory evolution at the whole-locus level in order to understand how interactions between enhancers and other regulatory levels shape the evolution of gene expression.Fundação Calouste Gulbenkian/Instituto Gulbenkian de Ciência; Toulouse RIO Imaging platform; Bloomington Drosophila Stock Center (Indiana, USA); Developmental Studies Hybridoma Bank (Iowa, USA); Drosophila Genomics Resource Center (Indiana, USA); NIH grant: (2P0OD010949); Agence Nationale de la Recherche grant: (ANR-13-ISV7-0001-01); Fundação para a Ciência e a Tecnologia grants: (SFRH/BPD/75139/2010, FCT-ANR/BIA-ANM/0003/2013, FCT-EXPL/BEX-GMG/2197/2013).info:eu-repo/semantics/acceptedVersio