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

Cross-validating precipitation datasets in the Indus River basin

Abstract. Large uncertainty remains about the amount of precipitation falling in the Indus River basin, particularly in the more mountainous northern part. While rain gauge measurements are often considered as a reference, they provide information for specific, often sparse, locations (point observations) and are subject to underestimation, particularly in mountain areas. Satellite observations and reanalysis data can improve our knowledge but validating their results is often difficult. In this study, we offer a cross-validation of 20 gridded datasets based on rain gauge, satellite, and reanalysis data, including the most recent and less studied APHRODITE-2, MERRA2, and ERA5. This original approach to cross-validation alternatively uses each dataset as a reference and interprets the result according to their dependency on the reference. Most interestingly, we found that reanalyses represent the daily variability of precipitation as well as any observational datasets, particularly in winter. Therefore, we suggest that reanalyses offer better estimates than non-corrected rain-gauge-based datasets where underestimation is problematic. Specifically, ERA5 is the reanalysis that offers estimates of precipitation closest to observations, in terms of amounts, seasonality, and variability, from daily to multi-annual scale. By contrast, satellite observations bring limited improvement at the basin scale. For the rain-gauge-based datasets, APHRODITE has the finest temporal representation of the precipitation variability, yet it importantly underestimates the actual amount. GPCC products are the only datasets that include a correction factor of the rain gauge measurements, but this factor likely remains too small. These findings highlight the need for a systematic characterisation of the underestimation of rain gauge measurements. European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 648609

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