Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under which these strongly converge, locally, to the solutions within an appropriate distance. We express the conditions for convergence in terms of H\"{o}lder stability of the inverse maps, which ties naturally to the analysis of inverse problems

Convergence Rates for Learning Linear Operators from Noisy Data

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator's eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and non-diagonal settings.Comment: To appear in SIAM/ASA Journal on Uncertainty Quantification (JUQ); 34 pages, 5 figures, 2 table

Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal

In the present paper an iterative time-reversal algorithm, that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The timereversal retrofocusing is analyzed from a boundary control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Improving evidence on women’s groups: a proposed typology and common reporting indicators

Women’s groups are a widely implemented and researched development intervention, particularly in South Asia and Africa. Groups encompass many models and aim to address a range of objectives. However, there is no consistent approach to describing their varied implementation models, which hinders the accurate interpretation of evidence and construct validity. Drawing from three recent evidence reviews and research experience with groups, we propose a typology and common reporting indicators to describe women’s groups. As large-scale investments in women’s groups grow, these tools can support the interpretation and transferability of evidence across models and settings

Landbouwpraktijk en waterkwaliteit op landbouwbedrijven aangemeld voor de derogatie. Beschrijving van de meetnetopzet voor de periode 2006-2009 en de inhoud van de rapportages vanaf 2008

Translation of RIVM report 680717001. Alleen digitaal verschenenHet RIVM en het LEI hebben in 2006 in Nederland een monitoringnetwerk opgezet dat de gevolgen meet als landbouwbedrijven mogen afwijken (derogatie) van de Europese gebruiksnorm voor dierlijke mest. Het meetnet volgt driehonderd landbouwbedrijven die zich hebben aangemeld voor derogatie. Het legt de gevolgen vast voor de landbouwpraktijk en de waterkwaliteit. In dit rapport is de opzet van het monitoringnetwerk beschreven, evenals de wijze waarop vanaf 2008 over de resultaten zal worden gerapporteerd. Het rapport geeft onder andere aan wanneer welke cijfers beschikbaar zijn, en welke rekenmethoden gebruikt zullen worden om onder andere de bemesting en gewasopbrengst te berekenen. De Europese Nitraatrichtlijn verplicht lidstaten het stikstofgebruik via dierlijke mest te beperken tot maximaal 170 kg per hectare. Een lidstaat kan de Europese Commissie vragen hiervan onder voorwaarden af te wijken. Nederland heeft in december 2005 toestemming gekregen om vanaf 2006 tot en met 2009 onder voorwaarden af te mogen wijken van de gestelde norm. Dit betekent dat landbouwbedrijven 250 kilo stikstof per hectare mogen toedienen via dierlijke mest afkomstig van graasdieren (vooral koeien). Een van die voorwaarden is dat minimaal 70 procent van het totale areaal grasland is. Daarnaast is de Nederlandse overheid verplicht een monitoringnetwerk in te richten en de Commissie over de resultaten daarvan te rapporteren. De driehonderd deelnemers die worden gevolgd, zijn een steekproef van de circa 27.000 Nederlandse landbouwbedrijven die zich hebben aangemeld voor derogatie. Het netwerk is een onderdeel van het Landelijk Meetnet effecten Mestbeleid (LMM).In 2006 RIVM and LEI set up a monitoring network that measures the consequences of the option for farmers to deviate from the European use-standard for animal manure (derogation). The monitoring network follows three hundred farms benefiting from individual derogations and records the consequences for agricultural practice and water quality. This report describes the design and set-up of the monitoring network, as well as the content and layout of the annual reports from 2008 onwards containing results of the monitoring network. The report indicates, for example, what data will be available at a certain point in time, and what methods will be used to calculate such factors as fertilisation and yield. The Nitrates Directive obliges Member States to limit the use of animal manure to a maximum of 170 kg of nitrogen per hectare. A Member State may request the European Commission to deviate from this obligation under certain conditions. In December 2005, the European Commission granted the Netherlands the right to derogate from the obligation from 2006 till 2009 inclusive, implying that farmers could use up to 250 kg of nitrogen via manure of grazing livestock (particularly cows). One of the conditions is that 70% or more of the acreage available for manure application is grass. The Netherlands authorities are also obliged to set up a monitoring network and to report the results of this network to the European Commission. The 300 farms participating in the monitoring represent a sample taken from the approximately 27,000 Netherlands farms benefiting from individual derogations. The network is part of the National Programme for Monitoring the Effectiveness of the Minerals Policy (LMM).VROM-BWLLNV-D

External Validation of Model-Based Dosing Guidelines for Vancomycin, Gentamicin, and Tobramycin in Critically Ill Neonates and Children: A Pragmatic Two-Center Study

Background: The Dutch Pediatric Formulary (DPF) increasingly bases its guidelines on model-based dosing simulations from pharmacokinetic studies. This resulted in nationwide dose changes for vancomycin, gentamicin, and tobramycin in 2015. Objective: We aimed to evaluate target attainment of these altered, model-based doses in critically ill neonates and children. Methods: This was a retrospective cohort study in neonatal intensive care unit (NICU) and pediatric ICU (PICU) patients receiving vancomycin, gentamicin, or tobramycin between January 2015 and March 2017 in two university hospitals. The first therapeutic drug monitoring concentration for each patient was collected, as was clinical and dosing information. Vancomycin and tobramycin target trough concentrations were 10–15 and ≤ 1 mg/L, respectively. Target gentamicin trough and peak concentrations were < 1 and 8–12 mg/L, respectively. Results: In total, 482 patients were included (vancomycin [PICU] n = 62, [NICU] n = 102; gentamicin [NICU] n = 97; tobramycin [NICU] n = 221). Overall, median trough concentrations were within the target range for all cohorts but showed large interindividual variability, causing nontarget attainment. Trough concentrations were outside the target range in 66.1%, 60.8%, 14.7%, and 23.1% of patients in these four cohorts, respectively. Gentamicin peak concentrations were outside the range in 69% of NICU patients (term neonates 87.1%, preterm infants 57.1%). Higher creatinine concentrations were associated with higher vancomycin and tobramycin trough concentrations. Conclusion: This study illustrates the need to validate model-based dosing advice in the real-world setting as both sub- and supratherapeutic concentrations of vancomycin, gentamicin, and tobramycin were very prevalent. Our data underline the necessity for further individualization by addressing the high interindividual variability to improve target attainment