Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

Analysis and imaging of biocidal agrochemicals using ToF-SIMS

ToF-SIMS has been increasingly widely used in recent years to look at biological matrices, in particular for biomedical research, although there is still a lot of development needed to maximise the value of this technique in the life sciences. The main issue for biological matrices is the complexity of the mass spectra and therefore the difficulty to specifically and precisely detect analytes in the biological sample. Here we evaluated the use of ToF-SIMS in the agrochemical field, which remains a largely unexplored area for this technique. We profiled a large number of biocidal active ingredients (herbicides, fungicides, and insecticides); we then selected fludioxonil, a halogenated fungicide, as a model compound for more detailed study, including the effect of co-occurring biomolecules on detection limits. There was a wide range of sensitivity of the ToF-SIMS for the different active ingredient compounds, but fludioxonil was readily detected in real-world samples (wheat seeds coated with a commercial formulation). Fludioxonil did not penetrate the seed to any great depth, but was largely restricted to a layer coating the seed surface. ToF-SIMS has clear potential as a tool for not only detecting biocides in biological samples, but also mapping their distribution

Study of the interaction of the Ig2 module of the fibroblast growth factor receptor, FGFR Ig2, with the fibroblast growth factor 1, FGF1, by means of NMR spectroscopy

AbstractFibroblast growth factor (FGF) receptor (FGFR) consists extracellularly of three immunoglobulin (Ig) modules (Ig1–3). Currently, there are two competing models (symmetric and asymmetric) of the FGF–FGFR–heparin complex based on crystal structures. Indirect evidence exists in support of both models. However, it is not clear which model is physiologically relevant. Our aim was to obtain direct, non-crystallographic evidence in support of them. We found by nuclear magnetic resonance that Ig2 could bind to FGF1 not only via the primary site (present in both models), but also via the secondary site (present only in the symmetric model). Thus, our data support the symmetric model