The Readiness of Water Molecules to Split into Hydrogen + Oxygen: A Proposed New Aspect of Water Splitting.

The potential of the anode, at which the evolution of oxygen begins, is a key parameter that describes how well water is split in water electrolyzers. Research efforts related to electrocatalytically initiated water splitting that aim at reducing the oxygen evolution reaction (OER) overpotential to date focus on the optimization of materials used to produce the electrodes. Descriptors for the readiness of the H2 O molecule itself to break down into its components have not been considered in water electrolysis experiments so far. In a simple set of experiments, it is found that adding dioxane to aqueous solutions leads to a substantial blueshift of the frequency of the OH stretch vibration which is a sign of an increased strength of the OH bond (intramolecular bonding). This phenomenon coincides with a significant increase in the OER onset potential as derived from cyclic voltammetry experiments. Thus, the OH stretch frequency can be an ideal indicator for the readiness of water molecules to be split in its cleavage products. This is thought to be first example of a study into the relationship between structural features of water as derived from Fourier transform infrared (FTIR) spectroscopic studies and key results derived from water electrolysis experiments.

Computational resolution in single molecule localization - impact of noise level and emitter density.

Classical fluorescence microscopy is a powerful technique to image biological specimen under close-to-native conditions, but light diffraction limits its optical resolution to 200-300 nm-two orders of magnitude worse than the size of biomolecules. Assuming single fluorescent emitters, the final image of the optical system can be described by a convolution with the point spread function (PSF) smearing out details below the size of the PSF. In mathematical terms, fluorescence microscopy produces bandlimited space-continuous images that can be recovered from their spatial samples under the conditions of the classical Shannon-Nyquist theorem. During the past two decades, several single molecule localization techniques have been established and these allow for the determination of molecular positions with sub-pixel accuracy. Without noise, single emitter positions can be recovered precisely - no matter how close they are. We review recent work on the computational resolution limit with a sharp phase transition between two scenarios: 1) where emitters are well-separated with respect to the bandlimit and can be recovered up to the noise level and 2) closely distributed emitters which results in a strong noise amplification in the worst case. We close by discussing additional pitfalls using single molecule localization techniques based on structured illumination.

A note on the iterative MRI reconstruction from nonuniform k-space data.

In magnetic resonance imaging (MRI), methods that use a non-Cartesian grid in k-space are becoming increasingly important. In this paper, we use a recently proposed implicit discretisation scheme which generalises the standard approach based on gridding. While the latter succeeds for sufficiently uniform sampling sets and accurate estimated density compensation weights, the implicit method further improves the reconstruction quality when the sampling scheme or the weights are less regular. Both approaches can be solved efficiently with the nonequispaced FFT. Due to several new techniques for the storage of an involved sparse matrix, our examples include also the reconstruction of a large 3D data set. We present four case studies and report on efficient implementation of the related algorithms.