Bayesian uncertainty evaluation applied to the tilted-wave interferometer.

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements, acquired with a special setup, and sophisticated mathematical evaluation procedures. To determine the form of the surface under test, a computational model is required that closely mimics the measurement process of the physical measurement instruments. The parameters of the computational model, comprising the surface under test sought, are then tuned by solving an inverse problem. Due to this embedded structure of the real experiment and computational model and the overall complexity, a thorough uncertainty evaluation is challenging. In this work, a Bayesian approach is proposed to tackle the inverse problem, based on a statistical model derived from the computational model of the tilted-wave interferometer. Such a procedure naturally allows for uncertainty quantification to be made. We present an approximate inference scheme to efficiently sample quantities of the posterior using Monte Carlo sampling involving the statistical model. In particular, the methodology derived is applied to the tilted-wave interferometer to obtain an estimate and corresponding uncertainty of the pixel-by-pixel form of the surface under test for two typical surfaces taking into account a number of key influencing factors. A statistical analysis using experimental design is employed to identify main influencing factors and a subsequent analysis confirms the efficacy of the method derived.

Ion type and valency differentially drive vimentin tetramers into intermediate filaments or higher order assemblies.

Vimentin intermediate filaments, together with actin filaments and microtubules, constitute the cytoskeleton in cells of mesenchymal origin. The mechanical properties of the filaments themselves are encoded in their molecular architecture and depend on their ionic environment. It is thus of great interest to disentangle the influence of both the ion type and their concentration on vimentin assembly. We combine small angle X-ray scattering and fluorescence microscopy and show that vimentin in the presence of the monovalent ions, K+ and Na+, assembles into "standard filaments" with a radius of about 6 nm and 32 monomers per cross-section. In contrast, di- and multivalent ions, independent of type and valency, lead to the formation of thicker filaments associating over time into higher order structures. Hence, our results may indeed be of relevance for living cells, as local ion concentrations in the cytoplasm during certain physiological activities may differ considerably from average intracellular concentrations.

Compressed FTIR spectroscopy using low-rank matrix reconstruction.

Fourier transform infrared (FTIR) spectroscopy is a powerful technique in analytical chemistry. Typically, spatially distributed spectra of the substance of interest are conducted simultaneously using FTIR spectrometers equipped with array detectors. Scanning-based methods such as near-field FTIR spectroscopy, on the other hand, are a promising alternative providing higher spatial resolution. However, serial recording severely limits their application due to the long acquisition times involved and the resulting stability issues. We demonstrate that it is possible to significantly reduce the measurement time of scanning methods by applying the mathematical technique of low-rank matrix reconstruction. Data from a previous pilot study of Leishmania strains are analyzed by randomly selecting 5% of the interferometer samples. The results obtained for bioanalytical fingerprinting using the proposed approach are shown to be essentially the same as those obtained from the full set of data. This finding can significantly foster the practical applicability of high-resolution serial scanning techniques in analytical chemistry and is also expected to improve other applications of FTIR spectroscopy and spectromicroscopy.