The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.     

High pressure-induced structural effects in plastic packaging

Today, flexible vacuum packages are predominantly used for products to be subjected to high pressure treatment. However, tray packages with a modified atmosphere are in demand, which provide a high failure rate with respect to gas and water vapour permeability and packaging integrity. Methods to follow permeation processes under high pressure were developed and used together with optical microscopy, confocal scanning laser microscopy, Raman spectroscopy and atomic force microscopy to identify the mechanisms for changes in permeability and damage to the packaging materials. Single film samples and pouch packages filled with model products were studied. Results indicate a reversible decrease in the coefficients of diffusion and permeation under the impact of high pressure, due to the compression of the polymeric bulk. Irreversible changes in the polymeric materials are associated with gases in the packaging head space, which cause high local temperatures and create damage due to rapid deliberation upon the pressure drop at the end of the high pressure cycle.     

Zero-temperature properties of randomly self-interacting polymers

We study the zero-temperature behavior of several simple models for randomly self-interacting polymers in one and 1+1 dimensions. Results are based on exact enumeration and closed-form expressions.     

Edge linking and image segmentation by combining optical and digital methods

We present a hybrid method for segmentation of intensity images, which combines an optical contouring technique and digital algorithms for linking edge points or image segmentation. In a first stage, the digital image to be processed is displayed in a twisted-nematic liquid-crystal display (LCD), which is placed between a polarizer–analyzer pair at 45 deg (instead of 90 deg as occurs in standard LCDs). It is not difficult to demonstrate that the proposed setup produces a resultant image with very pronounced dark contours at middle intensity. After the optical preprocessing, two different digital algorithms are applied: an edge linking algorithm (modified chain code) and a simple thresholding technique for image segmentation. The proposed procedure works well with monochromatic and color images. The method could be useful as a robust technique for segmentation of large images in real-time, which presents potential applications in medical and biological imaging.     

Surface structure of ultrathin Fe films on Cu(001) revisited

The structure and magnetism of ultrathin Fe films epitaxially grown on a Cu(001) surface are investigated by grazing scattering of fast H and He atoms or ions. By making use of a new variant of ion beam triangulation based on the detection of the number of emitted electrons, we obtain direct information on the structure of the film surface. We observe for room temperature growth a dominant and defined fcc-like structure. Complex surface reconstructions as reported in recent STM and LEED studies are observed only for cooling and H2 dosing.     

Ultra-fine grained Nd–Fe–B by high pressure reactive milling and desorption

This paper reports on the grain refinement in dynamic hydrogenation disproportionation desorption and recombination (d-HDDR) processed Nd-rich Nd₂Fe₁₄B and stoichiometric Nd₂Fe₁₄B powders using high pressure reactive milling (HPRM) followed by a subsequent desorption and recombination. In contrast to the dynamic-HDDR processed anisotropic powder with a grain size of the Nd₂Fe₁₄B phase of 300 nm, the new approach yields a further reduction of the Nd₂Fe₁₄B₁ grain size to less than 70 nm. Nd-rich Nd₂Fe₁₄B powder produced by HPRM and subsequent desorption exhibits a coercivity μ_0iH_c=1.35 T and a remanence of 0.80 T. In the stoichiometric material, the reduction of the Nd-content leads to an increase in remanence to 0.85 T. Additionally, it is demonstrated that highly anisotropic powders can also be obtained by dynamic-HDDR processing of stoichiometric Nd₂Fe₁₄B powders.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

On functions having Cauchy differences in some prescribed sets

Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK (6C) = {0}. If a functionh:E F is continuous at at least one point andh(x + y) – h(x) – h(y) K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E.