This paper studies the properties of a new lower bound for the natural pseudodistance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the L ∞ -norm. In order to obtain the lower bound, a suitable metric between size functions, called matching distance, is introduced. It compares size functions by solving an optimal matching problem between countable point sets. The matching distance is shown to be resistant to perturbations, implying that it is always smaller than the natural pseudo-distance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.

Fibrillogenesis of the small peptide Aβ(1-40) is considered to be the hallmark of Alzheimer's disease. Some evidence indicates small oligomers, rather than mature fibrils, as the key cytotoxic agents. The fluorescent dye Thioflavin T (ThT) is often used to detect amyloid deposits in both in vivo and in vitro experiments, and it is used to study kinetic measurements, under the fundamental hypothesis that this probe does not influence the aggregation processes. We report experimental data showing that ThT may promote the Aβ(1-40) peptide amyloid aggregation changing solvent-peptide interactions and stabilizing more ordered β-like conformation. This finding has a two-fold importance: It is a fundamental warning in all fibrillation experiments where ThT is used as fluorescent probe, and it suggests that ThT, accelerating fibril formation, could be used to reduce the presence of transient small oligomers, thus interfering with the pathogenic impact of Aβ peptide.

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Despite the great interest organic spintronics has recently attracted, there is only a partial understanding of the fundamental physics behind electron spin relaxation in organic semiconductors. Mechanisms based on hyperfine interaction have been demonstrated, but the role of the spin-orbit interaction remains elusive. Here, we report muon spin spectroscopy and time-resolved photoluminescence measurements on two series of molecular semiconductors in which the strength of the spin-orbit interaction has been systematically modified with a targeted chemical substitution of different atoms at a particular molecular site. We find that the spin-orbit interaction is a significant source of electron spin relaxation in these materials.