Amorphous Aggregation of Amyloid Beta 1‐40 Peptide in Confined Space

The amorphous aggregation of Aβ1‐40 peptide is addressed by using micromolding in capillaries. Both the morphology and the size of the aggregates are modulated by changing the contact angle of the sub‐micrometric channel walls. Upon decreasing the hydrophilicity of the channels, the aggregates change their morphology from small aligned drops to discontinuous lines, thereby keeping their amorphous structure. Aβ1‐40 fibrils are observed at high contact angles.     

Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

The effect of linear perturbations on the Yamabe problem

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold $\left( M,g\right) $ is compact. Established in the locally conformally flat case by Schoen (Lecture Notes in Mathematics, vol. 1365, pp. 120–154. Springer, Berlin 1989, Surveys Pure Application and Mathematics, 52 Longman Science, Technology, pp. 311–320. Harlow 1991) and for $n\le 24$ by Khuri–Marques–Schoen (J Differ Geom 81(1):143–196, 2009), it has revealed to be generally false for $n\ge 25$ as shown by Brendle (J Am Math Soc 21(4):951–979, 2008) and Brendle–Marques (J Differ Geom 81(2):225–250, 2009). A stronger version of it, the compactness under perturbations of the Yamabe equation, is addressed here with respect to the linear geometric potential $\frac{n-2}{4(n-1)} {{\mathrm{Scal}}}_g,\, {{\mathrm{Scal}}}_g$ being the Scalar curvature of $\left( M,g\right) $ . We show that a-priori $L^\infty $ –bounds fail for linear perturbations on all manifolds with $n\ge 4$ as well as a-priori gradient $L^2$ –bounds fail for non-locally conformally flat manifolds with $n\ge 6$ and for locally conformally flat manifolds with $n\ge 7$ . In several situations, the results are optimal. Our proof combines a finite dimensional reduction and the construction of a suitable ansatz for the solutions generated by a family of varying metrics in the conformal class of $g$ .     

From exaptation to radical niche construction in biological and technological complex systems

Biological adaptation assumes the evolution of structures toward better functions. Yet, the roots of adaptive trajectories usually entail subverted—perverted—structures, derived from a different function: what Gould and Vrba called “exaptation.” Generally, this derivation is regarded as contingent or serendipitous, but it also may have regularities, if not rules, in both biological evolution and technological innovation. On the basis of biological examples and examples from the history of technology, the authors demonstrate the centrality of exaptation for a modern understanding of niche, selection, and environment. In some cases, biological understanding illuminates technical exaptation. Thus, the driver of exaptation is not simply chance matching of function and form; it depends on particular, permissive contexts. © 2013 Wiley Periodicals, Inc. Complexity 18: 7–14, 2013