X-Ray Molecular Structure of a Red Bilin Derivative from Chlorella protothecoides. 4th communication on chlorophyll catabolism

The molecular structure of a chlorophyll a catabolite isolated from the culture medium of bleached Chlorella protothecoides cells has been determined by X-ray diffraction; the crystal structure shows a distorted helical arrangement of the pyrrole rings and consists of symmetrical dimers located at a crystallographic diad, which are stabilized by six intermolecular H-bonds.     

Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

Olefination of ketones using a gold(III)-catalyzed Meyer-Schuster rearrangement

An atom-economical and efficient olefination strategy for ketones is described. Ethoxyacetylide addition followed by a gold-catalyzed Meyer-Schuster rearrangement affords alpha,beta-unsaturated esters, generally in excellent overall yield from the starting ketones. The alkynophilicity of Au3+ promotes an interaction with the electron-rich acetylenes that catalyzes the Meyer-Schuster rearrangement selectively over other conceivable pathways.     

Fast Algorithms for Nonparametric Curve Estimation

Abstract

Naive implementations of local polynomial fits and kernel estimators require almost O(n ²) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n ^7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities.     

Isospectral Alexandrov spaces

We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results by the authors based on Schüth’s version of the torus method.     

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.     

Focused ion beam/scanning electron microscopy characterization of cell behavior on polymer micro-/nanopatterned substrates: a study of cell-substrate interactions

Topographic micro and nanostructures can play an interesting role in cell behaviour when cells are cultured on these kinds of patterned substrates. It is especially relevant to investigate the influence of the nanometric dimensions topographic features on cell morphology, proliferation, migration and differentiation. To this end, some of the most recent fabrication technologies, developed for the microelectronics industry, can be used to produce well-defined micro and nanopatterns on biocompatible polymer substrates. In this work, osteoblast-like cells are grown on poly(methyl methacrylate) substrates patterned by nanoimprint lithography techniques. Examination of the cell-substrate interface can reveal important details about the cell morphology and the distribution of the focal contacts on the substrate surface. For this purpose, a combination of focused ion beam milling and scanning electron microscopy techniques has been used to image the cell-substrate interface. This technique, if applied to samples prepared by freeze-drying methods, allows high-resolution imaging of cross-sections through the cell and the substrate, where the interactions between the nanopatterned substrate, the cell and the extracellular matrix, which are normally hidden by the bulk of the cell, can be studied.     

Positivity and Stability for One-Sided Coupled Operator Matrices

Many evolutionary systems can be described by an abstract Cauchy problem governed by an operator matrix. Assuming this problem to be one-sided coupled and well-posed we study in this paper the positivity and the stability of the associated matrix semigroup. The abstract results are illustrated by several examples.