Landau Damping in the Kuramoto Model

We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit, with individual frequencies drawn from a distribution with density of class \({C^n}\) (\({n\geq 4}\)). A criterion for linear stability of the uniform stationary state is established which, for basic examples in the literature, is equivalent to the standard condition on the coupling strength. We prove that, under this criterion, the Kuramoto order parameter, when evolved under the full nonlinear dynamics, asymptotically vanishes (with polynomial rate n) for every trajectory issued from a sufficiently small \({C^n}\) perturbation. The proof uses techniques from the Analysis of PDEs and closely follows recent proofs of the nonlinear Landau damping in the Vlasov equation and Vlasov-HMF model.     

Automated solid-phase synthesis of protected oligosaccharides containing beta-mannosidic linkages

For automated oligosaccharide synthesis to impact glycobiology, synthetic access to most carbohydrates has to become efficient and routine. Methods to install "difficult" glycosidic linkages have to be established and incorporated into the overall synthetic concept. Described here is the first automated solid-phase synthesis of oligosaccharides containing the challenging beta-mannosidic linkage. Carboxybenzyl mannoside building blocks proved effective beta-mannosylation agents and resulted in excellent conversion and good to moderate selectivities. [(Triisopropylsilyl)oxy]-methyl ether (Tom), served as an orthogonal, minimally intrusive, and readily cleavable protecting group for the elongation of the C3 position of mannose. The desired oligosaccharide products were readily separated from by-products containing unwanted stereoisomers using reverse-phase HPLC. The methods described here expand the scope of carbohydrates currently accessible by automation as many oligosaccharides of biological interest contain beta-mannosidic linkages.     

A comparative study of amide-bond forming reagents in aqueous media – Substrate scope and reagent compatibility

A survey of amidation reagents demonstrating DIC-HOPO, DMT-MM, COMU-collidine, TPTU-NMI, EEDQ, CDI and EDC-Oxyma to be effective for the coupling of carboxylic acids with amines in the presence of water and the absence of problematic dipolar aprotic solvents is reported. DMT-MM was shown to provide the best yields for the coupling of a secondary amine, TPTU-NMI and COMU-collidine for aniline, whilst the combination of DIC with HOPO afforded the broadest substrate scope and the highest yields for a sterically demanding carboxylic acid.     

An agent-based model for the bibliometric h-index

We model a virtual scientific community in which authors publish and cite articles. Citations are attributed according to a preferential attachment mechanism. From the numerical simulations, the h-index can be computed. This bottom-up approach reproduces well real bibliometric data. We consider two versions of our model. (1) The single-scientist is controlled by two parameters which can be tuned to reproduce the value of the h-index of many real scientists. Moreover, this model shows how the h-index grows with the number of citations, for a fixed number of articles. We also define an average h-index that can be used to compare the scientific productivity of institutions of different sizes. (2) The multi-scientist model considers a population of scientists and allows us to study the impact of removing citations from the low h-index researchers on the community. Simulations on real bibilometric data, as well as the predictions of the model, show that the h-index eco-system can be strongly affected by such a filtering.     

Shorter and modular synthesis of hemicryptophane-tren derivatives

Hemicryptophanes are host molecules with many applications as supramolecular catalysts or in ion selective recognition. A very convenient and efficient modular approach for the synthesis of hemicryptophane-tren (tren, tris(2-aminoethyl)-amine) derivatives has been developed. For instance, hemicryptophane 1 was synthesized at the gram scale in four steps from vanillyl alcohol compared to the previous seven-step procedure. The size, shape, and functionalities of the molecular cavity were also easily modified.     

Library of second-generation cycloruthenated compounds and evaluation of their biological properties as potential anticancer drugs: passing the nanomolar barrier

A library of 32 organoruthenium compounds has been synthesised. Known and novel C-N cyclometalated compounds as well as N-C-N and N-N-C pincer derivatives of this metal have been used in this purpose. Most of the compounds have been tested for their in vitro antitumoral behaviours, good to excellent activities have thus been found. Several of the newly synthesized compounds pass the symbolic barrier of the nanomolar range for their IC(50) indicating a critical improvement. The level of activity is tentatively correlated to physicochemical properties of the compounds such as their Ru(III/II) redox potential and their lipophilicity (log P).     

Asymmetric synthesis of the oxygenated polycyclic system of (+)-harringtonolide

A straightforward asymmetric synthesis of the cage oxygenated structure of (+)-harringtonolide has been accomplished for the first time. The key steps involved (i) a templated stereoselective IMDA reaction to build a highly functionalized cyclohexene ring D, (ii) functionalization of the cycloadduct, (iii) ring-closing metathesis providing the five-membered ring C, and finally (iv) a challenging one-step cascade cyclization of an epoxy-alcohol toward the target structure, whose mechanism was investigated.     

Fronts Between Periodic Patterns for Bistable Recursions on Lattices

Bistable space–time discrete systems commonly possess a large variety of stable stationary solutions with periodic profile. In this context, it is natural to ask about the fate of trajectories composed of interfaces between steady configurations with periodic pattern and in particular, to study their propagation as traveling fronts. Here, we investigate such fronts in piecewise affine bistable recursions on the one-dimensional lattice. By introducing a definition inspired by symbolic dynamics, we prove the existence of front solutions and uniqueness of their velocity, upon the existence of their ground patterns. Moreover, the velocity dependence on parameters and the co-existence of several fronts with distinct ground patterns are also described. Finally, robustness of the results to small $C^1$ -perturbations of the piecewise affine map is argued by mean continuation arguments.