Random sampling of bandlimited signals on graphs

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than $O(k\log ?(k))$ measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques.     

A cautionary warning on the use of electrochemical measurements to calculate comproportionation constants for mixed-valence compounds

The redox potentials for successive oxidations in a series of ligand-bridged dinuclear ruthenium complexes are shown to be dependent on the identity of the anion used as the electrolyte in the electrochemical measurements. Since the differences between these redox potentials (DeltaE(ox)) are often used to calculate the comproportionation equilibrium constants (K(c)) in mixed-valence species--and therefore the extent of inter-metal communication between the metal centres--the results demonstrate the need for extreme care in comparison of DeltaE(ox) data and of K(c) values derived from them.     

Solid-phase synthesis of phenolic steroids: from optimization studies to a convenient procedure for combinatorial synthesis of biologically relevant estradiol derivatives

During the course of our studies on therapeutic agents for the treatment of breast cancer, we became interested in the solid-phase combinatorial synthesis of estradiol derivatives that contain a functionalized side chain at either position 16 beta or 7 alpha. Both types of compounds have already demonstrated inhibitory activity toward both biosynthesis and action of estradiol. As a first step, two versatile precursors bearing an azidoalkyl side chain at either position 16 beta or 7 alpha of estradiol were synthesized using standard solution-phase methods. Afterward, the effectiveness of five linkers to attach the phenolic function of these estradiol derivatives to a polystyrene resin was investigated; they were benzylic ether (Merrifield), 4-alkoxy-benzylic ethers (Wang, Sheppard), tetrahydropyranyl ether (Ellman), benzoic ester, and o-nitrobenzyl ether. To test the linker in a synthetic context, a short sequence of reactions, including reduction of the azide and acylation of the corresponding amine, was performed on the polymer-bound estradiol derivative. While all of the tested linkers proved effective in attaching the phenol functionality of the precursor, only the o-nitrobenzyl ether photolabile linker enabled the release of the final products in acceptable purities. Consequently, this linker was used to perform successfully the solid-phase synthesis of four different classes of estradiol derivatives in acceptable yields and excellent purities. This study was preliminary to the combinatorial synthesis of larger libraries of biologically relevant estradiol derivatives.     

Recent advances in the anionic synthesis of chain-end functionalized polymers

Recent results for the preparation of chain-end functionalized polymers using alkyllithium-initiated anionic polymerization are described. Termination with 4-chloro-1,1,1-trimethoxybutane has been used to prepare trimethoxy ortho ester (carboxyl)-functionalized polymers. Functionalization with the oxiranes, glycidoxypropyltrimethoxysilane, 3,4-epoxy-1-butene and 1,1,1-trifluoro-2,3-epoxypropane, has been investigated to prepare trimethoxysilyl-functionalized polymers, 1,3-diene-functionalized macro monomers and trifluoromethyl-functionalized polymers, respectively. Secondary amine-functionalized polymers have been prepared by termination with N-(benzylidene)methylamine and also using an N-benzyl tertiary amine-functionalized alkyllithium initiator followed by hydrogenolysis of the benzyl group.     

Competition between antiferromagnetism and superconductivity in high-Tc cuprates

Using variational cluster perturbation theory we study the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the t-t(')-t(')-U Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of dSC that should be observable in photoemission experiments.     

Fluctuations about hydrodynamic nonequilibrium steady states

Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stationary state held away from global thermal equilibrium by a temperature gradient or shear flow. In the former case, the Brillouin peaks in the light scattering spectrum acquire an asymmetry that is qualitatively similat to earlier results but different in detail.     

Applications de la sonde moleculaire aux composites a teneur elevee en solides—II. Étude du vieillissement

Three types of highly filled polymers were studied by the molecular probe to evaluate the applicability of this technique to ageing studies. The probe was found efficient in characterizing the behaviour of a given composite under a given set of conditions, or the effect of the nature of the solid phase on the stability of the binder. Thus, the post-curing effect in composite containing NH,₄CLO₄ and Al was analysed in detail. ΔH_a = 15·8 kcal/mole was found for this first-order reaction. In a second example, Fe₂O₃ was shown to decrease the post-curing effect leading to a very thermally stable material. Finally, the absence of aluminium resulted in a reduced hydrolytic stability of the binder.     

The N-acyloxyiminium ion aza-Prins route to octahydroindoles: total synthesis and structural confirmation of the antithrombotic marine natural product oscillarin

The first enantiocontrolled total synthesis of the marine natural product oscillarin is described. The proposed structure and absolute configuration of oscillarin is thus confirmed, and a previously assigned structure of a subunit was shown to be incorrect. The X-ray structure of an oscillarin-thrombin complex was resolved at 2.0 A resolution, which validated its potent inhibitory activity against the enzyme with an IC(50) = 28 nM. Methodology was developed for the synthesis of enantiopure octahydroindole-2-carboxylic acids with usable functionality at C-6. The method consists of the halocarbocyclization of N-acyloxyiminium ions containing an olefinic tether in the presence of tin tetrachloride or tin tetrabromide. This N-acyloxyiminium ion aza-Prins carbocyclization proved to be general for the construction of octahydroindole and perhydroquinoline 2-carboxylic acids. Mechanistic rationales are based on an antiperiplanar attack of the terminal alkene on the iminium ion, leading to an incipient secondary carbocation which is trapped by halide via an equatorial attack. X-ray crystal structures of products corroborate the expected stereochemistry.