Complexity reduction of C-Algorithm

The C-Algorithm introduced in [5] is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case.The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in [1] and [2] to find many new examples of isochronous centers for the Liénard type equation.     

Measuring local and global vibration modes in model plants

Model plants are extensively used in biological studies, and their mechanical behaviour needs to be better understood, in relation to studies in mechanoperception for instance. We present here the first approach to derive experimentally the modal parameters of two of these plants, Arabidopsis thaliana and Populus tremula × alba. A classical sinusoidal sweep excitation is used, with a measurement of displacements based on LKT optical flow tracking, followed by a bi-orthogonal decomposition (BOD). This allows us to estimate several modal frequencies for each plant, as well as the corresponding spatial localizations of deformation. Analyzing the modal frequencies, we show that global and local modes correspond to distinct ranges of frequencies and depend differently on plant size. Possible phenotyping applications are then discussed.     

Two-dimensional motion of a set of particles in a free surface flow with image processing

A method to analyze bed load with image processing was developed. The motion of coarse spherical particles on a mobile bed entrained by a shallow turbulent flow down a steep channel was filmed with a high-speed camera. The water free surface and the particle positions were detected combining classical image processing algorithms. We developed a particle-tracking algorithm to calculate all particle trajectories and motion regimes, rolling or saltation. At constant slope, the contribution of the rolling particles to the solid discharge only slightly differed when the particle supply was increased. At a slope of 10%, it represented about 40%. In contrast, rolling became the major regime when the slope increased, at a slope of 15% it represented up to 80% of the total solid discharge.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Synthesis of L-Rhamnose and N -Acetyl-D-Glucosamine Derivatives Entering in the Composition of Bacterial Polysaccharides by Use of Glucansucrases

Transglucosylation reactions using sucrose as glucosyl donor and either N-acetyl-D-glucosamine, L-rhamnose, or methyl α -L-rhamnopyranoside as acceptors were carried out with recombinant glucansucrases from families 70 and 13 of glycoside-hydrolases. Depending on the enzyme specificity, various carbohydrate structures were synthesized and characterized including α -D-glucopyranosyl-(1 → 6)-N-acetyl-D-glucosamine, α -D-glucopyranosyl-(1 → 4)-N-acetyl-D-glucosamine, α -D-glucopyranosyl-(1 → 1)-β -L-rhamnopyranoside, α -D-glucopyranosyl-(1 → 4)-α -D-glucopyranosyl-(1 → 1)-β -L-rhamnopyranoside, methyl α -D-glucopyranosyl-(1 → 4)-α -L-rhamnopyranoside, and methyl α -D-glucopyranosyl-(1 → 3)-α -L-rhamnopyranoside. Disaccharides were obtained with yields going up to 64%. The structural diversity generated as well as the obtained yields appear to be related to enzyme active site architecture, which can be modulated and improved by enzyme engineering. Several of the obtained disaccharides enter in the composition of surface polysaccharides of pathogenic bacteria, among which is Shigella flexneri. Our results outline the potential of glucansucrases in the chemo-enzymatic synthesis of complex carbohydrates of biological interest whose chemical synthesis may be seen as a limitation.     

Small-time existence for the Navier-Stokes equations with a free surface

We prove the small-time existence of a solution of the Navier-Stokes equations, for any initial data, for a free boundary fluid with surface tension taken into account. A fixed point method is used. The linearized problem is hyperbolic and dissipative. The classical methods to solve it seem to fail and the method used here could perhaps be applied for equations of the same kind.     

Synthesis of polypropionate subunits from cyclopropanes

The oxymercuration-reductive demercuration of several cyclopropanealkanol or their derivatives bearing adjacent stereocenters has been investigated in order to synthesize polypropionate subunits. The crucial importance of the ester protecting group for the remote oxygenated moieties on the mechanism and the stereochemical outcome of these reactions has been rationalized.     

Design of Potent Mannose 6‐Phosphate Analogues for the Functionalization of Lysosomal Enzymes To Improve the Treatment of Pompe Disease

Improving therapeutics delivery in enzyme replacement therapy (ERT) for lysosomal storage disorders is a challenge. Herein, we present the synthesis of novel analogues of mannose 6‐phosphate (M6P), known as AMFAs and functionalized at the anomeric position for enzyme grafting. AMFAs are non‐phosphate serum‐resistant derivatives that efficiently bind the cation‐independent mannose 6‐phosphate receptor (CI‐M6PR), which is the main pathway to address enzymes to lysosomes. One of the AMFAs was used to improve the treatment of the lysosomal myopathy Pompe disease, in which acid α‐glucosidase (GAA) is defective. AMFA grafting on a M6P‐free recombinant GAA led to a higher uptake of the GAA in adult Pompe fibroblasts in culture as compared to Myozyme, the M6P recombinant GAA. Moreover, the treatment of Pompe adult mice with the AMFA‐grafted recombinant enzyme led to a remarkable improvement, even at low doses, in muscle functionality and regeneration, whereas Myozyme had limited efficacy.     

Improved oxygen mobility in nanosized mixed-oxide particles synthesized using a simple nanocasting route

This work reports the synthesis of homogeneously dispersed mixed-oxide nanoparticles (<5 nm) exhibiting improved lattice oxygen mobility (ca. two times higher than on bulk samples), using a novel synthesis procedure of nanocasting in mesoporous silica host support.     

Recent developments in the application of nanoparticles prepared from w/o microemulsions in heterogeneous catalysis

This paper reviews the use of microemulsions, especially the water-in-oil (w/o) microemulsions, for preparation of nanoparticles that are employed as catalyst components in heterogeneous catalytic reactions. The objective is to show the growing interest of using microemulsions in the preparation of different types of materials such as metals, single metal oxides or mixed metal oxides with a broad range of application in heterogeneous catalysis and also in electrocatalysis. In most cases, the catalytic material showed improved catalytic properties as a result of the special synthesis environment created by the microemulsions. Still, research is needed for a better understanding of such beneficial effects. In addition, this method needs improvements in order to produce, in an environmentally friendly way, a suitable amount of material for use in industrial-scale catalytic processes.