Weighted fusion graphs: Merging properties and watersheds

This paper deals with the mathematical properties of watersheds in weighted graphs linked to region merging methods, as used in image analysis.In a graph, a cleft (or a binary watershed) is a set of vertices that cannot be reduced, by point removal, without changing the number of regions (connected components) of its complement. To obtain a watershed adapted to morphological region merging, it has been shown that one has to use the topological thinnings introduced by M. Couprie and G. Bertrand. Unfortunately, topological thinnings do not always produce thin clefts.Therefore, we introduce a new transformation on vertex weighted graphs, called C-watershed, that always produces a cleft. We present the class of perfect fusion graphs, for which any two neighboring regions can be merged, while preserving all other regions, by removing from the cleft the points adjacent to both. An important theorem of this paper states that, on these graphs, the C-watersheds are topological thinnings and the corresponding divides are thin clefts. We propose a linear-time immersion-like algorithm to compute C-watersheds on perfect fusion graphs, whereas, in general, a linear-time topological thinning algorithm does not exist. Furthermore, we prove that this algorithm is monotone in the sense that the vertices are processed in increasing order of weight. Finally, we derive some characterizations of perfect fusion graphs based on the thinness properties of both C-watersheds and topological watersheds.     

The multidimensional Luzin theorem

Each measurable map of an open set U⊂Rn to Rn is equal almost everywhere to the gradient of a continuous almost everywhere differentiable function defined on Rn that vanishes, together with its gradient, outside U.     

Improving shock-free compressible RANS solvers for LES on unstructured meshes

Standard numerical methods used to solve the Reynolds averaged Navier–Stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model. A possible solution is to resort to non-dissipative central schemes. Unfortunately, these schemes are in general unstable. A way to reach stability is to select a central scheme that conserves the discrete kinetic energy. To that purpose, a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock-free flows on unstructured grids. A direct numerical simulation of the flow past a sphere at a Reynolds number of 300 and a large eddy simulation at a Reynolds number of 10,000 are performed to validate the methodology.     

Norm-to-Weak Upper Semi-Continuity of the Duality and Pre-Duality Mappings

We show that when the duality map is norm-to-weak upper semi-continuous at some point of a dual space, the pre-duality map shares this property. We show that if x is a point of very smoothness of a Banach space X, it fails in general to be a point of very smoothness of the bidual X ^**. This cannot happen however if the bidual X ^** is a Grothendieck space.     

Progress in solid core photonic bandgap fibers

We investigate both experimentally and numerically confinement and bend losses in solid-core photonic bandgap fibers. We proposed two designs, based on the addition of air regions in the cladding, allowing these losses to be reduced significantly while keeping the optical properties of bandgap fibers. We also present and discuss numerical results on the impact of transversal defects on the fiber confinement loss in the case of a realistic low loss fiber.     

A KAM phenomenon for singular holomorphic vector fields

Let X be a germ of holomorphic vector field at the origin of Cⁿ and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection of a polydisc with an analytic set of the form “resonant monomials = constants”. Such a biholomorphism conjugates the restriction of X to one of its invariant varieties to the restriction of a linear diagonal vector field to a toric variety. Moreover, we show that the set of “frequencies” defining the invariant sets is of positive measure.     

A straightforward synthesis of ynones by reaction of dimethylalkynylaluminum reagents with acid chlorides

Alkynyldimethylaluminum reagents react with various aromatic and aliphatic acid chlorides in a fast and efficient way. This reaction provides a simple entry to numerous ynones, using readily available, inexpensive, and nontoxic metalating agent, and does not require any transition metal as a catalyst.     

Analysis of carbohydrates in plants by high-performance anion-exchange chromatography coupled with electrospray mass spectrometry

A mass spectrometer was coupled to high-performance anion-exchange chromatography (HPAEC) with the help of electrochemical neutralization of the eluent and post-column addition of lithium chloride for carbohydrate analysis. Parallel selective channels (single ion monitoring) were used to decrease the detection limits and separate unresolved peaks. The mass specific detection allowed the simultaneous analysis of a wide range of sugar alcohols, mono-, di- and oligosaccharides. Carbohydrates extracted from leaves of poplar submitted to drought stress were analyzed using pulsed amperometric detection (PAD), then mass spectrometry. It allowed the confirmation of peak attribution and the identification of salicin as a major compound in the extracts. Different responses to water deficit and re-hydration were obtained for several carbohydrates, suggesting different roles in osmoprotection processes.     

Synthesis of Novel Fluorogenic L-Fmoc Lysine Derivatives as Potential Tools for Imaging Cells

Two coumarin-labeled lysines were conveniently prepared as fluorescent probes. 7-Methoxy and 7-diethylamino coumarin-3-carboxylic acids were synthesized according to a modification of known procedures. Labeling at lysine was achieved in solution via the active N-hydroxysuccinimide ester of the carboxylic acid coumarin derivatives to give the target compounds in good yield. Spectroscopic data (UV-vis and fluorescence) were recorded for all compounds.