Critical duality

We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special structure. We examine several examples. In particular, we consider some special classes of generalized convex functions.     

Metal-acetylide addition to tetracyanoethylene

Two push-pull chromophores that have shown utility in the field of molecular electronics and non-linear optics are DDMEBT (1, 2-(4-dimethylamino)phenyl)-3-((4-(dimethylamino)phenyl)ethynyl)buta-1,3-diene-1,1,4,4-tetracarbonitrile) and TDMEE (2, 4-(4-dimethylamino)phenyl)but-1-en-3-yne-1,1,2-tricarbonitrile). Unfortunately, the methods reported for their synthesis give variable yields, use toxic solvents, and only provide small amounts of material. We report improved synthetic protocols, providing access to larger quantities of material. By investigating multiple metal-acetylides of 4-ethynyl-N,N-dimethylaniline and their subsequent addition to TCNE, we obtained various products depending on the identity of the metal ion. This led to the simple synthesis of push-pull chromophoric compounds.     

Investigating the relationship between cell cycle stage and diosgenin-induced megakaryocytic differentiation of HEL cells using sedimentation field-flow fractionation

Differentiation therapy could be one strategy for stopping cancer cell proliferation. A plant steroid, diosgenin, is known to induce megakaryocytic differentiation in human erythroleukemia (HEL) cells. In recent studies, the use of sedimentation field-flow fractionation (SdFFF) allowed the preparation of subpopulations that may differ in regard to sensitivity to differentiation induction. The specific goal of this study was to determine the relationship between cell cycle stage and sensitivity to megakaryocytic differentiation induction of HEL cells. After first confirming the capacity of diosgenin to specifically select targets, hyperlayer SdFFF cell sorting was used to prepare fractions according to cell cycle position from crude HEL cells. The sensitivities of these fractions to diosgenin-induced differentiation were then tested. The coupling of SdFFF cell separation to imaging flow cytometry showed that G1-phase cells were more sensitive to differentiation induction than S/G2M-phase cells, confirming the relationship between cell status at the start of induction, the extent of the biological event, and the potential of SdFFF in cancer research.     

Use of polymer-supported phenyltin for the creation of aryl-aryl or aryl-heteroaryl bonds via Stille cross-coupling reactions

An insoluble polymer-supported phenyltin reagent was successfully used in Stille cross-coupling reactions with aryl- and heteroaryl-halides. Cross-coupling products were isolated in good to high yields with very low contamination by tin and palladium residues after removal of the residual supported organotin halide. The regeneration and recyclability of the supported phenyltin reagent were also examined and proved to be possible, but required palladium cleaning of the grafted polymer to be efficient along 4 cycles when Pd(PPh₃)₄ was used as catalyst.     

Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems

Numerous planning problems can be formulated as multi-stage stochastic programs and many possess key discrete (integer) decision variables in one or more of the stages. Progressive hedging (PH) is a scenario-based decomposition technique that can be leveraged to solve such problems. Originally devised for problems possessing only continuous variables, PH has been successfully applied as a heuristic to solve multi-stage stochastic programs with integer variables. However, a variety of critical issues arise in practice when implementing PH for the discrete case, especially in the context of very difficult or large-scale mixed-integer problems. Failure to address these issues properly results in either non-convergence of the heuristic or unacceptably long run-times. We investigate these issues and describe algorithmic innovations in the context of a broad class of scenario-based resource allocation problem in which decision variables represent resources available at a cost and constraints enforce the need for sufficient combinations of resources. The necessity and efficacy of our techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages.     

Comparison of three methods for fractionation and enrichment of low molecular weight proteins for SELDI-TOF-MS differential analysis

In most diseases, the clinical need for serum/plasma markers has never been so crucial, not only for diagnosis, but also for the selection of the most efficient therapies, as well as exclusion of ineffective or toxic treatment. Due to the high sample complexity, prefractionation is essential for exploring the deep proteome and finding specific markers.In this study, three different sample preparation methods (i.e., highly abundant protein precipitation, restricted access materials (RAM) combined with IMAC chromatography and peptide ligand affinity beads) were investigated in order to select the best fractionation step for further differential proteomic experiments focusing on the LMW proteome (MW inferior to 40,000 Da). Indeed, the aim was not to cover the entire plasma/serum proteome, but to enrich potentially interesting tissue leakage proteins. These three methods were evaluated on their reproducibility, on the SELDI-TOF-MS peptide/protein peaks generated after fractionation and on the information supplied.The studied methods appeared to give complementary information and presented good reproducibility (below 20%). Peptide ligand affinity beads were found to provide efficient depletion of HMW proteins and peak enrichment in protein/peptide profiles.     

Are dualities appropriate for duality theories in optimization?

We raise some questions about duality theories in global optimization. The main one concerns the possibility to extend the use of conjugacies to general dualities for studying dual optimization problems. In fact, we examine whether dualities are the most general concepts to get duality results. We also consider the passage from a Lagrangian approach to a perturbational approach and the reverse passage in the framework of general dualities. Since a notion of subdifferential can be defined for any duality, it is natural to examine whether the familiar interpretation of multipliers as generalized derivatives of the performance function associated with a dualizing parameterization of the given problem is still valid in the general framework of dualities.     

A (1→4)-β-D-Glucuronan Excreted by a Mutant of the Rhizobium Meliloti M5N1 Strain

Abstract

A mutant of the R. meliloti M5N1 strain has been selected. This strain, R. meliloti M5N1 CS (NCIMB 40472), excretes an extracellular material composed of 2-O-Ac-β-GlcpA, 3-O-Ac-β-GlcpA, 2,3-di-O-Ac-β-GlcpA and three species of β-GlcpA residues 1→4 linked. For the culture conditions used, the weight average molecular weight of the polymer varied in the range of 6 × 10⁴ < Mw < 4 × 10⁵. High molecular weight glucuronate forms thermoreversible gels at 5 g L^?l. In the presence of divalent cation such as Ca²⁺ or trivalent cations such as Cr³⁺ or Fe^{3 +}, cross linking of the polymer occurs. This polysaccharide is the first exocellular (1→4)-β-D-glucuronan produced by a R. meliloti strain.