Benders decomposition, Lagrangean relaxation and metaheuristic design

Large part of combinatorial optimization research has been devoted to the study of exact methods leading to a number of very diversified solution approaches. Some of those older frameworks can now be revisited in a metaheuristic perspective, as they are quite general frameworks for dealing with optimization problems. In this work, we propose to investigate the possibility of reinterpreting decompositions, with special emphasis on the related Benders and Lagrangean relaxation techniques. We show how these techniques, whose heuristic effectiveness is already testified by a wide literature, can be framed as a “master process that guides and modifies the operations of subordinate heuristics”, i.e., as metaheuristics. Obvious advantages arise from these approaches, first of all the runtime evolution of both upper and lower bounds to the optimal solution cost, thus yielding both a high-quality heuristic solution and a runtime quality certificate of that same solution.     

Testing the structure of multistage stochastic programs

A fixed topology of stages and/or a fixed branching scheme are common assumptions for applications and numerical solution of scenario based multistage stochastic programs. Using contamination technique to test this structure, we extend the results of Dupačová (Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds) Prague stochastics. Matfyzpress, Praha, pp 91–101, 2006a) to stochastic programs with multistage polyhedral risk objectives. The ideas are exemplified by bond portfolio management problems and complemented by illustrative numerical results.     

The extracellular matrix of the human aortic wall: ultrastructural observations by FEG-SEM and by tapping-mode AFM

Fragments of human ascending aorta harvested during heart surgery were cryofractured and observed by scanning electron microscopy (SEM) and atomic force microscopy (AFM). Elastic fibers appear as irregular, undulated laminae of variable size and shape. Their surface shows an evident fibrous texture suggestive of a criss-crossed, delicate filamentous scaffold and is marked by a number of features such as ridges, holes and protruding ribs. At higher magnification, both SEM and AFM show the surface composed of a finely granular material, with a bead size of approximately 20 nm. However, the thickness of the metal coating in one case, and the tip convolution effect on the other, may equally result in an artifactual enlargement of the structures, so that the beads may be significantly smaller. The surfaces created by the fracture always appear smooth and compact and with this technique do not reveal significant detail. The collagen component is mostly represented by small, uniform fibrils gathered in flexuous bundles and following a wavy course not unlike that of the elastic laminae. An orthogonal lattice of small proteoglycans is readily evident even without a specific treatment. Occasionally, the fibrils appear encrusted or engulfed in a grainy matrix reminiscent of the elastic fiber surface. Fluid Tapping-Mode Atomic Force Microscopy simultaneously reveals the surface-bound proteoglycans and the inner architecture of the fibrils, composed of smaller subunits following a spiral course with a winding angle of approximately 17 degrees.     

The female gonad of the epizoic platyhelminth Troglocaridicola sp. (Rhabdocoela, Temnocephalida, Scutariellidae): ultrastructural and cytochemical investigations

The cytoarchitecture of the female gonad of the scutariellid Troglocaridicola sp. has been investigated by means of electron microscopy and cytochemical techniques. It consists of a single germarium and two rows of vitelline follicles, both enveloped by an outer extracellular lamina (EL) and an inner cellular tunica constituted by accessory cells. Some ultrastructural features which differ from the basic pattern of all the other Rhabdocoela studied so far have been found. In the germarium the following are observed: (a) The presence in the oocytes of peripheral translucent vesicles containing glycoproteins, which differ in diameter and substructure from the peripheral egg granules observed in all the other neoophoran Platyhelminthes. These vesicles can be considered an autapomorphic feature of the taxon Troglocaridicola; (b) The presence of proteinaceous acorn-shaped granules which remain scattered in the ooplasm throughout oogenesis and can be interpreted as residual yolk. This situation is shared with some Proseriata and Tricladida; (c) The precence of accessory cell processes between growing and mature oocytes, as is typical of some Proseriata and Tricladida. In the vitellarium, the presence of polyphenolic shell globules whose substructure does not correspond either to the multigranular pattern prevailing in representatives of Eulecithophora (Prolecithophora+Rhabdocoela) or to the homogeneous pattern found in Lecithoepitheliata. They have a meandering/concentric pattern of the content similar to that described in some Proseriata and Tricladida. On the basis of the ultrastructural characteristics of the female gonad described above, the position of Troglocaridicola in the taxon Rhabdocoela is discussed.     

Functionalization of Reduced Graphite Oxide Sheets with a Zwitterionic Surfactant

Films of a few layers in thickness of reduced graphite oxide (RGO) sheets functionalized by the zwitterionic surfactant N‐dodecyl‐N,N‐dimethyl‐3‐ammonio‐1‐propanesulfonate (DDPS) are obtained by using the Langmuir–Blodgett method. The quality of the RGO sheets is checked by analyzing the degrees of reduction and defect repair by means of X‐ray photoelectron spectroscopy, atomic force microscopy (AFM), field‐emission scanning electron microscopy (SEM), micro‐Raman spectroscopy, and electrical conductivity measurements. A modified Hummers method is used to obtain highly oxidized graphite oxide (GO) together with a centrifugation‐based method to improve the quality of GO. The GO samples are reduced by hydrazine or vitamin C. Functionalization of RGO with the zwitterionic surfactant improves the degrees of reduction and defect repair of the two reducing agents and significantly increases the electrical conductivity of paperlike films compared with those prepared from unfunctionalized RGO.     

Dynamic combinatorial libraries for the recognition of heavy metal ions

We present the use of hydrazone dynamic combinatorial libraries (DCLs) to identify macrocyclic receptors that are selective for alkaline earth metal ions over alkali metal ions. In particular, the toxic heavy metal ions Sr(2+) and Ba(2+) induce characteristic changes in the DCLs. Four macrocycles were isolated and characterised by LCMS, HRMS, NMR and X-ray crystallography; binding studies by UV-Vis spectroscopy confirm the selectivity observed in the DCLs.     

Existence and concentration of positive solutions for a super-critical fourth order equation

In this paper we investigate the problem of existence of solutions for a super-critical fourth order Yamabe type equation and we exhibit a family of solutions concentrating at two points, provided the domain contains one hole and we give a multiplicity result if we are given multiple holes.     

Silicon nitride PhC nanocavities as versatile platform for visible spectral range devices

We propose silicon nitride two-dimensional photonic crystal resonators as flexible platform to realize photonic devices based on spontaneous emission engineering of nanoemitters in the visible spectral range. The versatility of our approach is demonstrated by coupling the two dipole-like modes of a closed band gap H1 nanocavity with: (i) DNA strands marked with Cyanine 3 organic dyes, (ii) antibodies bounded to fluorescent proteins and (iii) colloidal semiconductor nanocrystals localized in the maximum of the resonant electric field. The experimental results are in good agreement with the numerical simulations, highlighting the good coupling of the nanocavities with both organic and inorganic light emitters.     

On some auxiliary mappings generated by nonexpansive and strictly pseudo-contractive mappings

Starting by a finite family of mappings, we define the concept of procedure with Lipschitzian dependence of the coefficients. We give seven concrete examples of such procedures and prove the strong convergence of two viscosity methods.