Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Optimizing the Curie temperature of pseudo-binary RxR2-x ' Fe-17 (R, R ' = rare earth) for magnetic refrigeration

Several pseudo-binary RxR2-x'Fe-17 alloys (with R = Y, Ce, Pr, Gd and Dy) were synthesized with rhombohedral Th2Zn17-type crystal structure determined from x-ray and neutron powder diffraction. The choice of compositions was done with the aim of tuning the Curie temperature (T-C) in the 270 +/- 20 K temperature range, in order to obtain the maximum magneto-caloric effect around room temperature. The investigated compounds exhibit broad isothermal magnetic entropy changes, Delta S-M(T), with moderate values of the refrigerant capacity, even though the values of Delta S-M(Peak) are relatively low compared with those of the R2Fe17 compounds with R = Pr or Nd. The reduction on the Delta S-M(Peak) is explained in terms of the diminution in the saturation magnetization value. Furthermore, the Delta S-M(T) curves exhibit a similar caret-like behavior, suggesting that the magneto-caloric effect is mainly governed by the Fe-sublattice. A single master curve for Delta S-M/Delta S-M(Peak)(T) under different values of the magnetic field change are obtained for each compound by rescaling of the temperature axis.

Petrarca y los De viris illustribus

Anejos de Veleia, Series Minor, 26. Editado por Vitalino Valcárcel.

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

El mundo intelectual del ‘antiguo autor’: las Auctoritates Aristotelis en la Celestina primitiva

El primer acto de La Celestina, escrito por un autor anónimo, contiene abundantes citas de Aristóteles, Séneca, Boecio y pseudo Boecio: a partir de aquí la filología celestinista ha solido deducir filiaciones e intenciones diversas para esta primera parte de la obra. En este artículo se demuestra que todas y cada una de dichas citas proceden de un florilegio filosófico muy difundido en la época —sobre todo en las facultades de artes— conocido como Auctoritates Aristotelis o Parvi flores: este hallazgo sitúa al anónimo autor de la Celestina primitiva —y probablemente a su público— en un ambiente netamente universitario, define con precisión la frontera entre la parte del antiguo autor y la parte de Rojas y obliga a revisar las afinidades ideológicas y filosóficas que se le venían suponiendo al anónimo —sobre todo en relación a su presunto senequismo— así como la intención que se le atribuía a este primer acto.

Unveiling the factors shaping the distribution of widely distributed alpine vertebrates, using multi-scale ecological niche modelling of the bat Plecotus macrobullaris

Several alpine vertebrates share a distribution pattern that extends across the South-western Palearctic but is limited to the main mountain massifs. Although they are usually regarded as cold-adapted species, the range of many alpine vertebrates also includes relatively warm areas, suggesting that factors beyond climatic conditions may be driving their distribution. In this work we first recognize the species belonging to the mentioned biogeographic group and, based on the environmental niche analysis of Plecotus macrobullaris, we identify and characterize the environmental factors constraining their ranges. Distribution overlap analysis of 504 European vertebrates was done using the Sorensen Similarity Index, and we identified four birds and one mammal that share the distribution with P. macrobullaris. We generated 135 environmental niche models including different variable combinations and regularization values for P. macrobullaris at two different scales and resolutions. After selecting the best models, we observed that topographic variables outperformed climatic predictors, and the abruptness of the landscape showed better predictive ability than elevation. The best explanatory climatic variable was mean summer temperature, which showed that P. macrobullaris is able to cope with mean temperature ranges spanning up to 16 degrees C. The models showed that the distribution of P. macrobullaris is mainly shaped by topographic factors that provide rock-abundant and open-space habitats rather than climatic determinants, and that the species is not a cold-adapted, but rather a cold-tolerant eurithermic organism. P. macrobullaris shares its distribution pattern as well as several ecological features with five other alpine vertebrates, suggesting that the conclusions obtained from this study might be extensible to them. We concluded that rock-dwelling and open-space foraging vertebrates with broad temperature tolerance are the best candidates to show wide alpine distribution in the Western Palearctic.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Double layers in gravity theories

Gravitational double layers, unlike their classical electromagnetic counterparts, are thought to be forbidden in gravity theories. It has been recently shown, however, that they are feasible in, for instance, gravity theories with a Lagrangian quadratic in the curvature. This is surprising with many potential consequences and the possibility of new physical behaviours. While a clear interpretation seems elusive, several lines of research are open. I present the field equations for double layers, the new physical quantities arising, and several explicit examples

Two new species of Zospeum Bourguignat, 1856 from the Basque-Cantabrian Mountains, Northern Spain (Eupulmonata, Ellobioidea, Carychiidae)

Two new species of the genus Zospeum Bourguignat, 1856 are described from caves in the Sierra de Aitzgorri (Gipuzkoa) and the Sierra Salvada (Burgos) in Northern Spain. The taxa Z. vasconicum sp. n. and Z. zaldivarae sp. n. have recently, without a formal name, been included in a molecular study of worldwide members of the Carychiidae. In the present paper, the shell morphology and variation of these species is described and illustrated.