Robust branch-cut-and-price for the Capacitated Minimum Spanning Tree problem over a large extended formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms: powerful new cuts expressed over a very large set of variables are added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very significant improvements over previous algorithms. Several open instances could be solved to optimality.     

The diameter of the acyclic Birkhoff polytope

In this work we give an interpretation of vertices and edges of the acyclic Birkhoff polytope, T_n=Ω_n(T), where T is a tree with n vertices, in terms of graph theory. We generalize a recent result relatively to the diameter of the graph G(T_n).     

Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

Two-photon induced anisotropy in PMMA film doped with Disperse Red 13

In this paper we present optical anisotropy induced by 150-fs laser pulses operating at 775 nm in poly(methyl methacrylate) (PMMA) films doped with Disperse Red 13 (DR13). Two-photon absorption of DR13 induces reversible birefringence in the sample, a feature associated with the molecular orientation caused by isomerization of the azochromophores. No irreversible anisotropy, associated with photobleaching of the chromophore was observed. The slope of 2 obtained for the induced birefringence as a function of the excitation irradiance corroborates the two-photon nature of the process.     

Accuracy and time performance of different schemes of the local field correction PIV technique

Local field correction particle image velocimetry (LFC-PIV) has become an established alternative among high-resolution PIV techniques. Previous works by the authors introduced its implementation by means of simple algorithms. In these works the initial limitation of the method, which was related to the mean distance between particles, was removed. Comparison with other contemporary high-resolution techniques indicates that it offers advantages in robustness and accuracy. The trade-off for this better performance is a heavier computing load. Until now, the computing time that this load requires has not been characterized in detail, since this computing time could be substantially reduced by accepting a reduction in accuracy. This paper focuses on the characterization of the trade-off between time and accuracy, thus offering a new perspective to PIV. In this field, LFC-PIV offers a wide range of possibilities that are described in the paper. Several alternative schemes for LFC-PIV are tested, together with an analysis of the influence of the number of iterations. Performance figures for both accuracy and expended time are given. Metrological evaluation is carried out over synthetic images. A test of coherence between these results and the performance on real images is also presented. The paper shows that even for a limited number of iterations this technique offers advantages.     

Enhancing Intersystem Crossing in Phenotiazinium Dyes by Intercalation into DNA

Phenothiazinium dyes are used as photosensitizers in photodynamic therapy. Their mode of action is related to the generation of triplet excited states by intersystem crossing. Therefore, rationalizing the factors that influence intersystem crossing is crucial to improve the efficacy of photodynamic therapy. Here we employ quantum mechanics/molecular mechanics calculations to investigate the effect of aqueous and nucleic acid environments on the intersystem crossing mechanism in methylene blue. We find that the mechanism by which the triplet states are generated depends strongly on the environment. While intersystem crossing in water is mediated exclusively by vibronic spin–orbit coupling, it is enhanced in DNA due to a second pathway driven by electronic spin–orbit coupling. Competing charge‐transfer processes, which are also possible in the presence of DNA, can therefore be suppressed by a suitable structural functionalization, thereby increasing the efficacy of photodynamic therapy.     

Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions

Elsewhere in this volume (Nogueira et al. (2005) Exp Fluids, in press), the conceptual background that explains the possibility of resolving wavelengths smaller than the size of the interrogation window, with no basic restrictions but sampling, has been explained. Here, a practical implementation of the concepts is performed. To achieve this resolution in iterative PIV processing, an appropriate weighting function can be used, as commented in that reference. Here, the constraints for the design of such weighting functions are presented and analysed. This opens a line of work on possible weighting functions to develop, since the weightings used in these iterative methods, like local field correction particle image velocimetry (LFC-PIV) (Nogueira et al. (1999) Exp Fluids 27(2):107–116), have not been optimised yet. As an example, different weighting functions are commented and tested both on synthetic and real images. The results on these new weightings indicate that the current ones can be improved and the optimisation criteria are open for further advancement.