Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Gravitational Entropy in Cosmological Models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI _h models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor. PACS: 04.20.-q 95.30.Sf 98.80.Jk     

Reactions of dimethyldivinylsilane,dimethyldivinyltin and allyltrimethyltin with diethylene (tertiary) phosphine)platinum complexes

The compounds [Pt(C₂H₄)₂(PR₃)] [PR₃ = P-tBu₂Me, P(C₆H₁₁)₃, PPh₃] react dimethyldivinylsilane or dimethyldivinyltin to give chelate complexes [Pt{(CH₂CH)₂MMe₂} (PR₃)] (M = Si or Sn). allyltrimethyltin reacts with various diethylene (tertiary phosphine)platinum compounds with cleavage of the allyl group to afford complexes [Pt(SnMe₃)(η³-C₃H₅)(PR₂)]. The NMR spectra (¹³C, ¹H and ³¹P) of the new compounds have been recorded, and the data are discussed in terms of the structures proposed.     

Thermal wave photopyroelectric characterization of advanced materials: State of the art

This article reviews the history, background, theoretical basis, development, attempts to optimize, and experimental performance of the photopyroelectric technique for the optothermal characterization of advanced materials such as semiconductors, superconductors, pure metals and alloys, quantum wells, liquid crystals, paramagnetic and ferromagnetic materials, as well as solar cells. The state of the art in the experimental processes in this field is also reviewed. This new photothermal technique can be used after a careful optimization, as a highly sensitive method for photopyroelectric spectroscopy and general thermal wave measurements. It has been shown to be a highly sensitive spectroscopic method for the nondestructive evaluation of advanced materials. This review presents the main photopyroelectric theoretical models that have been used for the extraction of some important optoelectronic properties such as the optical absorption coefficient and the nonradiative quantum efficiency spectra, as well as some thermal properties such as the thermal diffusivity, thermal conductivity, and specific heat. The applicability of the general basic theoretical model with its many special cases is also described in detail. This review demonstrates how photopyroelectric spectroscopy can be complementary to the conventional spectroscopic methods. The different experimental modes of the technique are also discussed. Moreover, some ideas concerning future perspectives of applying the technique to other scientific fields are outlined. This article does not aspire to an in-depth analysis of the experimental results in the field; rather, it focuses on the technique itself.     

The thresholds for diameter 2 in random Cayley graphs

Given a group G, the model denotes the probability space of all Cayley graphs of G where each element of the generating set is chosen independently at random with probability p. In this article we show that for any and any family of groups G_k of order n_k for which , a graph with high probability has diameter at most 2 if and with high probability has diameter greater than 2 if . We also provide examples of families of graphs which show that both of these results are best possible. Of particular interest is that for some families of groups, the corresponding random Cayley graphs achieve Diameter 2 significantly faster than the Erd?s‐Renyi random graphs. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 218–235, 2014     

Novel proresolving aspirin-triggered DHA pathway

Endogenous mechanisms in the resolution of acute inflammation are of interest because excessive inflammation underlies many pathologic abnormalities. We report an aspirin-triggered DHA metabolome that biosynthesizes a potent product in inflammatory exudates and human leukocytes, namely aspirin-triggered Neuroprotectin D1/Protectin D1 [AT-(NPD1/PD1)]. The complete stereochemistry of AT-(NPD1/PD1) proved to be 10R,17R-dihydroxydocosa-4Z,7Z,11E,13E,15Z,19Z-hexaenoic acid. The chirality of hydroxyl groups and geometry of the conjugated triene system essential for bioactivity were established by matching biological materials with stereochemically pure isomers prepared by organic synthesis. AT-(NPD1/PD1) reduced neutrophil (PMN) recruitment in murine peritonitis in a dose-dependent fashion whereby neither a Δ(15)-trans-isomer nor DHA was effective. With human cells, AT-(NPD1/PD1) decreased transendothelial PMN migration as well as enhanced efferocytosis of apoptotic human PMN by macrophages. These results indicate that AT-(NPD1/PD1) is a potent anti-inflammatory proresolving molecule.     

Real R&;D options with time-to-learn and learning-by-doing

We model R&D efforts to enhance the value of a product or technology before final development. Such efforts may be directed towards improving quality, adding new features, or adopting technological innovations. They are implemented as optional, costly and interacting control actions expected to enhance value but with uncertain outcome. We examine the interesting issues of the optimal timing of R&D, the impact of lags in the realization of the R&D outcome, and the choice between accelerated versus staged (sequential) R&D. These issues are also especially interesting since the history of decisions affects future decisions and the distributions of asset prices and induces path-dependency. We show that the existence of optional R&D efforts enhances the investment option value significantly. The impact of a dividend-like payout rate or of project volatility on optimal R&D decisions may be different with R&D timing flexibility than without. The attractiveness of sequential strategies is enhanced in the presence of learning-by-doing and decreasing marginal reversibility of capital effects.     

Algorithms for large scale set covering problems

This paper is concerned with the set covering problem (SCP), and in particular with the development of a new algorithm capable of solving large-scale SCPs of the size found in real-life situations. The set covering problem has a wide variety of practical applications which, in general, yield large and sparse instances, normally with hundreds of rows and thousands of columns. In this paper, we present an algorithm capable of solving problems of this size and test problems up to 400 rows and 4000 columns are solved. The method developed in this paper consists of a tree-search procedure based on a combination of decomposition and state space relaxation which is a technique developed for obtaining lower bounds on the dynamic program associated with a combinatorial optimization problem. The large size SCPs are decomposed into many smaller SCPs which are then solved or bounded by state space relaxation (SSR). Before using the decomposition and SSR, reductions both in the number of columns and the number of rows of the problem are made by applying Lagrangian relaxation, linear programming and heuristic methods.     

Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem

In this paper we present a lower bound for the capacitated warehouse location problem based upon the Lagrangean relaxation of a mixed-integer formulation of the problem, where we use subgradient optimisation in an attempt to maximise this lower bound. Problem reduction tests based upon this lower bound and the original problem are given. Incorporating this bound and the reduction tests into a tree search procedure enables us to solve problems involving up to 50 warehouses and 150 customers.