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     

Algebraic classification of higher dimensional spacetimes

We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes.We discuss some consequences of this work.     

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.     

A restricted Lagrangean approach to the traveling salesman problem

We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially bounded procedures for generating valid inequalities and taking them into the Lagrangean function with a positive multiplier without violating the constraints, so as to strengthen the current lower bound. Upper bounds are generated by a fast tour-building heuristic. When the bound-strengthening techniques are exhausted without matching the upper with the lower bound, we branch by using two different rules, according to the situation: the usual subtour breaking disjunction, and a new disjunction based on conditional bounds. We discuss computational experience on 120 randomly generated asymmetric TSP's with up to 325 cities, the maximum time used for any single problem being 82 seconds. This is a considerable improvement upon earlier methods. Though the algorithm discussed here is for the asymmetric TSP, the approach can be adapted to the symmetric TSP by using the 2-matching problem instead of AP.Research supported by the National Science Foundation through grant no. MCS76-12026 A02 and the U.S. Office of Naval Research through contract no. N0014-75-C-0621 NR 047-048.     

A unified framework for the numerical solution of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: N.karcanias{at}city.ac.uk^**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature.     

Sizing the slenderness of free-standing rocking columns to withstand earthquake shaking

This paper investigates the problem of sizing the width of tall free-standing columns with a given height which are intended to rock, yet shall remain stable during the maximum expected earthquake shaking. The motivation for this study is the emerging seismic design concept of allowing tall rigid structures to uplift and rock in order to limit base moments and shears. The paper first discusses the mathematical characterization of pulse-like ground motions and the dimensionless products that govern the dynamics of the rocking response of a free-standing block and subsequently, using basic principles of dynamics, derives a closed-form expression that offers the minimum design slenderness that is sufficient for a free-standing column with a given size to survive a pulse-like motion with known acceleration amplitude and duration.     

A smoothed particle hydrodynamics-based fluid model with a spatially dependent viscosity: application to flow of a suspension with a non-Newtonian fluid matrix

A smoothed particle hydrodynamics approach is utilized to model a non-Newtonian fluid with a spatially varying viscosity. In the limit of constant viscosity, this approach recovers an earlier model for Newtonian fluids of Español and Revenga (Phys Rev E 67:026705, 2003). Results are compared with numerical solutions of the general Navier–Strokes equation using the “regularized” Bingham model of Papanastasiou (J Rheol 31:385–404, 1987) that has a shear-rate-dependent viscosity. As an application of this model, the effect of having a non-Newtonian fluid matrix, with a shear-rate-dependent viscosity in a moderately dense suspension, is examined. Simulation results are then compared with experiments on mono-size silica spheres in a shear-thinning fluid and for sand in a calcium carbonate paste. Excellent agreement is found between simulation and experiment. These results indicate that measurements of the shear viscosity of simple shear-rate-dependent non-Newtonian fluids may be used in simulation to predict the viscosity of concentrated suspensions having the same matrix fluid.