Constructive Heuristics for the Minimum Labelling Spanning Tree Problem: a preliminary comparison

This report studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge), the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest possible number of distinct labels. The model can represent many real-world problems in telecommunication networks, electric networks, and multimodal transportation networks, among others, and the problem has been shown to be NP-complete even for complete graphs. A primary heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of this constructive heuristic have been proposed to improve its efficiency. Here we describe the problem, review the literature and compare some variants of this algorithm

Solving the minimum labelling spanning tree problem using hybrid local search

Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the MLST problem has been shown to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA and PILOT. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic

Enhanced electron correlations, local moments, and Curie temperature in strained MnAs nanocrystals embedded in GaAs

We have studied the electronic structure of hexagonal MnAs, as epitaxial continuous film on GaAs(001) and as nanocrystals embedded in GaAs, by Mn 2p core-level photoemission spectroscopy. Configuration-interaction analyses based on a cluster model show that the ground state of the embedded MnAs nanocrystals is dominated by a d5 configuration that maximizes the local Mn moment. Nanoscaling and strain significantly alter the properties of MnAs. Internal strain in the nanocrystals results in reduced p-d hybridization and enhanced ionic character of the Mn-As bonding interactions. The spatial confinement and reduced p-d hybridization in the nanocrystals lead to enhanced d-electron localization, triggering d-d electron correlations and enhancing local Mn moments. These changes in the electronic structure of MnAs have an advantageous effect on the Curie temperature of the nanocrystals, which is measured to be remarkably higher than that of bulk MnAs.Comment: 4 figures, 2 table

Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model

Transport measurements on the cuprates suggest the presence of a quantum critical point hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single particle quantities, such as the spectral function, the quasiparticle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudogap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbor hopping t' we find a classical critical point at temperature T_c. This classical critical point is found to be associated with a phase separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudogap state, respectively. Since the critical temperature T_c extrapolates to zero as t' vanishes, we conclude that a quantum critical point connects the Fermi-liquid to the pseudogap region, and that the marginal-Fermi-liquid behavior in its vicinity is the analogous of the supercritical region in the liquid-gas transition.Comment: 18 pages, 9 figure

Análisis de evidencias de pensamiento funcional en estudiantes de 5º curso primaria

Esta investigación tiene como objetivo identificar evidencias de pensamiento funcional en estudiantes de quinto curso de educación primaria, en el marco de la propuesta de innovación curricular y línea de investigación conocida como Early-Algebra (Molina, 2009)

The effect of the relative orientation between the coronal field and new emerging flux: I Global Properties

The emergence of magnetic flux from the convection zone into the corona is an important process for the dynamical evolution of the coronal magnetic field. In this paper we extend our previous numerical investigations, by looking at the process of flux interaction as an initially twisted flux tube emerges into a plane parallel, coronal magnetic field. Significant differences are found in the dynamical appearance and evolution of the emergence process depending on the relative orientation between the rising flux system and any preexisting coronal field. When the flux systems are nearly anti-parallel, the experiments show substantial reconnection and demonstrate clear signatures of a high temperature plasma located in the high velocity outflow regions extending from the reconnection region. However, the cases that have a more parallel orientation of the flux systems show very limited reconnection and none of the associated features. Despite the very different amount of reconnection between the two flux systems, it is found that the emerging flux that is still connected to the original tube, reaches the same height as a function of time. As a compensation for the loss of tube flux, a clear difference is found in the extent of the emerging loop in the direction perpendicular to the main axis of the initial flux tube. Increasing amounts of magnetic reconnection decrease the volume, which confines the remaining tube flux.Comment: 21 pages, 16 figures Accepted for Ap

The role of consumption in material reduction opportunities: the impact of product lifetime in supplying the UK steel demand

Most of the products purchased in the UK are manufactured in other countries. As a result, worldwide greenhouse gases (GHG) emissions released to manufacture all products purchased in the UK are significantly higher than the UK territorial emissions. More than one half of global industrial emissions result from the use of steel, cement, paper, plastics, and aluminium. In this paper, the UK consumption of products that embody these five materials is estimated. For steel, which is the most widely used among these five materials, consumption and accumulation patterns are examined across four product categories. The impact of steel product lifetime extension is examined for the UK as one option for material demand reduction at the consumption stage of the supply chain. Different levels of steel product lifetimes are simulated for the UK in 2050 and their impacts are examined in terms of UK steel production, implicit steel imports, and global carbon dioxide emissions. Steel product lifetime extension promotes a reduction in the need for steel imports, by reducing the demand for new steel, which leads to lower carbon dioxide emissions required to supply the UK steel demand. The results demonstrate the criticality of a focus on the consumption stage, since any interventions made towards demand reduction of end-use goods leads to material reduction across the supply chain

Thermodynamics of the Quantum Critical Point at Finite Doping in the 2D Hubbard Model: A Dynamical Cluster Approximation Study

We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approximation. We use continuous time quantum Monte Carlo as a cluster solver to avoid the systematic error which complicates the calculation of the entropy and potential energy (double occupancy). We find that at a critical filling, there is a pronounced peak in the entropy divided by temperature, S/T, and in the normalized double occupancy as a function of doping. At this filling, we find that specific heat divided by temperature, C/T, increases strongly with decreasing temperature and kinetic and potential energies vary like T^2 ln(T). These are all characteristics of quantum critical behavior.Comment: 4 pages, 4 figures. Submitted to Phys. Rev. B Rapid Communications on June 27, 200