Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games

Cooperative games provide a framework for fair and stable profit allocation in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are such solution concepts that characterize stability of cooperation. In this paper, we study the algorithmic issues on the least-core and nucleolus of threshold cardinality matching games (TCMG). A TCMG is defined on a graph $G=(V,E)$ and a threshold $T$, in which the player set is $V$ and the profit of a coalition $S\subseteq V$ is 1 if the size of a maximum matching in $G[S]$ meets or exceeds $T$, and 0 otherwise. We first show that for a TCMG, the problems of computing least-core value, finding and verifying least-core payoff are all polynomial time solvable. We also provide a general characterization of the least core for a large class of TCMG. Next, based on Gallai-Edmonds Decomposition in matching theory, we give a concise formulation of the nucleolus for a typical case of TCMG which the threshold $T$ equals $1$. When the threshold $T$ is relevant to the input size, we prove that the nucleolus can be obtained in polynomial time in bipartite graphs and graphs with a perfect matching

Ab-initio investigation of the covalent bond energies in the metallic covalent superconductor MgB2 and in AlB2

The contributions of the covalent bond energies of various atom pairs to the cohesive energy of MgB2 and AlB2 are analysed with a variant of our recently developed energy-partitioning scheme for the density-functional total energy. The covalent bond energies are strongest for the intralayer B-B pairs. In contrast to the general belief, there is also a considerable covalent bonding between the layers, mediated by the metal atom. The bond energies between the various atom pairs are analysed in terms of orbital- and energy-resolved contributions.Comment: 6 pages, 1 figure, 2 tables, submitted to PR

Quantum Control of Light through an Atom-Molecule Dark State

We propose to use a quantized version of coherent two-color photoassociation to realize a hybrid device for quantum control of light. The dynamical features of this system are exhibited, including the slowing down or storage of light and the molecular matter-wave solitons. This may indicate a hybrid atom-molecule quantum device for storage and retrieve of optical information.Comment: with several detailed derivations in comparison with the published version Phys. Rev. A 80, 025601 (2009)

Signal processing in high speed OTDM networks

This paper presents the design and experimental results of an optical packet-switching testbed capable of performing message routing with single wavelength TDM packet bit rates as high as 100 Gb/s

Discovery of Extended Main Sequence Turn-offs in Four Young Massive Clusters in the Magellanic Clouds

An increasing number of young massive clusters (YMCs) in the Magellanic Clouds have been found to exhibit bimodal or extended main sequences (MSs) in their color--magnitude diagrams (CMDs). These features are usually interpreted in terms of a coeval stellar population with different stellar rotational rates, where the blue and red MS stars are populated by non- (or slowly) and rapidly rotating stellar populations, respectively. However, some studies have shown that an age spread of several million years is required to reproduce the observed wide turn-off regions in some YMCs. Here we present the ultraviolet--visual CMDs of four Large and Small Magellanic Cloud YMCs, NGC 330, NGC 1805, NGC 1818, and NGC 2164, based on high-precision Hubble Space Telescope photometry. We show that they all exhibit extended main-sequence turn-offs (MSTOs). The importance of age spreads and stellar rotation in reproducing the observations is investigated. The observed extended MSTOs cannot be explained by stellar rotation alone. Adopting an age spread of 35--50 Myr can alleviate this difficulty. We conclude that stars in these clusters are characterized by ranges in both their ages and rotation properties, but the origin of the age spread in these clusters remains unknown.Comment: 14 pages, 9 figures, ApJ accepte

The radial distributions of the two main-sequence components in the young massive star cluster NGC 1856

The recent discovery of double main sequences in the young, massive star cluster NGC 1856 has caught significant attention. The observations can be explained by invoking two stellar generations with different ages and metallicities or by a single generation of stars composed of two populations characterized by different rotation rates. We analyzed the number ratios of stars belonging to both main-sequence components in NGC 1856 as a function of radius. We found that their number ratios remain approximately unchanged from the cluster's central region to its periphery, indicating that both components are homogeneously distributed in space. Through a comparison of the loci of the best-fitting isochrones with the ridge lines of both stellar components, we found that both multiple stellar populations and rapid stellar rotation can potentially explain the observed main-sequence bifurcation in NGC 1856. However, if NGC1856 were a young representative of the old globular clusters, then the multiple stellar populations model would not be able to explain the observed homogeneity in the spatial distributions of these two components, since all relevant scenarios would predict that the second stellar generation should be formed in a more compact configuration than that of the first stellar generation, while NGC 1856 is too young for both stellar generations to have been fully mixed dynamically. We speculate that the rapid stellar rotation scenario would be the favored explanation of the observed multiple stellar sequences in NGC 1856.Comment: 11 pages, 6 figures, ApJ accepte