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

Response to 'Fear of death and the symmetry argument'

This article is a response to 'Fear of death and the symmetry argument', in this issue. In that article, the author discusses the above Lucretian symmetry argument, and proposes a view that justifies the existing asymmetry in our attitudes towards birth and death. I begin by distinguishing this symmetry argument from a different one, also loosely inspired by Lucretius, which also plays a role in the article. I then describe what I take to be the author's solution to the original symmetry argument (i.e. the one above) and explain why I am unpersuaded by it.This response was written while I was a member of the Templeton World Charity Foundation project 'Theology, Philosophy of Religion, and the Natural Science

Evidence for the Collective Nature of the Reentrant Integer Quantum Hall States of the Second Landau Level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature

The statistical properties of galaxy morphological types in compact groups of Main galaxies from the SDSS Data Release 4

In order to explore the statistical properties of galaxy morphological types in compact groups (CGs), we construct a random group sample which has the same distributions of redshift and number of member galaxies as those of the CG sample. It turns out that the proportion of early-type galaxies in different redshift bins for the CG sample is statistically higher than that for random group sample, and with growing redshift z this kind of difference becomes more significant. This may be due to the existence of interactions and mergers within a significant fraction of SDSS CGs. We also compare statistical results of CGs with those of more compact groups and pairs, but do not observe as large statistical difference as Hickson (1982)'results.Comment: 12 pages, 9 figure

Flux rope, hyperbolic flux tube, and late EUV phases in a non-eruptive circular-ribbon flare

We present a detailed study of a confined circular flare dynamics associated with 3 UV late phases in order to understand more precisely which topological elements are present and how they constrain the dynamics of the flare. We perform a non-linear force free field extrapolation of the confined flare observed with the HMI and AIA instruments onboard SDO. From the 3D magnetic field we compute the squashing factor and we analyse its distribution. Conjointly, we analyse the AIA EUV light curves and images in order to identify the post-flare loops, their temporal and thermal evolution. By combining both analysis we are able to propose a detailed scenario that explains the dynamics of the flare. Our topological analysis shows that in addition to a null-point topology with the fan separatrix, the spine lines and its surrounding Quasi-Separatix Layers halo (typical for a circular flare), a flux rope and its hyperbolic flux tube (HFT) are enclosed below the null. By comparing the magnetic field topology and the EUV post-flare loops we obtain an almost perfect match 1) between the footpoints of the separatrices and the EUV 1600~\AA{} ribbons and 2) between the HFT's field line footpoints and bright spots observed inside the circular ribbons. We showed, for the first time in a confined flare, that magnetic reconnection occured initially at the HFT, below the flux rope. Reconnection at the null point between the flux rope and the overlying field is only initiated in a second phase. In addition, we showed that the EUV late phase observed after the main flare episode are caused by the cooling loops of different length which have all reconnected at the null point during the impulsive phase.Comment: Astronomy & Astrophysics, in pres