31,253 research outputs found
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
and a threshold , in which the player set is and the profit of
a coalition is 1 if the size of a maximum matching in
meets or exceeds , 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 equals . When
the threshold 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
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