20,640 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
Reduction of -Regular Noncrossing Partitions
In this paper, we present a reduction algorithm which transforms -regular
partitions of to -regular partitions of .
We show that this algorithm preserves the noncrossing property. This yields a
simple explanation of an identity due to Simion-Ullman and Klazar in connection
with enumeration problems on noncrossing partitions and RNA secondary
structures. For ordinary noncrossing partitions, the reduction algorithm leads
to a representation of noncrossing partitions in terms of independent arcs and
loops, as well as an identity of Simion and Ullman which expresses the Narayana
numbers in terms of the Catalan numbers
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
Heavy Pentaquarks
We construct the spin-flavor wave functions of the possible heavy pentaquarks
containing an anti-charm or anti-bottom quark using various clustered quark
models. Then we estimate the masses and magnetic moments of the or heavy pentaquarks. We emphasize the difference in the
predictions of these models. Future experimental searches at BESIII, CLEOc,
BELLE, and LEP may find these interesting states
State-independent experimental test of quantum contextuality in an indivisible system
We report the first state-independent experimental test of quantum
contextuality on a single photonic qutrit (three-dimensional system), based on
a recent theoretical proposal [Yu and Oh, Phys. Rev. Lett. 108, 030402 (2012)].
Our experiment spotlights quantum contextuality in its most basic form, in a
way that is independent of either the state or the tensor product structure of
the system
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