27,600 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
Handling Attrition in Longitudinal Studies: The Case for Refreshment Samples
Panel studies typically suffer from attrition, which reduces sample size and
can result in biased inferences. It is impossible to know whether or not the
attrition causes bias from the observed panel data alone. Refreshment samples -
new, randomly sampled respondents given the questionnaire at the same time as a
subsequent wave of the panel - offer information that can be used to diagnose
and adjust for bias due to attrition. We review and bolster the case for the
use of refreshment samples in panel studies. We include examples of both a
fully Bayesian approach for analyzing the concatenated panel and refreshment
data, and a multiple imputation approach for analyzing only the original panel.
For the latter, we document a positive bias in the usual multiple imputation
variance estimator. We present models appropriate for three waves and two
refreshment samples, including nonterminal attrition. We illustrate the
three-wave analysis using the 2007-2008 Associated Press-Yahoo! News Election
Poll.Comment: Published in at http://dx.doi.org/10.1214/13-STS414 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Mechanical Properties of Glass Forming Systems
We address the interesting temperature range of a glass forming system where
the mechanical properties are intermediate between those of a liquid and a
solid. We employ an efficient Monte-Carlo method to calculate the elastic
moduli, and show that in this range of temperatures the moduli are finite for
short times and vanish for long times, where `short' and `long' depend on the
temperature. By invoking some exact results from statistical mechanics we offer
an alternative method to compute shear moduli using Molecular Dynamics
simulations, and compare those to the Monte-Carlo method. The final conclusion
is that these systems are not "viscous fluids" in the usual sense, as their
actual time-dependence concatenates solid-like materials with varying local
shear moduli
Quantum secret sharing between m-party and n-party with six states
We propose a quantum secret sharing scheme between -party and -party
using three conjugate bases, i.e. six states. A sequence of single photons,
each of which is prepared in one of the six states, is used directly to encode
classical information in the quantum secret sharing process. In this scheme,
each of all members in group 1 choose randomly their own secret key
individually and independently, and then directly encode their respective
secret information on the states of single photons via unitary operations, then
the last one (the th member of group 1) sends of the resulting qubits
to each of group 2. By measuring their respective qubits, all members in group
2 share the secret information shared by all members in group 1. The secret
message shared by group 1 and group 2 in such a way that neither subset of each
group nor the union of a subset of group 1 and a subset of group 2 can extract
the secret message, but each whole group (all the members of each group) can.
The scheme is asymptotically 100% in efficiency. It makes the Trojan horse
attack with a multi-photon signal, the fake-signal attack with EPR pairs, the
attack with single photons, and the attack with invisible photons to be
nullification. We show that it is secure and has an advantage over the one
based on two conjugate bases. We also give the upper bounds of the average
success probabilities for dishonest agent eavesdropping encryption using the
fake-signal attack with any two-particle entangled states. This protocol is
feasible with present-day technique.Comment: 7 page
Implications of Cosmic Repulsion for Gravitational Theory
In this paper we present a general, model independent analysis of a recently
detected apparent cosmic repulsion, and discuss its potential implications for
gravitational theory. In particular, we show that a negatively spatially curved
universe acts like a diverging refractive medium, to thus naturally cause
galaxies to accelerate away from each other. Additionally, we show that it is
possible for a cosmic acceleration to only be temporary, with some accelerating
universes actually being able to subsequently recontract.Comment: RevTeX, 13 page
Analytical Solution of Electron Spin Decoherence Through Hyperfine Interaction in a Quantum Dot
We analytically solve the {\it Non-Markovian} single electron spin dynamics
due to hyperfine interaction with surrounding nuclei in a quantum dot. We use
the equation-of-motion method assisted with a large field expansion, and find
that virtual nuclear spin flip-flops mediated by the electron contribute
significantly to a complete decoherence of transverse electron spin correlation
function. Our results show that a 90% nuclear polarization can enhance the
electron spin time by almost two orders of magnitude. In the long time
limit, the electron spin correlation function has a non-exponential
decay in the presence of both polarized and unpolarized nuclei.Comment: 4 pages, 3 figure
Nonexistence of self-similar singularities for the 3D incompressible Euler equations
We prove that there exists no self-similar finite time blowing up solution to
the 3D incompressible Euler equations. By similar method we also show
nonexistence of self-similar blowing up solutions to the divergence-free
transport equation in . This result has direct applications to the
density dependent Euler equations, the Boussinesq system, and the
quasi-geostrophic equations, for which we also show nonexistence of
self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of
compact support for the vorticit
Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions
We present Monte Carlo simulations of the spanning-forest model (q \to 0
limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show
that, in contrast to the two-dimensional case, the model has a "ferromagnetic"
second-order phase transition at a finite positive value w_c. We present
numerical estimates of w_c and of the thermal and magnetic critical exponents.
We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has
expanded title as published in PR
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