7,597 research outputs found
(Non-)existence of Polynomial Kernels for the Test Cover Problem
The input of the Test Cover problem consists of a set of vertices, and a
collection of distinct subsets of , called
tests. A test separates a pair of vertices if A subcollection is a test cover if each
pair of distinct vertices is separated by a test in . The
objective is to find a test cover of minimum cardinality, if one exists. This
problem is NP-hard.
We consider two parameterizations the Test Cover problem with parameter :
(a) decide whether there is a test cover with at most tests, (b) decide
whether there is a test cover with at most tests. Both
parameterizations are known to be fixed-parameter tractable. We prove that none
have a polynomial size kernel unless . Our proofs use
the cross-composition method recently introduced by Bodlaender et al. (2011)
and parametric duality introduced by Chen et al. (2005). The result for the
parameterization (a) was an open problem (private communications with Henning
Fernau and Jiong Guo, Jan.-Feb. 2012). We also show that the parameterization
(a) admits a polynomial size kernel if the size of each test is upper-bounded
by a constant
Physical condition and spin-resolved exchange correlation kernels in an inhomogeneous many electron system
We first exploit the spin symmetry relation for the exact exchange correlation
kernel in an inhomogeneous many electron system
with arbitrary spin polarization . The physical condition required to
satisfy the specific symmetry relation is derived and examined for simple
ferromagnetic-nonmagnetic structure by taking the electrochemical potential
into account. The condition is then applied to several composite systems useful
in spintronics applications such as the magnetic system with net spin
polarization.Comment: 5 pages, 1 figur
Male Partners' Involvement Towards Prenatal Screening and Diagnostic Testing for Down Syndrome
Introduction: Now, male partners' involvement in prenatal screening and diagnostic testing for Down syndrome is becoming increasingly recognized as well to ensure that parents are well informed of the risks and benefits of screening. The aim of study was to understand the degree of male partners' involvement during pregnancy in Singapore population. Methods: A cross-sectional survey of male partners' attending prenatal counseling was performed. The instrument used to measure the level of involvement is a self-assessment questionnaire that identifies the role of male partners with a Likert scale. Descriptive statistics was used to analyze data gained. Result: A total of 107 participants completed the questionnaire. Sixty-seven percent of male partners were found to have a highlevel of involvement while 32.7% was found to have a medium level of involvement. Most of them stated that women can pursue prenatal testing without their permission. Male partners found it more important for them to accompany their spouse to amniocentesis or CVS than to the Down syndrome screening test. When participants were asked about how much information about Down syndrome they sought prior to the appointment, how much discussion they had with their spouse about Down syndrome testing, and about whether they or their spouse should be the first person to receive test results, most stated that they were undecided. Conclusion: These results revealed that male partners were very well involved in the Down syndrome testing during pregnancy and future studies should assess possible underlying factors that influence male partners' involvement
First-Order Transition and Critical End-Point in Vortex Liquids in Layered Superconductors
We calculate various thermodynamic quantities of vortex liquids in a layered
superconductor by using the nonperturbative parquet approximation method, which
was previously used to study the effect of thermal fluctuations in
two-dimensional vortex systems. We find there is a first-order transition
between two vortex liquid phases which differ in the magnitude of their
correlation lengths. As the coupling between the layers increases,the
first-order transition line ends at a critical point. We discuss the possible
relation between this critical end-point and the disappearance of the
first-order transition which is observed in experiments on high temperature
superconductors at low magnetic fields.Comment: 9 pages, 5 figure
Finite-size critical scaling in Ising spin glasses in the mean-field regime
We study in Ising spin glasses the finite-size effects near the spin-glass
transition in zero field and at the de Almeida-Thouless transition in a field
by Monte Carlo methods and by analytical approximations. In zero field, the
finite-size scaling function associated with the spin-glass susceptibility of
the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as
that of one-dimensional spin-glass models with power-law long-range
interactions in the regime where they can be a proxy for the Edwards-Anderson
short-range spin-glass model above the upper critical dimension. We also
calculate a simple analytical approximation for the spin-glass susceptibility
crossover function. The behavior of the spin-glass susceptibility near the de
Almeida-Thouless transition line has also been studied, but here we have only
been able to obtain analytically its behavior in the asymptotic limit above and
below the transition. We have also simulated the one-dimensional system in a
field in the non-mean-field regime to illustrate that when the Imry-Ma droplet
length scale exceeds the system size one can then be erroneously lead to
conclude that there is a de Almeida-Thouless transition even though it is
absent.Comment: 10 pages, 7 figure
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