112,072 research outputs found
Mapping functions and critical behavior of percolation on rectangular domains
The existence probability and the percolation probability of the
bond percolation on rectangular domains with different aspect ratios are
studied via the mapping functions between systems with different aspect ratios.
The superscaling behavior of and for such systems with exponents
and , respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev.
Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order
approximation of the mapping functions and for and ,
respectively; the exponents and can be obtained from numerically
determined mapping functions and , respectively.Comment: 17 pages with 6 figure
Geometry, thermodynamics, and finite-size corrections in the critical Potts model
We establish an intriguing connection between geometry and thermodynamics in
the critical q-state Potts model on two-dimensional lattices, using the q-state
bond-correlated percolation model (QBCPM) representation. We find that the
number of clusters of the QBCPM has an energy-like singularity for q different
from 1, which is reached and supported by exact results, numerical simulation,
and scaling arguments. We also establish that the finite-size correction to the
number of bonds, has no constant term and explains the divergence of related
quantities as q --> 4, the multicritical point. Similar analyses are applicable
to a variety of other systems.Comment: 12 pages, 6 figure
A Parameterized Post-Friedmann Framework for Modified Gravity
We develop a parameterized post-Friedmann (PPF) framework which describes
three regimes of modified gravity models that accelerate the expansion without
dark energy. On large scales, the evolution of scalar metric and density
perturbations must be compatible with the expansion history defined by distance
measures. On intermediate scales in the linear regime, they form a
scalar-tensor theory with a modified Poisson equation. On small scales in dark
matter halos such as our own galaxy, modifications must be suppressed in order
to satisfy stringent local tests of general relativity. We describe these
regimes with three free functions and two parameters: the relationship between
the two metric fluctuations, the large and intermediate scale relationships to
density fluctuations and the two scales of the transitions between the regimes.
We also clarify the formal equivalence of modified gravity and generalized dark
energy. The PPF description of linear fluctuation in f(R) modified action and
the Dvali-Gabadadze-Porrati braneworld models show excellent agreement with
explicit calculations. Lacking cosmological simulations of these models, our
non-linear halo-model description remains an ansatz but one that enables
well-motivated consistency tests of general relativity. The required
suppression of modifications within dark matter halos suggests that the linear
and weakly non-linear regimes are better suited for making complementary test
of general relativity than the deeply non-linear regime.Comment: 12 pages, 9 figures, additional references reflect PRD published
versio
MObile Technology for Improved Family Planning: update to randomised controlled trial protocol.
BACKGROUND: This update outlines changes to the MObile Technology for Improved Family Planning study statistical analysis plan and plans for long-term follow-up. These changes result from obtaining additional funding and the decision to restrict the primary analysis to participants with available follow-up data. The changes were agreed prior to finalising the statistical analysis plan and sealing the dataset. METHODS/DESIGN: The primary analysis will now be restricted to subjects with data on the primary outcome at 4-month follow-up. The extreme-case scenario, where all those lost to follow-up are counted as non-adherent, will be used in a sensitivity analysis. In addition to the secondary outcomes outlined in the protocol, we will assess the effect of the intervention on long-acting contraception (implant, intra-uterine device and permanent methods).To assess the long-term effect of the intervention, we plan to conduct additional 12-month follow-up by telephone self-report for all the primary and secondary outcomes used at 4 months. All participants provided informed consent for this additional follow-up when recruited to the trial. Outcome measures and analysis at 12 months will be similar to those at the 4-month follow-up. The primary outcomes of the trial will be the use of an effective modern contraceptive method at 4 months and at 12 months post-abortion. Secondary outcomes will include long-acting contraception use, self-reported pregnancy, repeat abortion and contraception use over the 12-month post-abortion period. DISCUSSION: Restricting the primary analysis to those with follow-up data is the standard approach for trial analysis and will facilitate comparison with other trials of interventions designed to increase contraception uptake or use. Undertaking 12-month trial follow-up will allow us to evaluate the long-term effect of the intervention. TRIAL REGISTRATION: ClinicalTrials.gov NCT01823861
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