Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at occupation probability 0.59274621(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the percolation transitio

The effects of postmenopausal hormone therapy on social activity, partner relationship, and sexual life – experience from the EPHT trial

<p>Abstract</p> <p>Background</p> <p>With the exception of sexual functioning and weight, social and behavioural effects of postmenopausal hormone therapy (HT) have not been reported from trials. This paper reports such results from the EPHT-trial in Estonia.</p> <p>Methods</p> <p>A randomized trial, with a blind and non-blind sub-trial in Estonia. From 1999–2001, 1778 women were recruited. The mean follow-up was 3.6 years. Women's experiences were asked in the first and final study year by mailed questionnaires (74 and 81% response rates). Comparisons of the groups were made by cross-tabulation and logistic regression, adjusting for age.</p> <p>Results</p> <p>There were no differences between the HT and non-HT groups in regard to being employed, the extent of social involvement or marital status or opinions on aging. There was no difference in the frequency of free-time exercise, or overweight. Some of the indicators suggested less sexual inactivity, but the differences were small.</p> <p>Conclusion</p> <p>In a trial setting, postmenopausal hormone therapy did not influence work or social involvement or health behaviour.</p> <p>Trial registration</p> <p>ISRCTN35338757</p

Percolation on two- and three-dimensional lattices

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.Comment: 15 pages, 6 figures, 3 table

Exact results at the 2-D percolation point

We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n_c in the infinite system limit; the bn correct bulk cumulants. b and b_n are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter

A fast Monte Carlo algorithm for site or bond percolation

We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.Comment: 17 pages, 13 figures. Corrections and some additional material in this version. Accompanying material can be found on the web at http://www.santafe.edu/~mark/percolation

Experiences of a long-term randomized controlled prevention trial in a maiden environment: Estonian Postmenopausal Hormone Therapy trial

<p>Abstract</p> <p>Background</p> <p>Preventive drugs require long-term trials to show their effectiveness or harms and often a lot of changes occur during post-marketing studies. The purpose of this article is to describe the research process in a long-term randomized controlled trial and discuss the impact and consequences of changes in the research environment.</p> <p>Methods</p> <p>The Estonian Postmenopausal Hormone Therapy trial (EPHT), originally planned to continue for five years, was planned in co-operation with the Women's International Study of Long-Duration Oestrogen after Menopause (WISDOM) in the UK. In addition to health outcomes, EPHT was specifically designed to study the impact of postmenopausal hormone therapy (HT) on health services utilization.</p> <p>Results</p> <p>After EPHT recruited in 1999–2001 the Women's Health Initiative (WHI) in the USA decided to stop the estrogen-progestin trial after a mean of 5.2 years in July 2002 because of increased risk of breast cancer and later in 2004 the estrogen-only trial because HT increased the risk of stroke, decreased the risk of hip fracture, and did not affect coronary heart disease incidence. WISDOM was halted in autumn 2002. These decisions had a major influence on EPHT.</p> <p>Conclusion</p> <p>Changes in Estonian society challenged EPHT to find a balance between the needs of achieving responses to the trial aims with a limited budget and simultaneously maintaining the safety of trial participants. Flexibility was the main key for success. Rapid changes are not limited only to transiting societies but are true also in developed countries and the risk must be included in planning all long-term trials.</p> <p>The role of ethical and data monitoring committees in situations with emerging new data from other studies needs specification. Longer funding for preventive trials and more flexibility in budgeting are mandatory. Who should prove the effectiveness of an (old) drug for a new preventive indication? In preventive drug trials companies may donate drugs but they take a financial risk, especially with licensed drugs. Public funding is crucial to avoid commercial biases. Legislation to share the costs of large post-marketing trials as well as regulation of manufacturer's participation is needed. [ISRCTN35338757]</p

Perinatal Risk Factors for Diabetes in Later Life

OBJECTIVE—Low birth weight is consistently associated with an increased risk of type 2 diabetes in adulthood, but the individual contributions from poor fetal growth and preterm birth are not known. We therefore investigated the significance of these two factors separately