Stochastic Renormalization Group in Percolation: I. Fluctuations and Crossover

A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical self-similarity through a non-stationary branching process. The SRG provides a theoretical basis for analytical or numerical approximations, both at and away from criticality, whenever the correlation length is much larger than the lattice spacing (regardless of the system size). For example, the SRG predicts order-parameter distributions and finite-size scaling functions for the complete crossover between phases. For percolation, the simplest SRG describes structural quantities conditional on spanning, such as the total cluster mass or the minimum chemical distance between two boundaries. In these cases, the Central Limit Theorem (for independent random variables) holds at the stable, off-critical fixed points, while a ``Fractal Central Limit Theorem'' (describing long-range correlations) holds at the unstable, critical fixed point. This first part of a series of articles explains these basic concepts and a general theory of crossover. Subsequent parts will focus on limit theorems and comparisons of small-cell SRG approximations with simulation results.Comment: 33 pages, 6 figures, to appear in Physica A; v2: some typos corrected and Eqs. (26)-(27) cast in a simpler (but equivalent) for

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

Relationships between Parental Education and Overweight with Childhood Overweight and Physical Activity in 9-11 Year Old Children: Results from a 12-Country Study

Background: Globally, the high prevalence of overweight and low levels of physical activity among children has serious implications for morbidity and premature mortality in adulthood. Various parental factors are associated with childhood overweight and physical activity. The objective of this paper was to investigate relationships between parental education or overweight, and (i) child overweight, (ii) child physical activity, and (iii) explore household coexistence of overweight, in a large international sample. Methods: Data were collected from 4752 children (9-11 years) as part of the International Study of Childhood Obesity, Lifestyle and the Environment in 12 countries around the world. Physical activity of participating children was assessed by accelerometry, and body weight directly measured. Questionnaires were used to collect parents' education level, weight, and height. Results: Maternal and paternal overweight were positively associated with child overweight. Higher household coexistence of parent-child overweight was observed among overweight children compared to the total sample. There was a positive relationship between maternal education and child overweight in Colombia 1.90 (1.23-2.94) [odds ratio (confidence interval)] and Kenya 4.80 (2.21-10.43), and a negative relationship between paternal education and child overweight in Brazil 0.55 (0.33-0.92) and the USA 0.54 (0.33-0.88). Maternal education was negatively associated with children meeting physical activity guidelines in Colombia 0.53 (0.33-0.85), Kenya 0.35 (0.19-0.63), and Portugal 0.54 (0.31-0.96). Conclusions: Results are aligned with previous studies showing positive associations between parental and child overweight in all countries, and positive relationships between parental education and child overweight or negative associations between parental education and child physical activity in lower economic status countries. Relationships between maternal and paternal education and child weight status and physical activity appear to be related to the developmental stage of different countries. Given these varied relationships, it is crucial to further explore familial factors when investigating child overweight and physical activity