Abstract We consider supercritical site percolation on the $d$ -dimensional hypercube $Q^d$ . show that typically all components in percolated hypercube, besides giant, are of size $O(d)$ This resolves a conjecture Bollobás, Kohayakawa, and Łuczak from 1994.

Effect size is becoming an increasingly popular measure of the importance of an effect, both in individual studies and in meta-analyses. However, a large effect size is not the only way to demonstrate that an effect is important. This article describes 2 alternative methodological strategies, in which importance is a function of how minimal a manipulation of the independent variable or how diff...

Given a range space (X,R), where X is a set equipped with probability measure P and the family of measurable subsets R ⊂ 2X , and ǫ > 0, an ǫ-net is a subset of X in the support of P , which intersects each R ∈ R with P (R) ≥ ǫ. In many interesting situations the size of ǫ-nets depends only on ǫ together with different complexity measures. The aim of this paper is to give a systematic treatment...

where they make those critical decisions that govern their lives. You who garden certainly know that plants have a mind of their own. Given that humans, and the majority of animals, solve many of their stressful problems (say, hunger) with a change in behavior (foraging for food), where are these decisions made in plants? An intriguing, and visually pleasing, example of such decision-making can...

Aggression is ubiquitous in the animal kingdom, whenever the interests of individuals conflict. In contests between animals, the larger opponent is often victorious. However, counter intuitively, an individual that has little chance of winning (generally smaller individuals) sometimes initiates contests. A number of hypotheses have been put forward to explain this behaviour, including the "desp...

here is a saying, popular amongst paediatricians, that ‘children are not small adults’ and perhaps this issue of the Journal of Virus Eradication illustrates the complexities of acquiring HIV-1 infection perinatally on an immature immune system. Reviews by Gianesen et al. and Cotugno et al. highlight the differences between perinatal and adult HIV-1 infection. Infants have a very small pool of ...