Convexity, superquadratic growth, and dot products.

Let be a point set with cardinality . We give an improved bound for the number of dot products determined by , proving that A crucial ingredient in the proof of this bound is a new superquadratic expander involving products and shifts. We prove that, for any finite set , there exist such that This is derived from a more general result concerning growth of sets defined via convexity and sum sets, and which can be used to prove several other expanders with better than quadratic growth.

Age-specific differences in the magnitude of malaria-related anemia during low and high malaria seasons in rural Zambian children.

Background: Malaria causes anemia by destruction of red blood cells and inhibition of erythropoiesis.

Objective: We assessed whether the magnitude of the malaria-specific effect on anemia differs by age, during low and high malaria seasons.

Method: In rural Zambian children participating in a pro-vitamin A efficacy trial, we estimated differences in the prevalence of anemia (defined as hemoglobin < 110 g/L for children < 60 months.