Most studies of virulence of infection focus on pairwise host-parasite interactions. However, hosts are almost universally co-infected by several parasite strains and/or genotypes of the same or different species. While theory predicts that co-infection favours more virulent parasite genotypes through intensified competition for host resources, knowledge of the effects of genotype by genotype (...

A compact (not necessarily connected) Lie group G carries a (unique) biinvariant probability measure. Using this measure, one can average orbits of actions of G on affine convex sets to obtain fixed points. In particular, if G acts on a manifoldM , G leaves invariant a riemannian metric onM , and this metric can sometimes be used to obtain fixed points for the nonlinear action of G on M itself....

We investigate the statistics of the number N(R, S) of lattice points, n E Z-', in an annular domain /7(R, w) = (R + w)A\RA, where R, w > 0. Here A is a fixed convex set with smooth boundary and w is chosen so that the area of/7(R, w) is S. The statistics comes from R being taken as random (with a smooth density) in some interval [c~ T, c, T], c2 > ct > 0. We find that in the limit T--* oo the ...