It is shown that ifG is a graph which is contractible or dismantlable or finitely ball-Helly, and without infinite paths; or which is bounded, finitely ball-Helly and without infinite simplices then: (i) any contraction ofG stabilizes a finite simplex; and (ii)G contains a finite simplex which is invariant under any automorphism.
We indicate some qualitative properties of Fleming--Viot second order differential operators on the d-dimensional simplex, such as an inductive characterization of its domain and some spectral properties connected with the
asymptotic behavior of the generated semigroup. These properties turn out to be very useful in the approximation of the solution
of the evolution problem associated with Fleming--Viot operators, which are very important as diffusion models in population
-simplex in ℜ n . Different schemes of perturbation can be considered under this methodology. Note that different patterns of variability of the weights generate different geometric areas to be considered in the Monte Carlo simulations. According to a