Generalizing the rotation interval to vertex maps on graphs

Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the rotation elements associated to periodic points in a given edge of the graph. Most of the results show that the existence of two periodic points with certain rotation elements will imply an infinite family of other periodic points with related rotation elements. These results for periodic points can be considered as generalizations of the rotation interval for degree one maps of the circle

A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\lambda_{ls}$ is weakly topological if B satisfies condition $(\hbar)$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement "The convergence $\lambda_{ls}$ on the collapsing algebra B=\ro ((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC

Generalizing the Causal Effect of Fertility on Female Labor Supply

Abstract We study the effect of fertility on labor supply in Argentina and Mexico exploiting a source of exogenous variability in family size first introduced by Angrist and Evans (1998) for the United States. Our results constitute the first external validation of the estimates obtained for the US. External validation of empirical results is central to the making of rigorous science, but there are very few attempts to establish it. We find that the estimates for the US can be generalized both qualitatively and quantitatively to the populations of two developing countries where, compared to the US, fertility is known to be higher, female education levels are much lower and there are fewer facilities for childcare.http://deepblue.lib.umich.edu/bitstream/2027.42/40011/2/wp625.pd