Some Hopf Algebras of Trees

This paper generalizes the operadic construction of the Connes-Kreimer Hopf algebra of rooted trees by Moerdijk. Examples of Hopf algebras obtained in this way include the Loday-Ronco Hopf algebra of planar binary trees and the Brouder-Frabetti pruning Hopf algebra. In some examples we obtain a natural pre-Lie or dendriform algebra structure on the dual Hopf algebra. v2: Proof in section 8 corrected. v3: more corrections.Comment: 24 pages, 3 figure

Commuting in multinodal urban systems: An empirical comparison of three alternative models

The paper analyses whether the basic monocentric model of urban structure and commuting explains actual commuting in Europe, i.e. the Netherlands. As in the United States much wasteful commuting is established. The basic model has a low degree of explanatory power. In order to get more in line with actual commuting, the paper elaborates two alternatives to the basic model. Besides a decon-centrated model, a cross-traffic model is developed. Particularly the latter is quite successful in explaining actual commuting. The paper pleads for endo-geni-zing employment and stresses heterogeneity in labour demand and supply.

Semiparametric theory

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified and unrestricted, and can often yield robust estimators that nonetheless behave similarly to those based on parametric likelihood assumptions, e.g., fast rates of convergence to normal limiting distributions. We discuss the basics of semiparametric theory, focusing on influence functions.Comment: arXiv admin note: text overlap with arXiv:1510.0474