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.

Multiple tests of association with biological annotation metadata

We propose a general and formal statistical framework for multiple tests of association between known fixed features of a genome and unknown parameters of the distribution of variable features of this genome in a population of interest. The known gene-annotation profiles, corresponding to the fixed features of the genome, may concern Gene Ontology (GO) annotation, pathway membership, regulation by particular transcription factors, nucleotide sequences, or protein sequences. The unknown gene-parameter profiles, corresponding to the variable features of the genome, may be, for example, regression coefficients relating possibly censored biological and clinical outcomes to genome-wide transcript levels, DNA copy numbers, and other covariates. A generic question of great interest in current genomic research regards the detection of associations between biological annotation metadata and genome-wide expression measures. This biological question may be translated as the test of multiple hypotheses concerning association measures between gene-annotation profiles and gene-parameter profiles. A general and rigorous formulation of the statistical inference question allows us to apply the multiple hypothesis testing methodology developed in [Multiple Testing Procedures with Applications to Genomics (2008) Springer, New York] and related articles, to control a broad class of Type I error rates, defined as generalized tail probabilities and expected values for arbitrary functions of the numbers of Type I errors and rejected hypotheses. The resampling-based single-step and stepwise multiple testing procedures of [Multiple Testing Procedures with Applications to Genomics (2008) Springer, New York] take into account the joint distribution of the test statistics and provide Type I error control in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics.Comment: Published in at http://dx.doi.org/10.1214/193940307000000446 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org