A Model for Scaling in Firms' Size and Growth Rate Distribution

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis that firms compete for a scarce quantity (either aggregate demand or workforce) which is allocated probabilistically. The model allows us to relate size and growth rate distributions. We compare the results of our model to simulations with other scaling relationships, and to similar models and relate it to existing theory. Effects arising from binning data are discussed.Comment: accepted for publication in Physica

Graph Kernels ― a Synthesis Note on Positive Definiteness

National audienceWe review the problem of extending the applicability of support vector machines (SVM) to graph data. Many similarity measures, generally called kernels, on graph data have been proposed in the last decade. Yet some of them, like the optimum assignment kernel (15), are not positive semidefinite, which limits their application in SVM. In this paper we recall the necessary conditions for using SVM. While the Mercer theorem gives necessary and sufficient conditions for vectorial data, we show that for graph data an embedding in a Hilbert space has to be defined explicitly, and that weaker conditions do not suffice. For several kernels proposed in the literature we demonstrate that an underlying Hilbert space does exist by specifying the corresponding basis.Our findings are illustrated with small examples from the graph kernel literature

Graph Kernels ― a Synthesis Note on Positive Definiteness

National audienceWe review the problem of extending the applicability of support vector machines (SVM) to graph data. Many similarity measures, generally called kernels, on graph data have been proposed in the last decade. Yet some of them, like the optimum assignment kernel (15), are not positive semidefinite, which limits their application in SVM. In this paper we recall the necessary conditions for using SVM. While the Mercer theorem gives necessary and sufficient conditions for vectorial data, we show that for graph data an embedding in a Hilbert space has to be defined explicitly, and that weaker conditions do not suffice. For several kernels proposed in the literature we demonstrate that an underlying Hilbert space does exist by specifying the corresponding basis.Our findings are illustrated with small examples from the graph kernel literature

The SH3 domain of the Saccharomyces cerevisiae peroxisomal membrane protein Pex13p functions as a docking site for Pex5p, a mobile receptor for the import PTS1-containing proteins

We identified a Saccharomyces cerevisiae peroxisomal membrane protein, Pex13p, that is essential for protein import. A point mutation in the COOH-terminal Src homology 3 (SH3) domain of Pex13p inactivated the protein but did not affect its membrane targeting. A two-hybrid screen with the SH3 domain of Pex13p identified Pex5p, a receptor for proteins with a type I peroxisomal targeting signal (PTS1), as its ligand. Pex13p SH3 interacted specifically with Pex5p in vitro. We determined, furthermore, that Pex5p was mainly present in the cytosol and only a small fraction was associated with peroxisomes. We therefore propose that Pex13p is a component of the peroxisomal protein import machinery onto which the mobile Pex5p receptor docks for the delivery of the selected PTS1 protei