Characteristic exponents of complex networks

We present a novel way to characterize the structure of complex networks by studying the statistical properties of the trajectories of random walks over them. We consider time series corresponding to different properties of the nodes visited by the walkers. We show that the analysis of the fluctuations of these time series allows to define a set of characteristic exponents which capture the local and global organization of a network. This approach provides a way of solving two classical problems in network science, namely the systematic classification of networks, and the identification of the salient properties of growing networks. The results contribute to the construction of a unifying framework for the investigation of the structure and dynamics of complex systems.Comment: 6 pages, 5 figures, 1 tabl

Phylogenetic analysis of cyrtocrinid crinoids and its influence on traditional classifications

The cyrtocrinids are a group of mostly Mesozoic articulated crinoids, with rare Cenozoic forms and only two extant taxa. A careful analysis of previous studies indicates that the systematic arrangement of cyrtocrinids is very weak and unsatisfactory for several reasons. In particular, most of the original descriptions and diagnosis date from the past century and are logically influenced by a classical typological philosophy. Not being based on phylogeny, the currently accepted groups for cyrtocrinids must be putatively regarded as “artificial”. In addition, an inappropriate use of characters has been used, typically considered as diagnostic in other groups of crinoids but only marginally applicable to cyrtocrinids (the latter differently characterized for several highly distinctive and autapomorphic characters). In order to mitigate these problems and to arrive at the definition of characters and clades based on unambiguous synapomorphies, we present in this paper a preliminary and exploratory phylogenetic analysis based on parsimony of cyrtocrinids. The obtained topology showed how the traditionally recognized groups prove to be highly paraphyletic and polyphyletic, indicating the need for a complete revision of cyrtocrinids taxonomy, based on phylogeny. The gap-weighting method used for codifying morphometric continuous character, has proved to be a powerful tool to obtain well-resolved and consistent cladograms, even with a limited number of characters