Unraveling the Phylogenetic Relationships of the Eccoptochilinae, an Enigmatic Array of Ordovician Cheirurid Trilobites

The Cheiruridae are a diverse group of trilobites and several subfamilies within the clade have been the focus of recent phylogenetic studies. This paper focuses on the relationships of one of those subfamilies, the Ordovician Eccoptochilinae. We analyze sixteen species from six genera within the traditionally defined group, using the pilekiid Anacheirurus frederici as an outgroup. To assess the monophyly of the Eccoptochilinae seven sphaerexochine species, Kawina arnoldi, Sphaerexochus arenosus, S. atacius, S. latifrons, S. mirus, S. parvus, and S. scabridus were included in the analysis as well. The results of this analysis show that the genus Eccoptochile represents a paraphyletic grade and species traditionally assigned to Parasphaerexochus and Skelipyx plot within Pseudosphaerexochus. Also, representative species of Sphaerexochinae plot within the traditionally defined Eccoptochilinae, suggesting Eccoptochilinae itself is paraphyletic. To resolve this, we propose all species of Pseudosphaerexochus be placed within Sphaerexochinae and Eccoptochilinae be restricted to a monotypic Eccoptochile clavigera.This research was supported by NSF DEB-0716162

Connections between L2-Model Reduction andBalanced Truncation

In this paper we investigate the connection between model reduction by balanced truncation and by L2 reduction. We show that locally, i.e., close to the set of lower order systems, balanced truncation and (un-weighted) L2 model reduction produce models that are almost identical. This implies that high order estimated models can be reduced by either L2 reduction or balanced truncation, both methods giving a low order model with the same asymptotic varaiance, if the true data generating model is in the class of low order models