'Magis rythmus quam metron': the structure of Seneca's anapaests, and the oral/aural nature of Latin poetry

The aim of this contribution is twofold. The empirical focus is the metrical structure of Seneca's anapaestic odes. On the basis of a detailed formal analysis, in which special attention is paid to the delimitation and internal structure of metrical periods, I argue against the dimeter colometry traditionally assumed. This conclusion in turn is based on a second, more methodological claim, namely that in establishing the colometry of an ancient piece of poetry, the modern metrician is only allowed to set apart a given string of metrical elements as a separate metron, colon or period, if this postulated metrical entity could 'aurally' be distinguished as such by the hearer

The distillability problem revisited

An important open problem in quantum information theory is the question of the existence of NPT bound entanglement. In the past years, little progress has been made, mainly because of the lack of mathematical tools to address the problem. (i) In an attempt to overcome this, we show how the distillability problem can be reformulated as a special instance of the separability problem, for which a large number of tools and techniques are available. (ii) Building up to this we also show how the problem can be formulated as a Schmidt number problem. (iii) A numerical method for detecting distillability is presented and strong evidence is given that all 1-copy undistillable Werner states are also 4-copy undistillable. (iv) The same method is used to estimate the volume of distillable states, and the results suggest that bound entanglement is primarily a phenomenon found in low dimensional quantum systems. (v) Finally, a set of one parameter states is presented which we conjecture to exhibit all forms of distillability.Comment: Several corrections, main results unchange

Noncommutative smoothness and coadjoint orbits

Raf Bocklandt and the author have proved in math.AG/0010030 that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace Lie algebra of the corresponding quiver. A conjectural ringtheoretical explanation of these results was given in terms of noncommutative smoothness in the sense of C. Procesi. In this paper we prove these conjectures. The main tool in the proof is the etale local description due to W. Crawley-Boevey in math.AG/0105247. Along the way we determine the smooth locus of the so called Marsden-Weinstein reductions for quiver representations