Non-Perturbative Topological Strings And Conformal Blocks

We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.Comment: 36 page

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

DNA Barcoding the Geometrid Fauna of Bavaria (Lepidoptera): Successes, Surprises, and Questions

BACKGROUND: The State of Bavaria is involved in a research program that will lead to the construction of a DNA barcode library for all animal species within its territorial boundaries. The present study provides a comprehensive DNA barcode library for the Geometridae, one of the most diverse of insect families. METHODOLOGY/PRINCIPAL FINDINGS: This study reports DNA barcodes for 400 Bavarian geometrid species, 98 per cent of the known fauna, and approximately one per cent of all Bavarian animal species. Although 98.5% of these species possess diagnostic barcode sequences in Bavaria, records from neighbouring countries suggest that species-level resolution may be compromised in up to 3.5% of cases. All taxa which apparently share barcodes are discussed in detail. One case of modest divergence (1.4%) revealed a species overlooked by the current taxonomic system: Eupithecia goossensiata Mabille, 1869 stat.n. is raised from synonymy with Eupithecia absinthiata (Clerck, 1759) to species rank. Deep intraspecific sequence divergences (>2%) were detected in 20 traditionally recognized species. CONCLUSIONS/SIGNIFICANCE: The study emphasizes the effectiveness of DNA barcoding as a tool for monitoring biodiversity. Open access is provided to a data set that includes records for 1,395 geometrid specimens (331 species) from Bavaria, with 69 additional species from neighbouring regions. Taxa with deep intraspecific sequence divergences are undergoing more detailed analysis to ascertain if they represent cases of cryptic diversity

Microsurgery can cure most intracranial dural arteriovenous fistulae of the sinus and non-sinus type

There is consensus that intracranial dural arteriovenous fistulae (dAVF) with direct (non-sinus-type) or indirect (sinus-type) retrograde filling of a leptomeningeal vein should be treated due to the high risk of neurological deficits and hemorrhage. No consensus exists on treatment modality (surgery and/or embolization) and, if surgery is performed, on the best surgical strategy. This series aims to evaluate the role of surgery in the management of aggressive dAVFs. Forty-two patients underwent surgery. Opening and packing the sinus with thrombogenic material was performed in 9 of the 12 sinus-type dAVFs. In two sinus-type fistulae of the cavernous sinus and 1 of the torcular, microsurgery was used as prerequisite for subsequent embolization by providing access to the sinus. In the 30 non-sinus-type dAVFs, surgery consisted of interruption of the draining vein at the intradural entry point. In 41 patients undergoing 43 operations, elimination of the dAVF was achieved (97.6%). In one case, a minimal venous drainage persisted after surgery. The transient surgical morbidity was 11.9% (n = 5) and the permanent surgical morbidity 7.1% (n = 3). Our surgical strategy was to focus on the arterialized leptomeningeal vein in the non-sinus-type and on the arterialized sinus segment in the sinus-type dAVFs allowing us to obliterate all but one dAVF with a low morbidity rate. We therefore propose that microsurgery should be considered early in the treatment of both types of aggressive dAVFs. In selected cases of cavernous sinus dAVFs, the role of microsurgery is reduced to that of an adjunct to endovascular therapy