Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of surfaces for which C^2 is not bounded below are in positive characteristic, and the general expectation is that no examples can arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field. The previous version of this paper claimed to give a counterexample to the Bounded Negativity Conjecture. The idea of the counterexample was to use Hecke translates of a smooth Shimura curve in order to create an infinite sequence of curves violating the Bounded Negativity Conjecture. To this end we applied Hirzebruch Proportionality to all Hecke translates, simultaneously desingularized by a version of Jaffee's Lemma which exists in the literature but which turns out to be false. Indeed, in the new version of the paper, we show that only finitely many Hecke translates of a special subvariety of a Hilbert modular surface remain smooth. This new result is based on work done jointly with Xavier Roulleau, who has been added as an author. The other results in the original posting of this paper remain unchanged.Comment: 14 pages, X. Roulleau added as author, counterexample to Bounded Negativity Conjecture withdrawn and replaced by a proof that there are only finitely many smooth Shimura curves on a compact Hilbert modular surface; the other results in the original posting of this paper remain unchange

A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.Comment: 11 pages, no figures, published versio

Invertebrate neurophylogeny: suggested terms and definitions for a neuroanatomical glossary

<p>Abstract</p> <p>Background</p> <p>Invertebrate nervous systems are highly disparate between different taxa. This is reflected in the terminology used to describe them, which is very rich and often confusing. Even very general terms such as 'brain', 'nerve', and 'eye' have been used in various ways in the different animal groups, but no consensus on the exact meaning exists. This impedes our understanding of the architecture of the invertebrate nervous system in general and of evolutionary transformations of nervous system characters between different taxa.</p> <p>Results</p> <p>We provide a glossary of invertebrate neuroanatomical terms with a precise and consistent terminology, taxon-independent and free of homology assumptions. This terminology is intended to form a basis for new morphological descriptions. A total of 47 terms are defined. Each entry consists of a definition, discouraged terms, and a background/comment section.</p> <p>Conclusions</p> <p>The use of our revised neuroanatomical terminology in any new descriptions of the anatomy of invertebrate nervous systems will improve the comparability of this organ system and its substructures between the various taxa, and finally even lead to better and more robust homology hypotheses.</p

Olfactory Interference during Inhibitory Backward Pairing in Honey Bees

Background: Restrained worker honey bees are a valuable model for studying the behavioral and neural bases of olfactory plasticity. The proboscis extension response (PER; the proboscis is the mouthpart of honey bees) is released in response to sucrose stimulation. If sucrose stimulation is preceded one or a few times by an odor (forward pairing), the bee will form a memory for this association, and subsequent presentations of the odor alone are sufficient to elicit the PER. However, backward pairing between the two stimuli (sucrose, then odor) has not been studied to any great extent in bees, although the vertebrate literature indicates that it elicits a form of inhibitory plasticity. Methodology/Principal Findings: If hungry bees are fed with sucrose, they will release a long lasting PER; however, this PER can be interrupted if an odor is presented 15 seconds (but not 7 or 30 seconds) after the sucrose (backward pairing). We refer to this previously unreported process as olfactory interference. Bees receiving this 15 second backward pairing show reduced performance after a subsequent single forward pairing (excitatory conditioning) trial. Analysis of the results supported a relationship between olfactory interference and a form of backward pairing-induced inhibitory learning/ memory. Injecting the drug cimetidine into the deutocerebrum impaired olfactory interference. Conclusions/Significance: Olfactory interference depends on the associative link between odor and PER, rather than between odor and sucrose. Furthermore, pairing an odor with sucrose can lead either to association of this odor to PER or t