Vector bundles on projective varieties and representations of quivers

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an application, we provide decomposability criteria for such bundles.Comment: 29 pages. Partially overlaps with arXiv:1210.7835. To appear in Algebra and Discrete Mathematic

Technical Note: The Use of RNA-interference as a Tool to Find Proteins Involved in Melanosome Formation or Transport

Melanosomes are lysosome-related organelles that produce and transport the pigment melanin within melanocytes. Mutations in proteins required for melanosome transport and formation lead to a range of pigmentation defects, manifested at the cellular level as perinuclear clustering of melanosomes, or reduced sorting of melanosomal cargo such as tyrosinase-related protein 1 (TYRP1). A pilot screen was carried out to investigate whether a combination of cellular imaging and RNA interference could be used to identify new proteins involved in pigmentation pathways. In this study, eleven genes known to play a role in melanosome transport/formation or other pigmentation properties were knocked down in mouse melanocytes with shRNAmir constructs. The investigated genes were TYRP1, pallidin, cappuccino, dysbindin, HPS5, LYST, Myosin Va, melanophilin, RhoA, UBPY and mahogunin. In a blinded confocal imaging experiment, the only reproducible change observed in cells in which these targets were knocked down was a decrease in TYRP1 levels upon transfection with knockdown constructs against TYRP1 itself, or one of three constructs targeting HPS5 (Hermansky-Pudlak Syndrome 5). Upon analysis with high-content imaging software, only the knockdown construct against TYRP1 itself was detected. RT-PCR analysis showed that many of the shRNAmir constructs did not reduce mRNA and proteins levels enough to detect effects on melanosome properties. This was further examined for melanophilin, a protein necessary for melanosome transport. Altogether, the data show that this system is currently not sensitive enough for use in a screen for unknown regulators of melanosome transport and formation. The main obstacle appears to be incomplete reduction of target protein levels. Our observation that a ~50% reduction in mRNA level is not sufficient to elicit an effect is supported by the fact that heterozygous carriers of melanosomal transport disorders (Griscelli Syndrome, Hermansky-Pudlak Syndrome) do not display diseases phenotypes. A further reduction in protein levels, for example by viral infection of shRNA, may be required

Characteristics of exotic ants in North America

The worldwide transport of species beyond their native range is an increasing problem, e.g. for global biodiversity. Many introduced species are able to establish in new environments and some even become invasive. However, we do not know which traits enable them to survive and reproduce in new environments. This study aims to identify the characteristics of exotic ants, and to quantitatively test previously postulated but insufficiently tested assumptions. We collected data on nine traits of 93 exotic ant species (42 of them being invasive) and 323 native ant species in North America. The dataset includes 2536 entries from over 300 different sources; data on worker head width were mostly measured ourselves. We analyzed the data with three complementary analyses: univariate and multivariate analyses of the raw data, and multivariate analyses of phylogenetically independent contrasts. These analyses revealed significant differences between the traits of native and exotic ant species. In the multivariate analyses, only one trait was consistently included in the best models, estimated with AICc values: colony size. Thus, of the nine investigated traits, the most important characteristic of exotic ants as compared to native ants appears to be their large colony size. Other traits are also important, however, indicating that native and exotic ants differ by a suite of traits

Cosmological solutions of emergent noncommutative gravity

Matrix models of Yang-Mills type lead to an emergent gravity theory, which may not require fine-tuning of a cosmological constant. We find cosmological solutions of Friedmann-Robertson-Walker type. They generically have a big bounce, and an early inflation-like phase with graceful exit. The mechanism is purely geometrical, no ad-hoc scalar fields are introduced. The solutions are stabilized through vacuum fluctuations and are thus compatible with quantum mechanics. This leads to a Milne-like universe after inflation, which appears to be in remarkably good agreement with observation and may provide an alternative to standard cosmology.Comment: 4 pages, 2 figures. V2: version accepted by Phys.Rev.Lett. plus one pictur

A synthetic perturbative hypothesis for multiscale analysis of bluff-body wake instability

(Abstract