Cohomology of toric line bundles via simplicial Alexander duality

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original algorithm but also a speed-up version of it. Our proof is independent from (in fact appeared earlier on the arXiv than) the proof by H. Roschy and T. Rahn (arXiv:1006.2392), and has several advantages such as being shorter and cleaner and can also settle the additional conjecture on "Serre duality for Betti numbers" which was raised but unresolved in arXiv:1006.2392.Comment: 9 pages. Theorem 1.1 and Corollary 1.2 improved; Abstract and Introduction modified; References updated. To appear in Journal of Mathematical Physic

The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers (1,1)

Calabi-Yau threefolds with h^11(X)=h^21(X)=1 are constructed as free quotients of a hypersurface in the ambient toric variety defined by the 24-cell. Their fundamental groups are SL(2,3), a semidirect product of Z_3 and Z_8, and Z_3 x Q_8.Comment: 22 pages, 3 figures, 3 table

Cohomology of Line Bundles: Applications

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute equivariant cohomology for line bundles, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev's formula and its generalizations can be given a one-to-one cohomological interpretation. This paper is considered the third in the row of arXiv:1003.5217 and arXiv:1006.2392.Comment: 56 pages, 8 tables, cohomCalg incl. Koszul extension available at http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg

On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page

Unlocking the Keyhole - H2 and PAH emission from molecular clumps in the Keyhole Nebula

To better understand the environment surrounding CO emission clumps in the Keyhole Nebula, we have made images of the region in H2 1-0 S(1) (2.122 um) emission and polycyclic aromatic hydrocarbon (PAH) emission at 3.29 um. Our results show that the H2 and PAH emission regions are morphologically similar, existing as several clumps, all of which correspond to CO emission clumps and dark optical features. The emission confirms the existence of photodissociation regions (PDRs) on the surface of the clumps. By comparing the velocity range of the CO emission with the optical appearance of the H2 and PAH emission, we present a model of the Keyhole Nebula in which the most negative velocity clumps are in front of the ionization region, the clumps at intermediate velocities are in it, and those which have the least negative velocities are at the far side. It may be that these clumps, which appear to have been swept up from molecular gas by the stellar winds from eta Car, are now being over-run by the ionization region and forming PDRs on their surfaces. These clumps comprise the last remnants of the ambient molecular cloud around eta Car.Comment: 8 pages, 4 figures, to be published in MNRA

The Nikolaevskiy equation with dispersion

The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral, Goldstone mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilise some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram (Busse balloon) for the traveling waves can be remarkably complicated.Comment: 24 pages; accepted for publication in Phys. Rev.

Micromechanics of fatigue in woven and stitched composites

The goal is to determine how microstructural factors, especially the architecture of microstructural factors, control fatigue damage in 3D reinforced polymer composites. Test materials were fabricated from various preforms, including stitched quasi-isotropic laminates, and through-the-thickness angle interlock, layer-to-layer angle interlock, and through-the-thickness stitching effect weaves. Preforms were impregnated with a tough resin by a special vacuum infiltration method. Most tests are being performed in uniaxial compression/compression loading. In all cases to date, failure has occurred not by delamination, but by shear failure, which occurs suddenly rather than by gradual macroscopic crack growth. Some theoretical aspects of bridging are also examined

Statistics of quantum transmission in one dimension with broad disorder

We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the logarithm of the transmission probability through this unit. Unit actions and lengths are independent random variables, with a common distribution that is either narrow or broad. This investigation is motivated by results on disordered systems with non-stationary random potentials whose fluctuations grow with distance. In the statistical ensemble at fixed total sample length four phases can be distinguished, according to the values of the indices characterizing the distribution of the unit actions and lengths. The sample action, which is proportional to the logarithm of the conductance across the sample, is found to obey a fluctuating scaling law, and therefore to be non-self-averaging, in three of the four phases. According to the values of the two above mentioned indices, the sample action may typically grow less rapidly than linearly with the sample length (underlocalization), more rapidly than linearly (superlocalization), or linearly but with non-trivial sample-to-sample fluctuations (fluctuating localization).Comment: 26 pages, 4 figures, 1 tabl

On the Joint Distribution of Energy Levels of Random Schroedinger Operators

We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals, with the corresponding eigenfunctions being separately localized within prescribed regions. The bound generalizes the Wegner estimate on the density of states. The analysis proceeds through a new multiparameter spectral averaging principle

The polymeric stability of the Escherichia coli F4 (K88) fimbriae enhances its mucosal immunogenicity following oral immunization

&lt;p&gt;Only a few vaccines are commercially available against intestinal infections since the induction of a protective intestinal immune response is difficult to achieve. For instance, oral administration of most proteins results in oral tolerance instead of an antigen-specific immune response. We have shown before that as a result of oral immunization of piglets with F4 fimbriae purified from pathogenic enterotoxigenic Escherichia coli (ETEC), the fimbriae bind to the F4 receptor (F4R) in the intestine and induce a protective F4-specific immune response. F4 fimbriae are very stable polymeric structures composed of some minor subunits and a major subunit FaeG that is also the fimbrial adhesin. In the present study, the mutagenesis experiments identified FaeG amino acids 97 (N to K) and 201 (I to V) as determinants for F4 polymeric stability. The interaction between the FaeG subunits in mutant F4 fimbriae is reduced but both mutant and wild type fimbriae behaved identically in F4R binding and showed equal stability in the gastro-intestinal lumen. Oral immunization experiments indicated that a higher degree of polymerisation of the fimbriae in the intestine was correlated with a better F4-specific mucosal immunogenicity. These data suggest that the mucosal immunogenicity of soluble virulence factors can be increased by the construction of stable polymeric structures and therefore help in the development of effective mucosal vaccines.&lt;/p&gt;</p