On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

The nil Hecke ring and singularity of Schubert varieties

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Comment: AMSTE

Identification of polymorphisms and balancing selection in the male infertility candidate gene, ornithine decarboxylase antizyme 3

Abstract Background The antizyme family is a group of small proteins that play a role in cell growth and division by regulating the biosynthesis of polyamines (putrescine, spermidine, spermine). Antizymes regulate polyamine levels primarily through binding ornithine decarboxylase (ODC), an enzyme key to polyamine production, and targeting ODC for destruction by the 26S proteosome. Ornithine decarboxylase antizyme 3 (OAZ3) is a testis-specific antizyme paralog and the only antizyme expressed in the mid to late stages of spermatogenesis. Methods To see if mutations in the OAZ3 gene are responsible for some cases of male infertility, we sequenced and evaluated the genomic DNA of 192 infertile men, 48 men of known paternity, and 34 African aborigines from the Mbuti tribe in the Democratic Republic of the Congo. The coding sequence of OAZ3 was further screened for polymorphisms by SSCP analysis in the infertile group and an additional 250 general population controls. Identified polymorphisms in the OAZ3 gene were further subjected to a haplotype analysis using PHASE 2.02 and Arlequin 2.0 software programs. Results A total of 23 polymorphisms were identified in the promoter, exons or intronic regions of OAZ3. The majority of these fell within a region of less than two kilobases. Two of the polymorphisms, -239 A/G in the promoter and 4280 C/T, a missense polymorphism in exon 5, may show evidence of association with male infertility. Haplotype analysis identified 15 different haplotypes, which can be separated into two divergent clusters. Conclusion Mutations in the OAZ3 gene are not a common cause of male infertility. However, the presence of the two divergent haplotypes at high frequencies in all three of our subsamples (infertile, control, African) suggests that they have been maintained in the genome by balancing selection, which was supported by a test of Tajima's D statistic. Evidence for natural selection in this region implies that these haplotypes may be associated with a trait other than infertility. This trait may be related to another function of OAZ3 or a region in tight linkage disequilibrium to the gene.</p

Residues and World-Sheet Instantons

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0,2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. Here, we show that this cancellation follows directly from a residue theorem, whose proof relies only upon the right-moving world-sheet supersymmetries and suitable compactness properties of the (0,2) linear sigma model. Our residue theorem also extends to a new class of "half-linear" sigma models. Using these half-linear models, we show that heterotic compactifications on the quintic hypersurface in CP^4 for which the gauge bundle pulls back from a bundle on CP^4 are stable. Finally, we apply similar ideas to compute the superpotential contributions from families of membrane instantons in M-theory compactifications on manifolds of G_2 holonomy.Comment: 47 page

GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator

We present the recent discovery of a new subdwarf B variable (sdBV), with an exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1. With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever found. Photometry from three different observatories reveals a temporal spectrum with eleven clearly detected periods in the range 376 to 566 s, and at least five more close to our detection limit. These periods are unusually long for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for p- and g-modes close to the radial fundamental, given its low surface gravity. Of the ~50 short period sdB pulsators known to date, only a single one has been found to have comparable spectroscopic parameters to J20136+0928. This is the enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is the second example of this rare subclass of sdB pulsators located well above the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Academic Performance and Behavioral Patterns

Identifying the factors that influence academic performance is an essential part of educational research. Previous studies have documented the importance of personality traits, class attendance, and social network structure. Because most of these analyses were based on a single behavioral aspect and/or small sample sizes, there is currently no quantification of the interplay of these factors. Here, we study the academic performance among a cohort of 538 undergraduate students forming a single, densely connected social network. Our work is based on data collected using smartphones, which the students used as their primary phones for two years. The availability of multi-channel data from a single population allows us to directly compare the explanatory power of individual and social characteristics. We find that the most informative indicators of performance are based on social ties and that network indicators result in better model performance than individual characteristics (including both personality and class attendance). We confirm earlier findings that class attendance is the most important predictor among individual characteristics. Finally, our results suggest the presence of strong homophily and/or peer effects among university students