Complex quotients by nonclosed groups and their stratifications

We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural generalization to the nonrational case of the notion of toric variety associated with a rational convex polytope.Comment: Research announcement. Updated version, shortened, exposition improved, 8 p

Betti numbers of the geometric spaces associated to nonrational simple convex polytopes

We compute the Betti numbers of the geometric spaces associated to nonrational simple convex polytopes and find that they depend on the combinatorial type of the polytope exactly as in the rational case. This shows that the combinatorial features of the starting polytope are encoded in these generalized toric spaces as they are in their rational counterparts.Comment: 8 page

Nonrational, nonsimple convex polytopes in symplectic geometry

In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting. We provide here the explicit construction of these spaces, and a thorough description of the stratification.Comment: LaTeX, 7 page

Nonrational Symplectic Toric Cuts

In this article we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds and orbifolds in nonrational directions.Comment: 17 pages, 7 figures, minor changes in last version, to appear in Internat. J. Mat

The Drosophila histone variant H2A.V works in concert with HP1 to promote kinetochore-driven microtubule formation

Unlike other organisms that have evolved distinct H2A variants for different functions, Drosophila melanogaster has just one variant which is capable of filling many roles. This protein, H2A.V, combines the features of the conserved variants H2A.Z and H2A.X in transcriptional control/heterochromatin assembly and DNA damage response, respectively. Here we show that mutations in the gene encoding H2A.V affect chromatin compaction and perturb chromosome segregation in Drosophila mitotic cells. A microtubule (MT) regrowth assay after cold exposure revealed that loss of H2A.V impairs the formation of kinetochore-driven (k) fibers, which can account for defects in chromosome segregation. All defects are rescued by a transgene encoding H2A.V that lacks the H2A.X function in the DNA damage response, suggesting that the H2A.Z (but not H2A.X) functionality of H2A.V is required for chromosome segregation. We also found that loss of H2A.V weakens HP1 localization, specifically at the pericentric heterochromatin of metaphase chromosomes. Interestingly, loss of HP1 yielded not only telomeric fusions but also mitotic defects similar to those seen in H2A.V null mutants, suggesting a role for HP1 in chromosome segregation. We also show that H2A.V precipitates HP1 from larval brain extracts indicating that both proteins are part of the same complex. Moreover, we found that the overexpression of HP1 rescues chromosome missegregation and defects in the kinetochore-driven k-fiber regrowth of H2A.V mutants indicating that both phenotypes are influenced by unbalanced levels of HP1. Collectively, our results suggest that H2A.V and HP1 work in concert to ensure kinetochore-driven MT growth

Relational goods, sociability, and happiness.

The role of sociability and relational goods has generally been neglected in the formulation of standard economics textbook preferences. Our findings show that relational goods have significant and positive effects on self declared life satisfaction, net of the impact of other concurring factors. We also document that such effects persist when the equally significant inverse causality nexus is taken into account. This implies that a more intense relational life enhances life satisfaction and, at the same time, happier people have a more lively social life. Finally, we show that gender, age and education matter by showing that the effects of sociability on happiness are stronger for women, older and less educated individuals.

Nonrational Symplectic Toric Reduction

In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the torus.Comment: 13 pages, 2 figures. Final version, to appear in J. Geom. Phy