The mass of the product of spheres

Any compact manifold with positive scalar curvature has an associated asymptotically flat metric constructed using the Green's function of the conformal Laplacian, and the mass of this metric is an important geometric invariant. An explicit expression for the mass of the product of spheres $S^2 \times S^2$, both with the same Gaussian curvature, is given. Expressions for the masses of the quotient spaces $G(2,4)$, and $\mathbb{RP}^2 \times \mathbb{RP}^2$ are also given. The values of these masses arise in a construction of critical metrics on certain $4$-manifolds; applications to this problem will also be discussed.Comment: 25 page

Control of Arabidopsis apical-basal embryo polarity by antagonistic transcription factors.

Plants, similarly to animals, form polarized axes during embryogenesis on which cell differentiation and organ patterning programs are orchestrated. During Arabidopsis embryogenesis, establishment of the shoot and root stem cell populations occurs at opposite ends of an apical-basal axis. Recent work has identified the PLETHORA (PLT) genes as master regulators of basal/root fate, whereas the master regulators of apical/shoot fate have remained elusive. Here we show that the PLT1 and PLT2 genes are direct targets of the transcriptional co-repressor TOPLESS (TPL) and that PLT1/2 are necessary for the homeotic conversion of shoots to roots in tpl-1 mutants. Using tpl-1 as a genetic tool, we identify the CLASS III HOMEODOMAIN-LEUCINE ZIPPER (HD-ZIP III) transcription factors as master regulators of embryonic apical fate, and show they are sufficient to drive the conversion of the embryonic root pole into a second shoot pole. Furthermore, genetic and misexpression studies show an antagonistic relationship between the PLT and HD-ZIP III genes in specifying the root and shoot poles

Direct Detection Signals from Absorption of Fermionic Dark Matter

We present a new class of direct detection signals; absorption of fermionic dark matter. We enumerate the operators through dimension six which lead to fermionic absorption, study their direct detection prospects, and summarize additional constraints on their suppression scale. Such dark matter is inherently unstable as there is no symmetry which prevents dark matter decays. Nevertheless, we show that fermionic dark matter absorption can be observed in direct detection and neutrino experiments while ensuring consistency with the observed dark matter abundance and required lifetime. For dark matter masses well below the GeV scale, dedicated searches for these signals at current and future experiments can probe orders of magnitude of unexplored parameter space.Comment: 7 pages, 2 figures. v2: published in PRL with minor revisions and changes to Fig 2 (no change to results