Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Signatures of Star-planet interactions

Planets interact with their host stars through gravity, radiation and magnetic fields, and for those giant planets that orbit their stars within $\sim$10 stellar radii ($\sim$0.1 AU for a sun-like star), star-planet interactions (SPI) are observable with a wide variety of photometric, spectroscopic and spectropolarimetric studies. At such close distances, the planet orbits within the sub-alfv\'enic radius of the star in which the transfer of energy and angular momentum between the two bodies is particularly efficient. The magnetic interactions appear as enhanced stellar activity modulated by the planet as it orbits the star rather than only by stellar rotation. These SPI effects are informative for the study of the internal dynamics and atmospheric evolution of exoplanets. The nature of magnetic SPI is modeled to be strongly affected by both the stellar and planetary magnetic fields, possibly influencing the magnetic activity of both, as well as affecting the irradiation and even the migration of the planet and rotational evolution of the star. As phase-resolved observational techniques are applied to a large statistical sample of hot Jupiter systems, extensions to other tightly orbiting stellar systems, such as smaller planets close to M dwarfs become possible. In these systems, star-planet separations of tens of stellar radii begin to coincide with the radiative habitable zone where planetary magnetic fields are likely a necessary condition for surface habitability.Comment: Accepted for publication in the handbook of exoplanet

Local thermal adaptation and limited gene flow constrain future climate responses of a marine ecosystem engineer.

Rising ocean temperatures and extreme temperature events have precipitated declines and local extinctions in many marine species globally, but patterns of loss are often uneven across species ranges for reasons that are poorly understood. Knowledge of the extent of local adaptation and gene flow may explain such patterns and help predict future trajectories under scenarios of climate change. We test the extent to which local differentiation in thermal tolerance is influenced by gene flow and local adaptation using a widely distributed intertidal seaweed (Hormosira banksii) from temperate Australia. Population surveys across ~2,000 km of the species range revealed strong genetic structuring at regional and local scales (global F ST = 0.243) reflecting extremely limited gene flow, while common garden experiments (14-day exposures to 15, 18, 21°C) revealed strong site differences in early development and mortality in response to elevated temperature. Embryos from many sites spanning a longitudinal thermal gradient showed suppressed development and increased mortality to elevated water temperatures, but populations originating from warmer and more variable thermal environments tended to be less susceptible to warming. Notably, there was significant local-scale variation in the thermal responses of embryos within regions which was corroborated by the finding of small-scale genetic differences. We expect the observed genetic and phenotypic differentiation to lead to uneven responses to warming sea surface temperatures in this important marine foundation species. The study highlights the challenges of predicting species responses to thermal stress and the importance of management strategies that incorporate evolutionary potential for "climate-proofing" marine ecosystems

Large emissions from floodplain trees close the Amazon methane budget

Wetlands are the largest global source of atmospheric methane (CH4), a potent greenhouse gas. However, methane emission inventories from the Amazon floodplain, the largest natural geographic source of CH4 in the tropics, consistently underestimate the atmospheric burden of CH4 determined via remote sensing and inversion modelling, pointing to a major gap in our understanding of the contribution of these ecosystems to CH4 emissions. Here we report CH4 fluxes from the stems of 2,357 individual Amazonian floodplain trees from 13 locations across the central Amazon basin. We find that escape of soil gas through wetland trees is the dominant source of regional CH4 emissions. Methane fluxes from Amazon tree stems were up to 200 times larger than emissions reported for temperate wet forests6 and tropical peat swamp forests, representing the largest non-ebullitive wetland fluxes observed. Emissions from trees had an average stable carbon isotope value (δ13C) of −66.2 ± 6.4 per mil, consistent with a soil biogenic origin. We estimate that floodplain trees emit 15.1 ± 1.8 to 21.2 ± 2.5 teragrams of CH4 a year, in addition to the 20.5 ± 5.3 teragrams a year emitted regionally from other sources. Furthermore, we provide a ‘top-down’ regional estimate of CH4 emissions of 42.7 ± 5.6 teragrams of CH4 a year for the Amazon basin, based on regular vertical lower-troposphere CH4 profiles covering the period 2010–2013. We find close agreement between our ‘top-down’ and combined ‘bottom-up’ estimates, indicating that large CH4 emissions from trees adapted to permanent or seasonal inundation can account for the emission source that is required to close the Amazon CH4 budget. Our findings demonstrate the importance of tree stem surfaces in mediating approximately half of all wetland CH4 emissions in the Amazon floodplain, a region that represents up to one-third of the global wetland CH4 source when trees are combined with other emission sources

Anastrozole (‘Arimidex’) blocks oestrogen synthesis both peripherally and within the breast in postmenopausal women with large operable breast cancer

The effect of anastrozole on peripheral and tumour aromatase activity and oestrogen levels in postmenopausal patients with oestrogen receptor-rich breast tumours was investigated. Twenty-six patients were randomly allocated to treatment with anastrozole 1 mg (n=13) or 10 mg (n=13), once daily. Before and after 12 weeks' treatment, patients were infused with 3H-Δ4 androstenedione (20 MBq) and 14C-oestrone (E1) (1 MBq) for 18 h. Oestrogens were purified from excised tumours and plasma samples taken after each infusion. Peripheral and tumour aromatase activity and tumour E1 uptake were calculated from levels of 3H and 14C in purified E1 fractions from tumour and plasma. Endogenous tumour oestrogens were measured by radioimmunoassay. Twenty-three patients were available for analysis (1 mg group, n=12; 10 mg group, n=11). Following treatment, anastrozole (1 and 10 mg) markedly inhibited peripheral aromatase in all patients (the difference between pre- and on-treatment values being highly significant P<0.0001). In situ aromatase activity was also profoundly decreased by anastrozole treatment in 16 of 19 tumours (the difference with treatment also being highly significant P=0.0009). Most tumours were able to concentrate E1 beyond levels in the circulation; anastrozole treatment had no consistent effect on uptake of E1. Endogenous tumour levels of both E1 and oestradiol (E2) were significantly reduced with therapy (P=0.028 for E1 and P=0.0019 for E2). Anastrozole (1 and 10 mg daily) effectively suppresses aromatase activity, and subsequently oestrogen levels, within the breast tissue of postmenopausal women with large or locally advanced, operable, oestrogen receptor-rich breast cancers