A geometric model for Hochschild homology of Soergel bimodules

An important step in the calculation of the triply graded link homology theory of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as equivariant intersection homology of B x B-orbit closures in G. We show that, in type A these orbit closures are equivariantly formal for the conjugation T-action. We use this fact to show that in the case where the corresponding orbit closure is smooth, this Hochschild homology is an exterior algebra over a polynomial ring on generators whose degree is explicitly determined by the geometry of the orbit closure, and describe its Hilbert series, proving a conjecture of Jacob Rasmussen.Comment: 19 pages, no figure

MCMC with Strings and Branes: The Suburban Algorithm (Extended Version)

Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis-Hastings (MH) samplers, we place them on an auxiliary grid, and couple them together via nearest neighbor interactions. This leads to a class of "suburban samplers" (i.e., spread out Metropolis). Coupling the samplers in this way modifies the mixing rate and speed of convergence for the Markov chain, and can in many cases allow a sampler to more easily overcome free energy barriers in a target distribution. We test these general theoretical considerations by performing several numerical experiments. For suburban samplers with a fluctuating grid topology, performance is strongly correlated with the average number of neighbors. Increasing the average number of neighbors above zero initially leads to an increase in performance, though there is a critical connectivity with effective dimension d_eff ~ 1, above which "groupthink" takes over, and the performance of the sampler declines.Comment: v2: 55 pages, 13 figures, references and clarifications added. Published version. This article is an extended version of "MCMC with Strings and Branes: The Suburban Algorithm

Practical Application of NASA-Langley Advanced Satellite Products to In-Flight Icing Nowcasts

Experimental satellite-based icing products developed by the NASA Langley Research Center provide new tools to identify the locations of icing and its intensity. Since 1997, research forecasters at the National Center for Atmospheric Research (NCAR) have been helping to guide the NASA Glenn Research Center's Twin Otter aircraft into and out of clouds and precipitation for the purpose of characterizing in-flight icing conditions, including supercooled large drops, the accretions that result from such encounters and their effect on aircraft performance. Since the winter of 2003-04, the NASA Langley satellite products have been evaluated as part of this process, and are being considered as an input to NCAR s automated Current Icing Potential (CIP) products. This has already been accomplished for a relatively straightforward icing event, but many icing events have much more complex characteristics, providing additional challenges to all icing diagnosis tools. In this paper, four icing events with a variety of characteristics will be examined, with a focus on the NASA Langley satellite retrievals that were available in real time and their implications for icing nowcasting and potential applications in CIP

Aurora B answers an XIST-ential question

Mitotic release of chromatin-binding RNA gives insight into X chromosome silencing

The SAGA Survey: I. Satellite Galaxy Populations Around Eight Milky Way Analogs

We present the survey strategy and early results of the "Satellites Around Galactic Analogs" (SAGA) Survey. The SAGA Survey's goal is to measure the distribution of satellite galaxies around 100 systems analogous to the Milky Way down to the luminosity of the Leo I dwarf galaxy ($M_r < -12.3$). We define a Milky Way analog based on $K$-band luminosity and local environment. Here, we present satellite luminosity functions for 8 Milky Way analog galaxies between 20 to 40 Mpc. These systems have nearly complete spectroscopic coverage of candidate satellites within the projected host virial radius down to $r_o < 20.75$ using low redshift $gri$ color criteria. We have discovered a total of 25 new satellite galaxies: 14 new satellite galaxies meet our formal criteria around our complete host systems, plus 11 additional satellites in either incompletely surveyed hosts or below our formal magnitude limit. Combined with 13 previously known satellites, there are a total of 27 satellites around 8 complete Milky Way analog hosts. We find a wide distribution in the number of satellites per host, from 1 to 9, in the luminosity range for which there are five Milky Way satellites. Standard abundance matching extrapolated from higher luminosities predicts less scatter between hosts and a steeper luminosity function slope than observed. We find that the majority of satellites (26 of 27) are star-forming. These early results indicate that the Milky Way has a different satellite population than typical in our sample, potentially changing the physical interpretation of measurements based only on the Milky Way's satellite galaxies.Comment: 22 pages, 19 figures, 2 tables. Updated to published version. Survey website: http://sagasurvey.org

tert-Butyl N-hydr­oxy-N-[(1S*,2R*)-2-(1-naphth­yl)cyclo­pent-3-en-1-yl]carbamate

The relative stereochemistry of the title compound, C20H23NO3, was established by X-ray analysis. The asymmetric unit contains two independent mol­ecules. In the crystal structure, each type of mol­ecule forms a centrosymmetric dimer via pairs of inter­molecular O—H⋯O hydrogen bonds, resulting in an R 2 2(10) loop in each case

(4-Meth­oxy­phen­yl)methanaminium chloride

In the crystal structure of the title salt, C8H12NO+·Cl−, the methoxy group of the cation is co-planar with the phenylene moiety with an r.m.s. deviation from the mean plane of only 0.005 Å. The ammonium N atom deviates from this plane by 1.403 (1) Å. In the crystal, the (4-meth­oxy­phen­yl)methan­aminium cations and chloride anions are linked by N—H⋯Cl and C—H⋯O hydrogen bonds, resulting in an open framework architecture with hydrogen-bonded ammonium groups and chloride anions located in layers parallel to (011), separated by more hydrophobic layers with interdigitating anisole groups