Differential operators on the superline, Berezinians, and Darboux transformations

We consider differential operators on a supermanifold of dimension $1|1$. We define non-degenerate operators as those with an invertible top coefficient in the expansion in the "superderivative" $D$ (which is the square root of the shift generator, the partial derivative in an even variable, with the help of an odd indeterminate). They are remarkably similar to ordinary differential operators. We show that every non-degenerate operator can be written in terms of `super Wronskians' (which are certain Berezinians). We apply this to Darboux transformations (DTs), proving that every DT of an arbitrary non-degenerate operator is the composition of elementary first order transformations. Hence every DT corresponds to an invariant subspace of the source operator and, upon a choice of basis in this subspace, is expressed by a super-Wronskian formula. We consider also dressing transformations, i.e., the effect of a DT on the coefficients of the non-degenerate operator. We calculate these transformations in examples and make some general statements.Comment: 24 pages, LaTeX, some editorial changes (as compared with the earlier version

The High Chromospheres of the Late A Stars

We report the detection of N V 1239 A transition region emission in HST/GHRS spectra of the A7 V stars, Alpha Aql and Alpha Cep. Our observations provide the first direct evidence of 1-3 x 10^5 K material in the atmospheres of normal A-type stars. For both stars, and for the mid-A--type star Tau3 Eri, we also report the detection of chromospheric emission in the Si III 1206 A line. At a B-V color of 0.16 and an effective temperature of 8200 K, Tau3 Eri becomes the hottest main sequence star known to have a chromosphere and thus an outer convection zone. We see no firm evidence that the Si III line surface fluxes of the A stars are any lower than those of moderately active, solar-type, G and K stars. This contrasts sharply with their coronal X-ray emission, which is >100 times weaker than that of the later-type stars. Given the strength of the N V emission observed here, it now appears unlikely that the X-ray faintness of the A stars is due to their forming very cool, <= 1 MK coronae. An alternative explanation in terms of mass loss in coronal winds remains a possibility, though we conclude from moderate resolution spectra of the Si III lines that such winds, if they exist, do not penetrate into the chromospheric Si III--forming layers of the star, since the profiles of these lines are *not* blueshifted, and may well be redshifted with respect to the star.Comment: LaTex, 12 pages, 3 Postscript figures, uses aaspp4, accepted by Ap

Patterns of Design

In a straightforward meta-level shift of focus, we use design patterns as a medium and process for capturing insight about the process of design. We survey mainstream design genres, and draw conclusions about how they can help inform the design of intelligent systems

Co-expression of Gbeta 5 Enhances the Function of Two Ggamma Subunit-like Domain-containing Regulators of G Protein Signaling Proteins

Regulators of G protein signaling (RGS) stimulate the GTPase activity of G protein Galpha subunits and probably play additional roles. Some RGS proteins contain a Ggamma subunit-like (GGL) domain, which mediates a specific interaction with Gbeta 5. The role of such interactions in RGS function is unclear. RGS proteins can accelerate the kinetics of coupling of G protein-coupled receptors to G-protein-gated inwardly rectifying K+ (GIRK) channels. Therefore, we coupled m2-muscarinic acetylcholine receptors to GIRK channels in Xenopus oocytes to evaluate the effect of Gbeta 5 on RGS function. Co-expression of either RGS7 or RGS9 modestly accelerated GIRK channel kinetics. When Gbeta 5 was co-expressed with either RGS7 or RGS9, the acceleration of GIRK channel kinetics was strongly increased over that produced by RGS7 or RGS9 alone. RGS function was not enhanced by co-expression of Gbeta 1, and co-expression of Gbeta 5 alone had no effect on GIRK channel kinetics. Gbeta 5 did not modulate the function either of RGS4, an RGS protein that lacks a GGL domain, or of a functional RGS7 construct in which the GGL domain was omitted. Enhancement of RGS7 function by Gbeta 5 was not a consequence of an increase in the amount of plasma membrane or cytosolic RGS7 protein

Faster Family-wise Error Control for Neuroimaging with a Parametric Bootstrap

In neuroimaging, hundreds to hundreds of thousands of tests are performed across a set of brain regions or all locations in an image. Recent studies have shown that the most common family-wise error (FWE) controlling procedures in imaging, which rely on classical mathematical inequalities or Gaussian random field theory, yield FWE rates that are far from the nominal level. Depending on the approach used, the FWER can be exceedingly small or grossly inflated. Given the widespread use of neuroimaging as a tool for understanding neurological and psychiatric disorders, it is imperative that reliable multiple testing procedures are available. To our knowledge, only permutation joint testing procedures have been shown to reliably control the FWER at the nominal level. However, these procedures are computationally intensive due to the increasingly available large sample sizes and dimensionality of the images, and analyses can take days to complete. Here, we develop a parametric bootstrap joint testing procedure. The parametric bootstrap procedure works directly with the test statistics, which leads to much faster estimation of adjusted \emph{p}-values than resampling-based procedures while reliably controlling the FWER in sample sizes available in many neuroimaging studies. We demonstrate that the procedure controls the FWER in finite samples using simulations, and present region- and voxel-wise analyses to test for sex differences in developmental trajectories of cerebral blood flow

CO Line Emission and Absorption from the HL Tau Disk: Where is all the dust?

We present high-resolution infrared spectra of HL Tau, a heavily embedded young star. The spectra exhibit broad emission lines of hot CO gas as well as narrow absorption lines of cold CO gas. The column density for this cooler material (7.5+/-0.2 x 10^18 cm-2) indicates a large column of absorbing gas along the line of sight. In dense interstellar clouds, this column density of CO gas is associated with Av~52 magnitudes. However, the extinction toward this source (Av~23) suggests that there is less dust along the line of sight than inferred from the CO absorption data. We discuss three possibilities for the apparent paucity of dust along the line of sight through the flared disk: 1) the dust extinction has been underestimated due to differences in circumstellar grain properties, such as grain agglomeration; 2) the effect of scattering has been underestimated and the actual extinction is much higher; or (3) the line of sight through the disk is probing a gas-rich, dust-depleted region, possibly due to the stratification of gas and dust in a pre-planetary disk.Comment: To be published in The Astrophysical Journa

Near-Infrared Spectroscopy of McNeil's Nebula Object

We present 0.8-5.2 micron spectroscopy of the compact source at the base of a variable nebula (McNeil's Nebula Object) in the Lynds 1630 dark cloud that went into outburst in late 2003. The spectrum of this object reveals an extremely red continuum, CO bands at 2.3-2.5 microns in emission, a deep 3.0 micron ice absorption feature, and a solid state CO absorption feature at 4.7 microns. In addition, emission lines of H, Ca II, Mg I, and Na I are present. The Paschen lines exhibit P Cygni profiles, as do two lines of He I, although the emission features are very weak in the latter. The Brackett lines, however, are seen to be purely in emission. The P Cygni profiles clearly indicate that mass outflow is occurring in a wind with a velocity of ~400 km/s. The H line ratios do not yield consistent estimates of the reddening, nor do they agree with the extinction estimated from the ice feature (A_V ~ 11). We propose that these lines are optically thick and are produced in a dense, ionized wind. The near-infrared spectrum does not appear similar to any known FUor or EXor object. However, all evidence suggests that McNeil's Nebula Object is a heavily-embedded low-mass Class I protostar, surrounded by a disk, whose brightening is due to a recent accretion event.Comment: 11 pages, 2 ps figures, accepted for publication in ApJ Letter

Post-Outburst Observations of V1647 Ori: Detection of a Brief Warm, Molecular Outflow

We present new observations of the fundamental ro-vibrational CO spectrum of V1647 Ori, the young star whose recent outburst illuminated McNeil's Nebula. Previous spectra, acquired during outburst in 2004 February and July, had shown the CO emission lines to be broad and centrally peaked-similar to the CO spectrum of a typical classical T Tauri star. In this paper, we present CO spectra acquired shortly after the luminosity of the source returned to its pre-outburst level (2006 February) and roughly one year later (2006 December and 2007 February). The spectrum taken in 2006 February revealed blue-shifted CO absorption lines superimposed on the previously observed CO emission lines. The projected velocity, column density, and temperature of this outflowing gas was 30 km/s, 3^{+2}_{-1}E18 cm^{-2$, and 700^{+300}_{-100} K, respectively. The absorption lines were not observed in the 2006 December and 2007 February data, and so their strengths must have decreased in the interim by a factor of 9 or more. We discuss three mechanisms that could give rise to this unusual outflow.Comment: 14 pages, 2 figures, accepted for publication in ApJ