The curious nonexistence of Gaussian 2-designs

2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space L2(R). This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables, for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have an average state because the averaging integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and continuous quantum mechanics has important implications for optical state and process tomography.Comment: 9 pages, no pretty figures (sorry!

Illumination in symbiotic binary stars: Non-LTE photoionization models. II. Wind case

We describe a non-LTE photoionization code to calculate the wind structure and emergent spectrum of a red giant wind illuminated by the hot component of a symbiotic binary system. We consider spherically symmetric winds with several different velocity and temperature laws and derive predicted line fluxes as a function of the red giant mass loss rate, \mdot. Our models generally match observations of the symbiotic stars EG And and AG Peg for \mdot about 10^{-8} \msunyr to 10^{-7} \msunyr. The optically thick cross- section of the red giant wind as viewed from the hot component is a crucial parameter in these models. Winds with cross-sections of 2--3 red giant radii reproduce the observed fluxes, because the wind density is then high, about 10^9 cm^{-3}. Our models favor winds with acceleration regions that either lie far from the red giant photosphere or extend for 2--3 red giant radii.Comment: 51 pages, LaTeX including three tables, requires 15 Encapsulated Postscript figures, to appear in Ap

Biocatalytic, one-pot diterminal oxidation and esterification of n-alkanes for production of α,ω-diol and α,ω-dicarboxylic acid esters

Direct and selective terminal oxidation of medium-chain n-alkanes is a major challenge in chemistry. Efforts to achieve this have so far resulted in low specificity and overoxidized products. Biocatalytic oxidation of medium-chain n-alkanes – with for example the alkane monooxygenase AlkB from P. putida GPo1- on the other hand is highly selective. However, it also results in overoxidation. Moreover, diterminal oxidation of medium-chain n-alkanes is inefficient. Hence, α,ω-bifunctional monomers are mostly produced from olefins using energy intensive, multi-step processes. By combining biocatalytic oxidation with esterification we drastically increased diterminal oxidation upto 92 mol% and reduced overoxidation to 3% for n-hexane. This methodology allowed us to convert medium-chain n-alkanes into α,ω-diacetoxyalkanes and esterified α,ω-dicarboxylic acids. We achieved this in a one-pot reaction with resting-cell suspensions of genetically engineered Escherichia coli. The combination of terminal oxidation and esterification constitutes a versatile toolbox to produce α,ω-bifunctional monomers from n-alkanes

Spectral shape of the UV ionizing background and HeII absorption at redshifts 1.8 < z < 2.9

The shape of the UV ionizing background is reconstructed from optically thin metal absorption-line systems identified in spectra of HE2347-4342, Q1157+3143, and HS1700+6416 in the redshift interval 1.8 < z < 2.9. The systems are analyzed by means of the Monte Carlo Inversion method completed with the spectral shape recovering procedure. The UVB spectral shape fluctuates at 2.4 < z < 2.9 mostly due to radiative transfer processes in the clumpy IGM. At z < 1.8, the IGM becomes almost transparent both in the HI and HeII Lyman continua and the variability of the spectral shape comes from diversity of spectral indices describing the QSO/AGN intrinsic radiation. At z > 2.4, the recovered spectral shapes show intensity depression between 3 and 4 Ryd due to HeII Ly-alpha absorption in the IGM clouds (line blanketing) and continuous medium (true Gunn-Petersen effect). The mean HeII Ly-alpha opacity estimated from the depth of this depression corresponds within 1-2sigma to the values directly measured from the HI/HeII Ly-alpha forest towards the quasars studied. The observed scatter in eta = N(HeII)/N(HI) and anti-correlation between N(HI) and eta can be explained by the combined action of variable spectral softness and differences in the mean gas density between the absorbing clouds. Neither of the recovered spectral shapes show features which can be attributed to the putative input of radiation from soft sources like starburst galaxies.Comment: 20 pages, 20 figures. Accepted for publication in A&

Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb

This paper has been withdrawnComment: This paper has been withdraw

Manipulation of Fgf and Bmp signaling in teleost fishes suggests potential pathways for the evolutionary origin of multicuspid teeth

Teeth with two or more cusps have arisen independently from an ancestral unicuspid condition in a variety of vertebrate lineages, including sharks, teleost fishes, amphibians, lizards, and mammals. One potential explanation for the repeated origins of multicuspid teeth is the existence of multiple adaptive pathways leading to them, as suggested by their different uses in these lineages. Another is that the addition of cusps required only minor changes in genetic pathways regulating tooth development. Here we provide support for the latter hypothesis by demonstrating that manipulation of the levels of Fibroblast growth factor (Fgf) or Bone morphogenetic protein (Bmp) signaling produces bicuspid teeth in the zebrafish (Danio rerio), a species lacking multicuspid teeth in its ancestry. The generality of these results for teleosts is suggested by the conversion of unicuspid pharyngeal teeth into bicuspid teeth by similar manipulations of the Mexican Tetra (Astyanax mexicanus). That these manipulations also produced supernumerary teeth in both species supports previous suggestions of similarities in the molecular control of tooth and cusp number. We conclude that despite their apparent complexity, the evolutionary origin of multicuspid teeth is positively constrained, likely requiring only slight modifications of a pre-existing mechanism for patterning the number and spacing of individual teeth. © 2013 Wiley Periodicals, Inc

Dynamically Driven Evolution of the Interstellar Medium in M51

We report the highest-fidelity observations of the spiral galaxy M51 in CO emission, revealing the evolution of giant molecular clouds (GMCs) vis-a-vis the large-scale galactic structure and dynamics. The most massive GMCs (so-called GMAs) are first assembled and then broken up as the gas flow through the spiral arms. The GMAs and their H2 molecules are not fully dissociated into atomic gas as predicted in stellar feedback scenarios, but are fragmented into smaller GMCs upon leaving the spiral arms. The remnants of GMAs are detected as the chains of GMCs that emerge from the spiral arms into interarm regions. The kinematic shear within the spiral arms is sufficient to unbind the GMAs against self-gravity. We conclude that the evolution of GMCs is driven by large-scale galactic dynamics --their coagulation into GMAs is due to spiral arm streaming motions upon entering the arms, followed by fragmentation due to shear as they leave the arms on the downstream side. In M51, the majority of the gas remains molecular from arm entry through the inter-arm region and into the next spiral arm passage.Comment: 6 pages, including 3 figures. Accepted, ApJ

Drinking behaviour and alcohol-related harm amongst older adults: analysis of existing UK datasets.

Older adults experience age-related physiological changes that increase sensitivity and decrease tolerance to alcohol and there are a number of age-related harms such as falls, social isolation and elder abuse, which are compounded by alcohol misuse. Despite this unique vulnerability and the fact that the number of older adults is increasing, the literature on drinking behaviour and alcohol-related harm in older adults is sparse. This article describes a secondary analysis of UK data to address this knowledge gap

Predictors of and reasons for pacifier use in first-time mothers: an observational study

Background: The use of pacifiers is commonplace in Australia and has been shown to be negatively associated with breastfeeding duration. In order to influence behaviour related to the use of pacifiers it is important to understand the reasons for their use. The primary aim of this observational study was to investigate who (if anyone) advises first-time mothers to give a pacifier and the reasons for which they first give (or try to give) a pacifier to their infant. Additionally, this study investigated the predictors of pacifier use and the relationship between pacifier use and breastfeeding duration. Methods: In total, 670 Australian first-time mothers recruited as part of the NOURISH trial completed a questionnaire regarding infant feeding and pacifier use. Results: Pacifiers were introduced by 79% of mothers, of whom 28.7% were advised to use a pacifier by their mother/mother-in-law with a further 22.7% being advised by a midwife. The majority of mothers used a pacifier in order to soothe their infant (78.3%), to help put them to sleep (57.4%) and to keep them comforted and quiet (40.4%). Pacifiers given to infants before four weeks (adjHR 3.67; 95%CI 2.14–6.28) and used most days (adjHR 3.28; 95%CI 1.92–5.61) were significantly associated with shorter duration of breastfeeding. Conclusions: This study identifies an opportunity for educating new mothers and their support network, particularly their infant’s grandmothers, with regards to potential risks associated with the early and frequent use of a pacifier, and alternative methods for soothing their infant, in order to reduce the use of pacifiers and their potentially negative effect on breastfeeding duratio