Two-point function for the Maxwell field in flat Robertson-Walker spacetimes

We obtain an explicit two-point function for the Maxwell field in flat Roberson-Walker spaces, thanks to a new gauge condition which takes the scale factor into account and assume a simple form. The two-point function is found to have the short distance Hadamard behavior.Comment: 4 pages, Revte

Massive scalar field on (A)dS space from a massless conformal field in R6\mathbb{R}^6

We show how the equations for the scalar field (including the massive, massless, minimally and conformally coupled cases) on de Sitter and Anti-de Sitter spaces can be obtained from both the SO$(2,4)$-invariant equation $\square \phi = 0$ in $\mathbb{R}^6$ and two geometrical constraints defining the (A)dS space. Apart from the equation in $\mathbb{R}^6$, the results only follow from the geometry.Comment: Revtex 4.1, 6 pages. In v3: New material added (references, relation with mass ladder operator), accepted in JM

Maximizing the Strength of Fused-Deposition ABS Plastic Parts

Fused-Deposition (FD) creates parts using robotic extrusion of set.D.i-liquid .polymer fiber, which molecularly bonds with neighboring fibers via thermal-dlffuslo.n bonding. T~e strength ofthe. part depends on the bulk polymer strength, themesostructure ~flber layout, vOid geom~try, extent of fiber bonding), and thefiber-t~-fiber ~ond strength. The ~nfluence of these factors on the mechanical strength of FD-ABS.plasttc parts IS reported.along with the.FD process variable settingsfor maximum strength. Substantial increases in transverse strength are achieved at the optirnal settings and additional increases can be achieved by post..fabrication annealing. Keywords: Stratasys, fused-deposition, ABSplastic, functional parts, strength, mesostructure, polymer diffusion.Mechanical Engineerin

Permutation Inference for Canonical Correlation Analysis

Canonical correlation analysis (CCA) has become a key tool for population neuroimaging, allowing investigation of associations between many imaging and non-imaging measurements. As other variables are often a source of variability not of direct interest, previous work has used CCA on residuals from a model that removes these effects, then proceeded directly to permutation inference. We show that such a simple permutation test leads to inflated error rates. The reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption. Even in the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. The reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables. Here we propose solutions for both problems: in the case of nuisance variables, we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test; for more general cases, with or without nuisance variables, we propose estimating the canonical correlations in a stepwise manner, removing at each iteration the variance already explained, while dealing with different number of variables in both sides. We also discuss how to address the multiplicity of tests, proposing an admissible test that is not conservative, and provide a complete algorithm for permutation inference for CCA.Comment: 49 pages, 2 figures, 10 tables, 3 algorithms, 119 reference

Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval

We present a quantization scheme of an arbitrary measure space based on overcomplete families of states and generalizing the Klauder and the Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods like geometric quantization are uneasy to implement. The procedure is illustrated by (mostly two-dimensional) elementary examples in which the measure space is a $N$-element set and the unit interval. Spaces of states for the $N$-element set and the unit interval are the 2-dimensional euclidean $\R^2$ and hermitian \C^2 planes

Modelling CO emission from hydrodynamic simulations of nearby spirals, starbursting mergers, and high-redshift galaxies

We model the intensity of emission lines from the CO molecule, based on hydrodynamic simulations of spirals, mergers, and high-redshift galaxies with very high resolutions (3pc and 10^3 Msun) and detailed models for the phase-space structure of the interstellar gas including shock heating, stellar feedback processes and galactic winds. The simulations are analyzed with a Large Velocity Gradient (LVG) model to compute the local emission in various molecular lines in each resolution element, radiation transfer and opacity effects, and the intensity emerging from galaxies, to generate synthetic spectra for various transitions of the CO molecule. This model reproduces the known properties of CO spectra and CO-to-H2 conversion factors in nearby spirals and starbursting major mergers. The high excitation of CO lines in mergers is dominated by an excess of high-density gas, and the high turbulent velocities and compression that create this dense gas excess result in broad linewidths and low CO intensity-to-H2 mass ratios. When applied to high-redshift gas-rich disks galaxies, the same model predicts that their CO-to-H2 conversion factor is almost as high as in nearby spirals, and much higher than in starbursting mergers. High-redshift disk galaxies contain giant star-forming clumps that host a high-excitation component associated to gas warmed by the spatially-concentrated stellar feedback sources, although CO(1-0) to CO(3-2) emission is overall dominated by low-excitation gas around the densest clumps. These results overall highlight a strong dependence of CO excitation and the CO-to-H2 conversion factor on galaxy type, even at similar star formation rates or densities. The underlying processes are driven by the interstellar medium structure and turbulence and its response to stellar feedback, which depend on global galaxy structure and in turn impact the CO emission properties.Comment: A&A in pres