Causal conditioning and instantaneous coupling in causality graphs

The paper investigates the link between Granger causality graphs recently formalized by Eichler and directed information theory developed by Massey and Kramer. We particularly insist on the implication of two notions of causality that may occur in physical systems. It is well accepted that dynamical causality is assessed by the conditional transfer entropy, a measure appearing naturally as a part of directed information. Surprisingly the notion of instantaneous causality is often overlooked, even if it was clearly understood in early works. In the bivariate case, instantaneous coupling is measured adequately by the instantaneous information exchange, a measure that supplements the transfer entropy in the decomposition of directed information. In this paper, the focus is put on the multivariate case and conditional graph modeling issues. In this framework, we show that the decomposition of directed information into the sum of transfer entropy and information exchange does not hold anymore. Nevertheless, the discussion allows to put forward the two measures as pillars for the inference of causality graphs. We illustrate this on two synthetic examples which allow us to discuss not only the theoretical concepts, but also the practical estimation issues.Comment: submitte

Anisotropy Studies of the Unresolved Far-infrared Background

Dusty, starforming galaxies and active galactic nuclei that contribute to the integrated background intensity at far-infrared wavelengths trace the large-scale structure. Below the point source detection limit, correlations in the large-scale structure lead to clustered anisotropies in the unresolved component of the far-infrared background (FIRB). The angular power spectrum of the FIRB anisotropies could be measured in large-area surveys with the Spectral and Photometric Imaging Receiver (SPIRE) on the upcoming Herschel observatory. To study statistical properties of these anisotropies, the confusion from foreground Galactic dust emission needs to be reduced even in the ``cleanest'' regions of the sky.The multi-frequency coverage of SPIRE allows the foreground dust to be partly separated from the extragalactic background composed of dusty starforming galaxies as well as faint normal galaxies. The separation improves for fields with sizes greater than a few hundred square degrees and when combined with Planck data. We show that an area of about $\sim$ 400 degrees$^2$ observed for about 1000 hours with Herschel-SPIRE and complemented by Planck provides maximal information on the anisotropy power spectrum. We discuss the scientific studies that can be done with measurements of the unresolved FIRB anisotropies including a determination of the large scale bias and the small-scale halo occupation distribution of FIRB sources with fluxes below the point-source detection level.Comment: 10 pages, 8 figures, replaced to match the extended version, accepted by Ap

Lensing and Supernovae: Quantifying The Bias on the Dark Energy Equation of State

The gravitational magnification and demagnification of Type Ia supernovae (SNe) modify their positions on the Hubble diagram, shifting the distance estimates from the underlying luminosity-distance relation. This can introduce a systematic uncertainty in the dark energy equation of state (EOS) estimated from SNe, although this systematic is expected to average away for sufficiently large data sets. Using mock SN samples over the redshift range $0 < z \leq 1.7$ we quantify the lensing bias. We find that the bias on the dark energy EOS is less than half a percent for large datasets ($\gtrsim$ 2,000 SNe). However, if highly magnified events (SNe deviating by more than 2.5$\sigma$) are systematically removed from the analysis, the bias increases to $\sim$ 0.8%. Given that the EOS parameters measured from such a sample have a 1$\sigma$ uncertainty of 10%, the systematic bias related to lensing in SN data out to $z \sim 1.7$ can be safely ignored in future cosmological measurements.Comment: 5 pages, 4 figures; one figure and references added; minor modifications to text; reflects version accepted for publication in Ap

Structure of microbial communities in Sphagnum peatlands and effect of atmospheric carbon dioxide enrichment

Little is known about the structure of microbial communities in Sphagnum peatlands, and the potential effects of the increasing atmospheric C02 concentration on these communities are not known. We analyzed the structure of microbial communities in five Sphagnum-dominated peatlands across Europe and their response to C02 enrichment using miniFACE systems. After three growing seasons, Sphagnum samples were analyzed for heterotrophic bacteria, cyanobacteria, microalgae, heterotrophic flagellates, ciliates, testate amoebae, fungi, nematodes, and rotifers. Heterotrophic organisms dominated the microbial communities and together represented 78% to 97% of the total microbial biomass. Testate amoebae dominated the protozoan biomass. A canonical correspondence analysis revealed a significant correlation between the microbial community data and four environmental variables (Na+, DOC, water table depth, and DIN), reflecting continentality, hydrology, and nitrogen deposition gradients. Carbon dioxide enrichment modified the structure of microbial communities, but total microbial biomass was unaffected. The biomass of heterotrophic bacteria increased by 48%, and the biomass of testate amoebae decreased by 13%. These results contrast with the absence of overall effect on methane production or on the vegetation, but are in line with an increased below-ground vascular plant biomass at the same sites. We interpret the increase in bacterial biomass as a response to a C02-induced enhancement of Sphagnum exudation. The causes for the decrease of testate amoebae are unclear but could indicate a top-down rather than a bottom-up control on their densit

Submillimetre galaxies reside in dark matter haloes with masses greater than 3 × 10^(11) solar masses

The extragalactic background light at far-infrared wavelengths comes from optically faint, dusty, star-forming galaxies in the Universe with star formation rates of a few hundred solar masses per year. These faint, submillimetre galaxies are challenging to study individually because of the relatively poor spatial resolution of far-infrared telescopes. Instead, their average properties can be studied using statistics such as the angular power spectrum of the background intensity variations. A previous attempt at measuring this power spectrum resulted in the suggestion that the clustering amplitude is below the level computed with a simple ansatz based on a halo model. Here we report excess clustering over the linear prediction at arcminute angular scales in the power spectrum of brightness fluctuations at 250, 350 and 500 µm. From this excess, we find that submillimetre galaxies are located in darkmatter haloes with a minimum mass, M_(min), such that log_(10)[M_(min)/M_⊙] = 11.5^(+0.7)_(-0.2) at 350 µm, where M_⊙ is the solar mass. This minimum dark matter halo mass corresponds to the most efficient mass scale for star formation in the Universe, and is lower than that predicted by semi-analytical models for galaxy formation