Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background (CMB) data, such as the imprint of topological defects, in particular cosmic strings, and for their reconstruction after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for publication in MNRAS. Version 3 (identical to version 2) posted for code release announcement - "Steerable scale discretised wavelets on the sphere" - S2DW code available for download at http://www.mrao.cam.ac.uk/~jdm57/software.htm

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Cellular metabolism constrains innate immune responses in early human ontogeny

Pathogen immune responses are profoundly attenuated in fetuses and premature infants, yet the mechanisms underlying this developmental immaturity remain unclear. Here we show transcriptomic, metabolic and polysome profiling and find that monocytes isolated from infants born early in gestation display perturbations in PPAR-γ-regulated metabolic pathways, limited glycolytic capacity and reduced ribosomal activity. These metabolic changes are linked to a lack of translation of most cytokines and of MALT1 signalosome genes essential to respond to the neonatal pathogen Candida. In contrast, they have little impact on house-keeping phagocytosis functions. Transcriptome analyses further indicate a role for mTOR and its putative negative regulator DNA Damage Inducible Transcript 4-Like in regulating these metabolic constraints. Our results provide a molecular basis for the broad susceptibility to multiple pathogens in these infants, and suggest that the fetal immune system is metabolically programmed to avoid energetically costly, dispensable and potentially harmful immune responses during ontogeny

Multi-scale modeling of the evolution of the transport properties of cement pastes subject to leaching and carbonation

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