Equivalence after extension for compact operators on Banach spaces

In recent years the coincidence of the operator relations equivalence after extension and Schur coupling was settled for the Hilbert space case, by showing that equivalence after extension implies equivalence after one-sided extension. In this paper we investigate consequences of equivalence after extension for compact Banach space operators. We show that generating the same operator ideal is necessary but not sufficient for two compact operators to be equivalent after extension. In analogy with the necessary and sufficient conditions on the singular values for compact Hilbert space operators that are equivalent after extension, we prove the necessity of similar relationships between the $s$-numbers of two compact Banach space operators that are equivalent after extension, for arbitrary $s$-functions. We investigate equivalence after extension for operators on $\ell^{p}$-spaces. We show that two operators that act on different $\ell^{p}$-spaces cannot be equivalent after one-sided extension. Such operators can still be equivalent after extension, for instance all invertible operators are equivalent after extension, however, if one of the two operators is compact, then they cannot be equivalent after extension. This contrasts the Hilbert space case where equivalence after one-sided extension and equivalence after extension are, in fact, identical relations. Finally, for general Banach spaces $X$ and $Y$, we investigate consequences of an operator on $X$ being equivalent after extension to a compact operator on $Y$. We show that, in this case, a closed finite codimensional subspace of $Y$ must embed into $X$, and that certain general Banach space properties must transfer from $X$ to $Y$. We also show that no operator on $X$ can be equivalent after extension to an operator on $Y$, if $X$ and $Y$ are essentially incomparable Banach spaces

Sea anemone model has a single Toll-like receptor that can function in pathogen detection, NF-κB signal transduction, and development

In organisms from insects to vertebrates, Toll-like receptors (TLRs) are primary pathogen detectors that activate downstream pathways, specifically those that direct expression of innate immune effector genes. TLRs also have roles in development in many species. The sea anemone Nematostella vectensis is a useful cnidarian model to study the origins of TLR signaling because its genome encodes a single TLR and homologs of many downstream signaling components, including the NF-κB pathway. We have characterized the single N. vectensis TLR (Nv-TLR) and demonstrated that it can activate canonical NF-κB signaling in human cells. Furthermore, we show that the intracellular Toll/IL-1 receptor (TIR) domain of Nv-TLR can interact with the human TLR adapter proteins MAL and MYD88. We demonstrate that the coral pathogen Vibrio coralliilyticus causes a rapidly lethal disease in N. vectensis and that heat-inactivated V. coralliilyticus and bacterial flagellin can activate a reconstituted Nv-TLR–to–NF-κB pathway in human cells. By immunostaining of anemones, we show that Nv-TLR is expressed in a subset of cnidocytes and that many of these Nv-TLR–expressing cells also express Nv-NF-κB. Additionally, the nematosome, which is a Nematostella-specific multicellular structure, expresses Nv-TLR and many innate immune pathway homologs and can engulf V. coralliilyticus. Morpholino knockdown indicates that Nv-TLR also has an essential role during early embryonic development. Our characterization of this primitive TLR and identification of a bacterial pathogen for N. vectensis reveal ancient TLR functions and provide a model for studying the molecular basis of cnidarian disease and immunity.IOS-1354935 - National Science Foundation (NSF); GRFP - National Science Foundation (NSF); GRFP - National Science Foundation (NSF); 1262934 - National Science Foundation (NSF); 2014-BSP - Arnold and Mabel Beckman Foundatio

Atmospheric greenhouse gases retrieved from SCIAMACHY: comparison to ground-based FTS measurements and model results

SCIAMACHY onboard ENVISAT (launched in 2002) enables the retrieval of global long-term column-averaged dry air mole fractions of the two most important anthropogenic greenhouse gases carbon dioxide and methane (denoted XCO_2 and XCH_4). In order to assess the quality of the greenhouse gas data obtained with the recently introduced v2 of the scientific retrieval algorithm WFM-DOAS, we present validations with ground-based Fourier Transform Spectrometer (FTS) measurements and comparisons with model results at eight Total Carbon Column Observing Network (TCCON) sites providing realistic error estimates of the satellite data. Such validation is a prerequisite to assess the suitability of data sets for their use in inverse modelling. It is shown that there are generally no significant differences between the carbon dioxide annual increases of SCIAMACHY and the assimilation system CarbonTracker (2.00 ± 0.16 ppm yr^(−1) compared to 1.94 ± 0.03 ppm yr−1 on global average). The XCO_2 seasonal cycle amplitudes derived from SCIAMACHY are typically larger than those from TCCON which are in turn larger than those from CarbonTracker. The absolute values of the northern hemispheric TCCON seasonal cycle amplitudes are closer to SCIAMACHY than to CarbonTracker and the corresponding differences are not significant when compared with SCIAMACHY, whereas they can be significant for a subset of the analysed TCCON sites when compared with CarbonTracker. At Darwin we find discrepancies of the seasonal cycle derived from SCIAMACHY compared to the other data sets which can probably be ascribed to occurrences of undetected thin clouds. Based on the comparison with the reference data, we conclude that the carbon dioxide data set can be characterised by a regional relative precision (mean standard deviation of the differences) of about 2.2 ppm and a relative accuracy (standard deviation of the mean differences) of 1.1–1.2 ppm for monthly average composites within a radius of 500 km. For methane, prior to November 2005, the regional relative precision amounts to 12 ppb and the relative accuracy is about 3 ppb for monthly composite averages within the same radius. The loss of some spectral detector pixels results in a degradation of performance thereafter in the spectral range currently used for the methane column retrieval. This leads to larger scatter and lower XCH_4 values are retrieved in the tropics for the subsequent time period degrading the relative accuracy. As a result, the overall relative precision is estimated to be 17 ppb and the relative accuracy is in the range of about 10–20 ppb for monthly averages within a radius of 500 km. The derived estimates show that the SCIAMACHY XCH_4 data set before November 2005 is suitable for regional source/sink determination and regional-scale flux uncertainty reduction via inverse modelling worldwide. In addition, the XCO2 monthly data potentially provide valuable information in continental regions, where there is sparse sampling by surface flask measurements

Calibration of TCCON column-averaged CO2: the first aircraft campaign over European TCCON sites

The Total Carbon Column Observing Network (TCCON) is a ground-based network of Fourier Transform Spectrometer (FTS) sites around the globe, where the column abundances of CO2, CH4, N2O, CO and O2 are measured. CO2 is constrained with a precision better than 0.25% (1-σ). To achieve a similarly high accuracy, calibration to World Meteorological Organization (WMO) standards is required. This paper introduces the first aircraft calibration campaign of five European TCCON sites and a mobile FTS instrument. A series of WMO standards in-situ profiles were obtained over European TCCON sites via aircraft and compared with retrievals of CO2 column amounts from the TCCON instruments. The results of the campaign show that the FTS measurements are consistently biased 1.1% ± 0.2% low with respect to WMO standards, in agreement with previous TCCON calibration campaigns. The standard a priori profile for the TCCON FTS retrievals is shown to not add a bias. The same calibration factor is generated using aircraft profiles as a priori and with the TCCON standard a priori. With a calibration to WMO standards, the highly precise TCCON CO2 measurements of total column concentrations provide a suitable database for the calibration and validation of nadir-viewing satellite