The characteristic Cauchy problem for Dirac fields on curved backgrounds

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in $L^2$ and we give an explicit definition of the space of data on the light-cone producing a solution in $H^1$. The method is based on energy estimates following L. H\"ormander (J.F.A. 1990). The data for the characteristic Cauchy problem are only a half of the field, the other half is recovered from the characteristic data by integration of the constraints, consisting of the restriction of the Dirac equation to the cone. A precise analysis of the dynamics of light rays near the vertex of the cone is done in order to understand the integrability of the constraints; for this, the Geroch-Held-Penrose formalism is used.Comment: 39 pages. An error in lemma 3.1 in the first version has been corrected. Moreover, the treatment of the constraints (restriction of the equations to the null cone) has been considerably extended and is now given in full details. To appear in Journal of Hyperbolic Differential Equation

Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

We describe an expansion of the solution of the wave equation in the De Sitter - Schwarzschild metric in terms of resonances. The main term in the expansion is due to a zero resonance. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an small derivative loss in the angular directions.Comment: 22 pages, 5 figure

Tyrosine phosphatase PTPN11/SHP2 in solid tumors - bull’s eye for targeted therapy?

Encoded by PTPN11, the Src-homology 2 domain-containing phosphatase 2 (SHP2) integrates signals from various membrane-bound receptors such as receptor tyrosine kinases (RTKs), cytokine and integrin receptors and thereby promotes cell survival and proliferation. Activating mutations in the PTPN11 gene may trigger signaling pathways leading to the development of hematological malignancies, but are rarely found in solid tumors. Yet, aberrant SHP2 expression or activation has implications in the development, progression and metastasis of many solid tumor entities. SHP2 is involved in multiple signaling cascades, including the RAS-RAF-MEK-ERK-, PI3K-AKT-, JAK-STAT- and PD-L1/PD-1- pathways. Although not mutated, activation or functional requirement of SHP2 appears to play a relevant and context-dependent dichotomous role. This mostly tumor-promoting and infrequently tumor-suppressive role exists in many cancers such as gastrointestinal tumors, pancreatic, liver and lung cancer, gynecological entities, head and neck cancers, prostate cancer, glioblastoma and melanoma. Recent studies have identified SHP2 as a potential biomarker for the prognosis of some solid tumors. Based on promising preclinical work and the advent of orally available allosteric SHP2-inhibitors early clinical trials are currently investigating SHP2-directed approaches in various solid tumors, either as a single agent or in combination regimes. We here provide a brief overview of the molecular functions of SHP2 and collate current knowledge with regard to the significance of SHP2 expression and function in different solid tumor entities, including cells in their microenvironment, immune escape and therapy resistance. In the context of the present landscape of clinical trials with allosteric SHP2-inhibitors we discuss the multitude of opportunities but also limitations of a strategy targeting this non-receptor protein tyrosine phosphatase for treatment of solid tumors

From tropical shelters to temperate defaunation: the relationship between agricultural transition stage and the distribution of threatened mammals

Aim Agriculture is a key threat to biodiversity, however its relationship with biodiversity patterns is understudied. Here, we evaluate how the extent, intensity, and history of croplands relate to the global distribution of threatened mammals. We propose two hypotheses to explain these relationships: shelter, which predicts that threatened species concentrate in areas with low human land use; and threat, according to which threatened species should concentrate in areas of high human land use. Location Global. Time period c.B.C.6000 - 2014. Major taxa studied Terrestrial mammals. Methods We used boosted regression trees (BRT) that include spatial autocorrelation to investigate the relationship between the proportion of threatened terrestrial mammals (as defined by the IUCN Red List) and multiple metrics describing agricultural extent, intensity and history derived from remote sensing data and statistical projections. Data were analysed with a grain size of ~110 x 110 km at both global and biogeographic-realm scales. Results Agricultural extent and intensity were the most relevant indicator types, with specific metrics important for each realm. Forest cover (extent) was identified as important in several regions. Tropical regions in early agricultural transition stages (e.g., frontier landscapes) were consistent with the shelter hypothesis, whereas patterns found for regions in later stages (e.g., intensified agricultural landscapes) were mostly found in temperate regions and agreed with the threat hypothesis. Main conclusions These results highlight the need to consider multiple land-use indicators when addressing threats to biodiversity and to separately assess areas with divergent human and ecological histories in global-scale studies. Different relationships associated with different agricultural transition stages suggest that high concentrations of threatened species may have contrasting meanings in different regions worldwide. We propose a new unifying hypothesis following a cyclic relationship along agricultural transition stages resulting in alternating negative and positive relationships between agriculture and threatened species richness

Proliferation of Acid-Secretory Cells in the Kidney during Adaptive Remodelling of the Collecting Duct

The renal collecting duct adapts to changes in acid-base metabolism by remodelling and altering the relative number of acid or alkali secreting cells, a phenomenon termed plasticity. Acid secretory A intercalated cells (A-IC) express apical H+-ATPases and basolateral bicarbonate exchanger AE1 whereas bicarbonate secretory B intercalated cells (B-IC) express basolateral (and apical) H+-ATPases and the apical bicarbonate exchanger pendrin. Intercalated cells were thought to be terminally differentiated and unable to proliferate. However, a recent report in mouse kidney suggested that intercalated cells may proliferate and that this process is in part dependent on GDF-15. Here we extend these observations to rat kidney and provide a detailed analysis of regional differences and demonstrate that differentiated A-IC proliferate massively during adaptation to systemic acidosis. We used markers of proliferation (PCNA, Ki67, BrdU incorporation) and cell-specific markers for A-IC (AE1) and B-IC (pendrin). Induction of remodelling in rats with metabolic acidosis (with NH4Cl for 12 hrs, 4 and 7 days) or treatment with acetazolamide for 10 days resulted in a larger fraction of AE1 positive cells in the cortical collecting duct. A large number of AE1 expressing A-IC was labelled with proliferative markers in the cortical and outer medullary collecting duct whereas no labeling was found in B-IC. In addition, chronic acidosis also increased the rate of proliferation of principal collecting duct cells. The fact that both NH4Cl as well as acetazolamide stimulated proliferation suggests that systemic but not urinary pH triggers this response. Thus, during chronic acidosis proliferation of AE1 containing acid-secretory cells occurs and may contribute to the remodelling of the collecting duct or replace A-IC due to a shortened life span under these conditions