Spacelike hypersurfaces in standard static spacetimes

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic angle or bounded height is maximal. Our conclusions follow from general mean curvature estimates for spacelike hypersurfaces. In case where the spacetime is a Lorentzian product with spatial factor of nonnegative Ricci curvature and sectional curvatures bounded below, we also show that a complete maximal hypersurface not intersecting a spacelike slice is itself a slice. This result is obtained from a gradient estimate for parametric maximal hypersurfaces.Comment: 50 page

Rigidity results for complete spacelike submanifolds in plane fronted waves

New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is contained in a characteristic lightlike hypersurface. Moreover, for a complete codimension two extremal submanifold in a plane fronted wave we show sufficient conditions to guarantee that it is a (totally geodesic) wavefront.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBU

Completeness of uniformly accelerated observers in Galilean spacetimes

We analyze the concept of uniformly accelerated observer in Galilean spacetimes in the context of Newton–Cartan theory and find natural geometric assumptions to ensure that an inextensible uniformly accelerated observer in a Galilean spacetime does not disappear in a finite proper time

Development of an activity disease score in patients with uveitis (UVEDAI)

To develop a disease activity index for patients with uveitis (UVEDAI) encompassing the relevant domains of disease activity considered important among experts in this field. The steps for designing UVEDAI were: (a) Defining the construct and establishing the domains through a formal judgment of experts, (b) A two-round Delphi study with a panel of 15 experts to determine the relevant items, (c) Selection of items: A logistic regression model was developed that set ocular inflammatory activity as the dependent variable. The construct "uveitis inflammatory activity" was defined as any intraocular inflammation that included external structures (cornea) in addition to uvea. Seven domains and 15 items were identified: best-corrected visual acuity, inflammation of the anterior chamber (anterior chamber cells, hypopyon, the presence of fibrin, active posterior keratic precipitates and iris nodules), intraocular pressure, inflammation of the vitreous cavity (vitreous haze, snowballs and snowbanks), central macular edema, inflammation of the posterior pole (the presence and number of choroidal/retinal lesions, vascular inflammation and papillitis), and global assessment from both (patient and physician). From all the variables studied in the multivariate model, anterior chamber cell grade, vitreous haze, central macular edema, inflammatory vessel sheathing, papillitis, choroidal/retinal lesions and patient evaluation were included in UVEDAI. UVEDAI is an index designed to assess the global ocular inflammatory activity in patients with uveitis. It might prove worthwhile to motorize the activity of this extraarticular manifestation of some rheumatic diseases

Positively selected amino acid replacements within the RuBisCO enzyme of oak trees are associated with ecological adaptations

Phylogenetic analysis by maximum likelihood (PAML) has become the standard approach to study positive selection at the molecular level, but other methods may provide complementary ways to identify amino acid replacements associated with particular conditions. Here, we compare results of the decision tree (DT) model method with ones of PAML using the key photosynthetic enzyme RuBisCO as a model system to study molecular adaptation to particular ecological conditions in oaks (Quercus). We sequenced the chloroplast rbcL gene encoding RuBisCO large subunit in 158 Quercus species, covering about a third of the global genus diversity. It has been hypothesized that RuBisCO has evolved differentially depending on the environmental conditions and leaf traits governing internal gas diffusion patterns. Here, we show, using PAML, that amino acid replacements at the residue positions 95, 145, 251, 262 and 328 of the RuBisCO large subunit have been the subject of positive selection along particular Quercus lineages associated with the leaf traits and climate characteristics. In parallel, the DT model identified amino acid replacements at sites 95, 219, 262 and 328 being associated with the leaf traits and climate characteristics, exhibiting partial overlap with the results obtained using PAML

Stable maximal hypersurfaces in Lorentzian spacetimes

We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on the geometry of the ambient spacetime (e.g., the validity of TCC) to ensure stability. Some rigidity results and height estimates are also proven in GRW spacetimes. In the last part of the paper we consider k-stability of spacelike hypersurfaces, a concept related to mean curvatures of higher orders