The energy-critical defocusing NLS on T^3

We prove global well-posedness in H^1(T^3) for the energy-critical defocusing NLS.Comment: 24 page

On Hawking's Local Rigidity Theorems for Charged Black Holes

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, R\'{a}cz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symmetry plays a fundamental role in the classification theory of stationary black holes.Comment: 20 page

Improving the Reliability of Decision-Support Systems for Nuclear Emergency Management by Leveraging Software Design Diversity

This paper introduces a novel method of continuous verification of simulation software used in decision-support systems for nuclear emergency management (DSNE). The proposed approach builds on methods from the field of software reliability engineering, such as N-Version Programming, Recovery Blocks, and Consensus Recovery Blocks. We introduce a new acceptance test for dispersion simulation results and a new voting scheme based on taxonomies of simulation results rather than individual simulation results. The acceptance test and the voter are used in a new scheme, which extends the Consensus Recovery Block method by a database of result taxonomies to support machine-learning. This enables the system to learn how to distinguish correct from incorrect results, with respect to the implemented numerical schemes. Considering that decision-support systems for nuclear emergency management are used in a safety-critical application context, the methods introduced in this paper help improve the reliability of the system and the trustworthiness of the simulation results used by emergency managers in the decision making process. The effectiveness of the approach has been assessed using the atmospheric dispersion forecasts of two test versions of the widely used RODOS DSNE system

GATA6 Is a Crucial Regulator of Shh in the Limb Bud

In the limb bud, patterning along the anterior-posterior (A-P) axis is controlled by Sonic Hedgehog (Shh), a signaling molecule secreted by the “Zone of Polarizing Activity”, an organizer tissue located in the posterior margin of the limb bud. We have found that the transcription factors GATA4 and GATA6, which are key regulators of cell identity, are expressed in an anterior to posterior gradient in the early limb bud, raising the possibility that GATA transcription factors may play an additional role in patterning this tissue. While both GATA4 and GATA6 are expressed in an A-P gradient in the forelimb buds, the hindlimb buds principally express GATA6 in an A-P gradient. Thus, to specifically examine the role of GATA6 in limb patterning we generated Prx1-Cre; GATA6fl/fl mice, which conditionally delete GATA6 from their developing limb buds. We found that these animals display ectopic expression of both Shh and its transcriptional targets specifically in the anterior mesenchyme of the hindlimb buds. Loss of GATA6 in the developing limbs results in the formation of preaxial polydactyly in the hindlimbs. Conversely, forced expression of GATA6 throughout the limb bud represses expression of Shh and results in hypomorphic limbs. We have found that GATA6 can bind to chromatin (isolated from limb buds) encoding either Shh or Gli1 regulatory elements that drive expression of these genes in this tissue, and demonstrated that GATA6 works synergistically with FOG co-factors to repress expression of luciferase reporters driven by these sequences. Most significantly, we have found that conditional loss of Shh in limb buds lacking GATA6 prevents development of hindlimb polydactyly in these compound mutant embryos, indicating that GATA6 expression in the anterior region of the limb bud blocks hindlimb polydactyly by repressing ectopic expression of Shh

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Preliminary Investigation of Experimental Research on Savory (Satureja hortensis L.) In Vitro Modeling Possibility Using the Calogenesis Technique

Investigating the possibilities for in vitro plant modeling by using the calogenesis technique is one of the ways to exploit cell plasticity – the vegetable type, which plant biotechnology now offers an alternative for obtaining biomass as a source of raw material in various industries. One of the known plants cultivated by humans since ancient time, and recognized in the contemporary period as a dedicated source of plant material for different industries, because it has properties that recommend its use in food, medicine and beekeeping, is savory (Satureja hortensis L.). Our preliminary experimental research aimed at investigating the possibility of in vitro modeling of savory (Satureja hortensis L.) by using the calogenesis technique. This paper presents the experimental results which have been achieved by investigating the possibility of practical achievement, both by establishing aseptic cultures using savory (Satureja hortensis L.) seeds, and also by in vitro modeling of savory (Satureja hortensis L.) explants, considering the leaf, cotyledon, epicotyl, hypocotyl and radicle, in under to obtain callus by the influence of exogenous phytohormones (BA, TDZ and 2,4-D)