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

Quantifying dimensions of physical behavior in chronic pain conditions.

BACKGROUND: Chronic pain, defined as persistent or recurrent pain lasting longer than 3 months, is a frequent condition affecting an important percent of population worldwide. Pain chronicity can be caused by many different factors and is a frequent component of many neurological disorders. An important aspect for clinical assessment and design of effective treatment and/or rehabilitation strategies is to better understand the impact of pain on domains of functioning in everyday life. The aim of this study was to identify the objectively quantifiable features of physical functioning in daily life and to evaluate their effectiveness to differentiate behavior among subjects with different pain conditions. METHOD: Body worn sensors were used to record movement data during five consecutive days in 92 subjects. Sensor data were processed to characterize the physical behavior in terms of type, intensity, duration and temporal pattern of activities, postures and movements performed by subjects in daily life. Metrics quantifying these features were subsequently used to devise composite scores using a factor analysis approach. The severity of clinical condition was assessed using a rating of usual pain intensity on a 10-cm visual analog scale. The relationship between pain intensity and the estimated metrics/composite scores was assessed using multiple regression and discriminant analysis. RESULTS: According to the factor analysis solution, two composite scores were identified, one integrating the metrics quantifying the amount and duration of activity periods, and the other the metrics quantifying complexity of temporal patterns, i.e., the diversity of body movements and activities, and the manner in which they are organized throughout time. All estimated metrics and composite scores were significantly different between groups of subjects with clinically different pain levels. Moreover, analysis revealed that pain intensity seemed to have a more significant impact on the overall physical behavior, as it was quantified by a global composite score, whereas the type of chronic pain appeared to influence mostly the complexity of the temporal pattern. CONCLUSION: The methodology described could be informative for the design of objective outcome measures in chronic pain management/rehabilitation programs