Global well-posedness and scattering for the defocusing energy-critical nonlinear Schr\"odinger equation in R1+4\R^{1+4}

We obtain global well-posedness, scattering, uniform regularity, and global $L^6_{t,x}$ spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schr\"odinger equation in $\R\times\R^4$. Our arguments closely follow those of Colliander-Keel-Staffilani-Takaoka-Tao, though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the $L^6_{t,x}$-norm

The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+5}

In this work, we consider the energy-supercritical defocusing cubic nonlinear wave equation in dimension d=5 for radially symmetric initial data. We prove that an a priori bound in the critical space implies global well-posedness and scattering. The main tool that we use is a frequency localized version of the classical Morawetz inequality, inspired by recent developments in the study of the mass and energy critical nonlinear Schr\"odinger equation.Comment: AMS Latex, 20 page

Smart City: Concepts and two Relevant Components

In the last 30 years, the Smart City (SC) definitions have changed, they expressed different meanings by different people, but still no universally accepted definition, yet. The paper aims to summarize the existing relevant definitions to and propose a concept for characterizing the smartness of a city through intelligent planning and monitoring, guided by actionable information that underpins computer-assisted decisions and institutional digital transformation. As a practical approach, the SC concept is promoted by two components namely: spatial urban territorial planning and cultural heritage via virtual exhibitions. The article highlights the schematic diagram of cross-sectoral interactions between different stakeholders grouped by roles, and the expected impact for these interactions, a proposed functional system architecture for cultural heritage digital transformation and concrete steps for virtual exhibitions implementation

Protection of outbred mice against a vaginal challenge by a Chlamydia trachomatis serovar E recombinant major outer membrane protein vaccine is dependent on phosphate substitution in the adjuvant.

Chlamydia trachomatis is the most common bacterial sexually-transmitted pathogen for which there is no vaccine. We previously demonstrated that the degree of phosphate substitution in an aluminum hydroxide adjuvant in a TLR-4-based C. trachomatis serovar E (Ser E) recombinant major outer membrane protein (rMOMP) formulation had an impact on the induced antibody titers and IFN-γ levels. Here, we have extended these observations using outbreed CD-1 mice immunized with C. trachomatis Ser E rMOMP formulations to evaluate the impact on bacterial challenge. The results confirmed that the rMOMP vaccine containing the adjuvant with the highest phosphate substitution induced the highest neutralizing antibody titers while the formulation with the lowest phosphate substitution induced the highest IFN-γ production. The most robust protection was observed in mice vaccinated with the formulation containing the adjuvant with the lowest phosphate substitution, as shown by the number of mice with positive vaginal cultures, number of positive cultures and number of C. trachomatis inclusion forming units recovered. This is the first report showing that vaccination of an outbred strain of mice with rMOMP induces protection against a vaginal challenge with C. trachomatis

Outcomes following aortic valve procedures in 201 complex congenital heart disease cases:results from the UK National Audit

OBJECTIVES: Some patients with complex congenital heart disease (cCHD) also require aortic valve (AoV) procedures. These cases are considered high risk but their outcome has not been well characterized. We aim to describe these scenarios in the current practice, and provide outcome data for counselling and decision-making. METHODS: This was a retrospective study using the UK National Congenital Heart Disease Audit data on cCHD patients undergoing aortic valve replacement, balloon dilation (balloon aortic valvuloplasty) or surgical repair (surgical aortic valve repair) between 2000 and 2012. Coarsened exact matching was used to pair cCHD with patients undergoing AoV procedures for isolated valve disease. RESULTS: A total of 201 patients with a varied spectrum of cCHD undergoing 242 procedures were included, median age 9.4 years (1 day–65 years). Procedure types were: balloon aortic valvuloplasty (n = 31, 13%), surgical aortic valve repair (n = 57, 24%) and aortic valve replacement (n = 154, 63%). Mortality at 30 days was higher in neonates (21.8% vs 5.3%, P = 0.02). Survival at 10 years was 83.1%, freedom from aortic valve replacement 83.8% and freedom from balloon aortic valvuloplasty/surgical aortic valve repair 86.3%. Neonatal age (P < 0.001), single ventricle (P = 0.08), concomitant Fontan/Glenn (P = 0.002) or aortic arch procedures (0.02) were associated with higher mortality. cCHD patients had lower survival at 30 days (93% vs 100%, P = 0.003) and at 10 years (86.4% vs 96.1%, P = 0.005) compared to matched isolated AoV disease patients. CONCLUSIONS: AoV procedures in cCHD can be performed with good results outside infancy, but with higher mortality than in isolated AoV disease. Neonates and patients with single ventricle defects, especially those undergoing concomitant Fontan/Glenn, have worse outcomes