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

Notice and the Deeds Out Problem

When a grantor conveys land which has been subjected to easements or equitable servitudes in favor. of adjacent land previously conveyed by the grantor, there arises the serious question whether such interests are enforceable if the purchaser has not expressly taken the land subject to them. A cursory inspection of primary and secondary authority on the subject of easements and equitable servitudes would indicate that the answer depends upon whether, at the time of the sale, the purchaser of the servient estate has notice of the burden to which his land is allegedly subjected. It is the purpose of this article to determine the significance of notice in these circumstances and to ascertain when the foregoing test should be applied

Detection of high-energy X-ray flare from a source in Crux

Balloonborne X ray telescopic observation of point source in Cru

A Strong Szego Theorem for Jacobi Matrices

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szego theorem for Jacobi matrices on $l^2(\N)$. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that $\sum_{k=n}^\infty b_k$ and $\sum_{k=n}^\infty (a_k^2 - 1)$ lie in $l^2_1$, the linearly-weighted $l^2$ space.Comment: 26 page

Continual variations in the high energy X-ray flux from Sco X-1

Balloon X ray observations of intensity fluctuations in Sco X-

Initial Metabolic Profiles Are Associated with 7-Day Survival among Infants Born at 22-25 Weeks of Gestation.

OBJECTIVE:To evaluate the association between early metabolic profiles combined with infant characteristics and survival past 7 days of age in infants born at 22-25 weeks of gestation. STUDY DESIGN:This nested case-control consisted of 465 singleton live births in California from 2005 to 2011 at 22-25 weeks of gestation. All infants had newborn metabolic screening data available. Data included linked birth certificate and mother and infant hospital discharge records. Mortality was derived from linked death certificates and death discharge information. Each death within 7 days was matched to 4 surviving controls by gestational age and birth weight z score category, leaving 93 cases and 372 controls. The association between explanatory variables and 7-day survival was modeled via stepwise logistic regression. Infant characteristics, 42 metabolites, and 12 metabolite ratios were considered for model inclusion. Model performance was assessed via area under the curve. RESULTS:The final model included 1 characteristic and 11 metabolites. The model demonstrated a strong association between metabolic patterns and infant survival (area under the curve [AUC] 0.885, 95% CI 0.851-0.920). Furthermore, a model with just the selected metabolites performed better (AUC 0.879, 95% CI 0.841-0.916) than a model with multiple clinical characteristics (AUC 0.685, 95% CI 0.627-0.742). CONCLUSIONS:Use of metabolomics significantly strengthens the association with 7-day survival in infants born extremely premature. Physicians may be able to use metabolic profiles at birth to refine mortality risks and inform postnatal counseling for infants born at <26 weeks of gestation

Socioeconomic Mediators of Racial and Ethnic Disparities in Congenital Heart Disease Outcomes: A Population-Based Study in California.

Background Racial/ethnic and socioeconomic disparities exist in outcomes for children with congenital heart disease. We sought to determine the influence of race/ethnicity and mediating socioeconomic factors on 1-year outcomes for live-born infants with hypoplastic left heart syndrome and dextro-Transposition of the great arteries. Methods and Results The authors performed a population-based cohort study using the California Office of Statewide Health Planning and Development database. Live-born infants without chromosomal anomalies were included. The outcome was a composite measure of mortality or unexpected hospital readmissions within the first year of life defined as >3 (hypoplastic left heart syndrome) or >1 readmissions (dextro-Transposition of the great arteries). Hispanic ethnicity was compared with non-Hispanic white ethnicity. Mediation analyses determined the percent contribution to outcome for each mediator on the pathway between race/ethnicity and outcome. A total of 1796 patients comprised the cohort (n=964 [hypoplastic left heart syndrome], n=832 [dextro-Transposition of the great arteries]) and 1315 were included in the analysis (n=477 non-Hispanic white, n=838 Hispanic). Hispanic ethnicity was associated with a poor outcome (crude odds ratio, 1.72; 95% confidence interval [CI], 1.37-2.17). Higher maternal education (crude odds ratio 0.5; 95% CI , 0.38-0.65) and private insurance (crude odds ratio, 0.65; 95% CI , 0.45-0.71) were protective. In the mediation analysis, maternal education and insurance status explained 33.2% (95% CI , 7-66.4) and 27.6% (95% CI , 6.5-63.1) of the relationship between race/ethnicity and poor outcome, while infant characteristics played a minimal role. Conclusions Socioeconomic factors explain a significant portion of the association between Hispanic ethnicity and poor outcome in neonates with critical congenital heart disease. These findings identify vulnerable populations that would benefit from resources to lessen health disparities

Low Birth Weight and Risk of Later-Life Physical Disability in Women

Background: There is strong evidence that low and high birth weight due to in-utero programming results in elevated risk for adult diseases, though less research has been performed examining the influence of birth weight and physical disability later in life. Methods: Baseline data from 76,055 postmenopausal women in the Women's Health Initiative, a large multi-ethnic cohort, were used to examine the association between self-reported birth weight category (<6 lbs, 6-7 lbs 15 oz, 8-9 lbs 15 oz, and ≥10 lbs) and the self-reported physical functioning score on the RAND 36-item Health Survey. Linear regression models were adjusted for age, education, race/ethnicity, body mass index, and a comorbidity score. Results: Unadjusted models indicate that women born in the lowest and highest birth weight categories have significantly lower physical functioning scores as compared to women born in the normal weight category (β = -2.22, p < .0001 and β = -3.56, p < .0001, respectively). After adjustments, the relationship between the lowest birth weight category and physical functioning score remained significant (β = -1.52, p < .0001); however, the association with the highest birth weight category dissipated. Conclusions: Preconception and prenatal interventions aimed at reducing the incidence of low birth weight infants may subsequently reduce the burden of later-life physical disability

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.Comment: 16 pages, references added and discussion expande

Comparison of model predictions of typhoid conjugate vaccine public health impact and cost-effectiveness

Models are useful to inform policy decisions on typhoid conjugate vaccine (TCV) deployment in endemic settings. However, methodological choices can influence model-predicted outcomes. To provide robust estimates for the potential public health impact of TCVs that account for structural model differences, we compared four dynamic and one static mathematical model of typhoid transmission and vaccine impact. All models were fitted to a common dataset of age-specific typhoid fever cases in Kolkata, India. We evaluated three TCV strategies: no vaccination, routine vaccination at 9 months of age, and routine vaccination at 9 months with a one-time catch-up campaign (ages 9 months to 15 years). The primary outcome was the predicted percent reduction in symptomatic typhoid cases over 10 years after vaccine introduction. For three models with economic analyses (Models A-C), we also compared the incremental cost-effectiveness ratios (ICERs), calculated as the incremental cost (US$) per disability-adjusted life-year (DALY) averted. Routine vaccination was predicted to reduce symptomatic cases by 10-46$95-789 per DALY averted; two models predicted the ICER of routine vaccination alone to be greater than with the addition of catch-up campaign. Despite differences in model-predicted vaccine impact and cost-effectiveness, routine vaccination plus a catch-up campaign is likely to be impactful and cost-effective in high incidence settings such as Kolkata