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

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

Effects of reproductive period duration and number of pregnancies on midlife ECG indices: a secondary analysis from the Women\u27s Health Initiative Clinical Trial

OBJECTIVES: Pregnancy, menses and menopause are related to fluctuations in endogenous sex hormones in women, which cumulatively may alter cardiac electrical conduction. Therefore, we sought to study the association between number of pregnancies and reproductive period duration (RD, time from menarche to menopause) with ECG intervals in the Women\u27s Health Initiative Clinical Trials. DESIGN: Secondary analysis of multicentre clinical trial. SETTING: USA. PRIMARY OUTCOME MEASURES: ECGintervals: PR interval, P-wave duration, P-wave dispersion, QTc interval. PARTICIPANTS: n=40 687 women (mean age=62 years) participating in the Women\u27s Health Initiative Clinical Trials. 82.5% were white, 9.3% black, 4% Hispanic and 2.7% Asian. METHODS: In primary analysis, we employed multivariable linear regression models relating number of pregnancies and RD with millisecond changes in intervals from enrolment ECG. We studied effect modification by hormone therapy use. RESULTS: Among participants, 5+ live births versus 0 prior pregnancies was associated with a 1.32 ms increase in PR interval (95% CI 0.25 to 2.38), with a graded association with longer QTc interval (ms) (none (prior pregnancy, no live births)=0.66 (-0.56 to 1.88), 1=0.15 (-0.71 to 1.02), 2-4=0.25 (-0.43 to 0.94) and 5+ live births=1.15 (0.33 to 1.98), p=0.008). RD was associated with longer PR interval and maximum P-wave duration (but not P-wave dispersion) among never users of hormone therapy: (PR (ms) per additional RD year: 0.10 (0.04 to 0.16); higher P-wave duration (ms): 0.09 (0.06 to 0.12)). For every year increase in reproductive period, QTc decreased by 0.04 ms (-0.07 to -0.01). CONCLUSIONS: An increasing number of live births is related to increased and RD to decreased ventricular repolarisation time. Both grand multiparity and longer RD are related to increased atrial conduction time. Reproductive factors that alter midlife cardiac electrical conduction system remodelling in women may modestly influence cardiovascular disease risk in later life. TRIAL REGISTRATION NUMBER: NCT00000611

Prediction of preterm birth with and without preeclampsia using mid-pregnancy immune and growth-related molecular factors and maternal characteristics.

OBJECTIVE:To evaluate if mid-pregnancy immune and growth-related molecular factors predict preterm birth (PTB) with and without (±) preeclampsia. STUDY DESIGN:Included were 400 women with singleton deliveries in California in 2009-2010 (200 PTB and 200 term) divided into training and testing samples at a 2:1 ratio. Sixty-three markers were tested in 15-20 serum samples using multiplex technology. Linear discriminate analysis was used to create a discriminate function. Model performance was assessed using area under the receiver operating characteristic curve (AUC). RESULTS:Twenty-five serum biomarkers along with maternal age <34 years and poverty status identified >80% of women with PTB ± preeclampsia with best performance in women with preterm preeclampsia (AUC = 0.889, 95% confidence interval (0.822-0.959) training; 0.883 (0.804-0.963) testing). CONCLUSION:Together with maternal age and poverty status, mid-pregnancy immune and growth factors reliably identified most women who went on to have a PTB ± preeclampsia

The dynamics of the 3D radial NLS with the combined terms

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in the energy space $H^1(\R^3)$. The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^4u$. This problem was proposed by Tao, Visan and Zhang in \cite{TaoVZ:NLS:combined}. The main difficulty is the lack of the scaling invariance. Illuminated by \cite{IbrMN:f:NLKG}, we need give the new radial profile decomposition with the scaling parameter, then apply it into the scattering theory. Our result shows that the defocusing, $\dot H^1$-subcritical perturbation $|u|^2u$ does not affect the determination of the threshold of the scattering solution of (CNLS) in the energy space.Comment: 46page

Linear Statistics of Point Processes via Orthogonal Polynomials

For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.Comment: Added references, corrected typos. To appear, J. Stat. Phy

Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n\mathbb{R}^{1+n}

Using the same induction on energy argument in both frequency space and spatial space simultaneously as in \cite{CKSTT07}, \cite{RyV05} and \cite{Vi05}, we obtain global well-posedness and scattering of energy solutions of defocusing energy-critical nonlinear Hartree equation in $\mathbb{R}\times \mathbb{R}^n$($n\geq 5$), which removes the radial assumption on the data in \cite{MiXZ07a}. The new ingredients are that we use a modified long time perturbation theory to obtain the frequency localization (Proposition \ref{freqdelocaimplystbound} and Corollary \ref{frequencylocalization}) of the minimal energy blow up solutions, which can not be obtained from the classical long time perturbation and bilinear estimate and that we obtain the spatial concentration of minimal energy blow up solution after proving that $L^{\frac{2n}{n-2}}_x$-norm of minimal energy blow up solutions is bounded from below, the $L^{\frac{2n}{n-2}}_x$-norm is larger than the potential energy.Comment: 41page

Second trimester inflammatory and metabolic markers in women delivering preterm with and without preeclampsia.

ObjectiveInflammatory and metabolic pathways are implicated in preterm birth and preeclampsia. However, studies rarely compare second trimester inflammatory and metabolic markers between women who deliver preterm with and without preeclampsia.Study designA sample of 129 women (43 with preeclampsia) with preterm delivery was obtained from an existing population-based birth cohort. Banked second trimester serum samples were assayed for 267 inflammatory and metabolic markers. Backwards-stepwise logistic regression models were used to calculate odds ratios.ResultsHigher 5-α-pregnan-3β,20α-diol disulfate, and lower 1-linoleoylglycerophosphoethanolamine and octadecanedioate, predicted increased odds of preeclampsia.ConclusionsAmong women with preterm births, those who developed preeclampsia differed with respect metabolic markers. These findings point to potential etiologic underpinnings for preeclampsia as a precursor to preterm birth

Human cytomegalovirus infection of langerhans-type dendritic cells does not require the presence of the gH/gL/UL128-131A complex and is blocked after nuclear deposition of viral genomes in immature cells

Human cytomegalovirus (CMV) enters its host via the oral and genital mucosae. Langerhans-type dendritic cells (LC) are the most abundant innate immune cells at these sites, where they constitute a first line of defense against a variety of pathogens. We previously showed that immature LC (iLC) are remarkably resistant to CMV infection, while mature LC (mLC) are more permissive, particularly when exposed to clinical-strain-like strains of CMV, which display a pentameric complex consisting of the viral glycoproteins gH, gL, UL128, UL130, and UL131A on their envelope. This complex was recently shown to be required for the infection of immature monocyte-derived dendritic cells. We thus sought to establish if the presence of this complex is also necessary for virion penetration of LC and if defects in entry might be the source of iLC resistance to CMV. Here we report that the efficiency of LC infection is reduced, but not completely abolished, in the absence of the pentameric complex. While virion penetration and nuclear deposition of viral genomes are not impaired in iLC, the transcription of the viral immediate early genes UL122 and UL123 and of the delayed early gene UL50 is substantially lower than that in mLC. Together, these data show that the UL128, UL130, and UL131A proteins are dispensable for CMV entry into LC and that progression of the viral cycle in iLC is restricted at the step of viral gene expression