Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

Pattern mixture models for clinical validation of biomarkers in the presence of missing data

Targeted therapies for cancers are sometimes only effective in a subset of patients with a particular biomarker status. In clinical development, the biomarker status is typically determined by an investigational-use-only/laboratory-developed test. A market ready test (MRT) is developed later to meet regulatory requirements and for future commercial use. In the USA, the clinical validation of MRT showing efficacy and safety profile of the targeted therapy in the biomarker subgroups determined by MRT is needed for pre-market approval. One of the major challenges in carrying out clinical validation is that the biomarker status per MRT is often missing for many subjects. In this paper, we treat biomarker status as a missing covariate and develop a novel pattern mixture model in the setting of a proportional hazards model for the time-to-event outcome variable. We specify a multinomial regression model for the missing biomarker statuses, and develop an expectation–maximization algorithm by the Method of Weights (Ibrahim, Journal of the American Statistical Association, 1990) to estimate the parameters in the regression model. We use Louis' formula (Louis, Journal of the Royal Statistical Society. Series B, 1982) to obtain standard errors estimates. We examine the performance of our method in extensive simulation studies and apply our method to a clinical trial in metastatic colorectal cancer

Biomarker threshold adaptive designs for survival endpoints

Due to the importance of precision medicine, it is essential to identify the right patients for the right treatment. Biomarkers, which have been commonly used in clinical research as well as in clinical practice, can facilitate selection of patients with a good response to the treatment. In this paper, we describe a biomarker threshold adaptive design with survival endpoints. In the first stage, we determine subgroups for one or more biomarkers such that patients in these subgroups benefit the most from the new treatment. The analysis in this stage can be based on historical or pilot studies. In the second stage, we sample subjects from the subgroups determined in the first stage and randomly allocate them to the treatment or control group. Extensive simulation studies are conducted to examine the performance of the proposed design. Application to a real data example is provided for implementation of the first-stage algorithms

Polarized photons in radiative muon capture

We discuss the measurement of polarized photons arising from radiative muon capture. The spectrum of left circularly polarized photons or equivalently the circular polarization of the photons emitted in radiative muon capture on hydrogen is quite sensitive to the strength of the induced pseudoscalar coupling constant $g_P$. A measurement of either of these quantities, although very difficult, might be sufficient to resolve the present puzzle resulting from the disagreement between the theoretical prediction for $g_P$ and the results of a recent experiment. This sensitivity results from the absence of left-handed radiation from the muon line and from the fact that the leading parts of the radiation from the hadronic lines, as determined from the chiral power counting rules of heavy-baryon chiral perturbation theory, all contain pion poles.Comment: 10 pages, 6 figure

Mechanical properties of atomically thin boron nitride and the role of interlayer interactions

Atomically thin boron nitride (BN) nanosheets are important two-dimensional nanomaterials with many unique properties distinct from those of graphene, but investigation into their mechanical properties remains incomplete. Here we report that high-quality single-crystalline mono-and few-layer BN nanosheets are one of the strongest electrically insulating materials. More intriguingly, few-layer BN shows mechanical behaviours quite different from those of few-layer graphene under indentation. In striking contrast to graphene, whose strength decreases by more than 30% when the number of layers increases from 1 to 8, the mechanical strength of BN nanosheets is not sensitive to increasing thickness. We attribute this difference to the distinct interlayer interactions and hence sliding tendencies in these two materials under indentation. The significantly better interlayer integrity of BN nanosheets makes them a more attractive candidate than graphene for several applications, for example, as mechanical reinforcements

Search for Invisible Decays of η\eta and η′\eta^\prime in J/ψ→ϕηJ/\psi \to \phi\eta and ϕη′\phi \eta^\prime

Using a data sample of $58\times 10^6$ $J/\psi$ decays collected with the BES II detector at the BEPC, searches for invisible decays of $\eta$ and $\eta^\prime$ in $J/\psi$ to $\phi\eta$ and $\phi\eta^\prime$ are performed. The $\phi$ signals, which are reconstructed in $K^+K^-$ final states, are used to tag the $\eta$ and $\eta^\prime$ decays. No signals are found for the invisible decays of either $\eta$ or $\eta^\prime$, and upper limits at the 90% confidence level are determined to be $1.65 \times 10^{-3}$ for the ratio $\frac{B(\eta\to \text{invisible})}{B(\eta\to\gamma\gamma)}$ and $6.69\times 10^{-2}$ for $\frac{B(\eta^\prime\to \text{invisible})}{B(\eta^\prime\to\gamma\gamma)}$. These are the first searches for $\eta$ and $\eta^\prime$ decays into invisible final states.Comment: 5 pages, 4 figures; Added references, Corrected typo

Observation of Two New N* Peaks in J/psi -> ppi−nˉp pi^- \bar n and pˉπ+n\bar p\pi^+n Decays

The $\pi N$ system in decays of $J/\psi\to\bar NN\pi$ is limited to be isospin 1/2 by isospin conservation. This provides a big advantage in studying $N^*\to \pi N$ compared with $\pi N$ and $\gamma N$ experiments which mix isospin 1/2 and 3/2 for the $\pi N$ system. Using 58 million $J/\psi$ decays collected with the Beijing Electron Positron Collider, more than 100 thousand $J/\psi \to p \pi^- \bar n + c.c.$ events are obtained. Besides two well known $N^*$ peaks at 1500 MeV and 1670 MeV, there are two new, clear $N^*$ peaks in the $p\pi$ invariant mass spectrum around 1360 MeV and 2030 MeV. They are the first direct observation of the $N^*(1440)$ peak and a long-sought "missing" $N^*$ peak above 2 GeV in the $\pi N$ invariant mass spectrum. A simple Breit-Wigner fit gives the mass and width for the $N^*(1440)$ peak as $1358\pm 6 \pm 16$ MeV and $179\pm 26\pm 50$ MeV, and for the new $N^*$ peak above 2 GeV as $2068\pm 3^{+15}_{-40}$ MeV and $165\pm 14\pm 40$ MeV, respectively

Data acquisition process for an intelligent decision support in gynecology and obstetrics emergency triage

Manchester Triage System is a reliable system of triage in the emergency department of a hospital. This system when applied to a specific patients’ condition such the pregnancy has several limitations. To overcome those limitations an alternative triage IDSS was developed in the MJD. In this approach the knowledge was obtained directly from the doctors’ empirical and scientific experience to make the first version of decision models. Due to the particular gynecological and/or obstetrics requests other characteristics had been developed, namely a system that can increase patient safety for women in need of immediate care and help low-risk women avoid high-risk care, maximizing the use of resources. This paper presents the arrival flowchart, the associated decisions and the knowledge acquisition cycle. Results showed that this new approach enhances the efficiency and the safety through the appropriate use of resources and by assisting the right patient in the right place.The work of Filipe Portela was supported by the grant SFRH/BD/70156/2010 from FC