Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity

The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes

In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted

Non-minimality of corners in subriemannian geometry

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.Comment: 11 pages, final versio

Evaluation of Indirect Fluorescent Antibody Assays Compared to Rapid Influenza Diagnostic Tests for the Detection of Pandemic Influenza A (H1N1) pdm09

Performance of indirect fluorescent antibody (IFA) assays and rapid influenza diagnostic tests (RIDT) during the 2009 H1N1 pandemic was evaluated, along with the relative effects of age and illness severity on test accuracy. Clinicians and laboratories submitted specimens on patients with respiratory illness to public health from April to mid October 2009 for polymerase chain reaction (PCR) testing as part of pandemic H1N1 surveillance efforts in Orange County, CA; IFA and RIDT were performed in clinical settings. Sensitivity and specificity for detection of the 2009 pandemic H1N1 strain, now officially named influenza A(H1N1)pdm09, were calculated for 638 specimens. Overall, approximately 30% of IFA tests and RIDTs tested by PCR were falsely negative (sensitivity 71% and 69%, respectively). Sensitivity of RIDT ranged from 45% to 84% depending on severity and age of patients. In hospitalized children, sensitivity of IFA (75%) was similar to RIDT (84%). Specificity of tests performed on hospitalized children was 94% for IFA and 80% for RIDT. Overall sensitivity of RIDT in this study was comparable to previously published studies on pandemic H1N1 influenza and sensitivity of IFA was similar to what has been reported in children for seasonal influenza. Both diagnostic tests produced a high number of false negatives and should not be used to rule out influenza infection

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

Measurement of D-s(+) and D-s(*+) production in B meson decays and from continuum e(+)e(-) annihilation at √s=10.6 GeV

This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APSNew measurements of Ds+ and Ds*+ meson production rates from B decays and from qq̅ continuum events near the Υ(4S) resonance are presented. Using 20.8 fb-1 of data on the Υ(4S) resonance and 2.6 fb-1 off-resonance, we find the inclusive branching fractions B(B⃗Ds+X)=(10.93±0.19±0.58±2.73)% and B(B⃗Ds*+X)=(7.9±0.8±0.7±2.0)%, where the first error is statistical, the second is systematic, and the third is due to the Ds+→φπ+ branching fraction uncertainty. The production cross sections σ(e+e-→Ds+X)×B(Ds+→φπ+)=7.55±0.20±0.34pb and σ(e+e-→Ds*±X)×B(Ds+→φπ+)=5.8±0.7±0.5pb are measured at center-of-mass energies about 40 MeV below the Υ(4S) mass. The branching fractions ΣB(B⃗Ds(*)+D(*))=(5.07±0.14±0.30±1.27)% and ΣB(B⃗Ds*+D(*))=(4.1±0.2±0.4±1.0)% are determined from the Ds(*)+ momentum spectra. The mass difference m(Ds+)-m(D+)=98.4±0.1±0.3MeV/c2 is also measured.This work was supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the Swiss NSF, A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation

Smoke-free legislation and child health

In this paper, we aim to present an overview of the scientific literature on the link between smoke-free legislation and early-life health outcomes. Exposure to second-hand smoke is responsible for an estimated 166 ,000 child deaths each year worldwide. To protect people from tobacco smoke, the World Health Organization recommends the implementation of comprehensive smoke-free legislation that prohibits smoking in all public indoor spaces, including workplaces, bars and restaurants. The implementation of such legislation has been found to reduce tobacco smoke exposure, encourage people to quit smoking and improve adult health outcomes. There is an increasing body of evidence that shows that children also experience health benefits after implementation of smoke-free legislation. In addition to protecting children from tobacco smoke in public, the link between smoke-free legislation and improved child health is likely to be mediated via a decline in smoking during pregnancy and reduced exposure in the home environment. Recent studies have found that the implementation of smoke-free legislation is associated with a substantial decrease in the number of perinatal deaths, preterm births and hospital attendance for respiratory tract infections and asthma in children, although such benefits are not found in each study. With over 80% of the world’s population currently unprotected by comprehensive smoke-free laws, protecting (unborn) children from the adverse impact of tobacco smoking and SHS exposure holds great potential to benefit public health and should therefore be a key priority for policymakers and health workers alike

Distinguishing Characteristics between Pandemic 2009–2010 Influenza A (H1N1) and Other Viruses in Patients Hospitalized with Respiratory Illness

BACKGROUND: Differences in clinical presentation and outcomes among patients infected with pandemic 2009 influenza A H1N1 (pH1N1) compared to other respiratory viruses have not been fully elucidated. METHODOLOGY/PRINCIPAL FINDINGS: A retrospective study was performed of all hospitalized patients at the peak of the pH1N1 season in whom a single respiratory virus was detected by a molecular assay targeting 18 viruses/subtypes (RVP, Luminex xTAG). Fifty-two percent (615/1192) of patients from October, 2009 to December, 2009 had a single respiratory virus (291 pH1N1; 207 rhinovirus; 45 RSV A/B; 37 parainfluenza; 27 adenovirus; 6 coronavirus; and 2 metapneumovirus). No seasonal influenza A or B was detected. Individuals with pH1N1, compared to other viruses, were more likely to present with fever (92% & 70%), cough (92% & 86%), sore throat (32% & 16%), nausea (31% & 8%), vomiting (39% & 30%), abdominal pain (14% & 7%), and a lower white blood count (8,500/L & 13,600/L, all p-values<0.05). In patients with cough and gastrointestinal complaints, the presence of subjective fever/chills independently raised the likelihood of pH1N1 (OR 10). Fifty-five percent (336/615) of our cohort received antibacterial agents, 63% (385/615) received oseltamivir, and 41% (252/615) received steroids. The mortality rate of our cohort was 1% (7/615) and was higher in individuals with pH1N1 compared to other viruses (2.1% & 0.3%, respectively; p = 0.04). CONCLUSIONS/SIGNIFICANCE: During the peak pandemic 2009-2010 influenza season in Rhode Island, nearly half of patients admitted with influenza-like symptoms had respiratory viruses other than influenza A. A high proportion of patients were treated with antibiotics and pH1N1 infection had higher mortality compared to other respiratory viruses