Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

Measuring patient-perceived quality of care in US hospitals using Twitter

BACKGROUND: Patients routinely use Twitter to share feedback about their experience receiving healthcare. Identifying and analysing the content of posts sent to hospitals may provide a novel real-time measure of quality, supplementing traditional, survey-based approaches. OBJECTIVE: To assess the use of Twitter as a supplemental data stream for measuring patient-perceived quality of care in US hospitals and compare patient sentiments about hospitals with established quality measures. DESIGN: 404 065 tweets directed to 2349 US hospitals over a 1-year period were classified as having to do with patient experience using a machine learning approach. Sentiment was calculated for these tweets using natural language processing. 11 602 tweets were manually categorised into patient experience topics. Finally, hospitals with ≥50 patient experience tweets were surveyed to understand how they use Twitter to interact with patients. KEY RESULTS: Roughly half of the hospitals in the US have a presence on Twitter. Of the tweets directed toward these hospitals, 34 725 (9.4%) were related to patient experience and covered diverse topics. Analyses limited to hospitals with ≥50 patient experience tweets revealed that they were more active on Twitter, more likely to be below the national median of Medicare patients (p<0.001) and above the national median for nurse/patient ratio (p=0.006), and to be a non-profit hospital (p<0.001). After adjusting for hospital characteristics, we found that Twitter sentiment was not associated with Hospital Consumer Assessment of Healthcare Providers and Systems (HCAHPS) ratings (but having a Twitter account was), although there was a weak association with 30-day hospital readmission rates (p=0.003). CONCLUSIONS: Tweets describing patient experiences in hospitals cover a wide range of patient care aspects and can be identified using automated approaches. These tweets represent a potentially untapped indicator of quality and may be valuable to patients, researchers, policy makers and hospital administrators

Isoperimetric inequalities for Schatten norms of Riesz potentials

In this note we prove that the ball is a maximiser for integer order Schatten p-norms of the Riesz potential operators among all domains of a given measure in R d . In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one considered by M. Kac in the case of the Laplacian, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of Rayleigh-Faber-Krahn and Hong-Krahn-Szegö inequalities

Simplicity of extremal eigenvalues of the Klein-Gordon equation

We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real intervals and the two inner boundary points are eigenvalues, we show that these extremal eigenvalues are simple and possess strictly positive eigenfunctions. Examples of electric potentials satisfying these assumptions are given

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Simple gene transfer technique based on I-SceI meganuclease and cytoplasmic injection in IVF bovine embryos

Although transgenic methods in mammals are inefficient, an easy and highly efficient transgenesis systemusing I-SceI meganuclease (intron-encoded endonuclease fromS. cerevisiae)was recently described in Xenopus. The method consisted of injection into fertilized eggs of an I-SceI reaction mixture with a plasmid DNA carrying the transgene, flanked by the meganuclease recognition sites (pIS). In the present study, the effects of I-SceI on gene transfer were tested apparently for the first time in mammals, in particular, in cattle. Various conditions were evaluated, including three concentrations of the plasmid pIS Pax6egfp, carrying I-SceI recognition sites flanking egfp under Pax6 promoter and two injection times (before IVM and after IVF) of pIS CAGegfp, carrying I-SceI sites fanking egfp under CAG promoter. In addition, the quantity of transgenewasmeasured using quantitative polymerase chain reaction, and presence of transgene signals was evaluated using fluorescence in situ hybridization analysis. Transgene expression rateswere higher (P< 0.05) for groups treated after IVF (79.1%, 91/115 and 63.0%, 75/ 119) than before IVM (32.6%, 31/95 and 34.7%, 33/95), with and without I-SceI, respectively. Interestingly, injectionwith pIS plus I-SceI after IVF increased frequency (P<0.05) of nonmosaic transgene-expressing embryos (58.3%, 42/72 vs. 29.7%, 25/84) for pIS plus I-SceI and pIS alone. Based on fluorescence in situ hybridization analysis, injectionwith I-SceI increased (P<0.05) the proportion of embryos with transgene signals in all blastomeres compared with pIS alone (44.0%,11/25 vs. 6.9%, 2/29) for pIS plus I-SceI and pIS alone. In addition, transgene copy number was numerically higher for the group treated with pIS plus I-SceI compared with pIS alone. In conclusion, I-SceI gene transfer increased transgene signals in bovine embryos.Fil: Bevacqua, Romina Jimena. Universidad de Buenos Aires. Facultad de Agronomía. Pabellón de Zootecnica. Laboratorio de Biotecnología Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; ArgentinaFil: Canel, Natalia Gabriela. Universidad de Buenos Aires. Facultad de Agronomía. Pabellón de Zootecnica. Laboratorio de Biotecnología Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; ArgentinaFil: Hiriart, María Inés. Universidad de Buenos Aires. Facultad de Agronomía. Pabellón de Zootecnica. Laboratorio de Biotecnología Animal; ArgentinaFil: Sipowicz, P.. Universidad Nacional de San Martín. Laboratorio de Neuro y Citogenética Molecular; ArgentinaFil: Rozenblum, G. T.. Universidad Maimónides. Area de Investigaciones Biomédicas y Biotecnológicas. Centro de Estudios Biomédicos, Biotecnológicos, Ambientales y de Diagnóstico; ArgentinaFil: Vitullo, Alfredo Daniel. Universidad Maimónides. Area de Investigaciones Biomédicas y Biotecnológicas. Centro de Estudios Biomédicos, Biotecnológicos, Ambientales y de Diagnóstico; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; ArgentinaFil: Radrizzani Helguera, Martin. Universidad Nacional de San Martín. Laboratorio de Neuro y Citogenética Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; ArgentinaFil: Fernández y Martín, Rafael. Universidad de Buenos Aires. Facultad de Agronomía. Pabellón de Zootecnica. Laboratorio de Biotecnología Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario; ArgentinaFil: Salamone, Daniel Felipe. Universidad de Buenos Aires. Facultad de Agronomía. Pabellón de Zootecnica. Laboratorio de Biotecnología Animal; Argentin