Lieb-Thirring inequalities for Schr\"odinger operators with complex-valued potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.Comment: 9 pages; typos correcte

Tetrahedral and Triangular Deformations of Z=NZ=N Nuclei in Mass Region A∼60−80A \sim 60-80

We study static non-axial octupole deformations in proton-rich $Z=N$ nuclei, $^{64}$Ge, $^{68}$Se, $^{72}$Kr, $^{76}$Sr, $^{80}$Zr and $^{84}$Mo, by using the Skyrme Hartree-Fock plus BCS calculation with no restrictions on the nuclear shape. The calculation predicts that the oblate ground state in $^{68}$Se is extremely soft for the $Y_{33}$ triangular deformation, and that in $^{80}$Zr the low-lying local minimum state coexisting with the prolate ground state has the $Y_{32}$ tetrahedral deformation.Comment: 8 pages, 4 Postscript figures, REVTE

A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions

In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time $T$ if and only if its energy is negative at some time before $T$. The proof of this result is based on a Gamma-convergence technique

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for x\in\RR^d, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution. The linearization of this flow is interpreted here as the heat flow of the Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}), with a metric ${\bf g}$ which is conformal to the standard \RR^d metric. Studying the pointwise heat kernel behaviour allows to prove {suitable Gagliardo-Nirenberg} inequalities associated to the generator. Such inequalities in turn allow to study the nonlinear evolution as well, and to determine its asymptotics, which is identical to the one satisfied by the linearization. In terms of the rescaled representation, which is a nonlinear Fokker--Planck equation, the convergence rate turns out to be polynomial in time. This result is in contrast with the known exponential decay of such representation for all other values of $m$.Comment: 37 page

Acceptability, usability and performance of lateral flow immunoassay tests for SARS-CoV-2 antibodies: REACT-2 study of self-testing in non-healthcare key workers

Background Seroprevalence studies are essential to understand the epidemiology of SARS-CoV-2. Various technologies, including laboratory assays and point-of-care self-tests, are available for antibody testing. The interpretation of seroprevalence studies requires comparative data on the performance of antibody tests. Methods In June 2020, current and former members of the UK Police forces and Fire service performed a self-test lateral flow immunoassay (LFIA), had a nurse-performed LFIA and provided a venous blood sample for ELISA . We present the prevalence of antibodies to SARS-CoV-2; the acceptability and usability of self-test LFIAs; and determine the sensitivity and specificity of LFIAs compared to laboratory ELISA. Results In this cohort of 5189 current and former members of the Police service and 263 members of the Fire service, 7.4% (396/5,348; 95% CI, 6.7-8.1) were antibody positive. Seroprevalence was 8.9% (6.9-11.4) in those under 40 years, 11.5% (8.8-15.0) in those of non-white ethnicity and 7.8% (7.1-8.7) in those currently working. Self-test LFIA had an acceptability of 97.7% and a usability of 90.0%. There was substantial agreement between within-participant LFIA results (kappa 0.80; 0.77-0.83). The LFIAs had a similar performance: compared to ELISA, sensitivity was 82.1% (77.7-86.0) self-test and 76.4% (71.9-80.5) nurse-performed with specificity of 97.8% (97.3-98.2) and 98.5% (98.1-98.8) respectively. Conclusion A greater proportion of this non-healthcare key worker cohort showed evidence of previous infection with SARS-CoV-2 than the general population at 6.0% (5.8-6.1) following the first wave in England. The high acceptability and usability reported by participants and similar performance of self-test and nurse-performed LFIAs indicate that the self-test LFIA is fit for purpose for home-testing in occupational and community prevalence studies

School self-evaluation and its impact on teachers’ work in England

This study, based on in-depth interview data from a sample of schools in the midlands of England, offers an analysis of UK teachers’ perceptions and understandings of school self evaluation at a point when national accountability procedures have required that all schools complete and constantly update a web-based self evaluation schedule, which is then used as the basis for high stakes external inspection. School systems and cultures of self evaluation were found to be diverse, complex and school-specific. Three broad cultural categories are proposed as a heuristic to illuminate: issues of compliance and resistance, teacher motivation and behaviours, understandings of professionalism and leadership, school ethos, job satisfaction, and the use and interpretation of school level data in relation to school self evaluation

Uptake of synthetic low density lipoprotein by leukemic stem cells — a potential stem cell targeted drug delivery strategy

Chronic Myeloid Leukemia (CML) stem/progenitor cells, which over-express Bcr-Abl, respond to imatinib by a reversible block in proliferation without significant apoptosis. As a result, patients are unlikely to be cured owing to the persistence of leukemic quiescent stem cells (QSC) capable of initiating relapse. Previously, we have reported that intracellular levels of imatinib in primary primitive CML cells (CD34&lt;sup&gt;+&lt;/sup&gt;38&lt;sup&gt;lo/−&lt;/sup&gt;), are significantly lower than in CML progenitor cells (total CD34&lt;sup&gt;+&lt;/sup&gt;) and leukemic cell lines. The aim of this study was to determine if potentially sub-therapeutic intracellular drug concentrations in persistent leukemic QSC may be overcome by targeted drug delivery using synthetic Low Density Lipoprotein (sLDL) particles. As a first step towards this goal, however, the extent of uptake of sLDL by leukemic cell lines and CML patient stem/progenitor cells was investigated. Results with non-drug loaded particles have shown an increased and preferential uptake of sLDL by Bcr-Abl positive cell lines in comparison to Bcr-Abl negative. Furthermore, CML CD34&lt;sup&gt;+&lt;/sup&gt; and primitive CD34&lt;sup&gt;+&lt;/sup&gt;38&lt;sup&gt;lo/−&lt;/sup&gt; cells accumulated significantly higher levels of sLDL when compared with non-CML CD34&lt;sup&gt;+&lt;/sup&gt; cells. Thus, drug-loading the sLDL nanoparticles could potentially enhance intracellular drug concentrations in primitive CML cells and thus aid their eradication

Racial and Ethnic Health Disparities among Fifth-Graders in Three Cities

http://dx.doi.org/10.1056/NEJMsa111435

Volcanism and the Greenland ice cores: A new tephrochronological framework for the last glacial-interglacial transition (LGIT) based on cryptotephra deposits in three ice cores

Chemical profiles from Greenland ice cores show that the frequency of volcanism was higher during the last glacial-interglacial transition (LGIT) and early Holocene, (17–9 ka b2k) than in any other period during the last 110 kyr. This increased frequency has partly been linked to climate-driven melting of the Icelandic ice sheet during the last deglaciation, with regional isostatic changes thought to alter mantle viscosity and lead to more eruptions. Our study is the first to construct a comprehensive tephrochronological framework from Greenland ice cores over the LGIT to aid in the reconstruction of volcanic activity over this period. The framework is based on extensive high-resolution sampling of three Greenland ice cores between 17.4 and 11.6 ka b2k and comprises a total of 64 cryptotephra deposits from the NGRIP, GRIP and NEEM ice cores. We show that many of these tephras are preserved within the core without an associated chemical signature in the ice, which implies that reconstructions of volcanism based solely on glacio-chemical indicators might underestimate the number of events. Single glass shards from each deposit were geochemically characterised to trace the volcanic source and many of these deposits could be correlated between cores. We show that the 64 deposits represent tephra deposits from 42 separate volcanic events, and of these, 39 are from Iceland, two from the north Pacific region (Japan and USA) and one has an unknown source. Six deposits can be correlated to terrestrial and/or marine tephra deposits in the Northern Hemisphere and the remaining 36 are unreported in other archives. We did not locate tephra from the compositionally distinctive Laacher See eruption (∼13 ka b2k) in our records. Combining our new discoveries with the previously published tephra framework, raises the number of individual tephra horizons found in Greenland ice over this interval to 50. This significantly improves the regional tephrochronological framework, our knowledge of the eruptive history of Iceland during the LGIT and provides new tephra constraints over key LGIT climate events. Consequentially, this framework can guide sampling strategies of future tephra studies in the terrestrial and marine realms aiming to link these records to the Greenland ice cores to assess regional climate synchroneity

Paraoxonase 2 protein is spatially expressed in the human placenta and selectively reduced in labour

Humans parturition involves interaction of hormonal, neurological, mechanical stretch and inflammatory pathways and the placenta plays a crucial role. The paraoxonases (PONs 1–3) protect against oxidative damage and lipid peroxidation, modulation of endoplasmic reticulum stress and regulation of apoptosis. Nothing is known about the role of PON2 in the placenta and labour. Since PON2 plays a role in oxidative stress and inflammation, both features of labour, we hypothesised that placental PON2 expression would alter during labour. PON2 was examined in placentas obtained from women who delivered by cesarean section and were not in labour and compared to the equivalent zone of placentas obtained from women who delivered vaginally following an uncomplicated labour. Samples were obtained from 12 sites within each placenta: 4 equally spaced apart pieces were sampled from the inner, middle and outer placental regions. PON2 expression was investigated by Western blotting and real time PCR. Two PON2 forms, one at 62 kDa and one at 43 kDa were found in all samples. No difference in protein expression of either isoform was found between the three sites in either the labour or non-labour group. At the middle site there was a highly significant decrease in PON2 expression in the labour group when compared to the non-labour group for both the 62 kDa form (p = 0.02) and the 43 kDa form (p = 0.006). No spatial differences were found within placentas at the mRNA level in either labour or non-labour. There was, paradoxically, an increase in PON2 mRNA in the labour group at the middle site only. This is the first report to describe changes in PON2 in the placenta in labour. The physiological and pathological significance of these remains to be elucidated but since PON2 is anti-inflammatory further studies are warranted to understand its role