Statistics of statisticians: Critical mass of statistics and operational research groups in the UK

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the quality of statistics and operational research groups and the quantity researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 $\pm$ 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is about twice this value

Analytical mode normalization and resonant state expansion for optical fibers - an efficient tool to model transverse disorder

We adapt the resonant state expansion to optical fibers such as capillary and photonic crystal fibers. As a key requirement of the resonant state expansion and any related perturbative approach, we derive the correct analytical normalization for all modes of these fiber structures, including leaky modes that radiate energy perpendicular to the direction of propagation and have fields that grow with distance from the fiber core. Based on the normalized fiber modes, an eigenvalue equation is derived that allows for calculating the influence of small and large perturbations such as structural disorder on the guiding properties. This is demonstrated for two test systems: a capillary fiber and an endlessly single mode fiber.Comment: 10 pages, 4 figure

High-precision measurements of seawater Pb isotope compositions by double spike thermal ionization mass spectrometry

A new method for the determination of seawater Pb isotope compositions and concentrations was developed, which combines and optimizes previously published protocols for the separation and isotopic analysis of this element. For isotopic analysis, the procedure involves initial separation of Pb from 1 to 2 L of seawater by co-precipitation with Mg hydroxide and further purification by a two stage anion exchange procedure. The Pb isotope measurements are subsequently carried out by thermal ionization mass spectrometry using a Pb-207-Pb-204 double spike for correction of instrumental mass fractionation. These methods are associated with a total procedural Pb blank of 28 +/- 21 pg(1sd) and typical Pb recoveries of 40-60%. The Pb concentrations are determined by isotope dilution (ID) on 50 mL of seawater, using a simplified version of above methods. Analyses of multiple aliquots of six seawater samples yield a reproducibility of about +/- 1to +/- 10%(1sd) for Pb concentrations of between 7 and 50 pmol/kg, where precision was primarily limited by the uncertainty of the blank correction (12 +/- 4 pg; 1sd). For the Pb isotope analyses, typical reproducibilities (+/- 2sd) of 700-1500 ppm and 1000-2000ppm were achieved for Pb-207/Pb-206, Pb-208/Pb-206 and Pb-206/Pb-204, Pb-207/Pb-204, Pb-208/Pb-204, respectively. These results are superior to literature data that were obtained using plasma source mass spectrometry and they are at least a factor of five more precise for ratios involving the minor Pb-204 isotope. Both Pb concentration and isotope data, furthermore, show good agreement with published results for two seawater intercomparison samples of the GEOTRACES program. Finally, the new methods were applied to a seawater depth profile from the eastern South Atlantic. Both Pb contents and isotope compositions display a smooth evolution with depth, and no obvious outliers. Compared to previous Pb isotope data for seawater, the Pb-206/Pb-204 ratios are well correlated with Pb-207/Pb-206, underlining the significant improvement achieved in the measurement of the minor Pb-204 isotope

Pulsation models for the roAp star HD 134214

Precise time-series photometry with the MOST satellite has led to identification of 10 pulsation frequencies in the rapidly oscillating Ap (roAp) star HD 134214. We have fitted the observed frequencies with theoretical frequencies of axisymmetric modes in a grid of stellar models with dipole magnetic fields. We find that, among models with a standard composition of $(X,Z) = (0.70,0.02)$ and with suppressed convection, eigenfrequencies of a $1.65\,{\rm M}_\odot$ model with $\log T_{\rm eff} = 3.858$ and a polar magnetic field strength of 4.1kG agree best with the observed frequencies. We identify the observed pulsation frequency with the largest amplitude as a deformed dipole ($\ell = 1$) mode, and the four next-largest-amplitude frequencies as deformed $\ell = 2$ modes. These modes have a radial quasi-node in the outermost atmospheric layers ($\tau \sim 10^{-3}$). Although the model frequencies agree roughly with observed ones, they are all above the acoustic cut-off frequency for the model atmosphere and hence are predicted to be damped. The excitation mechanism for the pulsations of HD 134214 is not clear, but further investigation of these modes may be a probe of the atmospheric structure in this magnetic chemically peculiar star.Comment: 9 pages, 6 figures; accepted for publication in MNRA

Violation of the Leggett-Garg Inequality in Neutrino Oscillations

The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than $6{\sigma}$ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.Comment: Updated to match published version. 6 pages, 2 figure

On the detection of Lorentzian profiles in a power spectrum: A Bayesian approach using ignorance priors

Aims. Deriving accurate frequencies, amplitudes, and mode lifetimes from stochastically driven pulsation is challenging, more so, if one demands that realistic error estimates be given for all model fitting parameters. As has been shown by other authors, the traditional method of fitting Lorentzian profiles to the power spectrum of time-resolved photometric or spectroscopic data via the Maximum Likelihood Estimation (MLE) procedure delivers good approximations for these quantities. We, however, show that a conservative Bayesian approach allows one to treat the detection of modes with minimal assumptions (i.e., about the existence and identity of the modes). Methods. We derive a conservative Bayesian treatment for the probability of Lorentzian profiles being present in a power spectrum and describe an efficient implementation that evaluates the probability density distribution of parameters by using a Markov-Chain Monte Carlo (MCMC) technique. Results. Potentially superior to "best-fit" procedure like MLE, which only provides formal uncertainties, our method samples and approximates the actual probability distributions for all parameters involved. Moreover, it avoids shortcomings that make the MLE treatment susceptible to the built-in assumptions of a model that is fitted to the data. This is especially relevant when analyzing solar-type pulsation in stars other than the Sun where the observations are of lower quality and can be over-interpreted. As an example, we apply our technique to CoRoT observations of the solar-type pulsator HD 49933.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Einsatz von gecufften Endotrachealtuben bei Kindern in der Notfall- und Rettungsmedizin

Zusammenfassung: Moderne Pädiatrietuben mit Cuff kommen in der Kinderanästhesie und Kinderintensivmedizin vermehrt zur Anwendung. Hohe Treffsicherheit bei der Tubusgrößenwahl sowie die zuverlässige Abdichtung des Atemwegssystems ohne den Einsatz übergroßer Tuben sind entscheidende Vorteile gecuffter Tuben auch bei Säuglingen und kleinen Kindern in der Notfall- und Rettungsmedizin. Für einen sicheren Einsatz gecuffter Tuben in dieser Altersgruppe ist die Auswahl eines Pädiatrietubus mit korrekt platziertem Hochvolumen-Niederdruck-Cuff und Intubationstiefenmarkierung sowie eine geprüfte Tubusgrößenauswahlliste die Vorraussetzung. Die Überprüfung des Tubus auf eine Luftleckage nach der Intubation bei noch entleertem Cuff, das Füllen des Cuffs unter Cuffdruckkontrolle sowie die Cuffdruckbegrenzung auf maximal 20cmH2O erlauben den sicheren Einsatz von gecufften Tuben bei Säuglingen und Kindern. Fehlen gute Kindertuben mit Cuff, Altersgrößenauswahlliste und Cuffmanometer, so dürfen gecuffte Tuben bei Säuglingen und Kindern in der Rettungs- und Notfallmedizin nicht eingesetzt werden. Dann sollten weiterhin ungecuffte Tuben zum Einsatz gelange

Friedel oscillations in disordered quantum wires: Influence of e-e interactions on the localization length

The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the disorder. Scaling of the average Friedel oscillations by this exponential term collapses the disordered samples data on the clean results. We show that the length scale governing the exponential decay may be associated with the Anderson localization length and thus be used as a convenient way to determine the dependence of the localization length on disorder and interactions. The localization length decreases as a function of the interaction strength, in accordance with previous predictions.Comment: 7 pages, 7 figure