The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of bivariate phase synchronization strength. The resulting method is able to identify clusters of synchronized oscillators, and to quantify their strength as well as the degree of involvement of an oscillator in a cluster. Since for the case of a single cluster the method gives similar results as our previous approach, it can be seen as a generalized Synchronization Cluster Analysis, extending its field of application to more complex situations. The performance of the method is tested by applying it to simulation data.Comment: Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually available Jan 200

Comment on 'Stability of the semiclassical Einstein equation'

Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev. D 40, (1989) 315] are corrected.Comment: 3 pages, LaTeX, reprinted from Phys. Rev. D 50 (1994) 545

A compact dual atom interferometer gyroscope based on laser-cooled rubidium

We present a compact and transportable inertial sensor for precision sensing of rotations and accelerations. The sensor consists of a dual Mach-Zehnder-type atom interferometer operated with laser-cooled $^{87}$Rb. Raman processes are employed to coherently manipulate the matter waves. We describe and characterize the experimental apparatus. A method for passing from a compact geometry to an extended interferometer with three independent atom-light interaction zones is proposed and investigated. The extended geometry will enhance the sensitivity by more than two orders of magnitude which is necessary to achieve sensitivities better than $10^{-8}$rad/s/$\sqrt{\rm Hz}$.Comment: 9 pages, 8 figure

Interaction-induced Renormalization of Andreev Reflection

We analyze the charge transport between a one-dimensional weakly interacting electron gas and a superconductor within the scaling approach in the basis of scattering states. We derive the renormalization group equations, which fully account for the intrinsic energy dependence due to Andreev reflection. A strong renormalization of the corresponding reflection phase is predicted even for a perfectly transparent metal-superconductor interface. The interaction-induced suppression of the Andreev conductance is shown to be highly sensitive to the normal state resistance, providing a possible explanation of experiments with carbon-nanotube/superconductor junctions by Morpurgo et al. [Science 286, 263 (2001)].Comment: 4 pages, 2 figure

Diagnostic error increases mortality and length of hospital stay in patients presenting through the emergency room

Background: Diagnostic errors occur frequently, especially in the emergency room. Estimates about the consequences of diagnostic error vary widely and little is known about the factors predicting error. Our objectives thus was to determine the rate of discrepancy between diagnoses at hospital admission and discharge in patients presenting through the emergency room, the discrepancies’ consequences, and factors predicting them. Methods: Prospective observational clinical study combined with a survey in a University-affiliated tertiary care hospital. Patients’ hospital discharge diagnosis was compared with the diagnosis at hospital admittance through the emergency room and classified as similar or discrepant according to a predefined scheme by two independent expert raters. Generalized linear mixed-effects models were used to estimate the effect of diagnostic discrepancy on mortality and length of hospital stay and to determine whether characteristics of patients, diagnosing physicians, and context predicted diagnostic discrepancy. Results: 755 consecutive patients (322 [42.7%] female; mean age 65.14 years) were included. The discharge diagnosis differed substantially from the admittance diagnosis in 12.3% of cases. Diagnostic discrepancy was associated with a longer hospital stay (mean 10.29 vs. 6.90 days; Cohen’s d 0.47; 95% confidence interval 0.26 to 0.70; P = 0.002) and increased patient mortality (8 (8.60%) vs. 25(3.78%); OR 2.40; 95% CI 1.05 to 5.5 P = 0.038). A factor available at admittance that predicted diagnostic discrepancy was the diagnosing physician’s assessment that the patient presented atypically for the diagnosis assigned (OR 3.04; 95% CI 1.33–6.96; P = 0.009). Conclusions: Diagnostic discrepancies are a relevant healthcare problem in patients admitted through the emergency room because they occur in every ninth patient and are associated with increased in-hospital mortality. Discrepancies are not readily predictable by fixed patient or physician characteristics; attention should focus on context

Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page

Spectroscopy of PTCDA attached to rare gas samples: clusters vs. bulk matrices. I. Absorption spectroscopy

The interaction between PTCDA (3,4,9,10-perylene-tetracarboxylic-dianhydride) and rare gas or para-hydrogen samples is studied by means of laser-induced fluorescence excitation spectroscopy. The comparison between spectra of PTCDA embedded in a neon matrix and spectra attached to large neon clusters shows that these large organic molecules reside on the surface of the clusters when doped by the pick-up technique. PTCDA molecules can adopt different conformations when attached to argon, neon and para-hydrogen clusters which implies that the surface of such clusters has a well-defined structure and has not liquid or fluxional properties. Moreover, a precise analysis of the doping process of these clusters reveals that the mobility of large molecules on the cluster surface is quenched, preventing agglomeration and complex formation

Influence of temperature fluctuations on plasma turbulence investigations with Langmuir probes

The reliability of Langmuir probe measurements for plasma-turbulence investigations is studied on GEMR gyro-fluid simulations and compared with results from conditionally sampled I-V characteristics as well as self-emitting probe measurements in the near scrape-off layer of the tokamak ASDEX Upgrade. In this region, simulation and experiment consistently show coherent in-phase fluctuations in density, plasma potential and also in electron temperature. Ion-saturation current measurements turn out to reproduce density fluctuations quite well. Fluctuations in the floating potential, however, are strongly influenced by temperature fluctuations and, hence, are strongly distorted compared to the actual plasma potential. These results suggest that interpreting floating as plasma-potential fluctuations while disregarding temperature effects is not justified near the separatrix of hot fusion plasmas. Here, floating potential measurements lead to corrupted results on the ExB dynamics of turbulent structures in the context of, e.g., turbulent particle and momentum transport or instability identification on the basis of density-potential phase relations

The link between great earthquakes and the subduction of oceanic fracture zones

Giant subduction earthquakes are known to occur in areas not previously identified as prone to high seismic risk. This highlights the need to better identify subduction zone segments potentially dominated by relatively long (up to 1000 yr and more) recurrence times of giant earthquakes. We construct a model for the geometry of subduction coupling zones and combine it with global geophysical data sets to demonstrate that the occurrence of great (magnitude ≥ 8) subduction earthquakes is strongly biased towards regions associated with intersections of oceanic fracture zones and subduction zones. We use a computational recommendation technology, a type of information filtering system technique widely used in searching, sorting, classifying, and filtering very large, statistically skewed data sets on the Internet, to demonstrate a robust association and rule out a random effect. Fracture zone–subduction zone intersection regions, representing only 25% of the global subduction coupling zone, are linked with 13 of the 15 largest (magnitude &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;w&lt;/sub&gt; ≥ 8.6) and half of the 50 largest (magnitude &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;w&lt;/sub&gt; ≥ 8.4) earthquakes. In contrast, subducting volcanic ridges and chains are only biased towards smaller earthquakes (magnitude &lt; 8). The associations captured by our statistical analysis can be conceptually related to physical differences between subducting fracture zones and volcanic chains/ridges. Fracture zones are characterised by laterally continuous, uplifted ridges that represent normal ocean crust with a high degree of structural integrity, causing strong, persistent coupling in the subduction interface. Smaller volcanic ridges and chains have a relatively fragile heterogeneous internal structure and are separated from the underlying ocean crust by a detachment interface, resulting in weak coupling and relatively small earthquakes, providing a conceptual basis for the observed dichotomy