Scaling of Self-Avoiding Walks in High Dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\mu_5=8.838544(3)$, $\mu_6=10.878094(4)$, $\mu_7=12.902817(3)$, $\mu_8=14.919257(2)$ and give a revised estimate of $\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).Comment: 14 pages, 2 figure

Aerosol backscatter profiles from ceilometers: validation of water vapor correction in the framework of CeiLinEx2015

With the rapidly growing number of automated single-wavelength backscatter lidars (ceilometers), their potential benefit for aerosol remote sensing received considerable scientific attention. When studying the accuracy of retrieved particle backscatter coefficients, it must be considered that most of the ceilometers are influenced by water vapor absorption in the spectral range around 910&thinsp;nm. In the literature methodologies have been proposed to correct for this effect; however, a validation was not yet performed. In the framework of the ceilometer intercomparison campaign CeiLinEx2015 in Lindenberg, Germany, hosted by the German Weather Service, it was possible to tackle this open issue. Ceilometers from Lufft (CHM15k and CHM15kx, operating at 1064&thinsp;nm), from Vaisala (CL51 and CL31) and from Campbell Scientific (CS135), all operating at a wavelength of approximately 910&thinsp;nm, were deployed together with a multi-wavelength research lidar (RALPH) that served as a reference. In this paper the validation of the water vapor correction is performed by comparing ceilometer backscatter signals with measurements of the reference system extrapolated to the water vapor regime. One inherent problem of the validation is the spectral extrapolation of particle optical properties. For this purpose AERONET measurements and inversions of RALPH signals were used. Another issue is that the vertical range where validation is possible is limited to the upper part of the mixing layer due to incomplete overlap and the generally low signal-to-noise ratio and signal artifacts above that layer. Our intercomparisons show that the water vapor correction leads to quite a good agreement between the extrapolated reference signal and the measurements in the case of CL51 ceilometers at one or more wavelengths in the specified range of the laser diode's emission. This ambiguity is due to the similar effective water vapor transmission at several wavelengths. In the case of CL31 and CS135 ceilometers the validation was not always successful. That suggests that error sources beyond the water vapor absorption might be dominant. For future applications we recommend monitoring the emitted wavelength and providing “dark” measurements on a regular basis.</p

Suggested Cut-Off Values for Vitamin D as a Risk Marker for Total and Cardiac Death in Patients with Suspected Acute Coronary Syndrome

Background: Several studies have demonstrated an association between low vitamin D levels and cardiovascular risk. Vitamin D cut-off levels are still under debate.Objectives: To assess two cut-off levels, 40 and 70 nmol/L, respectively, for vitamin D measured as 25-hydroxyvitamin D in chest pain patients with suspected acute coronary syndrome.Methods: We investigated 1853 patients from coastal-Norway and inland NorthernArgentina. A similar database was used for pooling of data. Two-year follow-up data including all-cause mortality, cardiac death, and sudden cardiac death in the total patient population were analyzed, applying univariate and multivariable analysis.Results: Two hundred fifty-five patients with known vitamin D concentrations died. In the multivariable analysis, there was a decrease in total mortality above a cut-off level of 40 nmol/L and a decrease in cardiac death above a cut-off level of 70 nmol/L [HRs of 0.66 (95% CI, 0.50?0.88), p = 0.004 and 0.46 (95% CI, 0.22?0.94), p = 0.034, respectively].Conclusion: Vitamin D cut-off levels of 40 and 70 nmol/L were related to total mortality and cardiac death, respectively.Fil: Naesgaard, Patrycja A.. Stavanger University Hospital; Noruega. University Of Bergen; NoruegaFil: Leon de la Fuente, Ricardo Alfonso. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Stavanger University Hospital; Noruega. University Of Bergen; Noruega. Universidad Católica de Salta; ArgentinaFil: Nilsen, Stein Tore. Stavanger University Hospital; Noruega. University Of Bergen; NoruegaFil: Pönitz, Volker. Stavanger University Hospital; NoruegaFil: Brügger Andersen, Trygve. Stavanger University Hospital; NoruegaFil: Grundt, Heidi. University Of Bergen; Noruega. Stavanger University Hospital; NoruegaFil: Staines, Harry. Sigma Statistical Services; Reino UnidoFil: Nilsen, Dennis W. T.. Stavanger University Hospital; Noruega. University Of Bergen; Norueg