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

Approximale Attrition der Frontzähne bei Erwachsenen

Aufbauend auf der Arbeit von Geim, welche die Inzisivi und Prämolaren bei Kindern und Jugendlichen im Alter von 7 bis 20 Jahren auf ihre approximale Attrition hin untersuchte, wurde in dieser Arbeit die approximale Attrition der unteren Frontzähne bei Erwachsenen bestimmt. Zu diesem zweck wurden bei 620 Gipsmodellen von Patienten mitteleuropäischer Herkunft die mesiodistalen Breiten der Incisivi des Unterkiefers gemessen und ausgewertet. Die Gipsmodelle stammten aus den keiferorthopädischen und endodontischen Arichen der zahnklinik der Philipps Universität Marburg von Patienten im Alter zwischen 20 und 60 Jahren

B-type natriuretic peptide is a long-term predictor of all-cause mortality, whereas high-sensitive C-reactive protein predicts recurrent short-term troponin T positive cardiac events in chest pain patients: a prognostic study

<p>Abstract</p> <p>Background</p> <p>Few studies have addressed whether the combined use of B-type natriuretic peptide (BNP) and high-sensitive C-reactive protein (hsCRP) improves risk stratification for mortality and cardiovascular events in a population with chest pain and suspected acute coronary syndromes (ACS). Therefore, we wanted to assess the incremental prognostic value of these biomarkers with respect to long-term all-cause mortality and recurrent troponin T (TnT) positive cardiac events in 871 patients admitted to the emergency department.</p> <p>Methods</p> <p>Blood samples were obtained immediately following admission.</p> <p>Results</p> <p>After a follow-up period of 24 months, 129 patients had died. The BNP levels were significantly higher among patients dying than in long-term survivors (401 (145–736) versus 75 (29–235) pq/mL [median, 25 and 75% percentiles], p = 0.000). In a multivariable Cox regression model for death within 2 years, the hazard ratio (HR) for BNP in the highest quartile (Q4) was 5.13 (95% confidence interval (CI), 1.97–13.38) compared to the lowest quartile (Q1) and was associated with all-cause mortality above and beyond age, congestive heart failure and the index diagnosis ST-segment elevation myocardial infarction. HsCRP rendered no prognostic information for all-cause mortality. However, within 30 days, the adjusted HR for patients with recurrent TnT cardiac positive events hsCRP in Q4 was 14.79 (95% CI, 1.89–115.63) compared with Q1 and was associated with recurrent ischemic events above and beyond age, hypercholesterolemia and TnT values at admission.</p> <p>Conclusion</p> <p>BNP may act as a clinically useful biomarker when obtained at admission in an unselected patient population following hospitalization with chest pain and potential ACS, and may provide complementary prognostic information to established risk determinants at long-term follow-up. Our data do not support the hypothesis that the additional assessment of hsCRP will lead to better risk stratification for survival than BNP alone.</p> <p>Trial registration</p> <p>NCT00521976</p