Background and Aims-Alpha-fetoprotein (AFP) is widely used as a surveillance test for Hepatocellular carcinoma (HCC) among patients with cirrhosis. Des-gamma carboxy-prothrombin (DCP) and lectin-bound AFP (AFP-L3) are potential surveillance tests for HCC. The aims of this study were to determine performance of DCP and AFP-L3 for the diagnosis of early HCC, whether they complement AFP, and what factors affect DCP, AFP-L3 or AFP levels.

939In biological oscillator communities the transmission of information between two oscillators needs a finite time r. We investigate the influence of this effect on the mutual entrainment of two limit cycle oscillators with different frequencies by coupling them with a time delay r. It is shown that for a finite delay time there exists a multitude of synchronized solutions in contrast to the situation without delay where one has at most one solution. § 1. IntroductionInteracting nonlinear oscillators with different individual frequencies can spontaneously synchronize themselves to a common frequency-if the coupling strength exceeds a certain threshold value. This phenomenon is of much relevance to the understanding of biological oscillators such as, e.g., coupled heart pacemaker cells. Inspired by Winfree's earlier ideas l ) there has been a great deal of theoretical work on self-synchronization especially by Kuramoto and his coworkers. 2H3 )In this article we want to take into account the fact that in biological oscillator communities the information transmission between two oscillators needs a finite time r. 14 ),15) Important examples would be neural assemblies which could be modelled by oscillator communities where the delay is caused by the finite velocity of the signal along the axons. 16H8 ) There the crucial question occurs whether synchronization is still possible if the inverse delay time becomes of the same order of magnitude as the oscillator frequencies. In order to investigate the effect of this time delay on the synchronization of nonlinear oscillators we study the following model equations for two limit cycle oscillators:Here if;1, if;2 are the phases of the oscillators with individual frequencies WI, W2, and the interaction terms K sin( if;1,2( t) -if;2,1 (t -r» with coupling strength K tend to synchronize both oscillators. Apart from the delay time r which takes into account that different oscillators know from each others phases only after a retardation time, these equations are (for r=O) just the model equations which have been extensively investigated by Kuramoto.

No abstract

s u m m a r y Accurate rainfall data are of prime importance for many environmental applications. To provide spatially distributed rainfall data, point measurements are interpolated. However, in low density measurement networks, the use of different interpolation methods may result in large differences and hence in deviations from the actual spatial distribution of rainfall. Our study aims at analyzing different rainfall interpolation schemes with regard to their suitability to produce spatial rainfall estimates in a monsoon dominated region with scarce rainfall measurements. The study was carried out in the meso-scale catchment of the Mula and the Mutha Rivers (2036 km 2 ) upstream of the city of Pune, India. Rainfall data from 16 rain gauges were spatially interpolated using seven different methods, including Thiessen polygons, statistical, and geostatistical approaches. The two most suitable covariates for rainfall interpolation were identified as (i) distance in wind direction from the main orographic barrier and as (ii) a 0.05°pattern of mean annual rainfall derived from satellite data acquired by the Tropical Rainfall Measuring Mission (TRMM). Consequently, these two covariates were used in the regression-based interpolation approaches. The quality of the different methods was assessed using a two step validation approach: (i) Cross-validation was used to evaluate the capability to reproduce measured data. (ii) Spatially integrated interpolation performance was assessed by using a hydrologic model to calculate runoff and compare modeled to measured runoff. By this assessment, the regression-based methods showed the best performance. We found that the choice of the covariate had a significant impact on precipitation and runoff amounts, as well as on the temporal course of runoff events. Our results show, that the decision on the suitable interpolation scheme should not only be based on the comparison with point measurements, but should also take the representativeness of the given measurement network as well as of the interpolated spatial rainfall distribution into account. The successful application of regression-based interpolation methods using a high resolution TRMM pattern as covariate is very promising as it is transferable to other data scarce regions.