Error Thresholds in Single-Peak Gaussian Distributed Fitness Landscapes

Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.

Extraction of cable forces due to dead load in cable-stayed bridges under random vehicle loads

To extract the cable forces due to dead load in cable-stayed bridges from the monitoring data,the effects of various factors are eliminated step by step by different statistical methods.The information of cable tension sensors recorded by the health monitoring system of Nanjing No.3 Yangtze River Bridge is taken as an example. Temperature effects are eliminated by linear fitting analysis;a 5-level wavelet de-noising method is applied to eliminate the noise signal by the wavelet basis function of DB8.The rest cable force data is tested by the method of extreme-value type-Ⅲ distribution, and the fitted location parameter is selected as the cable force due to dead load.The results show that the cable force has a linear relationship with temperature. Sometimes, the temperature effect is significant.Noise effect accounts for a small percentage,and the vehicle loads effect has twice the temperature effect on the traffic volume in 2007. The calculation results of other stay cables verify the reliability and validity of the proposed method.

Probability density function and estimation for error of digitized map coordinates in GIS

Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.