This paper proposes a method based on quaternion for characterization α helix of proteins. The method defines the parameter called Quaternion Helix Axis Spherical Distance (QHASD) on the basis of mapping protein Cα frames′ helical axis onto a unit sphere, and uses QHASD to characterize the α helix of the protein secondary structure. Application of this method has been verified based on the PDBselect database, with an α helix characterization accuracy of 91.7%. This method possesses significant advantages of high detection accuracy, low computation and clear geometric significance.
Missing data represent a general problem in many scientific fields, especially in medical survival analysis. Dealing with censored data, interpolation method is one of important methods. However, most of the interpolation methods replace the censored data with the exact data, which will distort the real distribution of the censored data and reduce the probability of the real data falling into the interpolation data. In order to solve this problem, we in this paper propose a nonparametric method of estimating the survival function of right-censored and interval-censored data and compare its performance to SC (self-consistent) algorithm. Comparing to the average interpolation and the nearest neighbor interpolation method, the proposed method in this paper replaces the right-censored data with the interval-censored data, and greatly improves the probability of the real data falling into imputation interval. Then it bases on the empirical distribution theory to estimate the survival function of right-censored and interval-censored data. The results of numerical examples and a real breast cancer data set demonstrated that the proposed method had higher accuracy and better robustness for the different proportion of the censored data. This paper provides a good method to compare the clinical treatments performance with estimation of the survival data of the patients. This provides some help to the medical survival data analysis.
Multivariate time series problems widely exist in production and life in the society. Anomaly detection has provided people with a lot of valuable information in financial, hydrological, meteorological fields, and the research areas of earthquake, video surveillance, medicine and others. In order to quickly and efficiently find exceptions in time sequence so that it can be presented in front of people in an intuitive way, we in this study combined the Riemannian manifold with statistical process control charts, based on sliding window, with a description of the covariance matrix as the time sequence, to achieve the multivariate time series of anomaly detection and its visualization. We made MA analog data flow and abnormal electrocardiogram data from MIT-BIH as experimental objects, and verified the anomaly detection method. The results showed that the method was reasonable and effective.
Traditional sample entropy fails to quantify inherent long-range dependencies among real data. Multiscale sample entropy (MSE) can detect intrinsic correlations in data, but it is usually used in univariate data. To generalize this method for multichannel data, we introduced multivariate multiscale entropy into multiscale signals as a reflection of the nonlinear dynamic correlation. But traditional multivariate multiscale entropy has a large quantity of computation and costs a large period of time and space for more channel system, so that it can not reflect the correlation between variables timely and accurately. In this paper, therefore, an improved multivariate multiscale entropy embeds on all variables at the same time, instead of embedding on a single variable as in the traditional methods, to solve the memory overflow while the number of channels rise, and it is more suitable for the actual multivariate signal analysis. The method was tested in simulation data and Bonn epilepsy dataset. The simulation results showed that the proposed method had a good performance to distinguish correlation data. Bonn epilepsy dataset experiment also showed that the method had a better classification accuracy among the five data set, especially with an accuracy of 100% for data collection of Z and S.
Diffusion tensor imaging (DTI) is a rapid development technology in recent years of magnetic resonance imaging. The diffusion tensor interpolation is a very important procedure in DTI image processing. The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy, but the method does not revise the size of tensors. The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation. Firstly, we decomposed diffusion tensors with the direction of tensors being represented by quaternion. Then we revised the size and direction of the tensor respectively according to different situations. Finally, we acquired the tensor of interpolation point by calculating the weighted average. We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data. The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy (FA) and the determinant of tensors, but also preserve the tensor anisotropy at the same time. In conclusion, the improved method provides a kind of important interpolation method for diffusion tensor image processing.