利用DNA序列的混沌游戏表示(chaos game representation,CGR),提出了将2维DNA图谱转化成相应的类谱格式的方法。该方法不仅提供了一个较好的视觉表示,而且可将DNA序列转化成一个时间序列。利用CGR坐标将DNA序列转化成CGR弧度序列,并引入长记忆ARFIMA(p,d,q)模型去拟合此类序列,发现此类序列中有显著的长相关性且拟合度很好。
We study projective synchronization with different scaling factors （PSDF） in N coupled chaotic systems networks. By using the adaptive linear control, some sufficient criteria for the PSDF in symmetrical and asymmetrical coupled networks are separately given based on the Lyapunov function method and the left eigenvalue theory. Numerical simulations for a generalized chaotic unified system are illustrated to verify the theoretical results.
根据可信第三方(Trusted third part,TTP)参与通信的方式,安全协议可以分为在线TTP型和离线TTP型两类。分析了两类协议的优缺点,提出了一种复合型安全协议,在同一协议中结合了两种方式,方式的选择由消息发送方和接收方共同决定。该协议由4条规则组成。为了描述协议的动态运行过程,对SVO逻辑系统进行了扩充,增加了3条公理,用于刻划消息接收者的不可否认性。基于扩充后的SVO逻辑系统对复合型安全协议进行了形式化描述,证明了该协议具有不可否认性。
Chaos game representation （CGR） is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to determine the coordinates of their positions in a continuous space. This distribution of positions has two features： one is unique, and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences. A CGR-walk model is proposed based on CGR coordinates for the DNA sequences. The CGR coordinates are converted into a time series, and a long-memory ARFIMA （p, d, q） model, where ARFIMA stands for autoregressive fractionally integrated moving average, is introduced into the DNA sequence analysis. This model is applied to simulating real CGR-walk sequence data of ten genomic sequences. Remarkably long-range correlations are uncovered in the data, and the results from these models are reasonably fitted with those from the ARFIMA （p, d, q） model.
