分形几何学是非线性科学中重要的数学理论和方法，在生物信息学中如癌症诊断、分子进化、DNA和蛋白质功能分析等方面已广为应用。序列复杂度通过因子复杂性刻画序列的组成特性，是分形、数论、计算机编码等领域中的重要数学工具。本项目拟重点研究分形与序列复杂度方法在两类DNA调控元件的预测中的应用。具体内容包括(1)发展基于迭代函数系统的混沌图表示以及在此基础上的计盒维数、李雅普诺夫指数等分形指标的计算方法;(2)发展基于序列复杂度函数的拓扑熵、增长指数等复杂性指标的计算方法;(3)综合应用这些分形指标和复杂性指标，数值化表示人类基因组中DNA甲基化位点和CTCF结合位点两类DNA区段，并借助深度学习等信息技术构建预测模型。我们的预期成果将丰富分形与序列复杂度研究领域中重要数学指标的计算方法，同时还将拓展这些方法在生物信息中的应用研究范畴，并力争开拓分形几何学与生物信息学两个学科之间新的交叉点。

Fractal is an important method in nonlinear science, and it is attached high importance in the applications in Bioinformatics due to numerous successful cases, such as cancer diagnosis, molecular evolution and function analysis of DNA and protein. Sequence complexity can describe compositional properties of sequences by using factor complexities, and it has been widely used in various research areas, such as fractal, number theory, computer coding. In this project, we will study fractal and sequence complexity methods and their applications in predictions of two kinds of DNA regulatory elements. They contain: (1)develop ‘iterated function system’-based chaos game representation and related fractal indexes, such as box-counting dimension、Lyapunov exponent; (2)develop ‘sequence complexity’-based complexity indexes, such as topological entropy; (3)integrate these fractal and complexity indexes to represent DNA fragments and develop prediction models of DNA methylation sites and CTCF binding sites by employing deep learning technology. Our expectant results will both enrich the computing methods of some important mathematical indexes in fractal, and will also branch the applications of these methods in the more Bioinformatics research areas.