Mathematical Sciences: Topics in Symbolic Dynamics

这项补充奖励是为了支持Selim Tuncel教授在首席研究员Lind教授的项目中的数学研究。这门学科是称为符号动力学的遍历理论的一个分支。符号动力系统是来自有限字母表的双向无限符号串的集合，满足一个形成规则，该规则指定当一个人沿着该串移动时，允许跟随哪些符号。如果两个这样的系统之间存在遵守移位操作的行为良好的双射，则这两个系统是等价的。这一领域的一个中心主题是符号动力系统的分类。Tuncel教授将研究这些系统和相关系统的不变量，包括马尔可夫链的Beta函数、由维度模块产生的代数不变量和称为脚手架的额外结构元素。元胞自动机和伯努利移位之间的分组码是另外的研究课题。本项目中研究的数学结构已被用作通信和数据系统的模型。

This supplementary award is to support the mathematical research of Professor Selim Tuncel on the project of the principal investigator, Professor Lind. The subject is a branch of ergodic theory called symbolic dynamics. A symbolic dynamical system is a collection of two-way infinite strings of symbols from a finite alphabet satisfying a formation rule that specifies which symbols are allowed to follow which as one moves along the string. Two such systems are equivalent if there is a well- behaved bijection between them that respects the operation of shifting. A central theme in this area is the classification of symbolic dynamical systems. Professor Tuncel will study invariants for these and related systems, including the beta function for Markov chains and an algebraic invariant resulting from dimension modules and an additional element of structure called the scaffold. Cellular automata and block codes between Bernoulli shifts are additional research topics. The mathematical structures studied in this project have found considerable use as models for communication and data systems.