Dynamic Data Structures for Complex Systems

My work concerns the dynamics of some data structures and complex systems. We presented a combinatorial approach of tableaux and permutations based on dynamics. This approach, which we call Dynamic Data Structures opens us the door towards applications in economy via complex systems. Increasing subsequences of length more than two, the rectangular standard Young tableaux with two lines, the Dyck words and the codes which link these data structures. We have proposed an economic model which models the benefit of a bank account whose possible enumeration of the configurations is done using an adapted code. The second application deals with the evolution of genetic automata populations. These populations are studied by spectral analysis. Experiments are given on probabilistic automata whose evolution results in controlling dissipation by auto-regulation. The aim of this work is to give some computation tools related to the dynamics of data structures to analyze the complexity of systems.