2018/10/08 by Daizhan Cheng, Cheng, Daizhan, Zhenhui Xu +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Protein Structure and Dynamics #Topological and Geometric Data Analysis #math.DS
paper · pdf · doi:10.48550/arxiv.1810.03520
14 pages,7 figures
openalex publication_date 2018/10/08 · arxiv created 2019/04/16 · arxiv updated 2019/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space. This distance leads to projections over different dimensional Euclidean spaces and the corresponding linear systems on them, which provide a connection among linear systems with different dimensions. Based on these projections, an equivalence of vectors and an equivalence of matrices over different dimensions are proposed. It follows that the dynamics on quotient space is obtained, which provides a proper model for cross-dimensional systems. Finally, using lifts of dynamic systems on quotient space to Euclidean spaces of different dimensions, a cross-dimensional model is proposed to deal with the dynamics of dimension-varying process of linear systems. On the cross-dimensional model a control is designed to realize the transfer between models on Euclidean spaces of different dimensions.