Dynamical complexity of discrete time regulatory networks

Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.

基因调控网络的稳定原理：离散动力系统视角下的通道化

Canalization as a stabilizing principle of gene regulatory networks: a discrete dynamical systems perspective

本文从离散动力系统角度探讨基因调控网络的稳定性原理，提出通道化作为稳定机制，并分析其数学基础、应用及面临的挑战。

Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared to other models of regulatory networks, these models have an additional parameter which is identified as quantifying interaction delays. In spite of their simplicity, their dynamics presents a rich variety of behaviours. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear disc…

布尔模型粗粒度采样调控网络的连续动力学

Boolean models coarsely sample continuous dynamics of regulatory networks

本文提出将单调布尔模型嵌入多级组合模型框架，证明布尔模型系统性地低估网络动力学，而DSGRN方法能高效捕获更丰富的动力学行为，为离散与连续建模提供数学桥梁。

Bounded complexity, mean equicontinuity and discrete spectrum

We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric $d_n$, the max-mean metric $\hat{d}_n$ and the mean metric $\bar{d}_n$, both in topological dynamics and ergodic theory. It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_n$ (resp. $\hat{d}_n$) if and only if it is equicontinuous (resp. equicontinuous in the mean). However, we construct minimal systems which have bounded complexity with respect to $\bar{d}_n$ but not equicontinuous in the mean. It turns out that an invariant measure $μ$ …

Discrete spectrum for amenable group actions

In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean.