介观尺度上的模块基因动力学与网络理论
Modular Gene Dynamics and Network Theory at Mesoscopic Scale
摘要：
复杂的动态系统通常被建模为网络，其中节点代表通过网络的链接进行交互的动态单元。基因调控网络负责细胞内蛋白质的产生，是可以被描述为相互作用的基因网络的系统的一个例子。一个复杂动力系统的行为特征是其单元在不同尺度上的协同性，从而导致与系统功能相关的涌现动力学。在有关复杂系统的关键问题中，有一个问题是它们在不同的内部和外部相互作用参数下运行的稳定性问题。在这篇论文中，我们研究了通过不同拓扑结构的无向网络耦合的二维混沌映射。我们使用一个非辛耦合，其中涉及的映射之间的相互作用的时间延迟。我们测试网络拓扑结构的稳定性，通过调查他们的集体运动，通过分析孤立的单位从混沌性质的偏离。该研究是在两个网络尺度上进行的：（a）全尺寸网络（计算机生成的无标度树和添加团的树）;（b）树的特征子图4星，作为树的典型动力学基序，它以尽可能少的节点捕获其拓扑结构，适合于时延交互。我们研究这两个网络结构之间的动力学关系，研究出现的合作在大规模（树）作为结果的中尺度动力学模式所表现出的4星。(FULL正文中的摘要）
英文摘要：
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example of system that can be described as a network of interacting genes. The behavior of a complex dynamical system is characterized by cooperativity of its units at various scales, leading to emergent dynamics which is related to the system's function. Among the key problems concerning complex systems is the issue of stability of their functioning, in relation to different internal and external interaction parameters. In this Thesis we study two-dimensional chaotic maps coupled through non-directed networks with different topologies. We use a non-symplectic coupling which involves a time delay in the interaction among the maps. We test the stability of network topologies through investigation of their collective motion, done by analyzing the departures from chaotic nature of the isolated units. The study is done on two network scales: (a) full-size networks (a computer generated scalefree tree and a tree with addition of cliques); (b) tree's characteristic sub-graph 4-star, as a tree's typical dynamical motif which captures its topology in smallest possible number of nodes and is suitable for time-delayed interaction. We study the dynamical relationship between these two network structures, examining the emergence of cooperativity on a large scale (trees) as a consequence of mesoscale dynamical patterns exhibited by the 4-star. (FULL ABSTRACT INSIDE THE TEXT)
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