论文标题
局部突变在二次迭代中的影响
Effects of local mutations in quadratic iterations
论文作者
论文摘要
我们在复制系统中介绍突变，其中完整复制机制是通过家庭$ f_c（z）= z^2+c $的复杂二次映射的离散迭代来执行的。更具体地说，我们考虑一个“正确”函数$ f_ {C_1} $作用在复杂平面上（代表要复制的RNA）。一个“突变” $ f_ {c_0} $是作用在给定半径$ r $围绕突变焦点$ξ^*$的位点上的不同（“错误”）映射。突变的效果是径向插值的，以最终恢复原始地图$ f_ {C_1} $，当达到外半径$ r $。我们称结果地图为“突变”地图。 在突变迭代的理论框架中，我们研究突变（复制误差）如何在细胞分化的背景下影响系统的时间演变。我们使用该系统的囚犯组合在突变地图下同时量化整个空间的长期行为。我们分析突变的位置，时机和大小如何改变系统的长期演变（如囚犯拓扑中编码）。在遗传学的背景下，在与干细胞分化的过程中，该框架可能会增加我们对塑造遗传表达的因素和机制的理解。
We introduce mutations in replication systems in which the intact copying mechanism is performed by discrete iterations of a complex quadratic map in the family $f_c(z) = z^2+c$. More specifically, we consider a "correct" function $f_{c_1}$ acting on the complex plane (representing the RNA to be copied). A "mutation" $f_{c_0}$ is a different ("erroneous") map acting on a locus of given radius $r$ around a mutation focal point $ξ^*$. The effect of the mutation is interpolated radially to eventually recover the original map $f_{c_1}$ when reaching an outer radius $R$. We call the resulting map a "mutated" map. In the theoretical framework of mutated iterations, we study how a mutation (replication error) affects the temporal evolution of the system, in the context of cellular differentiation. We use the prisoner set of the system to quantify simultaneously the long-term behavior of the entire space under mutated maps. We analyze how the position, timing and size of the mutation can alter the system's long-term evolution (as encoded in the topology of its prisoner set). In the context of genetics, this framework may increase our understanding of the factors and mechanisms that shape the genetic expression, in a specialized cell, in the process of differentiation from a stem cell.
