二次迭代中局部突变的影响
Effects of local mutations in quadratic iterations
AI总结：
本文在复二次映射离散迭代构成的复制系统中引入局部突变机制，通过径向插值构建突变映射，并利用囚徒集拓扑分析突变的位置、时机与大小对细胞分化系统长期演化及基因表达的影响。
摘要：
我们在复制系统中引入突变，其中完整的复制机制由复二次映射族 $f_c(z) = z^2+c$ 的离散迭代执行。更具体地说，我们考虑一个作用于复平面（代表待复制的 RNA）的“正确”函数 $f_{c_1}$。“突变” $f_{c_0}$ 是一个不同的（“错误的”）映射，作用于突变焦点 $ξ^*$ 周围给定半径 $r$ 的基因座上。突变的影响通过径向插值计算，最终在到达外半径 $R$ 时恢复原始映射 $f_{c_1}$。我们将所得映射称为“突变”映射。在突变迭代的理论框架下，我们在细胞分化的背景下研究突变（复制错误）如何影响系统的时间演化。我们利用系统的囚徒集来同时量化整个空间在突变映射下的长期行为。我们分析了突变的位置、时机和大小如何改变系统的长期演化（如其囚徒集的拓扑结构所编码）。在遗传学背景下，该框架可能增进我们对干细胞分化过程中特定细胞内塑造基因表达的因素和机制的理解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
