摘要翻译：
本文改进了Ehresmann和Vandremeersch[Bull.Math.Bio.49,13-50(1987)]的分层进化系统理论，将该理论的范畴看作模糊集，模糊集的元素是由其嵌入图的箭头和相应顶点构成的复合对象。这样，每个类别都可以表示为状态空间[0.1]**n中的一个点。引入微分同态，在这种情况下充当范畴之间的函子，允许定义一个保持测度的动力系统。特别地，我们应用这种形式主义来描述一个活的单细胞。我们提出了在给定时间内它的状态是一个具有三个水平（分子水平、粗粒水平和细胞水平）的多形范畴，这些水平由适当的大肠杆菌联系起来。每一层都涉及到单元可以划分的主要功能和结构模块。细胞的时间演化是由一个变换驱动的，这个变换是Ricker映射的n维推广，我们建议通过要求活细胞在混沌边缘演化作为其行为的标志来确定其参数。从动力学角度看，这一性质表现为最大Lyapunov指数等于零。由于在一个相当完整的活细胞模型中，涉及到大量的参数使计算变得困难，我们还提出了一个玩具模型，该模型需要确定的参数较少，强调了细胞的裂变。
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英文标题：
《Hierarchical evolutive systems, fuzzy categories and the living single
  cell》
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作者：
Alejandro M. Mes\'on, C. Manuel Carlevaro and Fernando Vericat
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最新提交年份：
2018
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  In this article, the theory of hierarchical evolutive systems of Ehresmann and Vandremeersch [Bull. Math. Bio. 49, 13-50 (1987)] is improved by considering the categories of the theory as fuzzy sets whose elements are the composite objects formed by the arrows and corresponding vertices of their embedded graphs. This way each category can be represented as a point in the states space [0.1]**N. The introduction of a diffeomorphism, that acts in this context as a functor between categories, allows to define a measure preserving dynamical system. In particular, we apply this formalism to describe a living single cell. We propose for its state at a given time a hirerchical category with three levels (molecular, coarse-grained and cellular levels) related by adequate colimits. Each level involves the main functional and structural modules in which the cell can be partitioned. The time evolution of the cell is drived by a transformation which is a N-dimensional generalization of the Ricker map whose parameters we propose to be determined by requiring that, as hallmark of its behavior, the living cell to evolve at the edge of chaos. From the dynamical point of view this property manifests in the fact that the largest Lyapunov exponent is equal to zero. Since in a rather complete model of the living cell the huge number of involved parameters can make of the calculations a hard task, we also propose a toy model, with fewer parameters to be determined, which emphasizes the cellular fission.
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PDF链接：
https://arxiv.org/pdf/1802.00858