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摘要翻译：
我们介绍了真核细胞和有机体几何的一种形式，认为细胞是星形凸的，具有良好的生物学依据。这允许一个方便的描述他们的范围在空间以及所有方式的细胞表面梯度。我们假设这些细胞表面标记的光谱决定了生物体形状的表观遗传密码。细胞在某一时刻在空间中的结合，从定义上说，是作为欧几里得空间的度量子空间的有机体，欧几里得空间可以进一步配备一个任意的度量。每个细胞确定空间中的一个点，从而为生物体分配空间中不同点的有限构型，并在该构型空间上引入一个束，与记录特定表观遗传数据的纤维-希尔伯特空间相连。在此基础上，基于Gromov-Hausdorff距离提出了一个形态发生动力学的拉格朗日公式，该公式同时描述了胚胎的发育和再生生长。
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英文标题：
《Geometry of Morphogenesis》
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作者：
Nadya Morozova and Robert Penner
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最新提交年份：
2014
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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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一级分类：Mathematics 数学
二级分类：Metric Geometry 度量几何学
分类描述：Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces
欧氏，双曲，离散，凸，粗几何，黎曼几何的比较，对称空间
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英文摘要：
We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell surface gradients. We assume that a spectrum of such cell surface markers determines an epigenetic code for organism shape. The union of cells in space at a moment in time is by definition the organism taken as a metric subspace of Euclidean space, which can be further equipped with an arbitrary measure. Each cell determines a point in space thus assigning a finite configuration of distinct points in space to an organism, and a bundle over this configuration space is introduced with fiber a Hilbert space recording specific epigenetic data. On this bundle, a Lagrangian formulation of morphogenetic dynamics is proposed based on Gromov-Hausdorff distance which at once describes both embryo development and regenerative growth.
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PDF链接：
https://arxiv.org/pdf/1410.0566
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