摘要翻译:
本文提出了一个描述生物时间某些特征的抽象数学框架。关键的一点是,在我们看来,时间的通常物理(线性)表示不足以理解生命的关键现象,如生理(昼夜节律、季节性……)和适当的生物(心脏跳动、呼吸、新陈代谢……)的节律。特别是,生物节律的作用在物理时钟的数学形式化中似乎没有任何对应的作用,物理时钟是基于通常(可能是热力学的,因此是定向的)时间的频率。然后我们提出了生物时间的二维流形函数表示,作为适应自主生物节律的数学框架。这样得到的节律的“视觉”表示,特别是心脏跳动,将通过几个例子,为我们的方法在理解种间差异或种内病理方面的可能应用提供提示。由于纯粹数学的原因而需要的三维嵌入空间允许为“表示时间”引入一个合适的额外维度,具有认知意义。
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英文标题:
《A 2-dimensional Geometry for Biological Time》
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作者:
Francis Bailly, Giuseppe Longo, Ma\"el Mont\'evil
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最新提交年份:
2012
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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:
This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal ...) and properly biological (heart beating, respiration, metabolic ...). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The "visual" representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3-dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for "representation time", with a cognitive significance.
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PDF链接:
https://arxiv.org/pdf/1004.4186