Real-Time Equivalence of Chemical Reaction Networks and Analog Computers
Real-Time Equivalence of Chemical Reaction Networks and Analog Computers
复制标题
化学反应网络与模拟计算机的实时等效
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
James I. Lathrop
中科院分区：
文献类型：
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作者：
Xiang Huang;T. Klinge;James I. Lathrop
本文研究了可由化学反应网络(Huang，Klinger，Lathrop，Li，Lutz，2019)实时计算的实数类(Mathbb{R}_{RTCRN})及其与通用模拟计算机的关系。粗略地说，如果存在一个具有积分速率常数和指定物种X的化学反应网络(CRN)，使得当所有物种的浓度初始化为零时，X迅速指数收敛到α。本文定义了一类可由通用模拟计算机实时计算的实数的相似类\(\mathbb{R}_{RTGPAC}\)，并利用与Fages、Le Guludec、Bournez和Pouly提出的差表示法类似的结构证明了\(\mathbb{R}_{RTGPAC}=\mathbb{R}_{RTCRN}\).我们证明了这一等价性，证明了\(\mathbb{R}_{RTCRN}\)是\(\mathbb{R}\)的一个子域，它解决了一个以前公开的问题。我们还证明了初始浓度为零的CRN可以模拟为初始浓度为整数的CRN。利用这些结果，我们给出了简单而自然的结构，证明了\(e\)和\(\pi\)是以前未知的\(mathbb{R}_{RTCRN})的成员。
This paper investigates the class \( \mathbb {R}_{RTCRN}\) of real numbers that are computable in real time by chemical reaction networks (Huang, Klinge, Lathrop, Li, Lutz, 2019), and its relationship to general purpose analog computers. Roughly, \( \alpha \in \mathbb {R}_{RTCRN}\) if there is a chemical reaction network (CRN) with integral rate constants and a designated species \( X \) such that, when all species concentrations are initialized to zero, \( X \) converges to \( \alpha \) exponentially quickly. In this paper, we define a similar class \( \mathbb {R}_{RTGPAC}\) of real numbers that are computable in real time by general purpose analog computers, and show that \( \mathbb {R}_{RTGPAC}= \mathbb {R}_{RTCRN}\) using a construction similar to that of the difference representation introduced by Fages, Le Guludec, Bournez, and Pouly. We prove this equivalence by showing that \( \mathbb {R}_{RTCRN}\) is a subfield of \( \mathbb {R}\) which solves a previously open problem. We also prove that a CRN with integer initial concentrations can be simulated by a CRN with all zero initial concentrations. Using these results, we give simple and natural constructions showing \( e \) and \( \pi \) are members of \( \mathbb {R}_{RTCRN}\), which was not previously known.
连续化学反应网络中的可组合速率无关计算
DOI：
10.1007/978-3-319-99429-1_15
发表时间：
2018
期刊：
Computational Methods in Systems Biology. CMSB 2018.
影响因子：
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作者：
Chalk, C;Kornerup, N;Reeves, W;Soloveichik, D
通讯作者：
Soloveichik, D