Einstein Institute of Mathematics, The Hebrew University of Jerusalem(1), 9190401, Jerusalem, Israel; Department of Mathematics, Rutgers University, Piscataway, NJ, 08854-8019, USA.
Institute of Mathematical Biology, Faculty of Computer Sciences, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.
Biosystems. 2021 Jun;204:104392. doi: 10.1016/j.biosystems.2021.104392. Epub 2021 Mar 14.
Is it possible to apply infinite combinatorics and (infinite) set theory in theoretical biology? We do not know the answer yet but in this article we try to present some techniques from infinite combinatorics and set theory that have been used over the last decades in order to prove existence results and independence theorems in algebra and that might have the flexibility and generality to be also used in theoretical biology. In particular, we will introduce the theory of forcing and an algebraic construction technique based on trees and forests using infinite binary sequences. We will also present an overview of the theory of circular codes. Such codes had been found in the genetic information and are assumed to play an important role in error detecting and error correcting mechanisms during the process of translation. Finally, examples and constructions of infinite mixed circular codes using binary sequences hopefully show some similarity between these theories - a starting point for future applications.
是否可以在理论生物学中应用无限组合学和（无限）集合论？我们还不知道答案，但在本文中，我们试图介绍过去几十年来在代数中用于证明存在性结果和独立性定理的一些无限组合学和集合论技术，这些技术可能具有足够的灵活性和普遍性，可以在理论生物学中应用。具体来说，我们将介绍迫在眉睫的理论和一种基于树和森林的使用无限二进制序列的代数构造技术。我们还将介绍循环码理论的概述。在遗传信息中发现了这样的代码，并假定它们在翻译过程中的纠错和纠错机制中起着重要作用。最后，使用二进制序列的无限混合循环码的示例和构造，希望展示这些理论之间的一些相似性——这是未来应用的起点。
