To what degree has the vast space of higher-order knowledge combinations been explored and how has it evolved over time? To address these questions, we first develop a systematic approach to measuring combinatorial innovation in the biomedical sciences based upon the comprehensive ontology of Medical Subject Headings (MeSH) developed and maintained by the US National Library of Medicine. As such, this approach leverages an expert-defined knowledge ontology that features both breadth (27,875 MeSH analyzed across 25 million articles indexed by PubMed that were published from 1902 onwards) and depth (we differentiate between Major and Minor MeSH terms to identify differences in the knowledge network representation constructed from primary research topics only). With this level of uniform resolution, we differentiate between three different modes of innovation contributing to the combinatorial knowledge network: (i) conceptual innovation associated with the emergence of new concepts and entities (measured as the entry of new MeSH) and (ii) recombinant innovation, associated with the emergence of new combinations, which itself consists of two types: peripheral (i.e. combinations involving new knowledge) and core (combinations comprised of pre-existing knowledge only). Another relevant question we seek to address is whether examining triplet and quartet combinations, in addition to the more traditional dyadic or pairwise combinations, provides evidence of any new phenomena associated with higher-order combinations. Analysis of the size, growth, and coverage of combinatorial innovation yield results that are largely independent of the combination order, with some subtle caveats identified at higher order (i.e. beyond the common dyadic or pairwise representation of combinations). Our main results are two-fold: (a) despite the persistent addition of new MeSH terms, the network is densifying over time meaning that scholars are increasingly exploringand realizing the vast space of all knowledge combinations and (b) conceptual innovation is increasingly concentrated within single research articles, a harbinger of the recent paradigm shift towards convergence science.

高阶知识组合的广阔空间被探索到了何种程度，随着时间的推移它是如何演变的？为了解决这些问题，我们首先基于美国国家医学图书馆开发和维护的医学主题词（MeSH）综合本体，开发了一种系统方法来衡量生物医学科学中的组合创新。因此，这种方法利用了专家定义的知识本体，该知识本体具有广度（27,875 MeSH 分析了 2500 万篇 PubMed 索引的文章，从 1902 年开始发表）和深度（我们区分主要和次要 MeSH 术语以识别仅从主要研究主题构建的知识网络表示）。有了这种水平的统一分辨率，我们区分了有助于组合知识网络的三种不同的创新模式：（i）与新概念和实体的出现相关的概念创新（以新 MeSH 的进入来衡量）和（ii）重组创新，与新组合，它本身由两种类型组成：外围（即涉及新知识的组合）和核心（仅由预先存在的知识组成的组合）。我们试图解决的另一个相关问题是，除了更传统的二元或成对组合之外，检查三重和四重组合是否提供了与高阶组合相关的任何新现象的证据。分析规模、增长、组合创新产生的结果在很大程度上独立于组合顺序，在更高的顺序上发现了一些微妙的警告（即超出了组合的常见二元或成对表示）。我们的主要结果有两个：（a）尽管不断添加新的 MeSH 术语，但随着时间的推移，网络正在变得更加密集，这意味着学者们越来越多地探索和意识到所有知识组合的广阔空间；（b）概念创新越来越集中在单一的研究文章，预示着最近范式转向融合科学。