It is widely understood that innovations tend to be concentrated in cities, which is evidenced by innovative output increasing disproportionately with city size. Yet, given the heterogeneity of countries and technologies, few studies explore the relationship between population and innovation numbers. For instance, in the USA, innovative output scaling is substantial and is particularly pronounced for complex technologies. Whether this is a universal pattern of complex technologies and a potential facilitator of scaling, is unknown. Our analysis compared urban scaling in urban areas across 33 countries and 569 technologies. Considerable variation was identified between countries, which is rooted in two fundamental mechanisms (sorting and boosting). The sorting of innovation-intensive technologies is found to drive larger innovation counts among cities. Among most countries, this mechanism contributes to scaling more than city size boosting innovation within specific technologies. While complex technologies are concentrated in large cities and benefit from the advantages of urbanization, their contribution to the urban scaling of innovations is limited.

中文翻译：

---

提升、排序和复杂性——全球创新的城市规模

众所周知，创新往往集中在城市，创新产出的增长与城市规模不成比例就证明了这一点。然而，鉴于国家和技术的异质性，很少有研究探讨人口与创新数量之间的关系。例如，在美国，创新的产出规模很大，对于复杂技术尤为明显。这是否是复杂技术的普遍模式和扩展的潜在促进因素，尚不得而知。我们的分析比较了 33 个国家和 569 种技术在城市地区的城市规模。国家之间存在相当大的差异，这植根于两个基本机制（排序和提升）。研究发现，创新密集型技术的分类可以推动城市中更大的创新数量。在大多数国家中，这种机制有助于扩大城市规模，促进特定技术的创新。虽然复杂技术集中在大城市并受益于城市化的优势，但它们对城市创新规模的贡献有限。