🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000793s)
  1. Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics (2020)

    Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami, Yasin Ozcan
    Abstract Where do firms innovate? Mapping their locations in technological space is difficult, because it is high dimensional and unstructured. We address this issue by using a method in computational topology called the Mapper algorithm, which combines local clustering with global reconstruction. We apply this method to a panel of 333 major firms’ patent portfolios in 1976–2005 across 430 technological areas. Results suggest the Mapper graph captures salient patterns in firms’ patenting histories, and our measures of their uniqueness (the length of “flares”) are correlated with firms’ financial performances in a statistically and economically significant manner. We then compare this approach with a widely used clustering method by Jaffe (1989) to highlight additional findings.
  2. The Emergence of Higher-Order Structure in Scientific and Technological Knowledge Networks (2020)

    Thomas Gebhart, Russell J. Funk
    Abstract The growth of science and technology is primarily a recombinative process, wherein new discoveries and inventions are generally built from prior knowledge. While the recent past has seen rapid growth in scientific and technological knowledge, relatively little is known about the manner in which science and technology develop and coalesce knowledge into larger structures that enable or constrain future breakthroughs. Network science has recently emerged as a framework for measuring the structure and dynamics of knowledge. While helpful, these existing approaches struggle to capture the global structural properties of the underlying networks, leading to conflicting observations about the nature of scientific and technological progress. We bridge this methodological gap using tools from algebraic topology to characterize the higher-order structure of knowledge networks in science and technology across scale. We observe rapid and varied growth in the high-dimensional structure in many fields of science and technology, and find this high-dimensional growth coincides with decline in lower-dimensional structure. This higher-order growth in knowledge networks has historically far outpaced the growth in scientific and technological collaboration networks. We also characterize the relationship between higher-order structure and the nature of the science and technology produced within these structural environments and find a positive relationship between the abstractness of language used within fields and increasing high-dimensional structure. We also find a robust relationship between high-dimensional structure and number of metrics for publication success, implying this high-dimensional structure may be linked to discovery and invention.