Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems
arXiv:2002.09770
Abstract
Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of `type calculus', for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry.
36 pages, 10 main figures, 15 inset figures, 1 table; online appendices: http://compstorylab.org/allotaxonometry/
References in corpus (13)
- Emergence of scaling in random networks
- Power laws, Pareto distributions and Zipf's law
- Robust estimation of microbial diversity in theory and in practice
- Characterizing the Google Books corpus: Strong limits to inferences of socio-cultural and linguistic evolution
- Empirical Tests of Zipf's law Mechanism In Open Source Linux Distribution
- Safe Leads and Lead Changes in Competitive Team Sports
- Scoring dynamics across professional team sports: tempo, balance and predictability
- Similarity of symbol frequency distributions with heavy tails
- Selection Bias Tracking and Detailed Subset Comparison for High-Dimensional Data
- The game story space of professional sports: Australian Rules Football
- Simon's fundamental rich-get-richer model entails a dominant first-mover advantage
- Hahahahaha, Duuuuude, Yeeessss!: A two-parameter characterization of stretchable words and the dynamics of mistypings and misspellings
- Why scatter plots suggest causality, and what we can do about it
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