{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/universal-deterministic-patterns-in","title":"Universal deterministic patterns in stochastic count data","arxiv_id":"2405.17530","date":"2024-05-27","proceeding":null,"authors":["Zhixing Cao","Yiling Wang","Ramon Grima"],"abstract":"We report the existence of deterministic patterns in plots showing the relationship between the mean and the Fano factor (ratio of variance and mean) of stochastic count data. These patterns are found in a wide variety of datasets, including those from genomics, paper citations, commerce, ecology, disease outbreaks, and employment statistics. We develop a theory showing that the patterns naturally emerge when data sampled from discrete probability distributions is organised in matrix form. The theory precisely predicts the patterns and shows that they are a function of only one variable - the sample size.","url_abs":"https://arxiv.org/abs/2405.17530v1","url_pdf":"https://arxiv.org/pdf/2405.17530v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"universal-deterministic-patterns-in","repo_url":"https://github.com/edwardcao3026/pattern","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}