Essential Simplices in Persistent Homology and Subtle Admixture Detection

Authors Saugata Basu , Filippo Utro , Laxmi Parida

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Author Details

Saugata Basu
  • Department of Mathematics, Purdue University, West Lafayette, IN 47906, USA
Filippo Utro
  • Computational Biology Center, IBM T. J. Watson Research, Yorktown Heights, NY 10598, USA
Laxmi Parida
  • Computational Biology Center, IBM T. J. Watson Research, Yorktown Heights, NY 10598, USA

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Saugata Basu, Filippo Utro, and Laxmi Parida. Essential Simplices in Persistent Homology and Subtle Admixture Detection. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 14:1-14:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We introduce a robust mathematical definition of the notion of essential elements in a basis of the homology space and prove that these elements are unique. Next we give a novel visualization of the essential elements of the basis of the homology space through a rainfall-like plot (RFL). This plot is data-centric, i.e., is associated with the individual samples of the data, as opposed to the structure-centric barcodes of persistent homology. The proof-of-concept was tested on data generated by SimRA that simulates different admixture scenarios. We show that the barcode analysis can be used not just to detect the presence of admixture but also estimate the number of admixed populations. We also demonstrate that data-centric RFL plots have the potential to further disentangle the common history into admixture events and relative timing of the events, even in very complex scenarios.

Subject Classification

ACM Subject Classification
  • Applied computing → Life and medical sciences
  • population admixture
  • topological data analysis
  • persistent homology
  • population evolution


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  1. Anna P. Carrieri, Filippo Utro, and Laxmi Parida. Sampling arg of multiple populations under complex configurations of subdivision and admixture. Bioinformatics, 32(7):1048-1056, 2016. Google Scholar
  2. Herbert Edelsbrunner and John L. Harer. Computational topology: An Introduction. American Mathematical Society, Providence, RI, 2010. Google Scholar
  3. Robin Forman. A user’s guide to discrete Morse theory. Sém. Lothar. Combin., 48:Art. B48c, 35, 2002. Google Scholar
  4. Matthew L. Freedman, Christopher A. Haiman, Nick Patterson, Gavin J. McDonald, Arti Tandon, Alicja Waliszewska, Kathryn Penney, Robert G. Steen, Kristin Ardlie, Esther M. John, Ingrid Oakley-Girvan, Alice S. Whittemore, Kathleen A. Cooney, Sue A. Ingles, David Altshuler, Brian E. Henderson, and David Reich. Admixture mapping identifies 8q24 as a prostate cancer risk locus in african-american men. Proceedings of the National Academy of Sciences, 103(38):14068-14073, 2006. Google Scholar
  5. Robert Ghrist. Barcodes: The persistent topology of data. Bulletin of the American Mathematical Society, 45:61-75, 2008. Google Scholar
  6. Mark Jobling, Edward Hollox, Matthew Hurles, Toomas Kivisild, and Chris Tyler-Smith. Human evolutionary genetics. Garland Science, UK, 2013. Google Scholar
  7. M.J. Kearsey and H.S. Pooni. The Genetical Analysis of Quantitative Traits. Stanley Thornes, UK, 2004. Google Scholar
  8. P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Alagappan, J. Carlsson, G. Carlsson, and Mikael Vilhelm Vejdemo Johansson. Extracting insights from the shape of complex data using topology. Scientific Reports, 3, 2013. Google Scholar
  9. Lammi Parida, Filippo Utro, Deniz Yorukoglu, Anna Paola Carrieri, David Kuhn, and Saugata Basu. Topological signatures for population admixture. In Teresa M. Przytycka, editor, Research in Computational Molecular Biology, pages 261-275. Springer International Publishing, 2015. Google Scholar
  10. Andrew Tausz, Mikael Vejdemo-Johansson, and Henry Adams. JavaPlex: A research software package for persistent (co)homology. In Han Hong and Chee Yap, editors, Proceedings of ICMS 2014, Lecture Notes in Computer Science 8592, pages 129-136, 2014. Software available at URL:
  11. J.D. Wall and M.F. Hammer. Archaic admixture in the human genome. Current opinion in genetics &development, 16(6):606-610, 2006. Google Scholar
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