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Fingerprints of cancer by persistent homology

View ORCID ProfileA. Carpio, View ORCID ProfileL. L. Bonilla, View ORCID ProfileJ. C. Mathews, A. R. Tannenbaum
doi: https://doi.org/10.1101/777169
A. Carpio
1Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
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L. L. Bonilla
2Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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  • For correspondence: bonilla@ing.uc3m.es
J. C. Mathews
3Department of Medical Physics, Memorial Sloan Kettering Cancer Center, NY 10065, USA
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A. R. Tannenbaum
3Department of Medical Physics, Memorial Sloan Kettering Cancer Center, NY 10065, USA
4Departments of Computer Science & Applied Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
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Abstract

We have carried out a topological data analysis of gene expressions for different databases based on the Fermat distance between the z scores of different tissue samples. There is a critical value of the filtration parameter at which all clusters collapse in a single one. This critical value for healthy samples is gapless and smaller than that for cancerous ones. After collapse in a single cluster, topological holes persist for larger filtration parameter values in cancerous samples. Barcodes, persistence diagrams and Betti numbers as functions of the filtration parameter are different for different types of cancer and constitute fingerprints thereof.

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Posted September 23, 2019.
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Fingerprints of cancer by persistent homology
A. Carpio, L. L. Bonilla, J. C. Mathews, A. R. Tannenbaum
bioRxiv 777169; doi: https://doi.org/10.1101/777169
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Fingerprints of cancer by persistent homology
A. Carpio, L. L. Bonilla, J. C. Mathews, A. R. Tannenbaum
bioRxiv 777169; doi: https://doi.org/10.1101/777169

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