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    Sample path properties of the average generation of a Bellman-Harris process

    Meli, Gianfelice and Weber, Tom S. and Duffy, Ken R. (2019) Sample path properties of the average generation of a Bellman-Harris process. Journal of Mathematical Biology, 79. pp. 673-704. ISSN 1432-1416

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    Motivated by a recently proposed design for a DNA coded randomised algorithm that enables inference of the average generation of a collection of cells descendent from a common progenitor, here we establish strong convergence properties for the average generation of a super-critical Bellman–Harris process. We further extend those results to a two-type Bellman–Harris process where one type can give rise to the other, but not vice versa. These results further affirm the estimation method’s potential utility by establishing its long run accuracy on individual sample-paths, and significantly expanding its remit to encompass cellular development that gives rise to differentiated offspring with distinct population dynamics.

    Item Type: Article
    Additional Information: This work was supported by Science Foundation Ireland Grant 12 IP 1263
    Keywords: Bellman–Harris process; Sample-path properties; Average generation inference; Average tree depth inference; DNA coded algorithm; Two-type process;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 13478
    Identification Number:
    Depositing User: Dr Ken Duffy
    Date Deposited: 03 Nov 2020 15:08
    Journal or Publication Title: Journal of Mathematical Biology
    Publisher: Springer
    Refereed: Yes
    Funders: Science Foundation Ireland (SFI)
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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