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Stochastic Models of Cell Proliferation Kinetics Based on Branching Processes

  • Nikolay M. YanevEmail author
Chapter
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Abstract

The aim of this memorial survey paper is to present some joint work with Andrei Yu. Yakovlev (http://www.biology-direct.com/content/3/1/10) focused on new ideas for the theory of branching processes arising in cell proliferation modeling. The following topics are considered: some basic characteristics of cell cycle temporal organization, distributions of pulse-labeled discrete markers in branching cell populations, distributions of a continuous label in proliferating cell populations, limiting age and residual lifetime distributions for continuous-time branching processes, limit theorems and estimation theory for multitype branching populations and relative frequencies with a large number of ancestor, age-dependent branching populations with randomly chosen paths of evolution. Some of the presented results have not been published yet.

Keywords

Branching processes Cell proliferation Discrete and continuous labels Label distributions Immigration Age and residual lifetime distributions Age-dependent processes Large number of ancestors Multitype branching processes Limiting distributions Asymptotic normality Statistical inference 

AMS 2000 Subject Classifications

Primary 60J80 60J85; Secondary 62P10 92D25 

Notes

Acknowledgements

The author is very grateful to the referee for the useful remarks. The paper is supported by NIH/NINDS grant NS39511, NIH/NCI R01 grant CA134839, NIH grant N01-AI-050020 and grant KP-6-H22/3 from the NSF of the Ministry of Education and Science of Bulgaria.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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