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A probabilistic model for the survivability of cells

Part of: Approximation methods and numerical treatment of dynamical systems Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Ilan Adler ,
Hyun-Soo Ahn ,
Richard M. Karp  and
Sheldon M. Ross
Ilan Adler*
Affiliation:
University of California, Berkeley
Hyun-Soo Ahn
Affiliation:
University of California, Berkeley
Richard M. Karp*
Affiliation:
University of California, Berkeley
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: [email protected]
∗∗∗Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA. Email address: [email protected]
∗∗∗∗Postal address: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: [email protected]
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Abstract

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Consider n cells, of which some are target cells, and suppose that each cell has a weight. The cells are killed in a sequential manner, with each currently live cell being the next one killed with a probability proportional to its weight. We study the distribution of the number of cells that are alive at the moment when all the target cells have been killed.

Keywords

Target cellcoupon typeChernoff boundsimulation

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 60C05: Combinatorial probability 37M05: Simulation
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 919 - 931
Copyright
© Applied Probability Trust 2005 

Footnotes

∗∗

Current address: Department of Operations and Management Science, Ross School of Business, University of Michigan, Ann Arbor, MI 48109, USA. Email address: [email protected]

Research supported by the National Science Foundation Grant DMI-9901053 with the University of California.

References

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Motwani, R. and Raghavan, P. (1995). Randomized Algorithms. Cambridge University Press.CrossRefGoogle Scholar
Ross, S. M. (2002). Simulation, 3rd edn. Academic Press, Burlington, MA.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.Google Scholar