Asymptotic behaviour of an operator exponential related to branching random walk models of dna repeats

Journal of Biological Systems

Volumn 7, Issue 1, 1999, Pages 33-43

  Bobrowski, Adam ^a   Kimmel, Marek ^b  

^a LUBLIN UNIVERSITY OF TECHNOLOGY   (Poland)

^b Rice University   (United States)

Author keywords

Asymptotic behaviour; Branching random walk; DNA repeats; Drug resistance; Operator exponential function

Indexed keywords

EID: 0347748133     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339099000048     Document Type: Article

References (14)

1. Arendt W. and Batty C. J. K., Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988) pp. 837-852.
2. Axelrod D. E., Baggerly K. A. and Kimmel M., Gene amplification by unequal sister chromatid exchange: Probabilistic modeling and analysis of drug resistance data, J. Theor. Biol. 168 (1994) pp. 151-159.
3. Batty C. J. K., Asymptotic behaviour of semigroups, in Banach Center Publications 30 (1994) pp. 35-52.
4. Feller W., An Introduction to Probability and its Applications, Vol. 1 (Wiley, New York 1961).
5. Jagers P., Branching Processes with Biological Applications (Wiley, New York, 1976).
6. Kimmel M., Rapid genome evolution and cancer: A modeling perspective, Applied Mathematics and Computer Science, Special Issue, ed. by Kimmel M. and A. Swierniak, 4 (1994) pp. 163-177.
7. Kimmel M., Quasistationarity in a branching model of division-within-division, Classical and Modern Branching Processes, ed. by P. Jagers and K. Athreya, The IMA Volumes in Mathematics and Its Applications, 84 (1996) pp. 157-164.
8. Kimmel M. and Axelrod D. E., Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity, Genetics 125 (1990) pp. 633-644.
9. Kimmel M. and Chakraborty R., Measures of variation at microsatellite loci under a general stepwise mutation model, Theor. Pop. Biol. 60 (1996) pp. 345-367.
10. Kimmel M., Chakraborty R., Stivers D. N. and Deka R., Dynamics of repeat polymorphisms under forward-backward mutation models: Within- and between-population variability at microsatellite loci, Genetics 143 (1996) pp. 549-555.
11. Kimmel M. and Stivers D., A time-continuous branching process model of unstable gene amplification, Bull. Math. Biol. 56 (1994) pp. 337-357.
12. Lyubich Yu. I. and Vū Qûoc Phong, Asymptotic stability of linear differential equations on Banach spaces, Studia Math. 88 (1988) pp. 37-42.
13. Sklyar G. M. and Shirman V. Ya., On the asymptotic stability of a linear differential equation in a Banach space, Teor. Funktsiǐ Funktsional. Anal. i Prilozhen 37 (1982) pp. 127-132 (in Russian).
14. Świerniak A., Polański A. and Kimmel M., Control problems arising in chemotherapy under evolving drug resistance, Preprints of the 13th World Congress of IFAC, Vol. B, pp. 411-416.