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Some recent results concerning generation and asymptotic properties of stochastic semigroups are presented. The general results are applied to biological models described by piecewise deterministic Markov processes: birth-death processes, the evolution of the genome, genes expression and physiologically structured models.
Wydawca
Czasopismo
Rocznik
Tom
Strony
463--494
Opis fizyczny
Bibliogr. 46 poz.
Twórcy
autor
- Institute of Mathematics Silesian University Bankowa 14 40 007 Katowice, Poland
autor
- Institute of Mathematics Polish Academy of Science Bankowa 14 40 007 Katowice, Poland
- Institute of Mathematics Silesian University Bankowa 14 40 007 Katowice, Poland
autor
- Institute of Mathematics Silesian University Bankowa 14 40 007 Katowice, Poland
Bibliografia
- [1] A. S. Ackleh, B. G. Fitzpatrick, Modeling aggregation and growth processes in an algal population model: analysis and computations, J. Math. Biol. 35 (1997), 480–502.
- [2] A. S. Ackleh, K. Deng, On the first order hyperbolic coagulation model, Math. Methods Appl. Sci. 26 (2003), 703–715.
- [3] O. Arino, M. Kimmel, Comparison of approaches to modeling of cell population dynamics, SIAM J. Appl. Math. 53 (1993), 1480–1504.
- [4] O. Arino, R. Rudnicki, Phytoplankton dynamics, C. R. Biologies 327 (2004), 961–969.
- [5] J. Banasiak, On an extension of the Kato–Voigt perturbation theorem for substochastic semigroups and its application, Taiwanese J. Math. 5 (2001), 169–191.
- [6] J. Banasiak, On conservativity and shattering for an equation of phytoplankton dynamics, C. R. Biologies 327 (2004), 1025–1036.
- [7] J. Banasiak, L. Arlotti, Perturbations of Positive Semigroups with Applications, Springer Monographs in Mathematics, Springer-Verlag London Ltd., London, 2006.
- [8] J. Banasiak, W. Lamb, Coagulation, fragmentation and growth processes in a size structured population, Discrete Contin. Dyn. Syst. - B 11 (2009), 563–585.
- [9] J. Banasiak, K. Pichór, R. Rudnicki, Asynchronous exponential growth of a structured population model, Acta Appl. Math., DOI:10.1007/s10440-011-9666-y.
- [10] G. I. Bell, E. C. Anderson, Cell growth and division: I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures, Biophysical Journal 7 (1967), 329–351.
- [11] A. Bobrowski, Functional Analysis for Probability and Stochastic Processes. An Introduction, Cambridge University Press, Cambridge, 2005.
- [12] A. Bobrowski, T. Lipniacki, K. Pichór, R. Rudnicki, Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression, J. Math. Anal. Appl. 333 (2007), 753–769.
- [13] M. H. A. Davis, Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models, J. Roy. Statist. Soc. Ser. B 46 (1984), 353–388.
- [14] M. H. A. Davis, Markov models and optimization, Monographs on Statistics and Applied Probability, vol. 49, Chapman & Hall, London, 1993.
- [15] O. Diekmann, H. J. A. M. Heijmans, H. R. Thieme, On the stability of the cell size distribution, J. Math. Biol. 19 (1984), 227–248.
- [16] N. Friedman, L. Cai, X. Xie, Linking stochastic dynamics to population distribution: An analytical framework of gene expression, Phys. Rev. Lett. 97 (2006), 168302–1/4.
- [17] M. Gyllenberg, H. J. A. M. Heijmans, An abstract delay-differential equation modeling size dependent cell growth and division, SIAM J. Math. Anal. 18 (1987), 74–88.
- [18] M. Gyllenberg, G. F. Webb, Age-size structure in populations with quiescence, Math. Biosci. 86 (1987), 67–95.
- [19] M. Gyllenberg, G. F. Webb, A nonlinear structured population model of tumor growth with quiescence, J. Math. Biol. 28 (1990), 671–694.
- [20] H. J. A. M. Heijmans, On the stable size distribution of populations reproducing by fission into two unequal parts, Math. Biosci. 72 (1984), 19–50.
- [21] E. Hille, R. S. Phillips, Functional Analysis and Semi-groups, AmericanMathematical Society Colloquium Publications 31, American Mathematical Society, Providence, R. I., 1957.
- [22] M. A. Huynen, E. van Nimwegen, The frequency distribution of gene family size in complete genomes, Molecular Biology Evolution 15 (1998), 583–589.
- [23] T. Kato, On the semi-groups generated by Kolmogoroff’s differential equations, J. Math. Soc. Japan 6 (1954), 1–15.
- [24] M. Kimmel, Z. Darzynkiewicz, O. Arino, F. Traganos, Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis, J. Theor. Biol. 110 (1984), 637–664.
- [25] M. Komorowski, J. Miękisz, A. M. Kierzek, Translational repression contributes greater noise to gene expression than transcriptional repression, Biophysical Journal 96 (2009), 372–384.
- [26] A. L. Koch, J. V. Holtje, A physical basis for the precise location of the division site of rod-shaped bacteria: the central stress model, Microbiology 13 (1995), 3171–3180.
- [27] A. Lasota, M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43–62.
- [28] A. Lasota, M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Springer Applied Mathematical Sciences 97, New York, 1994.
- [29] T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A. R. Brasier, M. Kimmel, ranscriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006), 348–367.
- [30] M. C. Mackey, R. Rudnicki, Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol. 33 (1994), 89–109.
- [31] M. C. Mackey, M. Tyran-Kamińska, Dynamics and density evolution in piecewise deterministic growth processes, Ann. Polon. Math. 94 (2008), 111–129.
- [32] M. C. Mackey, M. Tyran-Kamińska, R. Yvinec, Molecular distributions in gene regulatory dynamics, J. Theor. Biol. 274 (2011), 84–96.
- [33] J. A. J. Metz, O. Diekmann (eds.), The Dynamics of Physiologically Structured Populations, Springer Lecture Notes in Biomathematics 68, New York, 1986.
- [34] K. Pichór, R. Rudnicki, Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl. 249 (2000), 668–685.
- [35] K. Pichór, Asymptotic stability and sweeping of substochastic semigroups, Ann. Polon. Math. 103 (2012), 123–134.
- [36] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245–262.
- [37] R. Rudnicki, K. Pichór, Markov semigroups and stability of the cell maturation distribution, J. Biol. Systems 8 (2000), 69–94.
- [38] R. Rudnicki, J. Tiuryn, D. Wójtowicz, A model for the evolution of paralog families in genomes, J. Math. Biology 53 (2006), 759–770.
- [39] R. Rudnicki, R. Wieczorek, Fragmentation – coagulation models of phytoplankton, Bull. Pol. Acad. Sci. Math. 54 (2006), 175–191.
- [40] R. Rudnicki, R. Wieczorek, Phytoplankton dynamics: from the behaviour of cells to a transport equation, Math. Mod. Nat. Phenomena 1 (2006), 83–100.
- [41] R. Rudnicki. R. Wieczorek, Mathematical models of phytoplankton dynamics, in: Russo R. (Ed.) Aquaculture I. Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (Special Issue 1), (2008), 55–63.
- [42] P. P. Slonimski, M. O. Mosse, P. Golik, A. Henaût, Y. Diaz, J. L. Risler, J. P. Comet, J. C. Aude, A. Wozniak, E. Glemet, J. J. Codani, The first laws of genomics, Microbial Comp. Genomics 3 (1998), 46.
- [43] M. Tyran-Kamińska, Substochastic semigroups and densities of piecewise deterministic Markov processes, J. Math. Anal. Appl. 357 (2009), 385–402.
- [44] M. Tyran-Kamińska, Ergodic theorems and perturbations of contraction semigroups, Studia Math. 195 (2009), 147–155.
- [45] J. Voigt, On substochastic C0-semigroups and their generators, Transport Theory Statist. Phys. 16 (1987), 453–466.
- [46] G. W. Webb, Structured population dynamics, in: R. Rudnicki (eds.), Mathematical Modelling of Population Dynamics, Banach Center Publ. 63, 123–163, Warszawa (2004).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0034-0039