2659242003

5 Podsumowanie

Pełny zunifikowany opis zjawiska różnicowania się komórek wymaga zbadania wielu problemów. W tej rozprawie rozwiązujemy najważniejsze z nich. Pozostałe, nie mniej ciekawe, będą tematem dalszych badań.

Literatura

[ 1] J. David Sweatt Mechanisms of memory Elsevier 2003.

|2] P.Gwiazda and G. Jararóz and Anna Marciniak-Czochra Models of discrete and continuous celi differentiation in the framework of transport eguation, SIAM Journal on Mathematical Analysis. Submitted.

[3] G. Jamróz Transport equation with non-Radon uelocity as embedding of system of ODEs. Comptes Rendus Ma-thematiąue. Submitted.

|4| G. Jamróz Nonuniqueness of Solutions - friend or enemy. Prom transport equation to modeling discrete-continuous celi dynamics. Lecture notes.

[5] L. Ambrosio and G. Crippa, Ezistence, Uniąueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields, Lecture Notes of the Unione Matematica Italiana, Springer, 5: 3-57, 2008.

|6] J. Belair, M.C. Mackey and J. Mahaffy (1995), Age structured and two delay models for erythropoiesis, Math. Biosci. 128: 317-346.

|7| M. Doumic, A. Marciniak-Czochra, B. Perthame and J. Zubelli (2011) Structured population model of stem celi diiferentiation. SIAM J. Appl. Math. 71, pp. 1918-1940.

|8] P. Gwiazda, T. Lorenz and A. Marciniak-Czochra (2010) A nonlinear structured population model: Lipschitz continuity of measure valued Solutions with respect to model ingredients. J. Diff. Eg. 248: 2703- 2735.

|9] A. Kriegstein and A. Alvarez-Buylla (2009) The Glial Naturę of Embryonic and Adult Neural Stem Cells. Annu. Rev. Neurosci. 32: 149-184

[10]    S. Maniglia Fine properties and well-posedness of Solutions of transport eąuations and of the lst order associated ODE PhD Thesis. Universita di Pisa, 2006.

[11]    A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. Jager and W. Wagner (2008) Modeling asymmetric celi division in hematopoietic stem cells - regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 17: 1-10.

[12]    MacArthur, Ben D, Ma’ayan, Avi, Lemischka, Ihor R. (2009) Systems biology of stem celi fate and cellular reprogramming Nat Rev Mol Celi Biol 10: 672-681. http://dx.doi.org/10.1038/nrm2766

[13]    Kazutoshi Takahashi and Shinya Yamanaka (August 2006) Induction of Pluripotent Stem Cells from Mouse Embryonic and Adult Fibroblast Cultures by Defined Factors Celi, Yolume 126, Issue 4, 663-676

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