Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Analytic and probabilistic methods to study biological models

2017/27/B/ST1/00100

Keywords:

piecewise deterministic Markov processes angielskim: Markov processes semigroups of positive operators evolution equations asymptotic stability population dynamics gene expression

Descriptors:

  • ST1_18: Control theory and optimisation
  • ST1_13: Probability and statistics
  • ST1_11: Partial differential equations

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Instytut Matematyczny Polskiej Akademii Nauk

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Ryszard Rudnicki 

Number of co-investigators in the project: 5

Call: OPUS 14 - announced on 2017-09-15

Amount awarded: 327 000 PLN

Project start date (Y-m-d): 2018-06-29

Project end date (Y-m-d): 2023-06-28

Project duration:: 60 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Komputer stacjonarny.
  2. notebook (5 000 PLN)

Information in the final report

  • Publication in academic press/journals (22)
  • Book publications / chapters in book publications (5)
  1. Dynamics of antibody levels: Asymptotic properties
    Authors:
    K. Pichór, R. Rudnicki
    Academic press:
    Math. Meth. Appl. Sci. (rok: 2020, tom: 43, strony: 10490-10499), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6536 - link to the publication
  2. How can we describe density evolution under delayed dynamics?
    Authors:
    M. C. Mackey, M. Tyran-Kamińska
    Academic press:
    Chaos: An Interdisciplinary Journal of Nonlinear Science (rok: 2021, tom: 31, strony: 043114 (1-13)), Wydawca: American Institute of Physics Publishing
    Status:
    Published
    DOI:
    10.1063/5.003831 - link to the publication
  3. Positive semigroups and perturbations of boundary conditions
    Authors:
    Piotr Gwiżdż, Marta Tyran-Kamińska
    Academic press:
    Positivity (rok: 2019, tom: 23, strony: 921–939), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11117-019-00644-w - link to the publication
  4. The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks
    Authors:
    Mateusz Falfus, Michael C. Mackey, Marta Tyran-Kamińska
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2019, tom: 470, strony: 931-953), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.042 - link to the publication
  5. A model of seasonal savanna dynamics
    Authors:
    P. Klimasara, M. Tyran-Kamińska
    Academic press:
    SIAM Journal on Applied Mathematics (rok: 2023, tom: 83, strony: 122-143), Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/21M1461393 - link to the publication
  6. Hydrodynamic limit of a stochastic model of proliferating cells with chemotaxis
    Authors:
    R. Wieczorek
    Academic press:
    Kinetic and Related Models (rok: 2023, tom: 16, strony: 373-393), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/krm.2022032 - link to the publication
  7. Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators
    Authors:
    B. Lods, M. Mokhtar-Kharroubi, R. Rudnicki
    Academic press:
    Ann. I. H. Poincare AN (rok: 2020, tom: 37, strony: 877-923), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.anihpc.2020.02.004 - link to the publication
  8. A hybrid stochastic model of retinal angiogenesis
    Authors:
    V. Capasso, R. Wieczorek
    Academic press:
    Math. Meth. Appl. Sci. (rok: 2020, tom: 43, strony: 10578-10592), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6725 - link to the publication
  9. Application of the Goodwin model to autoregulatory feedback for stochastic gene expression
    Authors:
    A.Kozdęba, A.Tomski
    Academic press:
    Math. Biosci. (rok: 2020, tom: 327, strony: 108413 (12 str)), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.mbs.2020.108413 - link to the publication
  10. Asymptotic properties of a general model of immune status
    Authors:
    K. Pichór, R. Rudnicki
    Academic press:
    SIAM Journal on Applied Mathematics (rok: 2023, tom: 83, strony: 172-193), Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/21M1466906 - link to the publication
  11. Cell cycle length and long-time behavior of an age-size model
    Authors:
    K. Pichór, R. Rudnicki
    Academic press:
    Mathematical Methods in the Applied Sciences (rok: 2022, tom: 45, strony: 5797-5820.), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.8139 - link to the publication
  12. Ergodic properties of a semilinear partial differential equation
    Authors:
    Ryszard Rudnicki
    Academic press:
    Journal of Differential Equations (rok: 2023, tom: 372, strony: 235--253), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2023.06.046 - link to the publication
  13. On convergence and asymptotic behaviour of semigroups of operators
    Authors:
    A. Bobrowski, R. Rudnicki
    Academic press:
    Phil. Trans. R. Soc. A. (rok: 2020, tom: 378, strony: 20190613 (18 str.)), Wydawca: The Royal Society Publishing
    Status:
    Published
    DOI:
    10.1098/rsta.2019.0613 - link to the publication
  14. PDE model of cell cycle dynamics and clustering in yeast
    Authors:
    Radosław Wieczorek
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2020, tom: 482 (2), strony: 123483), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2019.123483 - link to the publication
  15. Transport equations and perturbations of boundary conditions
    Authors:
    M. Tyran-Kamińska
    Academic press:
    Math. Meth. Appl. Sci. (rok: 2020, tom: 43, strony: 10511-10531), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6611 - link to the publication
  16. Applications of stochastic semigroups to cell cycle models
    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Academic press:
    Discrete and Continuous Dynamical Systems - Series B (rok: 2019, tom: 24 (5), strony: 2365-2381), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2019099 - link to the publication
  17. Densities for piecewise deterministic Markov processes with boundary
    Authors:
    Piotr Gwiżdż, Marta Tyran-Kamińska
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2019, tom: 479, strony: 384--425), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2019.06.032 - link to the publication
  18. From nest site lottery to host lottery: continuous model of growth suppression driven by the availability of nest sites for newborns or hosts for parasites and its impact on the selection of life history strategies
    Authors:
    Krzysztof Argasinski, Ryszard Rudnicki
    Academic press:
    Theory in Biosciences (rok: 2020, tom: 139, strony: 171-188), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12064-019-00307-0 - link to the publication
  19. Replicator dynamics for the game theoretic selection models based on state
    Authors:
    K.Argasinski, R. Rudnicki
    Academic press:
    Journal of Theoretical Biology (rok: 2021, tom: 526, strony: 110540 (1-24)), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jtbi.2020.110540 - link to the publication
  20. Stochastic gene expression revisited MDPI 2021 IF: 4.096
    Authors:
    A. Tomski, M. Zakarczemny
    Academic press:
    Genes (rok: 2021, tom: 12, strony: 648 (1-19)), Wydawca: MDPI
    Status:
    Published
    DOI:
    10.3390/genes12050648 - link to the publication
  21. One and two-phase cell cycle models
    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Academic press:
    Biomath (rok: 2019, tom: 8, strony: 1905261 (15 stron)), Wydawca: Biomath Forum
    Status:
    Published
    DOI:
    10.11145/j.biomath.2019.05.261 - link to the publication
  22. Randomly switching evolution equations
    Authors:
    P. Klimasara, M. C. Mackey, A. Tomski, M. Tyran-Kamińska
    Academic press:
    Nonlinear Analysis: Hybrid Systems (rok: 2021, tom: 39, strony: 100948 (1-15)), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.nahs.2020.100948 - link to the publication
  1. I. Podstawy teorii prawdopodobieństwa, II. Łańcuchy Markowa i ich zastosowania, III. Układy dynamiczne i teoria ergodyczna, IV. Kawałkami deterministyczne procesy Markowa, V. Równania stochastyczne i ich zastosowania,VI. Wybrane zaawansowane modele i metody stochastyczne, A. Operatory i półgrupy Markowa, B. Twierdzenia ergodyczne
    Authors:
    R. Rudnicki
    Book:
    Modele i Metody Biologii Matematycznej, Część II: Modele Probabilistyczne (rok: 2022, tom: Księgozbiór Matematyczny tom 4, strony: 1-729), Wydawca: Instytut Matematyczny Polskiej Akademii Nauk
    Status:
    Published
  2. Ergodic and chaotic properties of some biological models
    Authors:
    Ryszard Rudnicki
    Book:
    Lecture Notes on Mathematical Modellling in the Life Sciences - in honor of Michael Mackey , Wydawca: Springer
    Status:
    Submitted
  3. Asymptotic properties of stochastic semigroups with applications to piecewise deterministic Markov processes
    Authors:
    K. Pichór, R. Rudnicki
    Book:
    Semigroups of Operators: Theory and Applications SOTA-2018 (rok: 2020, tom: 325, strony: 329-347), Wydawca: Springer Proceedings in Mathematics & Statistics
    Status:
    Published
  4. Density Evolution Under Delayed Dynamics. An Open Problem (książka)
    Authors:
    Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska
    Book:
    Density Evolution Under Delayed Dynamics. An Open Problem (rok: 2020, tom: 38, strony: IX, 138), Wydawca: Fields Institute Monograph, Springer
    Status:
    Published
  5. Transformation semigroups and their applications
    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Book:
    Classical & Constructive Semigroups and Applications, in book series "Mathematics in Mind'' , Wydawca: Springer
    Status:
    Accepted for publication

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