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Analytic and probabilistic methods to study biological models

2017/27/B/ST1/00100

Keywords

Descriptors

  • ST1_18: Zastosowania matematyki w innych naukach
  • ST1_13: Rachunek prawdopodobieństwa i statystyka matematyczna
  • ST1_11: Równania różniczkowe cząstkowe

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

Voivodeship: mazowieckie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Ryszard Jan 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
2018-06-29
Project end date
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. Cost: 5 000 PLN

Information in the final report

Publication in academic press/journals (22)

  1. 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 (year: 2020, volume: 37, pages: 877-923), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.anihpc.2020.02.004 – link to the publication

  2. Dynamics of antibody levels: Asymptotic properties

    Authors:
    K. Pichór, R. Rudnicki
    Academic press:
    Math. Meth. Appl. Sci. (year: 2020, volume: 43, pages: 10490-10499), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6536 – link to the publication

  3. Densities for piecewise deterministic Markov processes with boundary

    Authors:
    Piotr Gwiżdż, Marta Tyran-Kamińska
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2019, volume: 479, pages: 384--425), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2019.06.032 – link to the publication

  4. 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 (year: 2020, volume: 139, pages: 171-188), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s12064-019-00307-0 – link to the publication

  5. One and two-phase cell cycle models

    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Academic press:
    Biomath (year: 2019, volume: 8, pages: 1905261 (15 stron)), Publisher: Biomath Forum
    Status:
    Published
    DOI:
    10.11145/j.biomath.2019.05.261 – link to the publication

  6. Application of the Goodwin model to autoregulatory feedback for stochastic gene expression

    Authors:
    A.Kozdęba, A.Tomski
    Academic press:
    Math. Biosci. (year: 2020, volume: 327, pages: 108413 (12 str)), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.mbs.2020.108413 – link to the publication

  7. Positive semigroups and perturbations of boundary conditions

    Authors:
    Piotr Gwiżdż, Marta Tyran-Kamińska
    Academic press:
    Positivity (year: 2019, volume: 23, pages: 921–939), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11117-019-00644-w – link to the publication

  8. Randomly switching evolution equations

    Authors:
    P. Klimasara, M. C. Mackey, A. Tomski, M. Tyran-Kamińska
    Academic press:
    Nonlinear Analysis: Hybrid Systems (year: 2021, volume: 39, pages: 100948 (1-15)), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.nahs.2020.100948 – link to the publication

  9. Replicator dynamics for the game theoretic selection models based on state

    Authors:
    K.Argasinski, R. Rudnicki
    Academic press:
    Journal of Theoretical Biology (year: 2021, volume: 526, pages: 110540 (1-24)), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jtbi.2020.110540 – link to the publication

  10. 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 (year: 2022, volume: 45, pages: 5797-5820.), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.8139 – link to the publication

  11. 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 (year: 2021, volume: 31, pages: 043114 (1-13)), Publisher: American Institute of Physics Publishing
    Status:
    Published
    DOI:
    10.1063/5.003831 – link to the publication

  12. Applications of stochastic semigroups to cell cycle models

    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Academic press:
    Discrete and Continuous Dynamical Systems - Series B (year: 2019, volume: 24 (5), pages: 2365-2381), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2019099 – link to the publication

  13. Stochastic gene expression revisited MDPI 2021 IF: 4.096

    Authors:
    A. Tomski, M. Zakarczemny
    Academic press:
    Genes (year: 2021, volume: 12, pages: 648 (1-19)), Publisher: MDPI
    Status:
    Published
    DOI:
    10.3390/genes12050648 – link to the publication

  14. A model of seasonal savanna dynamics

    Authors:
    P. Klimasara, M. Tyran-Kamińska
    Academic press:
    SIAM Journal on Applied Mathematics (year: 2023, volume: 83, pages: 122-143), Publisher: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/21M1461393 – link to the publication

  15. Ergodic properties of a semilinear partial differential equation

    Authors:
    Ryszard Rudnicki
    Academic press:
    Journal of Differential Equations (year: 2023, volume: 372, pages: 235--253), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2023.06.046 – link to the publication

  16. Asymptotic properties of a general model of immune status

    Authors:
    K. Pichór, R. Rudnicki
    Academic press:
    SIAM Journal on Applied Mathematics (year: 2023, volume: 83, pages: 172-193), Publisher: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/21M1466906 – link to the publication

  17. Hydrodynamic limit of a stochastic model of proliferating cells with chemotaxis

    Authors:
    R. Wieczorek
    Academic press:
    Kinetic and Related Models (year: 2023, volume: 16, pages: 373-393), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/krm.2022032 – link to the publication

  18. 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 (year: 2019, volume: 470, pages: 931-953), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2018.10.042 – link to the publication

  19. On convergence and asymptotic behaviour of semigroups of operators

    Authors:
    A. Bobrowski, R. Rudnicki
    Academic press:
    Phil. Trans. R. Soc. A. (year: 2020, volume: 378, pages: 20190613 (18 str.)), Publisher: The Royal Society Publishing
    Status:
    Published
    DOI:
    10.1098/rsta.2019.0613 – link to the publication

  20. PDE model of cell cycle dynamics and clustering in yeast

    Authors:
    Radosław Wieczorek
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2020, volume: 482 (2), pages: 123483), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2019.123483 – link to the publication

  21. A hybrid stochastic model of retinal angiogenesis

    Authors:
    V. Capasso, R. Wieczorek
    Academic press:
    Math. Meth. Appl. Sci. (year: 2020, volume: 43, pages: 10578-10592), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6725 – link to the publication

  22. Transport equations and perturbations of boundary conditions

    Authors:
    M. Tyran-Kamińska
    Academic press:
    Math. Meth. Appl. Sci. (year: 2020, volume: 43, pages: 10511-10531), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.6611 – link to the publication

Book publications / chapters in book publications (4)

  1. 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 (year: 2020, volume: 325, pages: 329-347), Publisher: Springer Proceedings in Mathematics & Statistics
    Status:
    Published

  2. 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 (year: 2020, volume: 38, pages: IX, 138), Publisher: Fields Institute Monograph, Springer
    Status:
    Published

  3. 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 (year: 2022, volume: Księgozbiór Matematyczny tom 4, pages: 1-729), Publisher: Instytut Matematyczny Polskiej Akademii Nauk
    Status:
    Published

  4. Transformation semigroups and their applications

    Authors:
    Katarzyna Pichór, Ryszard Rudnicki
    Book:
    Classical & Constructive Semigroups and Applications, in book series Mathematics in Mind'', Publisher: Springer
    Status:
    Accepted for publication

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Graphic design and implementation: Jakub Piotrowski