Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Topological Dynamics in the Big Data problem

2019/35/B/ST1/00874

Keywords:

topological data analysis discrete Morse theory combinatorial dynamical systems Conley index Morse decomposition persistent homology

Descriptors:

  • ST1_010:
  • ST1_006:
  • ST1_014:

Panel:

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

Host institution :

Uniwersytet Jagielloński, Wydział Matematyki i Informatyki

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Marian Mrozek 

Number of co-investigators in the project: 7

Call: OPUS 18 - announced on 2019-09-16

Amount awarded: 899 388 PLN

Project start date (Y-m-d): 2020-07-10

Project end date (Y-m-d): 2025-07-09

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

Project status: Project completed

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.

Information in the final report

  • Publication in academic press/journals (10)
  • Articles in post-conference publications (1)
  1. The Morse Equation in the Conley Index Theory for Discrete Multivalued Dynamical Systems
    Authors:
    B. Batko
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2022, ), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10136-3 - link to the publication
  2. Persistence of the Conley-Morse Graph in Combinatorial Dynamical Systems
    Authors:
    T. Dey, M. Mrozek, and R. Slechta
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2022, tom: 21, strony: 817-839), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/21M143162X - link to the publication
  3. Computing Connection Matrices via Persistence-like Reductions.
    Authors:
    T. Dey, M. Lipinski, M. Mrozek, and R. Slechta
    Academic press:
    SIAM Journal on Applied Dynamical Systems, (rok: 2024, tom: 23, strony: 81-97), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/23M1562469 - link to the publication
  4. Identifying Nonlinear Dynamics with High Confidence from Sparse Data
    Authors:
    Bogdan Batko, Marcio Gameiro, Ying Hung, William Kalies, Konstantin Mischaikow, Ewerton Vieira
    Academic press:
    SIAM J. APPLIED DYNAMICAL SYSTEMS (rok: 2024, tom: 23, strony: 383-409), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/23M1560252 - link to the publication
  5. The Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations
    Authors:
    Mateusz Przybylski, Marian Mrozek, Jim Wiseman
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2023, tom: online first, strony: 13150), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-023-10332-9 - link to the publication
  6. Combinatorial vs. classical dynamics: Recurrence.
    Authors:
    M. Mrozek, R. Srzednicki, J. Thorpe and Th. Wanner
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2022, tom: 108, strony: 11689), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2021.106226 - link to the publication
  7. Morse Predecomposition of an Invariant Set
    Authors:
    Michał Lipiński, Konstantin Mischaikow, Marian Mrozek
    Academic press:
    Qualitative Theory of Dynamical Systems (rok: 2024, tom: 1,00347222222222, strony: 12055), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12346-024-01144-3 - link to the publication
  8. A complete invariant for shift equivalence for Boolean matrices and finite relations
    Authors:
    Ethan Akin, Marian Mrozek, Mateusz Przybylski, Jim Wiseman
    Academic press:
    Topology and its Applications (rok: 2024, tom: 357:109075, strony: 45670), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.topol.2024.109075 - link to the publication
  9. Computing Connection Matrices via Persistence-like Reductions
    Authors:
    Tamal K. Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2024, tom: 23, strony: 81--97), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/23M1562469 - link to the publication
  10. Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields
    Authors:
    M. Mrozek, Th. Wanner
    Academic press:
    Journal of Differential Equations (rok: 2021, tom: 304, strony: 375-434), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.001 - link to the publication
  1. Tracking Dynamical Features via Continuation and Persistence
    Authors:
    T. Dey, M. Lipiński, M. Mrozek, and R. Slechta
    Conference:
    Status:
    Accepted for publication

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