prof. dr hab. Marian Mrozek

Jednostki:

  • Wydział Matematyki i Informatyki UJ
  • Instytut Informatyki i Matematyki Komputerowej
  • Katedra Matematyki Obliczeniowej

Publikacje:

59.
Ethan Akin, Marian Mrozek, Mateusz Przybylski, Jim Wiseman
A complete invariant for shift equivalence for Boolean matrices and finite relations, Topology and its Applications vol. 357 (2024), 109075
58.
Mateusz Przybylski, Marian Mrozek, Jim Wiseman
The Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations, Journal of Dynamics and Differential Equations (2023),
57.
Michał Lipiński, Jacek Kubica, Marian Mrozek, Thomas Wanner
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces, Journal of Applied and Computational Topology vol. 7 (2023), 139–184
56.
Tamal Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta
Tracking dynamical features via continuation and persistence, International Symposium on Computational Geometry [SoCG], (2022), 35:1-35:17
55.
Tamal K. Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta
Tracking Dynamical Features via Continuation and Persistence, 38th International Symposium On Computational Geometry (socg 2022) (2022),
54.
Marian Mrozek, Roman Srzednicki, Justin Thorpe, Thomas Wanner
Combinatorial vs. classical dynamics: Recurrence, Communications in Nonlinear Science and Numerical Simulation vol. 108 (2022), 106226, 1-30
53.
Tamal Dey, Marian Mrozek, Ryan Slechta
Persistence of the Conley-Morse Graph in Combinatorial Dynamical Systems, SIAM Journal on Applied Dynamical Systems vol. 21 (2021), 817–839
52.
Laurent Fribourg, Eric Goubault, Sameh Mohamed, Marian Mrozek, Sylvie Putot
A topological method for finding invariant sets of continuous systems, Information and Computation vol. 277 (2021), 104581
51.
Marian Mrozek, Thomas Wanner
Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields, Journal of Differential Equations vol. 304 (2021), 375-434
50.
Tomasz Kapela, Marian Mrozek, Daniel Wilczak, Piotr Zgliczyński
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems , Communications in Nonlinear Science and Numerical Simulation vol. 101 (2021), 105578
49.
Tamal K. Dey, Marian Mrozek, Ryan Slechta
Persistence of the Conley Index in Combinatorial Dynamical Systems, International Symposium on Computational Geometry [SoCG] vol. 36 (2020), 37:1-37:17
48.
Ulrich Bauer, Herbert Edelsbrunner, Grzegorz Jabłoński, Marian Mrozek
Čech–Delaunay gradient flow and homology inference for self-maps, Journal of Applied and Computational Topology vol. 4 (2020), 455–480
47.
Jonathan Ariel Barmak, Marian Mrozek, Thomas Wanner
A Lefschetz fixed point theorem for multivalued maps of finite spaces, Mathematische Zeitschrift vol. 294 (2020), 1477–1497
46.
Bogdan Batko, K. Mischaikow, Marian Mrozek, Mateusz Przybylski
Conley Index Approach to Sampled Dynamics, SIAM Journal on Applied Dynamical Systems vol. 19-1 (2020), 665-704
45.
Bogdan Batko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner
Linking combinatorial and classical dynamics: Conley index and Morse decompositions, Foundations of Computational Mathematics vol. 20 (2020), 967— 1012
44.
Tamal Dey, Mateusz Juda, Tomasz Kapela, Jacek Kubica, Michał Lipiński, Marian Mrozek
Persistent Homology of Morse Decompositions in Combinatorial Dynamics, SIAM Journal on Applied Dynamical Systems vol. 18-1 (2019), 510-530
43.
Marc Ethier, Grzegorz Jabłoński, Marian Mrozek
Finding Eigenvalues of Self-maps with the Kronecker Canonical Form vol. 198 (2017), "Applications of Computer Algebra", Springer
42.
Marian Mrozek
Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes, Foundations of Computational Mathematics vol. 17 (2017), 1585-1633
41.
Andrzej Gryglewski, Brandon Michael Henry, Marian Mrozek, Krzysztof Piech, Krzysztof Tomaszewski, Marcin Żelawski
Sensitivity and Specificity of Fractal Analysis to Distinguish Between Healthy and Pathologic Rectal Mucosa Microvasculature Seen During Colonoscopy, Surgical Laparoscopy, Endoscopy and Percutaneous Techniques vol. 26(5) (2016), 358–363
40.
K. Mischaikow, Marian Mrozek, Frank Weilandt
Discretization strategies for computing Conley indices and Morse decompositions of flows, Journal of Computational Dynamics vol. 3 (2016), 1-16
39.
Tomasz Kaczynski, Marian Mrozek, Thomas Wanner
Towards a formal tie between combinatorial and classical vector field dynamics, Journal of Computational Dynamics vol. 3 (1) (2016), 17-50
38.
Bogdan Batko, Marian Mrozek
Weak index pairs and the Conley index for discrete multivalued dynamical systems, SIAM Journal on Applied Dynamical Systems vol. 15.2 (2016), 1143-1162
37.
Laurent Fribourg, Eric Goubault, Sameh Mohamed, Marian Mrozek, Sylvie Putot
A Topological Method for Finding Invariant Sets of Continuous Systems vol. Lecture Notes in Computer Science (2015), "Reachability Problems", Springer Verlag (połaczony z Kluwer Academic Publishing)
36.
Marian Mrozek, Roman Srzednicki, Frank Weilandt
A topological approach to the algorithmic computation of the Conley index for Poincaré maps, SIAM Journal on Applied Dynamical Systems vol. 14 (2015), 1348-1386
35.
Herbert Edelsbrunner, Grzegorz Jabłoński, Marian Mrozek
The Persistent Homology of a Self-Map, Foundations of Computational Mathematics vol. 15 (2015), 1213-1244
34.
Piotr Brendel, Paweł Dłotko, Graham Ellis, Mateusz Juda, Marian Mrozek
Computing fundamental groups from point clouds, Applicable Algebra in Engineering, Communications and Computing vol. 26 (2015), 27-48
33.
Mateusz Juda, Marian Mrozek
CAPD::RedHom v2 - Homology Software Based on Reduction Algorithms, Lecture Notes in Computer Science vol. 8592 (2014), 160-166
32.
Shaun Harker, K. Mischaikow, Marian Mrozek, Vidit Nanda
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps, Foundations of Computational Mathematics vol. 14 (2014), 151-184
31.
Tomasz Kaczynski, Marian Mrozek
Cubical Cohomology Ring: Algorithmic Approach, Foundations of Computational Mathematics vol. 13 (2013), 789-818
30.
Marian Mrozek
Topological Dynamics: Rigorous Numerics via Cubical Homology vol. 70 (2012), "Advances in Applied and Computational Topology: AMS Short Course Computational Topology", American Mathematical Society (AMS)
29.
Piotr Brendel, Paweł Dłotko, Marian Mrozek, Natalia Żelazna
Homology Computations via Acyclic Subspace, Lecture Notes in Computer Science vol. 7309 (2012), 117-127
28.
Paweł Dłotko, Marian Mrozek, Hubert Wagner
Computational Topology in Text Mining, Lecture Notes in Computer Science vol. 7309 (2012), 68 - 79
27.
Andrzej Gryglewski, Andrzej Krajniak, Marian Mrozek, Han Sejin, Marcin Żelawski
Homological methods for extraction and analysis of linear features in multidimensional images, Pattern Recognition vol. 45(1) (2012), 285-298
26.
Paweł Dłotko, Robert Ghrist, Mateusz Juda, Marian Mrozek
Distributed computation of coverage in sensor networks by homological methods, Applicable Algebra in Engineering, Communications and Computing vol. 23, Issue 1-2 (2012), 29-58
25.
Mateusz Juda, Marian Mrozek
Z_2-homology of weak (p-2)-faceless p-pseudomanifolds may be computed in O(n) time, Topological Methods in Nonlinear Analysis vol. 40 (2012), 137-159
24.
Paweł Dłotko, Tomasz Kaczynski, Marian Mrozek, Thomas Wanner
Coreduction Homology Algorithm for Regular CW-Complexes, Discrete and Computational Geometry vol. 46 (2011), 361-388
23.
Tomasz Baron, Marcin Cwynar, Tomasz Grodzicki, Barbara Gryglewska, Marian Mrozek, Mirosław Nęcki, Marcin Żelawski
Fractal dimensions of skin microcirculation flow in subjects with familial predisposition or newly diagnosed hypertension, Cardiology Journal, Formerly Folia Cardiologica vol. 18, No. 1 (2011), 26-32
22.
Paweł Dłotko, Tomasz Kaczynski, Marian Mrozek
Computing the cubical cohomology ring, Image A, Proceedings of the 3rd International Workshop On Computational Topology in Image Context (2010), 137-142
21.
Paweł Dłotko, Shaun Harker, Mateusz Juda, Konstantin Mischaikov, Marian Mrozek, Vidit Nanda, Hubert Wagner
The efficiency of a homology algorithm based on discrete Morse Theory and Coreductions, Image a Proceedings of the 3rd International Workshop On Computational Topology in Image Context (2010), 41-47
20.
Marian Mrozek, Thomas Wanner
Coreduction homology algorithm for inclusions and persistent homology, Computers and Mathematics with Applications vol. 60.10 (2010), 2812-2833
19.
Bogdan Batko, Marian Mrozek
Homology of representable sets, Annales Polonici Mathematici vol. 97,3 (2010), 243-252
18.
Marian Mrozek
ˇCech Type Approach to Computing Homology of Maps, Discrete and Computational Geometry vol. 44.3 (2010), 546–576
17.
Marian Mrozek
Homology of representable sets, Annales Polonici Mathematici vol. 97.3 (2010), 243–252
16.
Marian Mrozek, Roman Srzednicki
Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds, Foundations of Computational Mathematics (2010), 191-220
15.
Bogdan Batko, Marian Mrozek
Coreduction homology algorithm, Discrete and Computational Geometry vol. 41 (2009), 96-118
14.
Andrzej Gryglewski, Andrzej Krajniak, Marian Mrozek, Han Sejin, Marcin Żelawski
Homological Methods in Feature Extraction of Multidimensional Images, Proceedings of the 2009 2nd International Congress On Image and Signal Processing, Ieee (2009), 1061-1066
13.
Marian Mrozek, Roman Srzednicki
Conley index of Poincare maps in isolating segments, Nonlinear Analysis, Theory, Methods and Applications (2009), 2123—2131
12.
Marian Mrozek, Paweł Pilarczyk, Natalia Żelazna
Homology algorithm based on acyclic subspace, Computers and Mathematics with Applications vol. 55 (2008), 2395-2412
11.
Bogdan Batko, Marian Mrozek
The Euler-Poincare characteristic of index maps, Topology and its Applications vol. 154.4 (2007), 859-866
10.
Marian Mrozek, Klaudiusz Wójcik
Discrete version of a geometric method for detecting chaotic dynamics, Topology and its Applications vol. 152 (2005), 70-82
9.
Marian Mrozek, James F. Reineck, Roman Srzednicki, J.F.Reineck
The Conley index over the circle, J. DYNAM. DIFFERENTIAL EQUATIONS 12 (2000), no. 2, 385--409
8.
Marian Mrozek, James F. Reineck, Roman Srzednicki
The Conley index over a base, Transactions of the American Mathematical Society vol. 352 (2000), 4171-4194
7.
Tomasz Kaczynski, Marian Mrozek, Maciej Ślusarek
Homology Computation by Reduction of Chain Complexes, Computers and Mathematics with Applications vol. 35 (1998), 59-70
6.
Marian Mrozek, Roman Srzednicki
On time-duality of the Conley index, RESULTS MATH. 24 (1993), no. 1-2, 161--167
5.
Marian Mrozek, Roman Srzednicki
The continuity axiom in multi-valued dynamical systems, RIV. MAT. PURA APPL. no. 3 (1988), 87--97 (1989)
4.
Marian Mrozek, Marek Zaionc
A computer model of evolution and ecological processes, Modeling, Simulation & Control C (1984), 59-63
3.
Marian Mrozek
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps, Foundations of Computational Mathematics (),
2.
K. Mischaikow, Marian Mrozek, S. Harker, V. Nanda
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps, Foundations of Computational Mathematics (),
1.
Marian Mrozek, Roman Srzednicki, J.F.Reineck
On a generalization of the Conley index, CONLEY INDEX THEORY (WARSAW, 1997), 157--171, Banach Center Publ., 47, Polish Acad. Sci., Warsaw, 1999

Konferencje:

14.
Marian Mrozek.
Workshop on switching dynamics and verification, Institut pour le Contrôle et la Décision de l'Idex Paris-Saclay., Paryż, Francja, 2016-01-28 - 2016-01-29
13.
Marian Mrozek.
XXI Krajowa Konferencja Zastosowan Matematyki w Biologii i Medycynie, AGH, Regietów, Polska, 2015-09-22 - 2015-09-26
12.
Marian Mrozek.
VII Symposium on Nonlinear Analysis 2015, Centrum Badań Nieliniowych im. J.P. Schaudera, Toruń, Polska, 2015-09-14 - 2015-09-18
11.
Marian Mrozek, Rafał Czyż.
6 Forum Matematyków Polskich, PTM, Warszawa, Polska, 2015-09-07 - 2015-09-12
10.
Marian Mrozek.
Critical Point Theory and Nonlinear Differential Problems, University of Verona, Canazei, Włochy, 2015-09-01 - 2015-09-04
9.
Marian Mrozek.
Geometric and Topological Methods in Computer Science GETEO , Aalborg University, Aalborg, Dania, 2015-04-07 - 2015-04-10
8.
Marian Mrozek.
8th Conference on Foundations of Computational Mathematics - Computational Dynamics, FoCM, Montevideo, Urugwaj, 2014-12-10 - 2014-12-20
7.
Marian Mrozek.
8th Conference on Foundations of Computational Mathematics, FoCM, Montevideo, Urugwaj, 2014-12-01 - 2014-12-20
6.
Marian Mrozek, Mateusz Juda.
Seventh de Brún Workshop on Homological Perturbation Theory, NUI Galway, Galway, Ireland, 2014-12-01 - 2014-12-05
5.
Marian Mrozek.
Discrete, Computational and Algebraic Topology, University of Copenhagen, Kopenhaga, Dania, 2014-11-12 - 2014-11-15
4.
Marian Mrozek.
5th International Workshop on Computational Topology in Image Context CTIC2014, Eftimie Murgu University, Resita, Timisoara, Rumunia, 2014-09-22 - 2014-09-25
3.
Marian Mrozek.
Combinatorial/ Topological Frameworks for Multiparameter Nonlinear Dynamics, Lorentz Center, Leiden, Holandia, 2014-07-18 - 2014-08-22
2.
Marian Mrozek, Mateusz Juda.
Algebraic Topology in Dynamics, Differential Equations, and Experimental Data , Institute for Mathematics and its Applications, Minneapolis, USA, 2014-02-10 - 2014-02-14
1.
Marian Mrozek, Grzegorz Jabłoński.
Geometric and Topological Methods in Computer Science, Aalborg University, Aalborg, Dania, 2012-09-04 - 2012-09-07

Konferencje organizowane:

Doktoranci (po 27 października 2003 roku)

DoktorantOtwarcieZakonczenie
Paweł Dłotko2009-12-172012-01-26
Mateusz Juda2011-10-272013-03-28
Natalia Żelazna2007-09-272010-09-30
Kinga Stolot2001-05-312004-01-08
Andrzej Krajniak2012-06-28 
Hubert Wagner2012-10-252014-11-27
Piotr Brendel2013-06-272017-01-26
Grzegorz Jabłoński2013-06-272015-11-26
Frank Weilandt2013-09-262016-05-19
Michał Lipiński2019-03-282021-11-18
Mateusz Przybylski2019-03-282022-01-20

Recenzje (po 27 października 2003 roku)

RecenzowanyJednostkaTreść recenzji
Doktorat: Tomasz KapelaKatedra Matematyki Obliczeniowej 
Doktorat: Anna Gierzkiewicz-PieniążekKatedra Matematyki Obliczeniowej 
Doktorat: Zofia Mączyńska 
Habilitacja: Andrzej BieleckiKatedra Informatyki Stosowanej 
Habilitacja: Daniel WilczakKatedra Matematyki Obliczeniowej 

Granty (realizowane po maju 2009 roku)

TytułRolaRozpoczęcieZakończenie
Metody algorytmiczne w topologii obliczeniowej i obliczeniowej dynamice topologicznejKierownik2010-09-232013-09-22
Algorytmy redukcji w obliczeniowej teorii homologii i kohomologii z zastosowaniamiKierownik2010-10-142012-03-29
Topological complex systemsKierownik2012-09-142015-09-30
Topologiczne systemy złożoneKierownik2013-03-132015-09-30
Obliczeniowa dynamika topologicznaKierownik2015-10-012022-09-30
Dynamikas topologiczna w problemie Big DataKierownik2020-06-102023-06-09

Nagrody

RokRodzajRodzaj uhonorowanej działalnościTyp 
2011nagrodawybitny dorobek naukowy lub artystycznykrajowaSzczegóły
2013nagrodadziałalność naukowa lub naukowo-badawczakrajowaSzczegóły
2023nagrodadziałalność naukowa lub naukowo-badawczakrajowaSzczegóły