Grzegorz Graff - Publikacje - MOST Wiedzy

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Rok 2024
Rok 2023
Rok 2022
  • Generalized Dold sequences on partially-ordered sets
    Publikacja

    - ELECTRONIC JOURNAL OF COMBINATORICS - Rok 2022

    Dold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...

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  • Minimal Sets of Lefschetz Periods for Morse-Smale Diffeomorphisms of a Connected Sum of g Real Projective Planes
    Publikacja

    - Rok 2022

    The dataset titled Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes contains all of the values of the topological invariant called the minimal set of Lefschetz periods, computed for Morse-Smale diffeomorphisms of a non-orientable compact surface without boundary of genus g (i.e. a connected sum of g real projective planes), where g varies from 1 to...

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Rok 2021
Rok 2020
Rok 2019
  • Detecting coupling directions with transcript mutual information: A comparative study
    Publikacja

    - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Rok 2019

    Causal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...

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  • Generating sequences of Lefschetz numbers of iterates
    Publikacja
    • G. Graff
    • M. Lebiedź
    • P. Nowak-Przygodzki

    - MONATSHEFTE FUR MATHEMATIK - Rok 2019

    Du, Huang and Li showed in 2003 that the class of Dold–Fermat sequences coincides with the class of Newton sequences, which are defined in terms of socalled generating sequences. The sequences of Lefschetz numbers of iterates form an important subclass of Dold–Fermat (thus also Newton) sequences. In this paper we characterize generating sequences of Lefschetz numbers of iterates.

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  • Jak gładkość generuje punkty periodyczne
    Publikacja

    Jednym z ważnych problemów teorii układów dynamicznych i topologii jest pytanie, jaka jest najmniejsza liczba punktów stałych lub periodycznych w danej klasie odwzorowań. Na przykład klasyczne twierdzenie Brouwera stwierdza, że każde ciągłe odwzorowanie kuli domkniętej w siebie ma przynajmniej jeden punkt stały. Szczególnie interesujące staje się powyższe pytanie w odniesieniu do klasy homotopii danego odwzorowania f. Artykuł poświęcony...

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  • Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms

    We apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...

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  • Periodic Points for Sphere Maps Preserving MonopoleFoliations
    Publikacja

    Let S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...

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Rok 2018
Rok 2017
  • Visualization of short-term heart period variability with network tools as a method for quantifying autonomic drive
    Publikacja
    • D. Makowiec
    • B. Graff
    • A. Kaczkowska
    • G. Graff
    • D. Wejer
    • J. Wdowczyk-Szulc
    • M. Żarczyńska-Buchowiecka
    • M. Gruchała
    • Z. R. Struzik

    - Rok 2017

    We argue that network methods are successful in detecting nonlinear properties in the dynamics of autonomic nocturnal regulation in short-term variability. Two modes of visualization of networks constructed from RR-increments are proposed. The first is based on the handling of a state space. The state space of RR-increments can be modified by a bin size used to code a signal and by the role of a given vertex as the representation...

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Rok 2016
Rok 2015
Rok 2014
Rok 2013
Rok 2012
Rok 2011
Rok 2010
Rok 2009
Rok 2008
  • Entropia w badaniach zaburzeń rytmu serca
    Publikacja

    - Rok 2008

    Artykuł prezentuje zastosowanie ''Approximate Entropy'', będącej miarą stopnia złożoności szeregów czasowych, do analizy zmiennosci rytmu serca.

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