Grzegorz Graff
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Grzegorz Graff has a total of 63 co-authors. Here are the top co-authors by number of shared publications:
- Beata Graff
Department of Hypertension and Diabetology, Medical University of Gdansk, Gdansk, Poland
14 shared publications - Jerzy Jezierski
Institute of Applications of Mathematics, Warsaw University of Life Sciences (SGGW), Warsaw, Poland
12 shared publications - Paweł Pilarczyk
Faculty of Applied Physics and Mathematics and Digital Technologies Center, Gdańsk University of Technology, Gdańsk, Poland
7 shared publications Piotr Nowak-Przygodzki
Independent scholar
6 shared publications- Adrian Myszkowski
Independent Researcher, Poland
4 shared publications Agnieszka Kaczkowska
Gdansk University of Technology, Poland
4 shared publications
Latest Publications
- Open Access
- 16 October 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (4) , 91
Nielsen coincidence theory of ${\varvec{(n,m)}}$-valued pairs of maps- 16 October 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 28 (4) , 91
Open AccessNielsen coincidence theory of ${\varvec{(n,m)}}$-valued pairs of maps - Open Access
- 2 September 2026
- Published by Elsevier in Biomedical Signal Processing and Control
- Vol. 129
Ordinal patterns with ties and tolerance provide a physiology-driven method to quantify cardiorespiratory interactions
- 2 September 2026
- Published by Elsevier in Biomedical Signal Processing and Control
- Vol. 129
Open AccessOrdinal patterns with ties and tolerance provide a physiology-driven method to quantify cardiorespiratory interactions
- Open Access
- 22 July 2026
- Published by Springer Nature in The European Physical Journal Special Topics
- Vol. 235 (31) , 9053-9066
The Makowiec Generalised Asymmetry Index for assessing asymmetry in heart rate and blood pressure variability in obstructive sleep apnea and healthy men
The Makowiec Generalised Asymmetry Index, denoted by $${{\,\textrm{MI}\,}}(q)$$ , is a q -parameterised family of directional asymmetry measures for time series, computed from short-term recordings to quantify the imbalance between opposite changes (increases vs. decreases) across fluctuation magnitudes. In this study, we apply the Makowiec Generalised Asymmetry Index to daytime recordings of heart rate variability (HRV) and blood pressure variability (BPV) collected during wakefulness, and we evaluate its usefulness for the characterization of healthy men and obstructive sleep apnea (OSA) patients. Our findings suggest that asymmetry quantified by the Makowiec Generalised Asymmetry Index in daytime for blood pressure signals during wakefulness may serve as a noninvasive marker supporting OSA screening and risk stratification, motivating further validation in larger prospective cohorts.- 22 July 2026
- Published by Springer Nature in The European Physical Journal Special Topics
- Vol. 235 (31) , 9053-9066
Open AccessThe Makowiec Generalised Asymmetry Index for assessing asymmetry in heart rate and blood pressure variability in obstructive sleep apnea and healthy men
The Makowiec Generalised Asymmetry Index, denoted by $${{\,\textrm{MI}\,}}(q)$$ , is a q -parameterised family of directional asymmetry measures for time series, computed from short-term recordings to quantify the imbalance between opposite changes (increases vs. decreases) across fluctuation magnitudes. In this study, we apply the Makowiec Generalised Asymmetry Index to daytime recordings of heart rate variability (HRV) and blood pressure variability (BPV) collected during wakefulness, and we evaluate its usefulness for the characterization of healthy men and obstructive sleep apnea (OSA) patients. Our findings suggest that asymmetry quantified by the Makowiec Generalised Asymmetry Index in daytime for blood pressure signals during wakefulness may serve as a noninvasive marker supporting OSA screening and risk stratification, motivating further validation in larger prospective cohorts. - 23 April 2025
- Published by Springer Nature in Qualitative Theory of Dynamical Systems
- Vol. 24 (3) , 1-22
Dold Coefficients of Quasi-unipotent Homeomorphisms of Orientable Surfaces
- 23 April 2025
- Published by Springer Nature in Qualitative Theory of Dynamical Systems
- Vol. 24 (3) , 1-22
Dold Coefficients of Quasi-unipotent Homeomorphisms of Orientable Surfaces
- 18 April 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 436
Fixed point indices of iterates of orientation-reversing homeomorphisms
- 18 April 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 436
Fixed point indices of iterates of orientation-reversing homeomorphisms
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 45 (11) , 4510-4528
Every finite set of natural numbers is realizable as algebraic periods of a Morse–Smale diffeomorphism
A given self-map $ f\colon M\to M $ of a compact manifold determines the sequence $ (L(f^n)) $ of the Lefschetz numbers of its iterations. We consider its dual sequence $ (a_n(f)) $ given by the Möbius inversion formula. The set $ {\mathcal AP}(f) = \{ n\in \mathbb N \colon a_n(f)\neq 0\} $ is called the set of algebraic periods. We solve an open problem existing in literature by showing that for every finite subset $ {\mathcal A} $ of natural numbers, there exist an orientable surface $ S_{\rm g} $, as well as a non-orientable surface $ N_ \mathrm g $, of genus $ {\rm g} $, and a Morse–Smale diffeomorphism $ f $ of this surface such that $ \mathcal{AP}(f) = \mathcal{A} $. For such a map it implies the existence of points of a minimal period $ n $ for each odd $ n \in \mathcal{A} $. For the orientation-reversing Morse–Smale diffeomorphisms of $ S_ \mathrm g $, we identify strong restrictions on $ {\mathcal AP}(f) $. Our method also provides an estimate of the number of conjugacy classes of mapping classes containing Morse–Smale diffeomorphisms, which is exponential in $ \mathrm g $.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 45 (11) , 4510-4528
Every finite set of natural numbers is realizable as algebraic periods of a Morse–Smale diffeomorphism
A given self-map $ f\colon M\to M $ of a compact manifold determines the sequence $ (L(f^n)) $ of the Lefschetz numbers of its iterations. We consider its dual sequence $ (a_n(f)) $ given by the Möbius inversion formula. The set $ {\mathcal AP}(f) = \{ n\in \mathbb N \colon a_n(f)\neq 0\} $ is called the set of algebraic periods. We solve an open problem existing in literature by showing that for every finite subset $ {\mathcal A} $ of natural numbers, there exist an orientable surface $ S_{\rm g} $, as well as a non-orientable surface $ N_ \mathrm g $, of genus $ {\rm g} $, and a Morse–Smale diffeomorphism $ f $ of this surface such that $ \mathcal{AP}(f) = \mathcal{A} $. For such a map it implies the existence of points of a minimal period $ n $ for each odd $ n \in \mathcal{A} $. For the orientation-reversing Morse–Smale diffeomorphisms of $ S_ \mathrm g $, we identify strong restrictions on $ {\mathcal AP}(f) $. Our method also provides an estimate of the number of conjugacy classes of mapping classes containing Morse–Smale diffeomorphisms, which is exponential in $ \mathrm g $.- Open Access
- 23 May 2024
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 26 (2) , 1-21
Algebraic periods and minimal number of periodic points for smooth self-maps of $\textbf{1}$-connected $\textbf{4}$-manifolds with definite intersection formsLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map $$f:M \rightarrow M$$ . This task is related to determining a topological invariant $$D^4_r[f]$$ , defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of iterations. Previously, the invariant was computed for self-maps of some 3-manifolds. In this paper, we compute the invariants $$D^4_r[f]$$ for the self-maps of closed 1-connected smooth 4-manifolds with definite intersection forms (i.e., connected sums of complex projective planes). We also present some efficient algorithmic approach to investigate that problem- 23 May 2024
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
- Vol. 26 (2) , 1-21
Open AccessAlgebraic periods and minimal number of periodic points for smooth self-maps of $\textbf{1}$-connected $\textbf{4}$-manifolds with definite intersection formsLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map $$f:M \rightarrow M$$ . This task is related to determining a topological invariant $$D^4_r[f]$$ , defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of iterations. Previously, the invariant was computed for self-maps of some 3-manifolds. In this paper, we compute the invariants $$D^4_r[f]$$ for the self-maps of closed 1-connected smooth 4-manifolds with definite intersection forms (i.e., connected sums of complex projective planes). We also present some efficient algorithmic approach to investigate that problem - 29 February 2024
- Published by Elsevier in Communications in Nonlinear Science and Numerical Simulation
- Vol. 132
An absorbing set for the Chialvo map
- 29 February 2024
- Published by Elsevier in Communications in Nonlinear Science and Numerical Simulation
- Vol. 132
An absorbing set for the Chialvo map
- Open Access
- 1 October 2023
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 33 (10)
Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate–blood pressure coupling quantified by entropy-based indices
We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset of indices most suitable for our classification problem in order to build an optimal yet simple model for distinguishing between patients suffering from obstructive sleep apnea and a control group.
- 1 October 2023
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 33 (10)
Open AccessDifferentiating patients with obstructive sleep apnea from healthy controls based on heart rate–blood pressure coupling quantified by entropy-based indices
We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset of indices most suitable for our classification problem in order to build an optimal yet simple model for distinguishing between patients suffering from obstructive sleep apnea and a control group.
- 1 April 2023
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 33 (4) , 043110
Topological-numerical analysis of a two-dimensional discrete neuron model
We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects.
- 1 April 2023
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 33 (4) , 043110
Topological-numerical analysis of a two-dimensional discrete neuron model
We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects.