Wyszukiwarka
prof. dr hab. Grzegorz Graff
Zatrudnienie
- Kierownik Studiów Doktoranckich w Wydział Fizyki Technicznej i Matematyki Stosowanej
- Kierownik zakładu w Zakład Równań Różniczkowych i Zastosowań Matematyki
- Profesor w Instytut Matematyki Stosowanej
Obszary badawcze
Publikacje
Filtry
wszystkich: 64
Katalog Publikacji
Rok 2013
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
Rok 2006
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Algebraic periods of self-maps of a rational exterior space of rank 2
PublikacjaArtykuł stanowi kompletny opis okresów algebraicznych dla odwzorowań wymiernej przestrzeni zewnętrznej rangi 2 w siebie.
Rok 2024
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An absorbing set for the Chialvo map
PublikacjaThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
Rok 2015
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublikacjaFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope
PublikacjaSample entropy (SampEn) was reported to be useful in the assessment of the complexity of heart rate dynamics. Permutation entropy (PermEn) is a new measure based on the concept of order and was previously shown to be accurate for short, non-stationary datasets. The aim of the present study is to assess if SampEn and PermEn obtained from baseline recordings might differentiate patients with various outcomes of the head-up tilt test...
Rok 2023
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Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere
PublikacjaA class of dissipative orientation preserving homeomorphisms of the infinite annulus,pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere isconsidered. We prove that in some isotopy classes the local behavior of such homeomor-phisms at a fixed point, namely the existence of so-called inverse saddle, impacts thetopology of the attractor — it cannot be arcwise connected
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Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices
PublikacjaWe 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...
Rok 2012
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublikacjaLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Entropy measures of heart rate variability for short ECG datasets in patients with congestive heart failure
PublikacjaWe investigated the usefulness of entropy measures calculated for short ECG series in distinguishing healthy subjects from patients with congestive heart failure (CHF). Four entropy measures were tested: Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (FuzzyEn) and Permutation Entropy (PE), each computed for ECG series of 1000, 500, 250 and 100 RR intervals. We found that with a reduction of the data set length...
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Entropy Measures of heart rate variability for short ECG datasets in patients with congestive heart failure
PublikacjaWe investigated the usefulness of entropy measures calculated for short ECG series in distinguishing healthy subjects from patients with congestive heart failure (CHF). Four entropy measures were tested: Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (Fuzzy En) and Permutation Entropy (PE), each computed for ECG series of 1000, 500, 250 and 100 RR intervals. We found that with a reduction of the data set length...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublikacjaLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
Rok 2020
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
Rok 2016
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Computing algebraic transfer entropy and coupling directions via transcripts
PublikacjaMost random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer...
Rok 2019
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Detecting coupling directions with transcript mutual information: A comparative study
PublikacjaCausal 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...
Rok 2021
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Dold sequences, periodic points, and dynamics
PublikacjaIn this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Rok 2018
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Dynamics of Field Line Mappings in Magnetic Flux Tubes
PublikacjaWe study the topological constraints on the dynamics of magnetic field lines in flux tubes. Our approach is based on the application of the topological invariant: fixed point index. We consider periodic flux tubes and find various restrictions on the field lines that come from the sequence of fixed point indices of iterations. We also analyze the case of a tube with a cylindrical obstacle, deducing some special dynamical properties...
Rok 2011
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Electrophysiological features in patients with sinus node dysfunction and vasovagal syncope
PublikacjaThe aim of the study was to identify electrophysiological criteria that can be used for identification of patients with sinus node dysfunction and concurrent vasovagal syncope.
Rok 2008
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Entropia w badaniach zaburzeń rytmu serca
PublikacjaArtykuł prezentuje zastosowanie ''Approximate Entropy'', będącej miarą stopnia złożoności szeregów czasowych, do analizy zmiennosci rytmu serca.
Rok 2003
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Etyczne aspekty zaufania.
PublikacjaArtykuł analizuje komponenty składające się na fenomen zaufania, ze szczególnym uwzględnieniem sfery etycznej.
Rok 2007
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Existence of periodic orbits for a perturbed vector field
PublikacjaPrzy nałożeniu pewnego warunku na odwzorowanie Poincarego, wyrażonego w języku indeksów iteracji, dowodzi się istnienia orbit periodycznych dla zaburzonego pola wektorowego.
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