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
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Ordinal pattern statistics for the assessment of heart rate variability
PublikacjaThe recognition of all main features of a healthy heart rhythm (the so-called sinus rhythm) is still one of the biggest challenges in contemporary cardiology. Recently the interesting physiological phenomenon of heart rate asymmetry has been observed. This phenomenon is related to unbalanced contributions of heart rate decelerations and accelerations to heart rate variability. In this paper we apply methods based on the concept...
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Relationship between heart rate variability, blood pressure and arterial wall properties during air and oxygen breathing in healthy subjects
PublikacjaPrevious studies reported that normobaric hyperoxia influences heart rate, arterial pressure, cardiac output and systemic vascular resistance, but the mechanisms underlying these changes are still not fully understood. Several factors are considered including degeneration of endothelium-derived nitric oxide by reactive oxygen species, the impact of oxygen-free radicals on tissues and alterations of autonomic nervous system function....
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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...
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublikacjaWe give a complete description of possible sequences ofindices of iterations of f at an isolated fixed point, answering inaffirmative the Chow, Mallet-Paret and Yorke conjecture posed in[S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index whichis a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983,pp. 109-131].
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Minimizing the number of periodic points for smooth maps. Non-simply connected case
PublikacjaNiech f będzie gładkim odwzorowaniem zamkniętej rozmaitości o wymiarze wiekszym niż 2, a r ustaloną liczbą naturalną. W artykule zdefiniowany został niezmiennik topologiczny równy minimalnej liczbie punktów r-periodycznych w gładkiej klasie homotopii f.
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Persistent homology as a new method of the assessment of heart rate variability
PublikacjaHeart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...
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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...
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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.
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165-2169].
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Generating sequences of Lefschetz numbers of iterates
PublikacjaDu, 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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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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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.
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublikacjaWe 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...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublikacjaLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublikacjaLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Local fixed point indices of iterations of planar maps
PublikacjaW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublikacjaWe 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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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...
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