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

The database of normal RRintervals of length up to 512 of 41 patients at rest hospitalized due to the episode of acute ischemic stroke
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

The database of normal RRintervals of length up to 512 of 46 healthy subjects at rest
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

The database of interpolated RRintervals of length 512 of 46 healthy subjects at rest
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

The database of indices computed from RRintervals of length 512 of 46 healthy subjects at rest
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

The database of indices computed from RRintervals of length 512 of 41 patients at rest hospitalized due to the episode of acute ischemic stroke
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

The database of interpolated RRintervals of original length 512 of 41 patients at rest hospitalized due to the episode of acute ischemic stroke
Dane BadawczeThis dataset contains the data that was a basis for the results discussed in the paper “Persistent homology as a new method of the assessment of heart rate variability” by Grzegorz Graff, Beata Graff, Paweł Pilarczyk, Grzegorz Jabłoński, Dariusz Gąsecki, Krzysztof Narkiewicz, Plos One (2021), DOI: 10.1371/journal.pone.0253851.

Dataset of phase portraits of the fractional preypredator model with Holling typeII interaction (without predator harvesting)
Dane BadawczeThe need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.

Data obtained by computation for Xray imaging of grating with magnification factor equal 8 using oriented Gaussian beams
Dane BadawczeThe propagation of Xray waves through an optical system consisting of grating and Xray refractive lenses is considered. In this approach, the propagating wave is represented as a superposition of the oriented Gaussian beams. The direction of wave propagation in each Gaussian beam is consistent with the local propagation direction of the Xray wavefront.

Data obtained by computation for Xray imaging of grating with magnification factor equal 4 using oriented Gaussian beams
Dane BadawczeThe propagation of Xray waves through an optical system consisting of grating and Xray refractive lenses is considered. In this approach, the propagating wave is represented as a superposition of the oriented Gaussian beams. The direction of wave propagation in each Gaussian beam is consistent with the local propagation direction of the Xray wavefront.

Data obtained by computation for Xray imaging of grating with magnification factor equal 2 using oriented Gaussian beams
Dane BadawczeThe propagation of Xray waves through an optical system consisting of grating and Xray refractive lenses is considered. In this approach, the propagating wave is represented as a superposition of the oriented Gaussian beams. The direction of wave propagation in each Gaussian beam is consistent with the local propagation direction of the Xray wavefront.

Data obtained by computation for Xray imaging of grating without magnification using oriented Gaussian beams
Dane BadawczeThe propagation of Xray waves through an optical system consisting of grating and Xray refractive lenses is considered. In this approach, the propagating wave is represented as a superposition of the oriented Gaussian beams. The direction of wave propagation in each Gaussian beam is consistent with the local propagation direction of the Xray wavefront.

The values of Permutation Entropy for patients with Congestive Heart Failure
Dane BadawczeThe dataset consists of calculated values of entropy of 75 000 intervals between consecutive heartbeats (RR intervals) for 29 patients with congestive heart failure (CHF). The original data were taken from PhysioNet Congestive Heart Failure RR Interval Database (cf. Goldberger A., Amaral L., Glass L., Hausdorff J., Ivanov P.C., Mark R., Mietus J.E.,...

The values of Block Entropy for patients with Congestive Heart Failure
Dane BadawczeThe dataset consists of calculated values of entropy of 75 000 intervals between consecutive heartbeats (RR intervals) for 29 patients with congestive heart failure (CHF). The original data were taken from PhysioNet Congestive Heart Failure RR Interval Database (cf. Goldberger A., Amaral L., Glass L., Hausdorff J., Ivanov P.C., Mark R., Mietus J.E.,...

The values of Block Entropy for individuals with Normal Sinus Rhythm
Dane BadawczeThe dataset consists of calculated values of entropy of 75 000 intervals between consecutive heartbeats (RR intervals) for 54 patients with normal sinus rhythm (NSR). The original data were taken from PhysioNet Normal Sinus Rhythm RR Interval Database (cf. Goldberger A., Amaral L., Glass L., Hausdorff J., Ivanov P.C., Mark R., Mietus J.E., Moody G.B.,...

The values of Permutation Entropy for individuals with Normal Sinus Rhythm
Dane BadawczeThe dataset consists of calculated values of entropy of 75 000 intervals between consecutive heartbeats (RR intervals) for 54 patients with normal sinus rhythm (NSR). The original data were taken from PhysioNet Normal Sinus Rhythm RR Interval Database (cf. Goldberger A., Amaral L., Glass L., Hausdorff J., Ivanov P.C., Mark R., Mietus J.E., Moody G.B.,...

Dataset of nonisomorphic graphs being coloring types (K3e,Kme;n), 2<m<8, 1<n<R(K3e,Kme)
Dane BadawczeFor K3e and Kme graphs, the type coloring (K3e,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K3e subgraph in the first color (no edge in the graph) or the Kme subgraph in the second color (exists edge in the graph). Kme means the full Km graph with one edge removed.The Ramsey number R(K3e,Kme) is the smallest...

Dataset of nonisomorphic graphs being coloring types (K6e,Kme;n), 2<m<5, 1<n<R(K6e,Kme)
Dane BadawczeFor K6e and Kme graphs, the type coloring (K6e,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K6e subgraph in the first color (no edge in the graph) or the Kme subgraph in the second color (exists edge in the graph). Kme means the full Km graph with one edge removed. The Ramsey number R(K6e,Kme) is the smallest...

Dataset of nonisomorphic graphs being coloring types (K5e,Kme;n), 2<m<5, 1<n<R(K5e,Kme)
Dane BadawczeFor K5e and Kme graphs, the type coloring (K5e,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K5e subgraph in the first color (no edge in the graph) or the Kme subgraph in the second color (exists edge in the graph). Kme means the full Km graph with one edge removed.The Ramsey number R(K5e,Kme) is the smallest...

Dataset of nonisomorphic graphs being coloring types (K4e,Kme;n), 2<m<7, 1<n<R(K4e,Kme)
Dane BadawczeFor K4e and Kme graphs, the type coloring (K4e,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K4e subgraph in the first color (no edge in the graph) or the Kme subgraph in the second color (exists edge in the graph). Kme means the full Km graph with one edge removed.The Ramsey number R(K4e,Kme) is the smallest...

The database of odd algebraic periods for quasiunipotent selfmaps of a space having the same homology group as the connected sum of g tori
Dane BadawczeThe dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasiunipotent selfmaps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz...

Database of the minimal sets of Lefschetz periods for MorseSmale diffeomorphisms of a connected sum of g tori
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of...

Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simplyconnected manifolds of dimension 8 and homology groups with the sum of ranks less or equal to 10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of selfmaps of a space. A closed smooth and simplyconnected manifolds of dimension 8 and its selfmaps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...

Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Dane BadawczePresented dataset is a result of the convergence analysis of the Mickenstype, nonlinear, finitedifference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...

Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simplyconnected manifolds of dimension 6 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of selfmaps of a space. A closed smooth and simplyconnected manifolds of dimension 6 and its selfmaps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...

Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simplyconnected manifolds of dimension 5 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of selfmaps of a space. A closed smooth and simplyconnected manifolds of dimension 5 and its selfmaps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...

Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simplyconnected manifolds of dimension 7 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of selfmaps of a space. A closed smooth and simplyconnected manifolds of dimension 7 and its selfmaps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...

Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simplyconnected manifolds of dimension 4 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of selfmaps of a space. A closed smooth and simplyconnected manifolds of dimension 4 and its selfmaps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...

Dynamics of Sunimodal maps used in population modeling.
Dane BadawczeSunimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of Sunimodal maps is now a welldeveloped branch of discrete dynamical systems, including famous Singer theorem which implies existence...

Dataset of nonisomorphic graphs of the coloring types (K3,Km;n), 2<m<7, 1<n<R(3,m)
Dane BadawczeFor K3 and Km graphs, a coloring type (K3,Km;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km subgraph in the second color (representing by edges in the graph).The Ramsey number R(3,m) is the smallest natural number n such that for any edge coloring...

Data obtained by computation for Xray focusing using oriented Gaussian beams
Dane BadawczeThe propagation of Xray waves through an optical system consisting of several Xray refractive lenses is considered. Gaussian beams are exact solutions of the paraxial equation. The Helmholtz equation describes the propagation of a monochromatic electromagnetic wave. Since the widths of the beams are much larger than the wavelength of Xrays, Gaussian...

A Fortran95 algorithm to solve the threedimensional Higgs boson equation in the de Sitter spacetime
Dane BadawczeA numerically efficient finitedifference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter spacetime is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a timedependent diffusion...

Data on solutions of Hes1 system
Dane BadawczeHes1 protein (hairy and enhancer of split 1) belongs to the helixloophelix (bHLH) family of transcription proteins, i.e. DNAbinding proteins in the promoter region or in another region where regulation of transcription processes occurs. The database collects data on solutions of the Hes1 systems with multiple binding sites and the dimer formation...

Dataset of nonisomorphic graphs of the coloring types (K4,Kme;n), 2<m<5, 1<n<R(K4,Kme)
Dane BadawczeFor K4 and Kme graphs, a coloring type (K4,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the Kme subgraph in the second color (representing by edges in the graph). Kme means the full Km graph with one edge removed.The Ramsey number R(K4,Kme)...

Database of the thermal ablation model
Dane BadawczeThermal ablation is a low invasive technique which eliminates cancerous tissue using high temperature. The presented database was used to show the temperature distribution for t=600[s] in two cases: when the value of the thermal conductivity of tissue k(x;T) is constant and for the variable k(x;T). In addition, using these data we showed the difference...

The Chow Ring of flag manifolds
Dane BadawczeSchubert calculus is the intersection theory of 19th century. Justifying this calculus is the content of the 15th problem of Hilbert. In the course to establish the foundation of algebraic geometry, Van der Vaerden and A. Weil attributed the problem to the determination of the chow ring of flag manifolds G/P, where G is a compact Lie group and P is...

Dataset of nonisomorphic graphs of the coloring types (Km,K3e;n), 4<m<8, 1<n<R(Km,K3e)
Dane BadawczeFor Km and K3e graphs, a coloring type (Km,K3e;n) is such an edge coloring of the full Kn graph, which does not have the Km subgraph in the first color (representing by no edges in the graph) or the K3e subgraph in the second color (representing by edges in the graph). K3e means the full Km graph with one edge removed.The Ramsey number R(Km,K3e)...

Dataset of nonisomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)
Dane BadawczeFor K4 graph, a coloring type (K4,K4;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the K4 subgraph in the second color (representing by edges in the graph).The Ramsey number R(4,4) is the smallest natural number n such that for any edge coloring of...

Estimates for minimal number of periodic points for smooth selfmaps of simplyconnected manifolds
Dane BadawczeWe consider a closed smooth connected and simplyconnected manifold of dimension at least 4 and its selfmap f. The topological invariant Dr[f] is equal to the minimal number of rperiodic points in the smooth homotopy class of f. We assume that r is odd and all coefficients b(k) of socalled periodic expansion of Lefschetz numbers of iterations are...

An facile Fortran95 algorithm to simulate complex instabilities in threedimensional hyperbolic systems
Dane BadawczeIt is well know that the simulation of fractional systems is a difficult task from all points of view. In particular, the computer implementation of numerical algorithms to simulate fractional systems of partial differential equations in three dimensions is a hard task which has no been solved satisfactorily. Here, we provide a Fortran95 code to solve...

Dataset of nonisomorphic graphs of the coloring types (K3,Kme;n), 2<m<7, 1<n<R(K3,Kme).
Dane BadawczeFor K3 and Kme graphs, a coloring type (K3,Kme;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Kme subgraph in the second color (representing by edges in the graph). Kme means the full Km graph with one edge removed.The Ramsey number R(K3,Kme)...

Database of the estimations of the numbers of simplices of triangulation of some classical Lie groups
Dane BadawczeIt is know that any smooth manifold can be triangulated. The number of simplices of triangulation of a given manifold depends on its topological and combinatorial structure. The data consists of the lower bounds for the numbers of simplices of each dimension of any triangulation of classical Lie groups U(n), SU(n), Sp(n), and SO(n) for n up to 25. Each...

Computing dynamical curlicues
Dane BadawczeA curlicue is a piecewise linear curve in the complex plane which can be generated by an arbitrary sequence of real numbers u_n. It can be interpreted as a trajectory of a particle in the plane which starts in the origin at time t=0 and moves with a constant velocity, changing its direction at instances t=0,1,2,3,..., where the new direction is given...

Stochastic intervals for the family of quadratic maps
Dane BadawczeNumerical analysis of chaotic dynamics is a challenging task. The oneparameter families of logistic maps and closely related quadratic maps f_a(x)=ax^2 are wellknown examples of such dynamical systems. Determining parameter values that yield stochasticlike dynamics is especially difficult, because although this set has positive Lebesgue measure,...

Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Dane BadawczeThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...

A collection of directed graphs for the minimum cycle mean weight computation
Dane BadawczeThis dataset contains definitions of the 16 directed graphs with weighted edges that were described in the following paper: Paweł Pilarczyk, A spaceefficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 349355, DOI: 10.22436/jmcs.020.04.08, URL: http://dx.doi.org/10.22436/jmcs.020.04.08 These...

Data obtained by numerical simulation for Xray focusing using a finite difference method
Dane BadawczeThe propagation of Xray waves through an optical system consisting of many Xray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finitedifference method is applied.

Minimal number of periodic points for smooth selfmaps of simplyconnected manifolds
Dane BadawczeThe problem of finding the minimal number of periodic points in a given class of selfmaps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simplyconnected manifold of dimension at least 4 and its selfmap f. The topological invariant D_r[f] is equal to the minimal number of rperiodic points...

Database of the minimal sets of Lefschetz periods for MorseSmale diffeomorphisms of a connected sum of g real projective planes.
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered...

Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Dane BadawczeThe presented dataset is a result of the convergence analysis of the Mickenstype, nonlinear, finitedifference discretization of a generalized Burgers–Huxley partial differential equation.
wyświetlono 3691 razy