Department of Differential Equations and Mathematical Applications - Administrative Units - MOST Wiedzy

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Department of Differential Equations and Mathematical Applications

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  • An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

    For 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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  • ANALYSIS OF THE p53 PROTEIN GENE EXPRESSION MODEL
    Publication

    - Year 2015

    We study the asymptotic behaviour of the solutions of the p53-Mdm2 model proposed by Monk (2003). The p53 gene is crucial for cellular inhibition of the angiogenesis process, while Mdm2 is a negative regulator of the p53 tumor-suppressor. We investigate the stability of the positive steady state and perform some numerical experiments.

  • Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization
    Publication
    • D. Makowiec
    • D. Wejer
    • A. Kaczkowska
    • M. Żarczyńska-Buchowiecka
    • Z. R. Struzik

    - Frontiers in Physiology - Year 2015

    Beat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3)...

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  • Efficient quadrature for fast oscillating integralof paraxial optics
    Publication

    The study concerns the determination of quadrature for the integral solutionof the paraxial wave equation. The difficulty in computation of the integral isassociated with the rapid change of the integrand phase. The developed quadraturetakes into account the fast oscillating character of the integrand. The presentedmethod is an alternative to the commonly used methods based on the use of theFourier transform. The determination...

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  • Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population
    Publication
    • D. Makowiec
    • A. Kaczkowska
    • D. Wejer
    • M. Żarczyńska-Buchowiecka
    • Z. R. Struzik

    - ENTROPY-SWITZ - Year 2015

    Two entropy-based approaches are investigated to study patterns describing differences in time intervals between consecutive heartbeats. The first method explores matrices arising from networks of transitions constructed following events represented by a time series. The second method considers distributions of ordinal patterns of length three, whereby patterns with repeated values are counted as different patterns. Both methods provide...

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  • Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope
    Publication

    - ENTROPY-SWITZ - Year 2015

    Sample 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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