Abstract. The 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 of ordinal pattern to the analysis of electrocardiograms (inter-peak intervals) of healthy subjects in the supine position. This way we observe new regularities of the heart rhythm related to the distribution of ordinal patterns of lengths 3 and 4.
Let f be a self-map of a smooth compact connected and simplyconnected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant D m r [f ] which is the best lower bound for the number of r-periodic points for all C 1 maps homotopic to f . In case m = 3 we give the formula for D 3 r [f ] and calculate it for self-maps of S 2 × I.2000 Mathematics Subject Classification. Primary 37C25, 55M20 Secondary 37C05.
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 (HUTT). Time-domain heart rate variability (HRV) indices and several nonlinear parameters were calculated using 500 RR interval-long ECG recordings done before tilting in patients with a history suggesting vasovagal syncope. Groups of patients with so-called cardiodepressive vasovagal syncope (VVS_2) during HUTT and patients who did not faint during the test were compared. Two types of HUT tests were analyzed: with spontaneous (SB) or controlled breathing (CB). In our study, SampEn was higher in VVS_2 patients during SB, and PermEn was higher in VVS_2 patients during CB. Irrespective of the type of breathing during the test, SampEn and PermEn were similar in patients with the Entropy 2015, 17 1008 same type of reaction during HUTT. The use of several entropy-based parameters seems to be useful in HRV assessment in patients with vasovagal fainting.
Let f be a smooth self-map of R m , when m is an arbitrary natural number. We give a complete description of possible sequences of indices of iterations of f at an isolated fixed point, answering in affirmative the Chow, Mallet-Paret and Yorke conjecture posed in [S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index which is a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,
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