MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
J. Levitana,d, M. Lewkowicza, N. Pozanovb, and Y. Ashkenazya,b
(a) Dept. of Physics, College of Judea and Samaria, Ariel, Israel
(b) The Research Inst., College of Judea and Samaria, Ariel, Israel
(c) Dept. of Physics, Bar-Ilan University, Ramat-Gan, Israel
(d) Dept. of Physics, The Technical University of Denmark, Lyngby, Denmark
We present a geometrical description of a two-dimensional plot of data points in terms of a gravitational multipole expansion where every data point is assigned a unit mass. The monopole moment represents the number of data points; the gravitational dipole moment is arranged to be zero by choosing the origin in the center of mass. The gravitational quadropole moment measures the deviation from a circular, disc-like, distribution of data points. These quadropole moments, calculated for the principal axes, offer a unique description of the mass distribution. The method is applied to the detrended time series created from R-R intervals obtained from a set of 32 individuals whose state of cardiac function is well known. The method succeeds to separate between individuals with normal and abnormal cardiac function. Finally the method is applied to some well-known attractors.