A Massively Parallel Algorithm for K2 Entropy Computation: Case Studies of Model Systems and in Vivo Data

Abstract

Grassberger and Procaccia's estimate of Kolmogorov entropy, i.e., K₂ entropy (Grassberger and Procaccia, 1983), is a commonly used measure of chaos present in complex dynamic systems. The design and imple mentation of a massively parallel algorithm on the MasPar MP-2 system for the computation of K₂ en tropy is presented. The parallel implementation on a 2,048-processor MasPar MP-2 system is shown to have a speedup of approximately 1,000. The parallel algo rithm for the computation of the correlation integral, in conjunction with the serial algorithm for the determi nation of an optimal scaling region in the correlation integral plot, are used as a computational tool to ana lyze the heart-rate dynamics of canine subjects intoxi cated with ethanol. Results indicate that the K₂ entropy and correlation dimension have an inverse correlation with the blood-ethanol concentration.

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