Information and entropy in strange attractors

“…As a primary definition, the entropy H (X) of a monodimensional discrete random variable X is H (X) = − x i ∈φ p(x i ) log p(x i ), where φ is the set of values and p(x i ) is the ith probability function. Other important definitions include the Kolmogorov-Sinai entropy [4], the K 2 entropy [5], and the marginal redundancy algorithm given by Fraser [6]. To compute these theoretical entropy indices, a large number of data points are needed to achieve convergence.…”

Section: Introductionmentioning

confidence: 99%

Inhomogeneous point-process entropy: An instantaneous measure of complexity in discrete systems

et al. 2014

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Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties.

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“…The analysis of deterministic chaos provides information on the system complexity and can explain a complex behaviour using a low-dimensional model (Fraser, 1989). The algorithm for nonlinear processing was developed in the seventies and eighties and has received noticeable attention in biomedical signal processing a decade later.…”

Section: Processing and Interpretation Of The Electromyogram Signalmentioning

confidence: 99%