Permutation entropy (PeEn) is a complexity measure that originated from dynamical systems theory. Specifically engineered to be robustly applicable to real-world data, the quantity has since been utilised for a multitude of time series analysis tasks. In electroencephalogram (EEG) analysis, value changes of PeEn correlate with clinical observations, among them the onset of epileptic seizures or...

Permutation entropy (PE) has a growing significance as a relative measure of complexity in nonlinear systems. It has been applied successfully to measuring complexity in nonlinear laser systems. Here, PE and weighted permutation entropy (WPE) are discovered to show an unexpected inversion to higher values, when characterizing the complexity at the characteristic frequencies of nonlinear drivers...

The study area, located in the southwest of Yunnan Province, has a distinct regional difference in both topography and climate system. Western region belongs to the Southwestern Yunnan mountainous area with varied landforms while eastern region is a part of Eastern Yunnan Plateau whose terrain is rather flat relatively. And different regions are influenced by different climates, which have resu...

In this paper we relate information theory and Kolmogorov Complexity (KC) to optimization in the black box scenario. We define the set of all possible decisions an algorithm might make during a run, we associate a function with a probability distribution over this set and define accordingly its entropy. We show that the expected KC of the set (rather than the function) is a better measure of pr...

Permutation relative entropy is proposed to quantify time irreversibility in our nonlinear dynamics analysis of electroencephalogram (EEG). Ordinal patterns in multi-dimension phase space of time series are symbolized, and the probabilistic divergences of all symmetric ordinal pairs are measured by relative entropy as time irreversibility. Analyzing multi-channel EEG from 18 healthy volunteers ...

We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplic...

Spontaneous reinnervation after diaphragmatic paralysis due to trauma, surgery, tumors and spinal cord injuries is frequently observed. A possible explanation could be collateral reinnervation, since the diaphragm is commonly double-innervated by the (accessory) phrenic nerve. Permutation entropy (PeEn), a complexity measure for time series, may reflect a functional state of neuromuscular trans...