Defective rotating machinery usually exhibits complex dynamic behavior. Therefore, feature representation of vibration signals is always critical for condition monitoring machinery. Permutation entropy (PeEn), an adaptive symbolic description, can measure complexities signals. However, PeEn, which compresses all the information into a single parameter, may lack capability to fully describe dyna...

The characterization of brain electrical activities in terms of neuronal complexity has recently received great attention. However, traditional complexity measures which are maximized for random sequences fail to quantify the inherent long-range correlation in brain dynamics. The recently introduced multiscale entropy (MSE) analysis accounts for the complexity over multiple time scales and ther...

We discuss robust methods of time series analysis which use only comparisons of values and not their actual size. Local and global order structure are defined as matrices or by rank numbers. Local ranks, autocorrelation by Kendall’s tau, and permutation entropy as complexity measure are introduced in such a way that they contain a scale parameter which allows to study time series on different s...

This paper presents a quasigroup encryptor that has very good data-scrambling properties and, therefore, it has potential uses in symmetric cryptography. The purpose of the scrambler is to maximize the entropy at the output, even in cases where the input is constant. The great complexity associated with the task of finding the scrambling transformation ensures the effectiveness of the encryptio...

This paper describes a new cryptanalytic technique that combines differential cryptanalysis with Shannon entropy. We call it differential entropy (DE). The objective is to exploit the non-uniform distribution of output differences from a given mapping as a distinguishing tool in cryptanalysis. Our preferred target is the IDEA block cipher [5] since we detected significantly low entropy at the o...

Entropy is a general concept that appears in different settings with different meanings. Thus, it measures disorder in physics, uncertainty in information theory, minimum code length in coding theory, (pseudo-)randomness in measure-preserving dynamical systems, complexity in topological dynamics, and algorithmic complexity in computer science. As for its importance, let us remind that it enters...

In this paper, by using the notion of fuzzy subsets, the concept of F-permutation is introduced. Then by applying this notion the concepts of presentation of an F-polygroup, graph of an F-permutation and F-permutation matrices are investigated.

Entropy measures have been extensively used to assess heart rate variability (HRV), a noninvasive marker of cardiovascular autonomic regulation. It is yet to be elucidated whether those entropy measures can sensitively respond to changes of autonomic balance and whether the responses, if there are any, are consistent across different entropy measures. Sixteen healthy subjects were enrolled in t...

This paper proposed a novel color image encryption scheme based on multiple chaotic systems. The ergodicity property of chaotic system is utilized to perform the permutation process; a substitution operation is applied to achieve the diffusion effect. In permutation stage, the 3D color plain-image matrix is converted to a 2D image matrix, then two generalized Arnold maps are employed to generat...