scholarly journals Ordinal Patterns in Heartbeat Time Series: An Approach Using Multiscale Analysis

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 583 ◽  
Author(s):  
María Muñoz-Guillermo
Keyword(s):  
Time Series ◽  
Multiscale Analysis ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Cardiac Diseases ◽  
Ordinal Patterns

In this paper, we simultaneously use two different scales in the analysis of ordinal patterns to measure the complexity of the dynamics of heartbeat time series. Rényi entropy and weighted Rényi entropy are the entropy-like measures proposed in the multiscale analysis in which, with the new scheme, four parameters are involved. First, the influence of the variation of the new parameters in the entropy values is analyzed when different groups of subjects (with cardiac diseases or healthy) are considered. Secondly, we exploit the introduction of multiscale analysis in order to detect differences between the groups.

Multiscale weighted Rényi entropy causality plane for financial time series

2019 ◽  
Vol 30 (05) ◽  
pp. 1950037 ◽  
Author(s):  
Jing Gao ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Financial Time Series ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Market Development ◽  
Permutation Entropy ◽  
Statistical Measure ◽  
Stock Market Development ◽  
Financial Time

The permutation entropy (PE) is a statistical measure which can describe complexity of time series. In recent years, the research on PE is increasing gradually. As part of its application, the complexity–entropy causality plane (CECP) and weighted CECP (WCECP) have been recently used to distinguish the stage of stock market development. In this paper, we focus on weighted Rényi entropy causality plane (WRECP), and then extend WCECP and WRECP into multiscale WCECP (MWCECP) and multiscale WRECP (MWRECP) by introducing a new parameter scale. By data simulating and analyzing, we show the power of WRECP. Besides, we discuss the MWCECP and the MWRECP of adjacent scales. It reveals a gradual relationship between adjacent weighted scale entropies.

Multiscale multifractal multiproperty analysis of financial time series based on Rényi entropy

2017 ◽  
Vol 28 (02) ◽  
pp. 1750028 ◽  
Author(s):  
Yang Yujun ◽  
Li Jianping ◽  
Yang Yimei
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Stock Indices ◽  
Generalized Hurst Exponent ◽  
Detrended Fluctuation

This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.

scholarly journals Detection of time reversibility in time series by ordinal patterns analysis

2018 ◽  
Vol 28 (12) ◽  
pp. 123111 ◽  
Author(s):  
J. H. Martínez ◽  
J. L. Herrera-Diestra ◽  
M. Chavez
Keyword(s):  
Time Series ◽  
Time Reversibility ◽  
Ordinal Patterns

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

scholarly journals Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 526
Author(s):  
Gautam Aishwarya ◽  
Mokshay Madiman
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Basic Properties ◽  
Reference Measure ◽  
Definition Of ◽  
Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

A new Rényi entropy-based local image descriptor for object recognition

2010 ◽  
Author(s):  
S. Gabarda ◽  
G. Cristóbal ◽  
P. Rodríguez ◽  
C. Miravet ◽  
J. M. del Cura
Keyword(s):  
Object Recognition ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Image Descriptor ◽  
Local Image Descriptor ◽  
Local Image
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