Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 365-372 ◽  
Author(s):  
KARTHI BALASUBRAMANIAN ◽  
SILPA S NAIR ◽  
NITHIN NAGARAJ
2010 ◽  
Vol 4 (1) ◽  
pp. 223-235 ◽  
Author(s):  
Carlos Gómez ◽  
Roberto Hornero

Alzheimer’s disease (AD) is one of the most frequent disorders among elderly population and it is considered the main cause of dementia in western countries. This irreversible brain disorder is characterized by neural loss and the appearance of neurofibrillary tangles and senile plaques. The aim of the present study was the analysis of the magnetoencephalogram (MEG) background activity from AD patients and elderly control subjects. MEG recordings from 36 AD patients and 26 controls were analyzed by means of six entropy and complexity measures: Shannon spectral entropy (SSE), approximate entropy (ApEn), sample entropy (SampEn), Higuchi’s fractal dimension (HFD), Maragos and Sun’s fractal dimension (MSFD), and Lempel-Ziv complexity (LZC). SSE is an irregularity estimator in terms of the flatness of the spectrum, whereas ApEn and SampEn are embbeding entropies that quantify the signal regularity. The complexity measures HFD and MSFD were applied to MEG signals to estimate their fractal dimension. Finally, LZC measures the number of different substrings and the rate of their recurrence along the original time series. Our results show that MEG recordings are less complex and more regular in AD patients than in control subjects. Significant differences between both groups were found in several brain regions using all these methods, with the exception of MSFD (p-value < 0.05, Welch’s t-test with Bonferroni’s correction). Using receiver operating characteristic curves with a leave-one-out cross-validation procedure, the highest accuracy was achieved with SSE: 77.42%. We conclude that entropy and complexity analyses from MEG background activity could be useful to help in AD diagnosis.


1994 ◽  
Vol 4 (1) ◽  
pp. 133-173 ◽  
Author(s):  
R. Wackerbauer ◽  
A. Witt ◽  
H. Atmanspacher ◽  
J. Kurths ◽  
H. Scheingraber
Keyword(s):  

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050129
Author(s):  
HAMIDREZA NAMAZI

Coronavirus disease (COVID-19) is a pandemic disease that has affected almost all around the world. The most crucial step in the treatment of patients with COVID-19 is to investigate about the coronavirus itself. In this research, for the first time, we analyze the complex structure of the coronavirus genome and compare it with the other two dangerous viruses, namely, dengue and HIV. For this purpose, we employ fractal theory, sample entropy, and approximate entropy to analyze the genome walk of coronavirus, dengue virus, and HIV. Based on the obtained results, the genome walk of coronavirus has greater complexity than the other two deadly viruses. The result of statistical analysis also showed the significant difference between the complexity of genome walks in case of all complexity measures. The result of this analysis opens new doors to scientists to consider the complexity of a virus genome as an index to investigate its danger for human life.


In this chapter, the author considers existing methods and means of forming pseudo-random sequences of numbers and also are described the main characteristics of random and pseudorandom sequences of numbers. The main theoretical aspects of the construction of pseudo-random number generators are considered. Classification of pseudorandom number generators is presented. The structures and models of the most popular pseudo-random number generators are considered, the main characteristics of generators that affect the quality of the formation of pseudorandom bit sequences are described. The models of the basic mathematical generators of pseudo-random numbers are considered, and also the principles of building hardware generators are presented.


2003 ◽  
Vol 13 (03) ◽  
pp. 733-742 ◽  
Author(s):  
FANJI GU ◽  
XIN MENG ◽  
ENHUA SHEN ◽  
ZHIJIE CAI

Several complexity measures, especially approximate entropy (ApEn) and a new defined complexity measure [Formula: see text], of EEG signals or the ones of the mutual information transmission between different channels of EEGs were calculated to distinguish different consciousness levels for different brain functional states. All of the measures decreased with the following order of brain states: rest with eyes open, eyes closed, light sleep and deep sleep. They decreased during epileptic seizures. On the contrary, the averaged mutual information between different channels increased significantly during the epileptic seizure; there is no significant difference among the averaged mutual information for the subject resting with eyes open, closed, being in light sleep and in deep sleep. Thus, the former indexes seem to be promising candidates to characterize different consciousness levels, while the latter seems not.


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