Tsallis entropy and cortical dynamics: the analysis of EEG signals

Capurro, Alberto; Diambra, Luis; Lorenzo, Daniel; Macadar, O.; Martín, María Teresa; Mostaccio, Catalina Alba; Plastino, A.; Rofman, Edmundo; Torres, Marı́a E.; Velluti, J.C.

doi:10.1016/s0378-4371(98)00137-x

Cited by 53 publications

(29 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…42,43 Previous EEG studies have successfully used the relative power distribution of wavelet coefficients to analyze different brain states in epilepsy. 9,33 Given the fact that the Tsallis entropy is a non-extensive measure, it is able to characterize a system where long-range interactions appear. 5 The degree of non-extensivity is stated by the entropic index q 2 <.…”

Section: Definition Of Spectral Entropiesmentioning

confidence: 99%

“…Previous studies have successfully applied several quantifiers based on extensive (e.g., Shannon and Re´nyi entropies) and non-extensive (e.g., Tsallis entropy) information measures to analyze EEG signals. 2,5,9,24,33,40,41 While extensive quantifiers, such as Shannon and Re´nyi entropies, have proved successful in describing systems with short-range interactions, non-extensive measures, such as Tsallis entropy, are able to describe a system where the effective interactions are of long-range. 5,40 In addition, MEG recordings, like EEG signals, are non-stationary and their characteristics may change over time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Regional Analysis of Spontaneous MEG Rhythms in Patients with Alzheimer’s Disease Using Spectral Entropies

et al. 2007

View full text Add to dashboard Cite

Alzheimer's disease (AD) is the most common form of dementia. Ageing is the greatest known risk factor for this disorder. Therefore, the prevalence of AD is expected to increase in western countries due to the rise in life expectancy. Nowadays, a low diagnosis accuracy is reached, but an early and accurate identification of AD should be attempted. In this sense, only a few studies have focused on the magnetoencephalographic (MEG) AD patterns. This work represents a new effort to explore the ability of three entropies from information theory to discriminate between spontaneous MEG rhythms from 20 AD patients and 21 controls. The Shannon (SSE), Tsallis (TSE), and Rényi (RSE) spectral entropies were calculated from the time-frequency distribution of the power spectral density (PSD). The entropies provided statistically significant lower values for AD patients than for controls in all brain regions (p < 0.0005). This fact suggests a significant loss of irregularity in AD patients' MEG activity. Maximal accuracy of 87.8% was achieved by both the TSE and RSE (90.0%, sensitivity; 85.7%, specificity). The statistically significant results obtained by both the extensive (SSE and RSE) and non-extensive (TSE) spectral entropies suggest that AD could disturb long and short-range interactions causing an abnormal brain function.

show abstract

Section: Definition Of Spectral Entropiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regional Analysis of Spontaneous MEG Rhythms in Patients with Alzheimer’s Disease Using Spectral Entropies

et al. 2007

View full text Add to dashboard Cite

show abstract

“…The Tsallis entropy evaluated by wavelet coefficients was analyzed for EEG signals in several works [24][25][26]. Though Tsallis entropy is also a viable method when applied within the scope of continuous concept, it may suffer from the q index parameter.…”

Section: Discussionmentioning

confidence: 99%

Continuous time wavelet entropy of auditory evoked potentials

Cek

Özgören

Savacı

2010

Computers in Biology and Medicine

View full text Add to dashboard Cite

a b s t r a c tIn this paper, the continuous time wavelet entropy (CTWE) of auditory evoked potentials (AEP) has been characterized by evaluating the relative wavelet energies (RWE) in specified EEG frequency bands. Thus, the rapid variations of CTWE due to the auditory stimulation could be detected in post-stimulus time interval. This approach removes the probability of missing the information hidden in short time intervals. The discrete time and continuous time wavelet based wavelet entropy variations were compared on non-target and target AEP data. It was observed that CTWE can also be an alternative method to analyze entropy as a function of time.

show abstract

“…NEXT's central concept is that of a non-additive (though extensive [4]) entropic information measure characterized by the real index q (with q = 1 recovering the standard BG entropy). Applications include cold atoms in dissipative optical lattices [5], dusty plasmas [6], trapped ions [7], spin glasses [8], turbulence in the heliosphere [9], self-organized criticality [10], high-energy experiments at LHC/CMS/CERN [11] and RHIC/PHENIX/Brookhaven [12], low-dimensional dissipative maps [13], finance [14], galaxies [15], Fokker-Planck equation's studies [16], EEG's [17], complex signals [18], Vlasov-Poisson equations [19], etc.…”

Section: Introductionmentioning

confidence: 99%

On the Nature of the Tsallis–Fourier Transform

Plastino

Rocca

2015

Mathematics

Self Cite

View full text Add to dashboard Cite

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis' q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT's non-invertibility issue, but discover a problem that remains open.

show abstract

Tsallis entropy and cortical dynamics: the analysis of EEG signals

Cited by 53 publications

References 4 publications

Regional Analysis of Spontaneous MEG Rhythms in Patients with Alzheimer’s Disease Using Spectral Entropies

Regional Analysis of Spontaneous MEG Rhythms in Patients with Alzheimer’s Disease Using Spectral Entropies

Continuous time wavelet entropy of auditory evoked potentials

On the Nature of the Tsallis–Fourier Transform

Contact Info

Product

Resources

About