Различные паттерны энтропии перестановок электроэнцефалограммы при эпилептиформной активности

Показано поведінку часової залежності ентропії перестановок при зміні порядку з третього до сьомого для електроенцефалограм, що містять епілептиформну активність. Встановлено, що зміна порядку в межах від трьох до семи не має істотного впливу на одержувані результати. Було виділено дві різні групи сигналів, що містять епілептиформну активність, одна зі зниженням ентропії перестановок в області з епілептиформною активністю, а інша – із збільшенням ентропії перестановок при епілептиформній активності.Behavior of permutation entropy for the orders from 3 to 7 was shown for the electroencephalogram (EEG) containing epileptiform activity. It was revealed that changing the order in the range from 3 to 7 has no significant effect on the results. Two different EEG groups containing epileptiform activity were distinguished, one with the tendency to a permutation entropy decrease in areas where epileptiform activity persists, another with increase of permutation entropy during epileptiform activity.Показано поведение временной зависимости энтропии перестановок при изменении порядка с третьего до седьмого для электроэнцефалограмм (ЭЭГ), содержащих эпилептиформную активность. Установлено, что изменение порядка в пределах от трех до семи не имеет существенного влияния на получаемые результаты. Было выделено две различные группы сигналов, содержащих эпилептиформную активность, одна со снижением энтропии перестановок в области с эпилептиформной активностью, а другая – с увеличением энтропии перестановок при эпилептиформной активности

Permutation entropy and its main biomedical and econophysics applications: a review

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.Facultad de Ingenierí

Increment entropy as a measure of complexity for time series

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters, one letter corresponding to direction and the other corresponding to magnitude. The Shannon entropy of the words is termed as increment entropy (IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have demonstrated its ability of detecting the abrupt change, regardless of energetic (e.g. spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series and it can be applicable to arbitrary real-world data.Comment: 12pages,7figure,2 table

Numerical and experimental study of the effects of noise on the permutation entropy

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an almost-deterministic regime, where the permutation entropy grows slower than linearly with the pattern dimension, to a noise-dominated regime, where the permutation entropy grows faster than linearly with the pattern dimension. We perform the same analysis on experimental time-series by considering the stochastic spiking output of a semiconductor laser with optical feedback. Because of the experimental conditions, the dynamics is found to be always in the noise-dominated regime. Nevertheless, the analysis allows to detect regularities of the underlying dynamics. By comparing the results of these three different examples, we discuss the possibility of determining from a time series whether the underlying dynamics is dominated by noise or not

Efficiency characterization of a large neuronal network: a causal information approach

When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution function associated to the interspike intervals and taking different degrees of inter-connectivity across neurons. More specifically we take into account the fine temporal ``structures'' of the complex neuronal signals not just by using the probability distributions associated to the inter spike intervals, but instead considering much more subtle measures accounting for their causal information: the Shannon permutation entropy, Fisher permutation information and permutation statistical complexity. This allows us to investigate how the information of the system might saturate to a finite value as the degree of inter-connectivity across neurons grows, inferring the emergent dynamical properties of the system.Comment: 26 pages, 3 Figures; Physica A, in pres

Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods

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