Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.Comment: Accepted for publication in PLoS On

Энтропия перестановок сердечного ритма плода при изъятии ударов сердца матери

Розробка і застосування методів ідентифікації фізіологічних станів для матері та плоду, заснованих на неінвазивному моніторингу серцевої діяльності, має велике клінічне значення під час вагітності. У даній роботі досліджуються нові можливості застосування ентропії перестановок (ЕП) – одного з нелінійних методів часового аналізу серцевих скорочень плода. ЕП використовується для описання ритмограм плоду з метою отримання нових даних щодо характеристик серцевого ритму плода. Використовується нова методика виділення фетальної електрокардіограми (фЕКГ), заснована на фільтрації у вейвлет-просторі та реконструкції фЕКГ з використанням коефіцієнтів деталізації. Ентропія перестановок застосовується для отримання числових значень та часових залежностей ЕП для серцевого ритму у випадку необроблених ритмограм плоду та ритмограм, отриманих з виділеними ударами серця матері. Припущення про необхідність видаляти удари серця матері із початкової ритмограми підтверджується різницею у значеннях ЕП для двох випадків.Development and application of maternal and fetal physiological states identification techniques based on the noninvasive electrical heart activity monitoring is of great clinical importance during pregnancy. In this paper, new possibilities of applying one of nonlinear measures of time series behavior analysis to the fetal heart rates are explored, and permutation entropy (PE) characteristics of fetal rhythmograms are used to get new insight on the fetal heart rhythm parameters. The new technique of fetal electrocardiogram (fECG) extraction is used, based on filtration in wavelet domain and reconstruction of fECG using detalization coefficients. Permutation entropy analysis is applied to obtain PE values and trends for the case of raw fetal rhythmograms and those obtained with excluded maternal heart beats. The assumption about the need to extract maternal heartbeats from initial rhythmogram is proven by the difference in PE values for two cases.Разработка и применение методов идентификации физиологических состояний матери и плода, основанных на неинвазивном мониторинге сердечной деятельности, имеет большое клиническое значение при беременности. В данной работе исследуются новые возможности применения энтропии перестановок (ЭП) – одного из нелинейных методов временного анализа сердечных сокращений плода. ЭП используется для описания ритмограмм плода с целью получения новых данных о характеристиках сердечного ритма плода. Используется новая методика выделения фетальной электрокардиограммы (фЭКГ), основанная на фильтрации в вейвлет-пространстве и реконструкции фЭКГ с использованием коэффициентов детализации. Энтропия перестановок применяется для получения числовых значений и временных зависимостей ЭП для сердечного ритма в случае необработанных ритмограмм плода и ритмограмм, полученных с выделенными ударами сердца матери. Предположение о необходимости удалять удары сердца матери из начальной ритмограммы подтверждается разницей в значениях ЭП для двух случаев

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

Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit highdimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the KolmogorovSinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.L.Z. and O.A.R. were supported by Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas (CONICET), Argentina. O.A.R. is PVE fellowship, CAPES, Brazil. Part of this work was funded by MEC (Spain), MICINN (Spain) and FEDER under Projects TEC2009-14101 (DeCoDicA) and FIS2007-60327 (FISICOS), and by the EC Project PHOCUS Grant 240763.Peer reviewe

Interaction between Thalamus and Hippocampus in Termination of Amygdala-Kindled Seizures in Mice

The thalamus and hippocampus have been found both involved in the initiation, propagation, and termination of temporal lobe epilepsy. However, the interaction of these regions during seizures is not clear. The present study is to explore whether some regular patterns exist in their interaction during the termination of seizures. Multichannel in vivo recording techniques were used to record the neural activities from the cornu ammonis 1 (CA1) of hippocampus and mediodorsal thalamus (MDT) in mice. The mice were kindled by electrically stimulating basolateral amygdala neurons, and Racine’s rank standard was employed to classify the stage of behavioral responses (stage 1~5). The coupling index and directionality index were used to investigate the synchronization and information flow direction between CA1 and MDT. Two main results were found in this study. (1) High levels of synchronization between the thalamus and hippocampus were observed before the termination of seizures at stage 4~5 but after the termination of seizures at stage 1~2. (2) In the end of seizures at stage 4~5, the information tended to flow from MDT to CA1. Those results indicate that the synchronization and information flow direction between the thalamus and the hippocampus may participate in the termination of seizures

Adaptive Neuro-Fuzzy Inference System for Classification of Background EEG Signals from ESES Patients and Controls

Background electroencephalography (EEG), recorded with scalp electrodes, in children with electrical status epilepticus during slow-wave sleep (ESES) syndrome and control subjects has been analyzed. We considered 10 ESES patients, all right-handed and aged 3-9 years. The 10 control individuals had the same characteristics of the ESES ones but presented a normal EEG. Recordings were undertaken in the awake and relaxed states with their eyes open. The complexity of background EEG was evaluated using the permutation entropy (PE) and sample entropy (SampEn) in combination with the ANOVA test. It can be seen that the entropy measures of EEG are significantly different between the ESES patients and normal control subjects. Then, a classification framework based on entropy measures and adaptive neuro-fuzzy inference system (ANFIS) classifier is proposed to distinguish ESES and normal EEG signals. The results are promising and a classification accuracy of about 89% is achieved

Adaptive Neuro-Fuzzy Inference System for Classification of Background EEG Signals from ESES Patients and Controls

Background electroencephalography (EEG), recorded with scalp electrodes, in children with electrical status epilepticus during slow-wave sleep (ESES) syndrome and control subjects has been analyzed. We considered 10 ESES patients, all right-handed and aged 3–9 years. The 10 control individuals had the same characteristics of the ESES ones but presented a normal EEG. Recordings were undertaken in the awake and relaxed states with their eyes open. The complexity of background EEG was evaluated using the permutation entropy (PE) and sample entropy (SampEn) in combination with the ANOVA test. It can be seen that the entropy measures of EEG are significantly different between the ESES patients and normal control subjects. Then, a classification framework based on entropy measures and adaptive neuro-fuzzy inference system (ANFIS) classifier is proposed to distinguish ESES and normal EEG signals. The results are promising and a classification accuracy of about 89% is achieved

The effects of graded levels of calorie restriction : VII. Topological rearrangement of hypothalamic aging networks

We would like to acknowledge the BSU staff for their invaluable help with caring for the animals. The work was supported by the UK Biotechnology and Biological Sciences Research Council BBSRC (BB/G009953/1 and BB/J020028/1) of JRS and SEM and a studentship of DD supported by the Centre for Genome Enabled Biology and Medicine, Aberdeen, UK. Joint meetings were funded by BBSRC grant (China partnering award BB/JO20028/1).Peer reviewedPublisher PD