We conceive a new recurrence quantifier for time series based on the concept of information entropy, in which the probabilities are associated with the presence of microstates defined on the recurrence matrix as small binary submatrices. The new methodology to compute the entropy of a time series has advantages compared to the traditional entropies defined in the literature, namely, a good correlation with the maximum Lyapunov exponent of the system and a weak dependence on the vicinity threshold parameter. Furthermore, the new method works adequately even for small segments of data, bringing consistent results for short and long time series. In a case where long time series are available, the new methodology can be employed to obtain high precision results since it does not demand large computational times related to the analysis of the entire time series or recurrence matrices, as is the case of other traditional entropy quantifiers. The method is applied to discrete and continuous systems.

Sleep plays a crucial role in the regulation of body homeostasis and rhythmicity in mammals. Recently, a specific component of the sleep structure has been proposed as part of its homeostatic mechanism, named micro-arousal. Here, we studied the unique progression of the dynamic behavior of cortical and hippocampal local field potentials (LFPs) during slow-wave sleep-related to motor-bursts (micro-arousals) in mice. Our main results comprised: (i) an abrupt drop in hippocampal LFP amplitude preceding micro-arousals which persisted until the end of motor-bursts (we defined as t interval, around 4s) and a similar, but delayed amplitude reduction in cortical (S1/M1) LFP activity occurring at micro-arousal onset; (ii) two abrupt frequency jumps in hippocampal LFP activity: from Theta (6–12 Hz) to Delta (2–4 Hz), also t seconds before the micro-arousal onset, and followed by another frequency jump from Delta to Theta range (5–7 Hz), now occurring at micro-arousal onset; (iii) a pattern of cortico-hippocampal frequency communication precedes micro-arousals: the analysis between hippocampal and cortical LFP fluctuations reveal high coherence during τ interval in a broader frequency band (2–12 Hz), while at a lower frequency band (0.5–2 Hz) the coherence reaches its maximum after the onset of micro-arousals. In conclusion, these novel findings indicate that oscillatory dynamics pattern of cortical and hippocampal LFPs preceding micro-arousals could be part of the regulatory processes in sleep architecture.

In recent decades, there has been a growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrated-and-Fire model (QIF-E) underwent an adjustment/improvement to include the ephaptic entrainment behavior between neurons and electric fields. Indeed, the aim of our study is to validate the QIF-E model, which is a model to estimate the influence of electric fields on neurons. For this purpose, we evaluated whether the main properties observed in an experiment by Anastassiou et al. (Nat Neurosci 14:217–223, 2011), which analyzed the effect of an electric field on cortical pyramidal neurons, are reproduced with the QIF-E model. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal (electrode) and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are used to estimate phase preferences and the entrainment intensity between the input stimulus and Action Potentials. The results observed are (i) in the subthreshold regime the values of the phase differences change with distinct frequencies of the input stimulus; (ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic phenomenon. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic communication in the brain, and its simplicity may open a door to simulate the ephaptic response in neuronal networks and assess the impact of ephaptic communication in such scenarios.

Recurrence entropy (S) is a novel time series complexity quantifier based on recurrence microstates. Here we show that max(S) is a parameter-free quantifier of time correlation of stochastic and chaotic signals, at the same time that it evaluates property changes of the probability distribution function (PDF) of the entire data set. max(S) can distinguish distinct temporal correlations of stochastic signals following a power-law spectrum, P (f ) ∝ 1/f α even when shuffled versions of the signals are used. Such behavior is related to its ability to quantify distinct subsets embedded in a time series. Applied to a deterministic system, the method brings new evidence about attractor properties and the degree of chaoticity. The development of a new parameter-free quantifier of stochastic and chaotic time series opens new perspectives to stochastic data and deterministic time series analyses and may find applications in many areas of science.