Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data.

Scale-free brain activity, linked with learning, the integration of different time scales, and the formation of mental models, is correlated with a metastable cognitive basis. The spectral slope, a key aspect of scale-free dynamics, was proposed as a potential indicator to distinguish between different sleep stages. Studies suggest that brain networks maintain a consistent scale-free structure across wakefulness, anesthesia, and recovery. Although differences in anesthetic sensitivity between the sexes are recognized, these variations are not evident in clinical electroencephalographic recordings of the cortex. Recently, changes in the slope of the power law exponent of neural activity were found to correlate with changes in Rényi entropy, an extended concept of Shannon's information entropy. These findings establish quantifiers as a promising tool for the study of scale-free dynamics in the brain. Our study presents a novel visual representation called the Rényi entropy-complexity causality space, which encapsulates complexity, permutation entropy, and the Rényi parameter q. The main goal of this study is to define this space for classical dynamical systems within theoretical bounds. In addition, the study aims to investigate how well different time series mimicking scale-free activity can be discriminated. Finally, this tool is used to detect dynamic features in intracranial electroencephalography (iEEG) signals. To achieve these goals, the study implementse the Bandt and Pompe method for ordinal patterns. In this process, each signal is associated with a probability distribution, and the causal measures of Rényi entropy and complexity are computed based on the parameter q. This method is a valuable tool for analyzing simulated time series. It effectively distinguishes elements of correlated noise and provides a straightforward means of examining differences in behaviors, characteristics, and classifications. For the iEEG experimental data, the REM state showed a greater number of significant sex-based differences, while the supramarginal gyrus region showed the most variation across different modes and analyzes. Exploring scale-free brain activity with this framework could provide valuable insights into cognition and neurological disorders. The results may have implications for understanding differences in brain function between the sexes and their possible relevance to neurological disorders.

Linear mixed-effect models for correlated response to process electroencephalogram recordings.

A data set of clinical studies of electroencephalogram recordings (EEG) following data acquisition protocols in control individuals (Eyes Closed Wakefulness - Eyes Open Wakefulness, Hyperventilation, and Optostimulation) are quantified with information theory metrics, namely permutation Shanon entropy and permutation Lempel Ziv complexity, to identify functional changes. This work implement Linear mixed-effects models (LMEMs) for confirmatory hypothesis testing. The results show that EEGs have high variability for both metrics and there is a positive correlation between them. The mean of permutation Lempel-Ziv complexity and permutation Shanon entropy used simultaneously for each of the four states are distinguishable from each other. However, used separately, the differences between permutation Lempel-Ziv complexity or permutation Shanon entropy of some states were not statistically significant. This shows that the joint use of both metrics provides more information than the separate use of each of them. Despite their wide use in medicine, LMEMs have not been commonly applied to simultaneously model metrics that quantify EEG signals. Modeling EEGs using a model that characterizes more than one response variable and their possible correlations represents a new way of analyzing EEG data in neuroscience.

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen-Shannon Distance.

Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen-Shannon distance. The influence that linear and nonlinear temporal correlations have on the discrimination is unveiled. Results obtained lead to significant conclusions that help to achieve an improved distinction between these resting brain states.

A Hybrid Cryptosystem Incorporating a New Algorithm for Improved Entropy.

Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie-Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are necessary for the symmetrical aspect to generate dynamic permutations, substitution boxes, and round keys. Following an encryption process with fourteen rounds, the encrypted images are processed by an algorithm proposed to enhance entropy, a critical metric for assessing encryption quality. It increases the frequencies of the basic colors to achieve a histogram closely resembling a uniform distribution, but it increases the image size by approximately 8%. This improves the entropy values achieved by the hybrid cryptosystem, bringing them remarkably close to the ideal value of 8.0. In specific instances, the entropy values were elevated from 7.99926 to 8.0. The proposed method exhibits resilience against various attacks, including differential, linear, brute force, and algebraic attacks, as evaluated through the entropy, correlation, goodness of fit, Discrete Fourier Transform (DFT), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Avalanche Criteria (AC), contrast, energy, and homogeneity. Further, encrypted images are subjected to noise attacks ranging from 20% to 50% noise, including additive, multiplicative, occlusion noise, as well as the newly introduced χ2 noise. The noise damage is quantified using the proposed Similarity Parameter (SP), and a 3 × 3 median filter is employed to enhance the visual quality.

A Permutation Entropy analysis to determine significant daily intervals to improve risk stratification tasks from COVID patients.

SARS-CoV-2 infection has a wide range of clinical manifestations making its diagnosis difficult, which is an important problem to solve. We evaluated heart rate data extracted from the Stanford University database. The data set considers heart rate and step records of 118 patients, where 90 correspond to healthy individuals and 28 patients with COVID. Each daily record was divided into 5-minute segments, providing 288 data per patient. The date of symptom onset was considered as a reference point to extract subsets of data whose variability was considerable, such as 30 days before the date and 30 days after it. Each of the 60 segments of 288 data per patient was treated using Permutation Entropy, Approximate Entropy, Spectral Entropy and Singular Value Decomposition Entropy. The average of the data from each group was used to construct the circadian profiles which were analyzed using the Mann-Whitney-Wilcoxon test, determining the most relevant 5-minute segments, whose p-value was less than 0.05. In this way, the Spectral Entropy was discarded as it did not show any significantly different segment. The efficiency of the method was reflected in the performance of a logistic model for binary classification proposed in this work, which reflected an accuracy of 94.12% in the PE case, 88% in the ApEn case and 94% in the SVDE case. The proposed analysis turns out to be highly efficient when detecting significant segments that allow improving the classification tasks carried out by Machine Learning models, which provides a basis for the study of statistics such as entropy to delimit databases and improve the performance of classifier models.

Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers.

This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen-Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.

Permutation Entropy Analysis to Intracranial Hypertension from a Porcine Model.

Intracranial pressure (ICP) monitoring is commonly used in the follow-up of patients in intensive care units, but only a small part of the information available in the ICP time series is exploited. One of the most important features to guide patient follow-up and treatment is intracranial compliance. We propose using permutation entropy (PE) as a method to extract non-obvious information from the ICP curve. We analyzed the results of a pig experiment with sliding windows of 3600 samples and 1000 displacement samples, and estimated their respective PEs, their associated probability distributions, and the number of missing patterns (NMP). We observed that the behavior of PE is inverse to that of ICP, in addition to the fact that NMP appears as a surrogate for intracranial compliance. In lesion-free periods, PE is usually greater than 0.3, and normalized NMP is less than 90% and p(s1)>p(s720). Any deviation from these values could be a possible warning of altered neurophysiology. In the terminal phases of the lesion, the normalized NMP is higher than 95%, and PE is not sensitive to changes in ICP and p(s720)>p(s1). The results show that it could be used for real-time patient monitoring or as input for a machine learning tool.

Rapid and non-destructive cinnamon authentication by NIR-hyperspectral imaging and classification chemometrics tools.

Cinnamon is a valuable aromatic spice widely used in pharmaceutical and food industry. Commonly, two-cinnamon species are available in the market, Cinnamomum verum (true cinnamon), cropped only in Sri Lanka, and Cinnamomum cassia (false cinnamon), cropped in different geographical origins. Thus, this work aimed to develop classification models based on NIR-hyperspectral imaging (NIR-HSI) coupled to chemometrics to classify C. verum and C. cassia sticks. First, principal component analysis (PCA) was applied to explore hyperspectral images. Scores surface displayed the high similarity between species supported by comparable macronutrient concentration. PC3 allowed better class differentiation compared to PC1 and PC2, with loadings exhibiting peaks related to phenolics/aromatics compounds, such as coumarin (C. cassia) or catechin (C. verum). Partial least square discriminant analysis (PLS-DA) and Support vector machine (SVM) reached similar performance to classify samples according to origin, with error = 3.3 % and accuracy = 96.7 %. A permutation test with p < 0.05 validated PLS-DA predictions have real spectral data dependency, and they are not result of chance. Pixel-wise (approach A) and sample-wise (approach B, C and D) classification maps reached a correct classification rate (CCR) of 98.3 % for C. verum and 100 % for C. cassia. NIR-HSI supported by classification chemometrics tools can be used as reliable analytical method for cinnamon authentication.

The effect of age on electroencephalogram measures of anesthesia hypnosis: A comparison of BIS, Alpha Power, Lempel-Ziv complexity and permutation entropy during propofol induction.

Background: Improving anesthesia administration for elderly population is of particular importance because they undergo considerably more surgical procedures and are at the most risk of suffering from anesthesia-related complications. Intraoperative brain monitors electroencephalogram (EEG) have proved useful in the general population, however, in elderly subjects this is contentious. Probably because these monitors do not account for the natural differences in EEG signals between young and older patients. In this study we attempted to systematically characterize the age-dependence of different EEG measures of anesthesia hypnosis. Methods: We recorded EEG from 30 patients with a wide age range (19-99 years old) and analyzed four different proposed indexes of depth of hypnosis before, during and after loss of behavioral response due to slow propofol infusion during anesthetic induction. We analyzed Bispectral Index (BIS), Alpha Power and two entropy-related EEG measures, Lempel-Ziv complexity (LZc), and permutation entropy (PE) using mixed-effect analysis of variances (ANOVAs). We evaluated their possible age biases and their trajectories during propofol induction. Results: All measures were dependent on anesthesia stages. BIS, LZc, and PE presented lower values at increasing anesthetic dosage. Inversely, Alpha Power increased with increasing propofol at low doses, however this relation was reversed at greater effect-site propofol concentrations. Significant group differences between elderly patients (>65 years) and young patients were observed for BIS, Alpha Power, and LZc, but not for PE. Conclusion: BIS, Alpha Power, and LZc show important age-related biases during slow propofol induction. These should be considered when interpreting and designing EEG monitors for clinical settings. Interestingly, PE did not present significant age differences, which makes it a promising candidate as an age-independent measure of hypnotic depth to be used in future monitor development.

PCAtest: testing the statistical significance of Principal Component Analysis in R.

Principal Component Analysis (PCA) is one of the most broadly used statistical methods for the ordination and dimensionality-reduction of multivariate datasets across many scientific disciplines. Trivial PCs can be estimated from data sets without any correlational structure among the original variables, and traditional criteria for selecting non-trivial PC axes are difficult to implement, partially subjective or based on ad hoc thresholds. PCAtest is an R package that implements permutation-based statistical tests to evaluate the overall significance of a PCA, the significance of each PC axis, and of contributions of each observed variable to the significant axes. Based on simulation and empirical results, I encourage R users to routinely apply PCAtest to test the significance of their PCA before proceeding with the direct interpretation of PC axes and/or the utilization of PC scores in subsequent evolutionary and ecological analyses.

Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine Learning.

Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series. The algorithm is trained using as input features the probabilities of ordinal patterns computed from FN time series, xαFN(t), generated with different values of α. Then, the ordinal probabilities computed from the time series of interest, x(t), are used as input features to the trained algorithm and that returns a value, αe, that contains meaningful information about the temporal correlations present in x(t). We have also shown that the difference, Ω, of the permutation entropy (PE) of the time series of interest, x(t), and the PE of a FN time series generated with α=αe, xαeFN(t), allows the identification of the underlying determinism in x(t). Here, we apply our methodology to different datasets and analyze how αe and Ω correlate with well-known quantifiers of chaos and complexity. We also discuss the limitations for identifying determinism in highly chaotic time series and in periodic time series contaminated by noise. The open source algorithm is available on Github.

From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology.

The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems' statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new "maps". From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.

Predictability of COVID-19 worldwide lethality using permutation-information theory quantifiers.

This paper examines the predictability of COVID-19 worldwide lethality considering 43 countries. Based on the values inherent to Permutation entropy ( H s ) and Fisher information measure ( F s ), we apply the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder an evaluate randomness present in the time series of daily death cases related to COVID-19 in each country. We also use Hs and Fs to rank the COVID-19 lethality in these countries based on the complexity hierarchy. Our results suggest that the most proactive countries implemented measures such as facemasks, social distancing, quarantine, massive population testing, and hygienic (sanitary) orientations to limit the impacts of COVID-19, which implied lower entropy (higher predictability) to the COVID-19 lethality. In contrast, the most reactive countries implementing these measures depicted higher entropy (lower predictability) to the COVID-19 lethality. Given this, our findings shed light that these preventive measures are efficient to combat the COVID-19 lethality.

Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective.

We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player's average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.

Augmenting Global Coherence in EEG Signals with Binaural or Monaural Noises.

Internal stochastic resonance (internal SR) is a phenomenon of non-linear systems in which the addition of a non-zero level of noise produces an enhancement in the coherence between two or more signals. In a previous study, we found that the simultaneous administration of multisensory visual and auditory noise augments global coherence in electroencephalographic (EEG) signals via this phenomenon. Here, we examined whether such global coherence can also be augmented with at least one noisy acoustic source. We performed experiments on healthy subjects and applied the following binaural and monaural noise-stimulation protocols. First, we administered to the left ear Gaussian noise of fixed intensity, while we delivered to the right ear a second Gaussian noise of variable intensity levels (binaural protocol). Second, we applied the Gaussian noise of the same variable intensity levels but only to one ear (monaural protocol). We performed a permutation test analysis, finding that during both noise protocols there was a significant enhancement in the global coherence in EEG signals via the occurrence of internal SR within central pathways of the auditory system.

Muscle fatigue analysis during dynamic contractions based on biomechanical features and Permutation Entropy.

Muscle fatigue is an important field of study in sports medicine and occupational health. Several studies in the literature have proposed methods for predicting muscle fatigue in isometric con-tractions using three states of muscular fatigue: Non-Fatigue, Transition-to-Fatigue, and Fatigue. For this, several features in time, spectral and time-frequency domains have been used, with good performance results; however, when they are applied to dynamic contractions the performance decreases. In this paper, we propose an approach for analyzing muscle fatigue during dynamic contractions based on time and spectral domain features, Permutation Entropy (PE) and biomechanical features. We established a protocol for fatiguing the deltoid muscle and acquiring surface electromiography (sEMG) and biomechanical signals. Subsequently, we segmented the sEMG and biomechanical signals of every contraction. In order to label the contraction, we computed some features from biomechanical signals and evaluated their correlation with fatigue progression, and the most correlated variables were used to label the contraction using hierarchical clustering with Ward's linkage. Finally, we analyzed the discriminant capacity of sEMG features using ANOVA and ROC analysis. Our results show that the biomechanical features obtained from angle and angular velocity are related to fatigue progression, the analysis of sEMG signals shows that PE could distinguish Non-Fatigue, Transition-to-Fatigue and Fatigue more effectively than classical sEMG features of muscle fatigue such as Median Frequency.

A New Methodology Based on EMD and Nonlinear Measurements for Sudden Cardiac Death Detection.

Heart diseases are among the most common death causes in the population. Particularly, sudden cardiac death (SCD) is the cause of 10% of the deaths around the world. For this reason, it is necessary to develop new methodologies that can predict this event in the earliest possible stage. This work presents a novel methodology to predict when a person can develop an SCD episode before it occurs. It is based on the adroit combination of the empirical mode decomposition, nonlinear measurements, such as the Higuchi fractal and permutation entropy, and a neural network. The obtained results show that the proposed methodology is capable of detecting an SCD episode 25 min before it appears with a 94% accuracy. The main benefits of the proposal are: (1) an improved detection time of 25% compared with previously published works, (2) moderate computational complexity since only two features are used, and (3) it uses the raw ECG without any preprocessing stage, unlike recent previous works.

Predicting Known Sentences: Neural Basis of Proverb Reading Using Non-parametric Statistical Testing and Mixed-Effects Models.

Predictions of future events play an important role in daily activities, such as visual search, listening, or reading. They allow us to plan future actions and to anticipate their outcomes. Reading, a natural, commonly studied behavior, could shed light over the brain processes that underlie those prediction mechanisms. We hypothesized that different mechanisms must lead predictions along common sentences and proverbs. The former ones are more based on semantic and syntactic cues, and the last ones are almost purely based on long-term memory. Here we show that the modulation of the N400 by Cloze-Task Predictability is strongly present in common sentences, but not in proverbs. Moreover, we present a novel combination of linear mixed models to account for multiple variables, and a cluster-based permutation procedure to control for multiple comparisons. Our results suggest that different prediction mechanisms are present during reading.

Genome-wide association studies pathway-based meta-analysis for residual feed intake in beef cattle.

Genome-wide association studies (GWASes) have been performed to search for genomic regions associated with residual feed intake (RFI); however inconsistent results have been obtained. A meta-analysis may improve these results by decreasing the false-positive rate. Additionally, pathway analysis is a powerful tool that complements GWASes, as it enables identification of gene sets involved in the same pathway that explain the studied phenotype. Because there are no reports on GWAS pathways-based meta-analyses for RFI in beef cattle, we used several GWAS results to search for significant pathways that may explain the genetic mechanism underlying this trait. We used an efficient permutation hypothesis test that takes into account the linkage disequilibrium patterns between SNPs and the functional feasibility of the identified genes over the whole genome. One significant pathway (valine, leucine and isoleucine degradation) related to RFI was found. The three genes in this pathway-methylcrotonoyl-CoA carboxylase 1 (MCCC1), aldehyde oxidase 1 (AOX1) and propionyl-CoA carboxylase alpha subunit (PCCA)-were found in three different studies. This same pathway was also reported in a transcriptome analysis from two cattle populations divergently selected for high and low RFI. We conclude that a GWAS pathway-based meta-analysis can be an appropriate method to uncover biological insights into RFI by combining useful information from different studies.

Protein topology determines substrate-binding mechanism in homologous enzymes.

During evolution, some homologs proteins appear with different connectivity between secondary structures (different topology) but conserving the tridimensional arrangement of them (same architecture). These events can produce two types of arrangements; circular permutation or non-cyclic permutations. The first one results in the N and C terminus transferring to a different position on a protein sequence while the second refers to a more complex arrangement of the structural elements. In ribokinase superfamily, two different topologies can be identified, which are related to each other as a non-cyclic permutation occurred during the evolution. Interestingly, this change in topology is correlated with the nucleotide specificity of its members. Thereby, the connectivity of the secondary elements allows us to distinguish an ATP-dependent and an ADP-dependent topology. Here we address the impact of introducing the topology of a homologous ATP-dependent kinase in an ADP-dependent kinase (Thermococcus litoralis glucokinase) in the structure, nucleotide specificity, and substrate binding order of the engineered enzyme. Structural evidence demonstrates that rewiring the topology of TlGK leads to an active and soluble enzyme without modifications on its three-dimensional architecture. The permuted enzyme (PerGK) retains the nucleotide preference of the parent TlGK enzyme but shows a change in the substrate binding order. Our results illustrate how the rearrangement of the protein folding topology during the evolution of the ribokinase superfamily enzymes may have dictated the substrate-binding order in homologous enzymes of this superfamily.