Ordinal pattern transition networks in eye tracking reading signals.

Eye tracking is an emerging technology with a wide spectrum of applications, including non-invasive neurocognitive diagnosis. An advantage of the use of eye trackers is in the improved assessment of indirect latent information about several aspects of the subjects' neurophysiology. The path to uncover and take advantage of the meaning and implications of this information, however, is still in its very early stages. In this work, we apply ordinal patterns transition networks as a means to identify subjects with dyslexia in simple text reading experiments. We registered the tracking signal of the eye movements of several subjects (either normal or with diagnosed dyslexia). The evolution of the left-to-right movement over time was analyzed using ordinal patterns, and the transitions between patterns were analyzed and characterized. The relative frequencies of these transitions were used as feature descriptors, with which a classifier was trained. The classifier is able to distinguish typically developed vs dyslexic subjects with almost 100% accuracy only analyzing the relative frequency of the eye movement transition from one particular permutation pattern (plain left to right) to four other patterns including itself. This characterization helps understand differences in the underlying cognitive behavior of these two groups of subjects and also paves the way to several other potentially fruitful analyses applied to other neurocognitive conditions and tests.

Detection of cardiac arrhythmia patterns in ECG through H × C plane.

The aim of this study is to formulate a new methodology based upon informational tools to detect patients with cardiac arrhythmias. As it is known, sudden death is the consequence of a final arrhythmia, and here lies the relevance of the efforts aimed at the early detection of arrhythmias. The information content in the time series from an electrocardiogram (ECG) signal is conveyed in the form of a probability distribution function, to compute the permutation entropy proposed by Bandt and Pompe. This selection was made seeking its remarkable conceptual simplicity, computational speed, and robustness to noise. In this work, two well-known databases were used, one containing normal sinus rhythms and another one containing arrhythmias, both from the MIT medical databank. For different values of embedding time delay τ, normalized permutation entropy and statistical complexity measure are computed to finally represent them on the horizontal and vertical axes, respectively, which define the causal plane H×C. To improve the results obtained in previous works, a feature set composed by these two magnitudes is built to train the following supervised machine learning algorithms: random forest (RF), support vector machine (SVM), and k nearest neighbors (kNN). To evaluate the performance of each classification technique, a 10-fold cross-validation scheme repeated 10 times was implemented. Finally, to select the best model, three quality parameters were computed, namely, accuracy, the area under the receiver operative characteristic (ROC) curve (AUC), and the F1-score. The results obtained show that the best classification model to detect the ECG coming from arrhythmic patients is RF. The values of the quality parameters were at the same levels reported in the available literature using a larger data set, thus supporting this proposal that uses a very small-sized feature space to train the model later used to classify. Summarizing, the attained results show the possibility to discriminate both groups of patients, with normal sinus rhythm or arrhythmic ECG, showing a promising efficiency in the definition of new markers for the detection of cardiovascular pathologies.

Dynamics in cortical activity revealed by resting-state MEG rhythms.

The brain is a biophysical system subject to information flows that may be thought of as a many-body architecture with a spatiotemporal dynamics described by its neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled oscillators forming a network where the node dynamics and that of the network topology can be studied. Quantifying its dynamics at various scales is an issue that claims to be explored for several brain activities, e.g., activity at rest. The resting-state (RS) associates the underlying brain dynamics of healthy subjects that are not actively compromised with sensory or cognitive processes. Studying its dynamics is highly non-trivial but opens the door to understand the general principles of brain functioning, as well as to contrast a passive null condition vs the dynamics of pathologies or non-resting activities. Here, we hypothesize about how the spatiotemporal dynamics of cortical fluctuations could be for healthy subjects at RS. To do that, we retrieve the alphabet that reconstructs the dynamics (entropy-complexity) of magnetoencephalography (MEG) signals. We assemble the cortical connectivity to elicit the dynamics in the network topology. We depict an order relation between entropy and complexity for frequency bands that is ubiquitous for different temporal scales. We unveiled that the posterior cortex conglomerates nodes with both stronger dynamics and high clustering for α band. The existence of an order relation between dynamic properties suggests an emergent phenomenon characteristic of each band. Interestingly, we find the posterior cortex as a domain of dual character that plays a cardinal role in both the dynamics and structure regarding the activity at rest. To the best of our knowledge, this is the first study with MEG involving information theory and network science to better understand the dynamics and structure of brain activity at rest for different bands and scales.

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach.

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.

Impairment of erythrocytes incubated in glucose medium: a wavelet-information theory analysis.

This study investigates the effects produced by an increased concentration of glucose in a suspending medium on the erythrocytes Information Theory quantifiers. Erythrocytes, which were obtained from eight healthy volunteers, were washed and incubated in vitro with glucose solutions at different concentrations. The measured Wavelet-based Information Theory quantifiers include the Relative Wavelet Energy (RWE), the Normalized Total Wavelet Shannon Entropy (NTWS), MPR-Statistical Complexity Measure (SCM) and entropy-complexity plane. The results show that the increase in glucose concentration does not produce significant changes on the RWE, while significant ones on the NTSE, which combined with SCM values allow to identify different behaviour for all the different populations in the entropy-complexity plane. Modification in the hemorheological properties of cells could be clearly detected with these Wavelet-based Information Theory quantifiers.

Permutation-information-theory approach to unveil delay dynamics from time-series analysis.

In this paper an approach to identify delay phenomena from time series is developed. We show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory, more precisely, permutation entropy and permutation statistical complexity. These quantifiers show clear extrema when the embedding delay τ of the symbolic reconstruction matches the characteristic time delay τ(S) of the system. Numerical data originating from a time delay system based on the well-known Mackey-Glass equations operating in the chaotic regime were used as test beds. We show that our method is straightforward to apply and robust to additive observational and dynamical noise. Moreover, we find that the identification of the time delay is even more efficient in a noise environment. Our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity.

Quantifiers for randomness of chaotic pseudo-random number generators.

We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely (i) its invariant measure and (ii) the mixing constant. This is of help in answering two questions that arise in applications: (i) which is the best PRNG among the available ones? and (ii) if a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure? Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.

Diabetic erythrocytes test by correlation coefficient.

Even when a healthy individual is studied, his/her erythrocytes in capillaries continually change their shape in a synchronized erratic fashion. In this work, the problem of characterizing the cell behavior is studied from the perspective of bounded correlated random walk, based on the assumption that diffractometric data involves both deterministic and stochastic components. The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. We have only a scalar signal and no governing equations; therefore the complete behavior has to be reconstructed in an artificial phase space. To analyze dynamics we used the technique of time delay coordinates suggested by Takens, May algorithm, and Fourier transform. The results suggest that on random-walk approach the samples from healthy controls exhibit significant differences from those from diabetic patients and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes' rheological properties.

Distinguishing noise from chaos.

Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.

Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools.

Efficient tools to characterize stochastic processes are discussed. Quantifiers originally proposed within the framework of information theory, like entropy and statistical complexity, are translated into wavelet language, which renders the above quantifiers into tools that exhibit the important "localization" advantages provided by wavelet theory. Two important and popular stochastic processes, fractional Brownian motion and fractional Gaussian noise, are studied using these wavelet-based informational tools. Exact analytical expressions are obtained for the wavelet probability distribution. Finally, numerical simulations are used to validate our analytical results.

Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

EEG analysis using wavelet-based information tools.

Wavelet-based informational tools for quantitative electroencephalogram (EEG) record analysis are reviewed. Relative wavelet energies, wavelet entropies and wavelet statistical complexities are used in the characterization of scalp EEG records corresponding to secondary generalized tonic-clonic epileptic seizures. In particular, we show that the epileptic recruitment rhythm observed during seizure development is well described in terms of the relative wavelet energies. In addition, during the concomitant time-period the entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus, for this kind of seizures, triggers a self-organized brain state characterized by both order and maximal complexity.

The Australian EEG database.

The Australian EEG Database is a web-based de-identified searchable database of 18,500 EEG records recorded at a regional public hospital over an 11-year period. Patients range in age from a premature infant born at 24 weeks gestation, through to people aged over 90 years. This paper will describe the history of the database, the range of patients represented in the database, and the nature of the text-based and digital data contained in the database. Preliminary results of the first two studies undertaken using the database are presented. Plans for sharing data from the Australian EEG database with researchers are discussed. We anticipate that such data will be useful in not only helping to answer clinical questions but also in the field of mathematical modeling of the EEG.

Analysis of wavelet-filtered tonic-clonic electroencephalogram recordings.

EEG signals obtained during tonic-clonic epileptic seizures can be severely contaminated by muscle and physiological noise. Heavily contaminated EEG signals are hard to analyse quantitatively and also are usually rejected for visual inspection by physicians, resulting in a considerable loss of collected information. The aim of this work was to develop a computer-based method of time series analysis for such EEGs. A method is presented for filtering those frequencies associated with muscle activity using a wavelet transform. One of the advantages of this method over traditional filtering is that wavelet filtering of some frequency bands does not modify the pattern of the remaining ones. In consequence, the dynamics associated with them do not change. After generation of a 'noise free' signal by removal of the muscle artifacts using wavelets, a dynamic analysis was performed using non-linear dynamics metric tools. The characteristic parameters evaluated (correlation dimension D2 and largest Lyapunov exponent lambda1) were compatible with those obtained in previous works. The average values obtained were: D2=4.25 and lambda1=3.27 for the pre-ictal stage; D2=4.03 and lambda1=2.68 for the tonic seizure stage; D2=4.11 and lambda1=2.46 for the clonic seizure stage.

A transient dominance of theta ERP component characterizes passive auditory processing: evidence from a developmental study.

This study analyzed relationships among co-existent EEG frequency responses during passive auditory stimulus processing. By applying quantifiers based on wavelet entropy, it is demonstrated that a short-lasting ordering of the complex post-stimulus EEG signal occurs as a result of a transient synchronization in the theta frequency channel. Further, by using a developmental model it is shown that, independently of the frequency content of the background EEG and ERPs, a highly-ordered microstate in the ERP is always determined by theta frequency. Thus, transient dominance of synchronized theta oscillations may reflect an important functional mechanism subserving stimulus information processing.

Wavelet entropy in event-related potentials: a new method shows ordering of EEG oscillations.

In this work we show the application of a measure of entropy defined from the wavelet transform, namely the wavelet entropy (WS), to the study of event-related potentials (ERPs). WS was computed for ERPs recorded from nine healthy subjects with three different types of stimuli, among them target stimuli in a cognitive task. A significant decrease of entropy was correlated with the responses to target stimuli (P300), thus showing that these responses correspond to a more "ordered" state than the spontaneous EEG. Furthermore, we propose the WS as a quantitative measure for such transitions between EEG ("disordered state") and ERP ("ordered state").

Wavelet entropy: a new tool for analysis of short duration brain electrical signals.

Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order/disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order/disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials.

Searching for hidden information with Gabor Transform in generalized tonic-clonic seizures.

The analysis of generalized tonic clonic seizures is usually difficult with scalp EEG due to muscle artifact. We applied Gabor Transform to evaluate 20 seizures from 8 consecutive patients admitted for video-EEG monitoring. We studied the relative intensity ratios of alpha, theta and delta bands over time. In 14/20 events we found a significant decremental activity in the delta band at the onset of the seizure indicating that this is dominated by theta and alpha bands. We conclude that GT is a useful auxiliary tool in the analysis of ictal activity that sheds light on the underlying pathophysiological mechanisms.