Recurrence plots of neuronal spike trains

Transition to chaos separates learning regimes and relates to measure of consciousness in recurrent neural networks

Recurrent neural networks exhibit chaotic dynamics when the variance in their connection strengths exceed a critical value. Recent work indicates connection variance also modulates learning strategies; networks learn "rich" representations when initialized with low coupling and "lazier" solutions with larger variance. Using Watts-Strogatz networks of varying sparsity, structure, and hidden weight variance, we find that the critical coupling strength dividing chaotic from ordered dynamics also differentiates rich and lazy learning strategies. Training moves both stable and chaotic networks closer to the edge of chaos, with networks learning richer representations before the transition to chaos. In contrast, biologically realistic connectivity structures foster stability over a wide range of variances. The transition to chaos is also reflected in a measure that clinically discriminates levels of consciousness, the perturbational complexity index (PCIst). Networks with high values of PCIst exhibit stable dynamics and rich learning, suggesting a consciousness prior may promote rich learning. The results suggest a clear relationship between critical dynamics, learning regimes and complexity-based measures of consciousness.

Studying the functional connectivity of the primary motor cortex with the binarized cross recurrence plot: The influence of Parkinson's disease

Two new recurrence plot methods (the binary recurrence plot and binary cross recurrence plot) were introduced here to study the long-term dynamic of the primary motor cortex and its interaction with the primary somatosensory cortex, the anterior motor thalamus of the basal ganglia motor loop and the precuneous nucleus of the default mode network. These recurrence plot methods: 1. identify short-term transient interactions; 2. identify long-lasting delayed interactions that are common in complex systems; 3. work with non-stationary blood oxygen level dependent (BOLD) data; 4. may study the relationship of centers with non-linear functional interactions; 5 may compare different experimental groups performing different tasks. These methods were applied to BOLD time-series obtained in 20 control subjects and 20 Parkinson´s patients during the execution of motor activity and body posture tasks (task-block design). The binary recurrence plot showed the task-block BOLD response normally observed in the primary motor cortex with functional magnetic resonance imaging methods, but also shorter and longer BOLD-fluctuations than the task-block and which provided information about the long-term dynamic of this center. The binary cross recurrence plot showed short-lasting and long-lasting functional interactions between the primary motor cortex and the primary somatosensory cortex, anterior motor thalamus and precuneous nucleus, interactions which changed with the resting and motor tasks. Most of the interactions found in healthy controls were disrupted in Parkinson's patients, and may be at the basis of some of the motor disorders and side-effects of dopaminergic drugs commonly observed in these patients.

Quantification of Dynamic Gastric Slow Wave Activity using Recurrence Plots

The genesis and maintenance of abnormal or dysrhythmic bio-electrical slow wave activity in the gut is poorly understood. The use of multi-electrode densely spaced electrodes to map in-vivo slow wave activity from the stomach surface provides a renewed understanding of gastric electro-physiology in health and disease. Analysis of the experimental data thus far have typically only utilized linear methods. Nonlinear methods such as the use of recurrence plots could provide key insights into physiological mechanisms. In this paper we applied recurrence analysis to synthetic propagation and experimental data, in cases where the activity was normal, abnormal and transitory. The recurrence plots were quantified using recurrence rate (RR) and diagonal length entropy (DLE). Normal activity had a higher mean RR than dysrhythmic and transition cases (0.08±0.01 vs 0.03±0.01 and 0.03±0.01). Transition cases had a lower mean DLE than dysrhythmic and normal activity (2.16±0.23 vs 3.30±0.58 and 3.01±0.42). The use of recurrence analysis in the gastrointestinal field will allow for a better understanding of normal activity, as well as provide insights into the mechanisms that are involved in initiating, maintaining and terminating dysrhythmic slow wave activity. It could also be used as a novel qualitative and quantitative approach to predict the progression of slow wave activity.

Recurrence quantification analysis of a three level trophic chain model

Recurrence plots and recurrence quantification analysis based measures - recurrence rate, determinism, divergence, entropy, laminarity and trapping time, are used to detect transitions between periodic and chaotic states and also the laminar states of the complex three species food web model with improved growth rate function and predatory ability. The study of dynamical equation of such a complex biological system with transients in terms of these measures results in localization of bifurcation behavior of the system.

Connectivity analysis of multichannel EEG signals using recurrence based phase synchronization technique

Real world biological systems such as the human brain are inherently nonlinear and difficult to model. However, most of the previous studies have either employed linear models or parametric nonlinear models for investigating brain function. In this paper, a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study connectivity in the brain has been proposed. Being non-parametric, this method makes very few assumptions, making it suitable for investigating brain function in a data-driven way. CPR's utility with application to multichannel electroencephalographic (EEG) signals has been demonstrated. Brain connectivity obtained using thresholded CPR matrix of multichannel EEG signals showed clear differences in the number and pattern of connections in brain connectivity between (a) epileptic seizure and pre-seizure and (b) eyes open and eyes closed states. Corresponding brain headmaps provide meaningful insights about synchronization in the brain in those states. K-means clustering of connectivity parameters of CPR and linear correlation obtained from global epileptic seizure and pre-seizure showed significantly larger cluster centroid distances for CPR as opposed to linear correlation, thereby demonstrating the superior ability of CPR for discriminating seizure from pre-seizure. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value.

Recurrence Quantification Analysis as a tool for complex fractionated atrial electrogram discrimination

Atrial fibrillation is the most encountered pathology of the heart rate. The reasons of its occurrence and its particular characteristics remain unknown, resulting from complex phenomena interaction. From these interactions emerges Complex Fractionated Atrial Electrograms (CFAE) which are useful for the ablation procedure. This study presents a method based on nonlinear data analysis, the Recurrence Quantification Analysis (RQA) applied on intracardiac atrial electrograms to detect CFAE particularities. The results obtained on areas previously tagged by a cardilogist show a good sensitivity to CFAE. Combination of RQA features offers a larger discrimination potential for future automated detection.

An interaction-dominant perspective on reading fluency and dyslexia

The background noise of response times is often overlooked in scientific inquiries of cognitive performances. However, it is becoming widely acknowledged in psychology, medicine, physiology, physics, and beyond that temporal patterns of variability constitute a rich source of information. Here, we introduce two complexity measures (1/f scaling and recurrence quantification analysis) that employ background noise as metrics of reading fluency. These measures gauge the extent of interdependence across, rather than within, cognitive components. In this study, we investigated dyslexic and non-dyslexic word-naming performance in beginning readers and observed that these complexity metrics differentiate reliably between dyslexic and average response times and correlate strongly with the severity of the reading impairment. The direction of change in the introduced metrics suggests that developmental dyslexia resides from dynamical instabilities in the coordination among the many components necessary to read, which could explain why dyslexic readers score below average on so many distinct tasks and modalities.

Recurrence Quantification Analysis of Spontaneous Electrophysiological Activity during Development: Characterization of In Vitro Neuronal Networks Cultured on Multi Electrode Array Chips

The combination of a nonlinear time series analysis technique, Recurrence Quantification Analysis (RQA) based on Recurrence Plots (RPs), and traditional statistical analysis for neuronal electrophysiology is proposed in this paper as an innovative paradigm for studying the variation of spontaneous electrophysiological activity of in vitro Neuronal Networks (NNs) coupled to Multielectrode Array (MEA) chips. Recurrence, determinism, entropy, distance of activity patterns, and correlation in correspondence to spike and burst parameters (e.g., mean spiking rate, mean bursting rate, burst duration, spike in burst, etc.) have been computed to characterize and assess the daily changes of the neuronal electrophysiology during neuronal network development and maturation. The results show the similarities/differences between several channels and time periods as well as the evolution of the spontaneous activity in the MEA chip. RPs could be used for graphically exploring possible neuronal dynamic breaking/changing points, whereas RQA parameters are suited for locating them. The combination of RQA with traditional approaches improves the identification, description, and prediction of electrophysiological changes and it will be used to allow intercomparison between results obtained from different MEA chips. Results suggest the proposed processing paradigm as a valuable tool to analyze neuronal activity for screening purposes (e.g., toxicology, neurodevelopmental toxicology).

Chaos game representation of human pallidal spike trains

Many studies have demonstrated the presence of scale invariance and long-range correlation in animal and human neuronal spike trains. The methodologies to extract the fractal or scale-invariant properties, however, do not address the issue as to the existence within the train of fine temporal structures embedded in the global fractal organisation. The present study addresses this question in human spike trains by the chaos game representation (CGR) approach, a graphical analysis with which specific temporal sequences reveal themselves as geometric structures in the graphical representation. The neuronal spike train data were obtained from patients whilst undergoing pallidotomy. Using this approach, we observed highly structured regions in the representation, indicating the presence of specific preferred sequences of interspike intervals within the train. Furthermore, we observed that for a given spike train, the higher the magnitude of its scaling exponent, the more pronounced the geometric patterns in the representation and, hence, higher probability of occurrence of specific subsequences. Given its ability to detect and specify in detail the preferred sequences of interspike intervals, we believe that CGR is a useful adjunct to the existing set of methodologies for spike train analysis.

Hierarchical organization of a reference system in newborn spontaneous movements

In this paper, we studied spontaneous newborn movements regarding the coordination of the four limbs, arms and legs, from a dynamic perspective. We used the method of recurrence plots to analyse the kinematic data from audiovisual recordings of neonates. We identified temporal and spatial synchronization of the four limbs that resulted in high recurrence patterns of biomechanical reference configurations. Furthermore, we identified transitions between linear and nonlinear epochs in the movement behavior of newborns on different time scales by means of recurrence quantification analysis. Results are discussed in the context of the concept of a structural hierarchy, in which different time scales correspond to hierarchical levels of organization.

Internal Pallidal Neuronal Activity During Mild Drug-Related Dyskinesias in Parkinson's Disease: Decreased Firing Rates and Altered Firing Patterns

The neuronal basis of hyperkinetic movement disorders has long been unclear. We now test the hypothesis that changes in the firing pattern of neurons in the globus pallidus internus (GPi) are related to dyskinesias induced by low doses of apomorphine in patients with advanced Parkinson's disease (PD). During pallidotomy for advanced PD, the activity of single neurons was studied both before and after administration of apomorphine at doses just adequate to induce dyskinesias (21 neurons, 17 patients). After the apomorphine injection, these spike trains demonstrated an initial fall in firing from baseline. In nine neurons, the onset of on was simultaneous with that of dyskinesias. In these spike trains, the initial fall in firing rate preceded and was larger than the fall at the onset of on with dyskinesias. Among the three neurons in which the onset of on occurred before that of dyskinesias, the firing rate did not change at the time of onset of dyskinesias. After injection of apomorphine, dyskinesias during on with dyskinesias often fluctuated between transient periods with dyskinesias and those without. Average firing rates were not different between these two types of transient periods. Transient periods with dyskinesias were characterized by interspike interval (ISI) independence, stationary spike trains, and higher variability of ISIs. A small but significant group of neurons demonstrated recurring ISI patterns during transient periods of on with dyskinesias. These results suggest that mild dyskinesias resulting from low doses of apomorphine are related to both low GPi neuronal firing rates and altered firing patterns.

Curved structures in recurrence plots: the role of the sampling time

We give a theoretical explanation of the formation of the curved macropatterns in the recurrence plots of sinusoidal signals, with nonstationarity in the phase or in the frequency. We show that the large time scales observed and the curved structures are the artificial product of the discretization of the signal. Recurrence plots are highly sensitive to the phase error introduced by the sampling, and we show that this characteristic can be used to detect very small (approximately 0.5%) phase or frequency shifts of the carrier frequency.

Synchronization likelihood with explicit time-frequency priors

Cognitive processing requires integration of information processed simultaneously in spatially distinct areas of the brain. The influence that two brain areas exert on each others activity is usually governed by an unknown function, which is likely to have nonlinear terms. If the functional relationship between activities in different areas is dominated by the nonlinear terms, linear measures of correlation may not detect the statistical interdependency satisfactorily. Therefore, algorithms for detecting nonlinear dependencies may prove invaluable for characterizing the functional coupling in certain neuronal systems, conditions or pathologies. Synchronization likelihood (SL) is a method based on the concept of generalized synchronization and detects nonlinear and linear dependencies between two signals (Stam, C.J., van Dijk, B.W., 2002. Synchronization likelihood: An unbiased measure of generalized synchronization in multivariate data sets. Physica D, 163: 236-241.). SL relies on the detection of simultaneously occurring patterns, which can be complex and widely different in the two signals. Clinical studies applying SL to electro- or magnetoencephalography (EEG/MEG) signals have shown promising results. In previous implementations of the algorithm, however, a number of parameters have lacked a rigorous definition with respect to the time-frequency characteristics of the underlying physiological processes. Here we introduce a rationale for choosing these parameters as a function of the time-frequency content of the patterns of interest. The number of parameters that can be arbitrarily chosen by the user of the SL algorithm is thereby decreased from six to two. Empirical evidence for the advantages of our proposal is given by an application to EEG data of an epileptic seizure and simulations of two unidirectionally coupled Hénon systems.

Using recurrence quantification analysis determinism for noise removal in cardiac optical mapping

Selecting signal processing parameters in optical imaging by utilizing the change in Determinism, a measure introduced in Recurrence Quantification Analysis, provides a novel method using the change in residual noise Determinism for improving noise quantification and removal across signals exhibiting disparate underlying tissue pathologies. The method illustrates an improved process for selecting filtering parameters and how using measured signal-to-noise ratio alone can lead to improper parameter selection.

Recurrence plots and unstable periodic orbits

A recurrence plot is a two-dimensional visualization technique for sequential data. These plots are useful in that they bring out correlations at all scales in a manner that is obvious to the human eye, but their rich geometric structure can make them hard to interpret. In this paper, we suggest that the unstable periodic orbits embedded in a chaotic attractor are a useful basis set for the geometry of a recurrence plot of those data. This provides not only a simple way to locate unstable periodic orbits in chaotic time-series data, but also a potentially effective way to use a recurrence plot to identify a dynamical system. (c) 2002 American Institute of Physics.

Recurrence plots of experimental data: To embed or not to embed?

A recurrence plot is a visualization tool for analyzing experimental data. These plots often reveal correlations in the data that are not easily detected in the original time series. Existing recurrence plot analysis techniques, which are primarily application oriented and completely quantitative, require that the time-series data first be embedded in a high-dimensional space, where the embedding dimension d(E) is dictated by the dimension d of the data set, with d(E)>/=2d+1. One such set of recurrence plot analysis tools, recurrence quantification analysis, is particularly useful in finding locations in the data where the underlying dynamics change. We have found that for certain low-dimensional systems the same results can be obtained with no embedding. (c) 1998 American Institute of Physics.