Recurrence microstates for machine learning classification.

Recurrence microstates are obtained from the cross recurrence of two sequences of values embedded in a time series, being the generalization of the concept of recurrence of a given state in phase space. The probability of occurrence of each microstate constitutes a recurrence quantifier. The set of probabilities of all microstates are capable of detecting even small changes in the data pattern. This creates an ideal tool for generating features in machine learning algorithms. Thanks to the sensitivity of the set of probabilities of occurrence of microstates, it can be used to feed a deep neural network, namely, a microstate multi-layer perceptron (MMLP) to classify parameters of chaotic systems. Additionally, we show that with more microstates, the accuracy of the MMLP increases, showing that the increasing size and number of microstates insert new and independent information into the analysis. We also explore potential applications of the proposed method when adapted to different contexts.

Phase-locking intermittency induced by dynamical heterogeneity in networks of thermosensitive neurons.

In this work, we study the phase synchronization of a neural network and explore how the heterogeneity in the neurons' dynamics can lead their phases to intermittently phase-lock and unlock. The neurons are connected through chemical excitatory connections in a sparse random topology, feel no noise or external inputs, and have identical parameters except for different in-degrees. They follow a modification of the Hodgkin-Huxley model, which adds details like temperature dependence, and can burst either periodically or chaotically when uncoupled. Coupling makes them chaotic in all cases but each individual mode leads to different transitions to phase synchronization in the networks due to increasing synaptic strength. In almost all cases, neurons' inter-burst intervals differ among themselves, which indicates their dynamical heterogeneity and leads to their intermittent phase-locking. We argue then that this behavior occurs here because of their chaotic dynamics and their differing initial conditions. We also investigate how this intermittency affects the formation of clusters of neurons in the network and show that the clusters' compositions change at a rate following the degree of intermittency. Finally, we discuss how these results relate to studies in the neuroscience literature, especially regarding metastability.

Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems.

The recurrence analysis of dynamic systems has been studied since Poincaré's seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy (Smax). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood (ϵ-vicinity), turning the analysis free of the vicinity parameter. In addition, ϵ turns out to be a novel quantifier of dynamical properties itself. We apply Smax and the optimum ϵ to deterministic and stochastic systems. The Smax quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series.

Correlated Brownian motion and diffusion of defects in spatially extended chaotic systems.

One of the spatiotemporal patterns exhibited by coupled map lattices with nearest-neighbor coupling is the appearance of chaotic defects, which are spatially localized regions of chaotic dynamics with a particlelike behavior. Chaotic defects display random behavior and diffuse along the lattice with a Gaussian signature. In this note, we investigate some dynamical properties of chaotic defects in a lattice of coupled chaotic quadratic maps. Using a recurrence-based diagnostic, we found that the motion of chaotic defects is well-represented by a stochastic time series with a power-law spectrum 1/fσ with 2.3≤σ≤2.4, i.e., a correlated Brownian motion. The correlation exponent corresponds to a memory effect in the Brownian motion and increases with a system parameter as the diffusion coefficient of chaotic defects.

Synchronous patterns and intermittency in a network induced by the rewiring of connections and coupling.

The connection architecture plays an important role in the synchronization of networks, where the presence of local and nonlocal connection structures are found in many systems, such as the neural ones. Here, we consider a network composed of chaotic bursting oscillators coupled through a Watts-Strogatz-small-world topology. The influence of coupling strength and rewiring of connections is studied when the network topology is varied from regular to small-world to random. In this scenario, we show two distinct nonstationary transitions to phase synchronization: one induced by the increase in coupling strength and another resulting from the change from local connections to nonlocal ones. Besides this, there are regions in the parameter space where the network depicts a coexistence of different bursting frequencies where nonstationary zig-zag fronts are observed. Regarding the analyses, we consider two distinct methodological approaches: one based on the phase association to the bursting activity where the Kuramoto order parameter is used and another based on recurrence quantification analysis where just a time series of the network mean field is required.

Neuron dynamics variability and anomalous phase synchronization of neural networks.

Anomalous phase synchronization describes a synchronization phenomenon occurring even for the weakly coupled network and characterized by a non-monotonous dependence of the synchronization strength on the coupling strength. Its existence may support a theoretical framework to some neurological diseases, such as Parkinson's and some episodes of seizure behavior generated by epilepsy. Despite the success of controlling or suppressing the anomalous phase synchronization in neural networks applying external perturbations or inducing ambient changes, the origin of the anomalous phase synchronization as well as the mechanisms behind the suppression is not completely known. Here, we consider networks composed of N = 2000 coupled neurons in a small-world topology for two well known neuron models, namely, the Hodgkin-Huxley-like and the Hindmarsh-Rose models, both displaying the anomalous phase synchronization regime. We show that the anomalous phase synchronization may be related to the individual behavior of the coupled neurons; particularly, we identify a strong correlation between the behavior of the inter-bursting-intervals of the neurons, what we call neuron variability, to the ability of the network to depict anomalous phase synchronization. We corroborate the ideas showing that external perturbations or ambient parameter changes that eliminate anomalous phase synchronization and at the same time promote small changes in the individual dynamics of the neurons, such that an increasing individual variability of neurons implies a decrease of anomalous phase synchronization. Finally, we demonstrate that this effect can be quantified using a well known recurrence quantifier, the "determinism." Moreover, the results obtained by the determinism are based on only the mean field potential of the network, turning these measures more suitable to be used in experimental situations.

Outcomes of 847 childhood-onset systemic lupus erythematosus patients in three age groups.

Objective The objective of this study was to assess outcomes of childhood systemic lupus erythematosus (cSLE) in three different age groups evaluated at last visit: group A early-onset disease (<6 years), group B school age (≥6 and <12 years) and group C adolescent (≥12 and <18 years). Methods An observational cohort study was performed in ten pediatric rheumatology centers, including 847 cSLE patients. Results Group A had 39 (4%), B 395 (47%) and C 413 (49%). Median disease duration was significantly higher in group A compared to groups B and C (8.3 (0.1-23.4) vs 6.2 (0-17) vs 3.3 (0-14.6) years, p < 0.0001). The median Systemic Lupus International Collaborating Clinics/American College of Rheumatology Damage Index (SLICC/ACR-DI) (0 (0-9) vs 0 (0-6) vs 0 (0-7), p = 0.065) was comparable in the three groups. Further analysis of organ/system damage revealed that frequencies of neuropsychiatric (21% vs 10% vs 7%, p = 0.007), skin (10% vs 1% vs 3%, p = 0.002) and peripheral vascular involvements (5% vs 3% vs 0.3%, p = 0.008) were more often observed in group A compared to groups B and C. Frequencies of severe cumulative lupus manifestations such as nephritis, thrombocytopenia, and autoimmune hemolytic anemia were similar in all groups ( p > 0.05). Mortality rate was significantly higher in group A compared to groups B and C (15% vs 10% vs 6%, p = 0.028). Out of 69 deaths, 33/69 (48%) occurred within the first two years after diagnosis. Infections accounted for 54/69 (78%) of the deaths and 38/54 (70%) had concomitant disease activity. Conclusions This large multicenter study provided evidence that early-onset cSLE group had distinct outcomes. This group was characterized by higher mortality rate and neuropsychiatric/vascular/skin organ damage in spite of comparable frequencies of severe cumulative lupus manifestations. We also identified that overall death in cSLE patients was an early event mainly attributed to infection associated with disease activity.

Spatial recurrence analysis: a sensitive and fast detection tool in digital mammography.

Efficient diagnostics of breast cancer requires fast digital mammographic image processing. Many breast lesions, both benign and malignant, are barely visible to the untrained eye and requires accurate and reliable methods of image processing. We propose a new method of digital mammographic image analysis that meets both needs. It uses the concept of spatial recurrence as the basis of a spatial recurrence quantification analysis, which is the spatial extension of the well-known time recurrence analysis. The recurrence-based quantifiers are able to evidence breast lesions in a way as good as the best standard image processing methods available, but with a better control over the spurious fragments in the image.

Suppression of bursting synchronization in clustered scale-free (rich-club) neuronal networks.

Functional brain networks are composed of cortical areas that are anatomically and functionally connected. One of the cortical networks for which more information is available in the literature is the cat cerebral cortex. Statistical analyses of the latter suggest that its structure can be described as a clustered network, in which each cluster is a scale-free network possessing highly connected hubs. Those hubs are, on their hand, connected together in a strong fashion ("rich-club" network). We have built a clustered scale-free network inspired in the cat cortex structure so as to study their dynamical properties. In this article, we focus on the synchronization of bursting activity of the cortical areas and how it can be suppressed by means of neuron deactivation through suitably applied light pulses. We show that it is possible to effectively suppress bursting synchronization by acting on a single, yet suitably chosen neuron, as long as it is highly connected, thanks to the "rich-club" structure of the network.

The role of individual neuron ion conductances in the synchronization processes of neuron networks.

The partial phase synchronization (sometimes called cooperation) of neurons is fundamental for the understanding of the complex behavior of the brain. The lack or the excess of synchronization can generate brain disorders like Parkinson's disease and epilepsy. The phase synchronization phenomenon is strongly related to the regular or chaotic dynamics of individual neurons. The individual dynamics themselves are a function of the ion channel conductances, turning the conductances into important players in the process of neuron synchronized health depolarization/repolarization processes. It is well known that many diseases are related to alterations of the ion-channel conductance properties. To normalize their functioning, drugs are used to block or activate specific channels, changing their conductances. We investigate the synchronization process of a Hodgkin-Huxley-type neural network as a function of the values of the individual neuron conductances, showing the dynamics of the neurons must be taken into account in the synchronization process. Particular sets of conductances lead to non-chaotic individual neuron dynamics allowing synchronization states for very weak coupling and resulting in a non-monotonic transition to synchronized states, as the coupling strength among neurons is varied. On the other hand, a monotonic transition to synchronized states is observed for individual chaotic dynamics of the neurons. We conclude the analysis of the individual dynamics of isolated neurons allows the prediction of the synchronization process of the network. We provide alternative ways to achieve the desired network state (phase synchronized or desynchronized) without any changes in the synaptic current of neurons but making just small changes in the neuron ion-channel conductances. The mechanism behind the control is the close relation between ion-channel conductance and the regular or chaotic dynamics of neurons. Finally, we show that by changing at least two conductances simultaneously the control may be much more efficient since the second conductance makes the synchronization possible just by performing a small change in the first. The study presented here may have an impact on new drug development research.

Bistability in the synchronization of identical neurons.

We investigate the role of bistability in the synchronization of a network of identical bursting neurons coupled through an generic electrical mean-field scheme. These neurons can exhibit distinct multistable states and, in particular, bistable behavior is observed when their sodium conductance is varied. With this, we consider three different initialization compositions: (i) the whole network is in the same periodic state; (ii) half of the network periodic, half chaotic; (iii) half periodic, and half in a different periodic state. We show that (i) and (ii) reach phase synchronization (PS) for all coupling strengths, while for (iii) small coupling regimes do not induce PS, and instead, there is a coexistence of different frequencies. For stronger coupling, case (iii) synchronizes, but after (i) and (ii). Since PS requires all neurons being in the same state (same frequencies), these different behaviors are governed by transitions between the states. We find that, during these transitions, (ii) and (iii) have transient chimera states and that (iii) has breathing chimeras. By studying the stability of each state, we explain the observed transitions. Therefore, bistability of neurons can play a major role in the synchronization of generic networks, with the simple initialization of the system being capable of drastically changing its asymptotic space.

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks.

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, [Formula: see text], that determines the strength of the correlation of the noise. To predict [Formula: see text] the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the [Formula: see text] value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same [Formula: see text] parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community.

Two-state on-off intermittency and the onset of turbulence in a spatiotemporally chaotic system.

We show the existence of two-state on-off intermittent behavior in spatially extended dynamical systems, using as an example the damped and forced drift wave equation. The two states are stationary solutions corresponding to different wave energies. In the language of (Fourier-mode) phase space these states are embedded in two invariant manifolds that become transversely unstable in the regime where two-state on-off intermittency sets in. The distribution of laminar duration sizes is compatible with the similar phenomenon occurring in time only in the presence of noise. In an extended system the noisy effect is provided by the spatial modes excited by the perturbation. We show that this intermittency is a precursor of the onset of strong turbulence in the system.

Management of Euxesta spp. in Sweet Corn with McPhail Traps.

Pests attacking the ear of sweet corn, such as Helicoverpa and Euxesta species, cause economic losses for the producer and the processing industry. Feeding on the style-stigmata preventing fertilization and on the developing grain and the association with pathogens are the main causes of product depreciation. The traditional control such as spraying with chemicals is not effective, even with several applications directed to the corn ear. Bacillus thuringiensis (Bt) corn also does not reach the fly. McPhail traps that have been used to monitor the pest can be a control strategy. This work evaluated the efficiency of food attractants placed inside McPhail traps to remove adult insects, in order to reduce ear damage. Twelve McPhail-type traps were installed in a randomized complete block design containing Bio Anastrepha® alone or combined with different doses of insecticide. Every 10 days, all the captured insects were counted and separated by species and sex. Only Euxesta eluta and Euxesta mazorca were found. The occurrence of insects was greater in the period between silk emergence and grain filling. The number of females was higher, probably due to the need to feed before oviposition. The number of E. mazorca females caught in the treatment containing only Bio Anastrepha® was higher compared with that of others. The mean ear damage was very low, and there was no interaction between the production parameters and the distance between the trap and the harvested plant. In short, the use of McPhail trap containing food attractants may be a viable alternative to control corn silk flies.

Transport properties in nontwist area-preserving maps.

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.

Erratum: Phase synchronization and intermittent behavior in healthy and Alzheimer-affected human-brain-based neural network [Phys. Rev. E 99, 022402 (2019)].

This corrects the article DOI: 10.1103/PhysRevE.99.022402.

Phase synchronization and intermittent behavior in healthy and Alzheimer-affected human-brain-based neural network.

We study the dynamical proprieties of phase synchronization and intermittent behavior of neural systems using a network of networks structure based on an experimentally obtained human connectome for healthy and Alzheimer-affected brains. We consider a network composed of 78 neural subareas (subnetworks) coupled with a mean-field potential scheme. Each subnetwork is characterized by a small-world topology, composed of 250 bursting neurons simulated through a Rulkov model. Using the Kuramoto order parameter we demonstrate that healthy and Alzheimer-affected brains display distinct phase synchronization and intermittence properties as a function of internal and external coupling strengths. In general, for the healthy case, each subnetwork develops a substantial level of internal synchronization before a global stable phase-synchronization state has been established. For the unhealthy case, despite the similar internal subnetwork synchronization levels, we identify higher levels of global phase synchronization occurring even for relatively small internal and external coupling. Using recurrence quantification analysis, namely the determinism of the mean-field potential, we identify regions where the healthy and unhealthy networks depict nonstationary behavior, but the results denounce the presence of a larger region or intermittent dynamics for the case of Alzheimer-affected networks. A possible theoretical explanation based on two locally stable but globally unstable states is discussed.

Mechanism for explosive synchronization of neural networks.

Here we investigate the mechanism for explosive synchronization (ES) of a complex neural network composed of nonidentical neurons and coupled by Newman-Watts small-world matrices. We find a range of nonlocal connection probabilities for which the network displays an abrupt transition to phase synchronization, characterizing ES. The mechanism behind the ES is the following: As the coupling parameter is varied in a network of distinct neurons, ES is likely to occur due to a bistable regime, namely a chaotic nonsynchronized and a regular phase-synchronized state in the phase space. In this case, even small coupling changes make possible a transition between them. The onset of ES occurs via a saddle-node bifurcation of a periodic orbit that leads the network dynamics to display a locally stable phase-synchronized state. The presence of this regime is accompanied by a hysteresis loop on the network dynamics as the coupling parameter is adiabatically increased and decreased. The end of the hysteresis loop is marked by a frontier crisis of the chaotic attractor which also determines the end of the coupling strength interval where ES is possible.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system.

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

Short-time memories in a network with randomly distributed connections.

Coupled map lattices are able to store short-term memories when an external periodic input is applied. We consider short-term memory formation in networks with both regular (nearest-neighbor) and randomly chosen connections. The regimes under which single or multiple memorized patterns are stored are studied in terms of the coupling and nonlinear parameters of the network.