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One of the interesting aspects of EEG data is the presence of temporally stable and spatially coherent patterns of activity, known as microstates, which have been linked to various cognitive and clinical phenomena. However, there is still no general agreement on the interpretation of microstate analysis. Various clustering algorithms have been used for microstate computation, and multiple studies suggest that the microstate time series may provide insight into the neural activity of the brain in the resting state. This study addresses two gaps in the literature. Firstly, by applying several state-of-the-art microstate algorithms to a large dataset of EEG recordings, we aim to characterise and describe various microstate algorithms. We demonstrate and discuss why the three “classically” used algorithms ((T)AAHC and modified K-Means) yield virtually the same results, while HMM algorithm generates the most dissimilar results. Secondly, we aim to test the hypothesis that dynamical microstate properties might be, to a large extent, determined by the linear characteristics of the underlying EEG signal, in particular, by the cross-covariance and autocorrelation structure of the EEG data. To this end, we generated a Fourier transform surrogate of the EEG signal to compare microstate properties. Here, we found that these are largely similar, thus hinting that microstate properties depend to a very high degree on the linear covariance and autocorrelation structure of the underlying EEG data. Finally, we treated the EEG data as a vector autoregression process, estimated its parameters, and generated surrogate stationary and linear data from fitted VAR. We observed that such a linear model generates microstates highly comparable to those estimated from real EEG data, supporting the conclusion that a linear EEG model can help with the methodological and clinical interpretation of both static and dynamic human brain microstate properties.

Background: Atrial fibrillation (AF) is associated with high risk of stroke preventable by timely initiation of anticoagulation. Currently available screening tools based on ECG are not optimal due to inconvenience and high costs. Aim of this study was to study the diagnostic value of apelin for AF in patients with high risk of stroke.Methods: We designed a multicenter, matched-cohort study. The population consisted of three study groups: a healthy control group (34 patients) and two matched groups of 60 patients with high risk of stroke (AF and non-AF group). Apelin levels were examined from peripheral blood.Results: Apelin was significantly lower in AF group compared to non-AF group (0.694 ± 0.148 vs. 0.975 ± 0.458 ng/ml, p = 0.001) and control group (0.982 ± 0.060 ng/ml, p < 0.001), respectively. Receiver operating characteristic (ROC) analysis of apelin as a predictor of AF scored area under the curve (AUC) of 0.658. Apelin's concentration of 0.969 [ng/ml] had sensitivity = 0.966 and specificity = 0.467. Logistic regression based on manual feature selection showed that only apelin and NT-proBNP were independent predictors of AF. Logistic regression based on selection from bivariate analysis showed that only apelin was an independent predictor of AF. A logistic regression model using repeated stratified K-Fold cross-validation strategy scored an AUC of 0.725 ± 0.131.Conclusions: Our results suggest that apelin might be used to rule out AF in patients with high risk of stroke.

Sleep manifests itself by the spontaneous emergence of characteristic oscillatory rhythms, which often timelock and are implicated in the memory formation. Here, we analyze a neural mass model of the thalamocortical loop of which the cortical node can generate slow oscillations (approx. 1 Hz) while its thalamic component can generate fast sleep spindles of σ-band activity (12–15 Hz). We study the dynamics for different coupling strengths between the thalamic and cortical nodes, for different conductance values of the thalamic node’s potassium leak and anomalous rectifying currents, and for different parameter regimes of the cortical node. The latter are: (1) a low activity (DOWN) state with noise-induced, transient excursions into a high activity (UP) state, (2) an adaptation induced slow oscillation limit cycle with alternating UP and DOWN states, and (3) a high activity (UP) state with noise-induced, transient excursions into the low activity (DOWN) state. During UP states, thalamic spindling is abolished or reduced. During DOWN states, the thalamic node generates sleep spindles, which in turn can cause DOWN to UP transitions in the cortical node. Consequently, this leads to spindle-induced UP state transitions in parameter regime (1), thalamic spindles induced in some but not all DOWN states in regime (2), and thalamic spindles following UP to DOWN transitions in regime (3). The spindle-induced σ-band activity in the cortical node, however, is typically strongest during the UP state, which follows a DOWN state “window of opportunity” for spindling. When the cortical node is parametrized in regime (3), the model well explains the interactions between slow oscillations and sleep spindles observed experimentally during Non-Rapid Eye Movement sleep. The model is computationally efficient and can be integrated into large-scale modeling frameworks to study spatial aspects like sleep wave propagation.

neurolib is a computational framework for whole-brain modeling written in Python. It provides a set of neural mass models that represent the average activity of a brain region on a mesoscopic scale. In a whole-brain network model, brain regions are connected with each other based on biologically informed structural connectivity, i.e., the connectome of the brain. neurolib can load structural and functional datasets, set up a whole-brain model, manage its parameters, simulate it, and organize its outputs for later analysis. The activity of each brain region can be converted into a simulated BOLD signal in order to calibrate the model against empirical data from functional magnetic resonance imaging (fMRI). Extensive model analysis is made possible using a parameter exploration module, which allows one to characterize a model’s behavior as a function of changing parameters. An optimization module is provided for fitting models to multimodal empirical data using evolutionary algorithms. neurolib is designed to be extendable and allows for easy implementation of custom neural mass models, offering a versatile platform for computational neuroscientists for prototyping models, managing large numerical experiments, studying the structure–function relationship of brain networks, and for performing in-silico optimization of whole-brain models.

Statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding and prediction of natural complex systems such as the Earth’s climate. This article introduces and applies information theory diagnostics to phase and amplitude time series of different oscillatory components of observed data that characterizes El Nino/Southern Oscillation. A suite of significant interactions between processes operating on different time scales is detected and shown to be important for emergence of extreme events. The mechanisms of these nonlinear interactions are further studied in conceptual low-order and state-of-the-art dynamical, as well as statistical climate models. Observed and simulated interactions exhibit substantial discrepancies, whose understanding may be the key to an improved prediction of ENSO. Moreover, the statistical framework applied here is suitable for inference of cross-scale interactions in human brain dynamics and other complex systems. Strong El Nino and La Nina events arise from the interaction and synchronization between El Nino Southern Oscillation (ENSO) cycles that operate on different time scales. The warm, El Nino, and cold, La Nina, phases of ENSO are irregular and occur every 2 to 7 years, governed by the interaction between the annual, biannual and interannual cycles. Milan Palus, from the Czech Academy of Sciences in Prague, and colleagues apply statistical diagnostics from information theory to ENSO data to detect the causal interactions between these three variability modes that lead to extreme El Nino/La Nina event. They find a particularly important role for the biannual cycle in these extreme events. The authors suggest that this statistical framework could also be used for inferring cross-scale interactions in neuronal networks in the human brain and other complex systems.

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two H\'enon systems, a unidirectional connection of chaotic systems of R\"ossler and Lorenz type and of two different R\"ossler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only $20\phantom{\rule{0.16em}{0ex}}000$ points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Air temperature variability on different time scales exhibits recurring patterns and quasi-oscillatory phenomena. Climate oscillations with the period about 7–8 years have been observed in many instrumental records in Europe. Although these oscillations are weak if considering their amplitude, they might have nonnegligible influence on temperature variability on shorter time scales due to cross-scale interactions recently observed by Palus (2014). In order to quantify the cross-scale influence, we propose a simple conditional mean approach which estimates the effect of the cycle with the period close to 8 years on the amplitude of the annual cycle in surface air temperature (SAT) in the range 0.7–1.4°C and the effect on the overall variability of the SAT anomalies (SATA) leads to the changes 1.5–1.7°C in the annual SATA means. The strongest effect in the winter SATA means reaches 4–5°C in central European station and reanalysis data.

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.

Complex systems are commonly characterized by the properties of their graph representation. Dynamical complex systems are then typically represented by a graph of temporal dependencies between time series of state variables of their subunits. It has been shown recently that graphs constructed in this way tend to have relatively clustered structure, potentially leading to spurious detection of small-world properties even in the case of systems with no or randomly distributed true interactions. However, the strength of this bias depends heavily on a range of parameters and its relevance for real-world data has not yet been established. In this work, we assess the relevance of the bias using two examples of multivariate time series recorded in natural complex systems. The first is the time series of local brain activity as measured by functional magnetic resonance imaging in resting healthy human subjects, and the second is the time series of average monthly surface air temperature coming from a large reanalysis of climatological data over the period 1948-2012. In both cases, the clustering in the thresholded correlation graph is substantially higher compared with a realization of a density-matched random graph, while the shortest paths are relatively short, showing thus distinguishing features of small-world structure. However, comparable or even stronger small-world properties were reproduced in correlation graphs of model processes with randomly scrambled interconnections. This suggests that the small-world properties of the correlation matrices of these real-world systems indeed do not reflect genuinely the properties of the underlying interaction structure, but rather result from the inherent properties of correlation matrix.

A directed climate network is constructed by Granger causality analysis of air temperature time series from a regular grid covering the whole Earth. Using winner-takes-all network thresholding approach, a structure of a smooth information flow is revealed, hidden to previous studies. The relevance of this observation is confirmed by comparison with the air mass transfer defined by the wind field. Their close relation illustrates that although the information transferred due to the causal influence is not a physical quantity, the information transfer is tied to the transfer of mass and energy.

It is well established that the global climate is a complex phenomenon with dynamics driven by the interaction of a multitude of identifiable but intertwined subsystems. The identification, at some level, of these subsystems is an important step towards understanding climate dynamics. We present a method to determine the number of principal components representing non-random correlation structures in climate data, or components that cannot be generated by a surrogate model of independent stochastic processes replicating the auto-correlation structure of each time series. The purpose of the method is to automatically reduce the dimensionality of large climate datasets into spatially localised components suitable for further interpretation or, for example, for use as nodes in a complex network analysis of large-scale climate dynamics. We apply the method to two 2.5° resolution NCEP/NCAR reanalysis global datasets of monthly means: the sea level pressure (SLP) and the surface air temperature (SAT), and extract 60 components explaining 87 % variance and 68 components explaining 72 % variance, respectively. The obtained components are in agreement with previous results in that they recover many well-known climate modes previously identified using other approaches including regionally constrained principal component analysis. Selected SLP components are discussed in more detail with respect to their correlation with important climate indices and their relationship to other SLP and SAT components. Finally, we consider a subset of the obtained components that have not yet been explicitly identified by other authors but seem plausible in the context of regional climate observations discussed in literature.