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Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks. [ABSTRACT FROM AUTHOR]

Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a resulting loss of information, this approach captures meaningful information about the temporal structure of the underlying system dynamics as well as about properties of interactions between coupled systems. This—together with its conceptual simplicity and robustness against measurement noise—makes ordinal time series analysis well suited to improve characterization of the still poorly understood spatiotemporal dynamics of the human brain. This minireview briefly summarizes the state-of-the-art of uni- and bivariate ordinal time-series-analysis techniques together with applications in the neurosciences. It will highlight current limitations to stimulate further developments, which would be necessary to advance characterization of evolving functional brain networks. [ABSTRACT FROM AUTHOR]

The collective dynamics of complex networks of FitzHugh–Nagumo units exhibits rare and recurrent events of high amplitude (extreme events) that are preceded by so-called proto-events during which a certain fraction of the units become excited. Although it is well known that a sufficiently large fraction of excited units is required to turn a proto-event into an extreme event, it is not yet clear how the other units are being recruited into the final generation of an extreme event. Addressing this question and mimicking typical experimental situations, we investigate the centrality of edges in time-dependent interaction networks. We derived these networks from time series of the units' dynamics employing a widely used bivariate analysis technique. Using our recently proposed edge-centrality concepts together with an edge-based network decomposition technique, we observe that the recruitment is primarily facilitated by sets of certain edges that have no equivalent in the underlying topology. Our finding might aid to improve the understanding of generation of extreme events in natural networked dynamical systems. [ABSTRACT FROM AUTHOR]

Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks. [ABSTRACT FROM AUTHOR]

Epilepsy is a common disorder characterized by recurrent seizures. An overwhelming majority of people with epilepsy regard the unpredictability of seizures as a major issue. More than 30 years of international effort have been devoted to the prediction of seizures, aiming to remove the burden of unpredictability and to couple novel, time-specific treatment to seizure prediction technology. A highly influential review published in 2007 concluded that insufficient evidence indicated that seizures could be predicted. Since then, several advances have been made, including successful prospective seizure prediction using intracranial EEG in a small number of people in a trial of a real-time seizure prediction device. In this Review, we examine advances in the field, including EEG databases, seizure prediction competitions, the prospective trial mentioned and advances in our understanding of the mechanisms of seizures. We argue that these advances, together with statistical evaluations, set the stage for a resurgence in efforts towards the development of seizure prediction methodologies. We propose new avenues of investigation involving a synergy between mechanisms, models, data, devices and algorithms and refine the existing guidelines for the development of seizure prediction technology to instigate development of a solution that removes the burden of the unpredictability of seizures. [ABSTRACT FROM AUTHOR]

Epilepsy is now conceptualized as a network disease. The epileptic brain network comprises structurally and functionally connected cortical and subcortical brain regions – spanning lobes and hemispheres –, whose connections and dynamics evolve in time. With this concept, focal and generalized seizures as well as other related pathophysiological phenomena are thought to emerge from, spread via, and be terminated by network vertices and edges that also generate and sustain normal, physiological brain dynamics. Research over the last years has advanced concepts and techniques to identify and characterize the evolving epileptic brain network and its constituents on various spatial and temporal scales. Network-based approaches further our understanding of how seizures emerge from the evolving epileptic brain network, and they provide both novel insights into pre-seizure dynamics and important clues for success or failure of measures for network-based seizure control and prevention. In this review, we summarize the current state of knowledge and address several important challenges that would need to be addressed to move network-based prediction and control of seizures closer to clinical translation. [ABSTRACT FROM AUTHOR]

We investigate the temporal and spatial variability of the importance of brain regions in evolving epileptic brain networks. We construct these networks from multiday, multichannel electroencephalographic data recorded from 17 epilepsy patients and use centrality indices to assess the importance of brain regions. Time-resolved indications of highest importance fluctuate over time to a greater or lesser extent, however, with some periodic temporal structure that can mostly be attributed to phenomena unrelated to the disease. In contrast, relevant aspects of the epileptic process contribute only marginally. Indications of highest importance also exhibit pronounced alternations between various brain regions that are of relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches. Nonetheless, these findings may guide new developments for individualized diagnosis, treatment, and control. [ABSTRACT FROM AUTHOR]

Nodes in large-scale epileptic networks that are crucial for seizure facilitation and termination can be regarded as potential targets for individualized focal therapies. Graph-theoretical approaches based on centrality concepts can help to identify such important nodes, however, they may be influenced by the way networks are derived from empirical data. Here we investigate evolving functional epileptic brain networks during 82 focal seizures with different anatomical onset locations that we derive from multichannel intracranial electroencephalographic recordings from 51 patients. We demonstrate how the various methodological steps (from the recording montage via node and link inference to the assessment of node centralities) affect importance estimation and discuss their impact on the interpretability of findings in the context of pathophysiological aspects of seizure dynamics. [ABSTRACT FROM AUTHOR]

We investigate the relative merit of phase-based methods for inferring directional couplings in complex networks of weakly interacting dynamical systems from multivariate time-series data. We compare the evolution map approach and its partialized extension to each other with respect to their ability to correctly infer the network topology in the presence of indirect directional couplings for various simulated experimental situations using coupled model systems. In addition, we investigate whether the partialized approach allows for additional or complementary indications of directional interactions in evolving epileptic brain networks using intracranial electroencephalographic recordings from an epilepsy patient. For such networks, both direct and indirect directional couplings can be expected, given the brain's connection structure and effects that may arise from limitations inherent to the recording technique. Our findings indicate that particularly in larger networks (number of nodes ≫ 10), the partialized approach does not provide information about directional couplings extending the information gained with the evolution map approach. [ABSTRACT FROM AUTHOR]

We study the impact of dynamical and structural heterogeneity on the collective dynamics of large small-world networks of pulse-coupled integrate-and-fire oscillators endowed with refractory periods and time delay. Depending on the choice of homogeneous control parameters (here, refractoriness and coupling strength), these networks exhibit a large spectrum of dynamical behaviors, including asynchronous, partially synchronous, and fully synchronous states. Networks exhibit transitions between these dynamical behaviors upon introducing heterogeneity. We show that the probability for a network to exhibit a certain dynamical behavior (network susceptibility) is affected differently by dynamical and structural heterogeneity and depends on the respective homogeneous dynamics. [ABSTRACT FROM AUTHOR]

We investigate a recently published analysis framework based on Bayesian inference for the time-resolved characterization of interaction properties of noisy, coupled dynamical systems. It promises wide applicability and a better time resolution than well-established methods. At the example of representative model systems, we show that the analysis framework has the same weaknesses as previous methods, particularly when investigating interacting, structurally different non-linear oscillators. We also inspect the tracking of time-varying interaction properties and propose a further modification of the algorithm, which improves the reliability of obtained results. We exemplarily investigate the suitability of this algorithm to infer strength and direction of interactions between various regions of the human brain during an epileptic seizure. Within the limitations of the applicability of this analysis tool, we show that the modified algorithm indeed allows a better time resolution through Bayesian inference when compared to previous methods based on least square fits. [ABSTRACT FROM AUTHOR]

Abstract: Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of time-varying edges, representing interactions between these systems. This approach is highly attractive to further our understanding of the physiological and pathophysiological dynamics in human brain networks. Indeed, there is growing evidence that the epileptic process can be regarded as a large-scale network phenomenon. We here review methodologies for inferring networks from empirical time series and for a characterization of these evolving networks. We summarize recent findings derived from studies that investigate human epileptic brain networks evolving on timescales ranging from few seconds to weeks. We point to possible pitfalls and open issues, and discuss future perspectives. [Copyright &y& Elsevier]

Abstract: Graph-theoretical analyses of complex brain networks is a rapidly evolving field with a strong impact for neuroscientific and related clinical research. Due to a number of confounding variables, however, a reliable and meaningful characterization of particularly functional brain networks is a major challenge. Addressing this problem, we present an analysis approach for weighted networks that makes use of surrogate networks with preserved edge weights or vertex strengths. We first investigate whether characteristics of weighted networks are influenced by trivial properties of the edge weights or vertex strengths (e.g., their standard deviations). If so, these influences are then effectively segregated with an appropriate surrogate normalization of the respective network characteristic. We demonstrate this approach by re-examining, in a time-resolved manner, weighted functional brain networks of epilepsy patients and control subjects derived from simultaneous EEG/MEG recordings during different behavioral states. We show that this surrogate-assisted analysis approach reveals complementary information about these networks, can aid with their interpretation, and thus can prevent deriving inappropriate conclusions. [Copyright &y& Elsevier]

We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module. [ABSTRACT FROM AUTHOR]

We propose a Markov chain method to efficiently generate surrogate networks that are random under the constraint of given vertex strengths. With these strength-preserving surrogates and with edge-weight-preserving surrogates we investigate the clustering coefficient and the average shortest path length of functional networks of the human brain as well as of the International Trade Networks. We demonstrate that surrogate networks can provide additional information about network-specific characteristics and thus help interpreting empirical weighted networks. [ABSTRACT FROM AUTHOR]

Abstract: Epilepsy is a malfunction of the brain that affects over 50 million people worldwide. Epileptic seizures are usually characterized by an abnormal synchronized firing of neurons involved in the epileptic process. In human epilepsy the exact mechanisms underlying seizure generation are still uncertain as are mechanisms underlying seizure spreading and termination. There is now growing evidence that an improved understanding of the epileptic process can be achieved through the analysis of properties of epileptic brain networks and through the analysis of interactions in such networks. In this overview, we summarize recent methodological developments to assess synchronization phenomena in human epileptic brain networks and present findings obtained from analyses of brain electromagnetic signals recorded in epilepsy patients. [Copyright &y& Elsevier]

Abstract: To improve the estimation of drift and diffusion coefficients of stochastic processes in case of a limited amount of usable data due to e.g. non-stationarity of natural systems we suggest to use kernel-based instead of histogram-based regression. We propose a method for bandwidth selection and compare it to a widely used cross-validation method. Kernel-based regression reveals an enhanced ability to estimate drift and diffusion especially for a small amount of data. This allows one to improve resolvability of changes in complex dynamical systems as evidenced by an exemplary analysis of electroencephalographic data recorded from a human epileptic brain. [Copyright &y& Elsevier]

We investigate numerically the collective dynamical behavior of pulse-coupled nonleaky integrate-and-fire neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for spontaneous firing for each neuron. We study network dynamics evolving from different sets of initial conditions in dependence on coupling strength and rewiring probability. Besides a homogeneous equilibrium state for low coupling strength, we observe different local patterns including cyclic waves, spiral waves, and turbulentlike patterns, which—depending on network parameters—interfere with the global collective firing of the neurons. We attribute the various network dynamics to distinct regimes in the parameter space. For the same network parameters different network dynamics can be observed depending on the set of initial conditions only. Such a multistable behavior and the interplay between local pattern formation and global collective firing may be attributable to the spatiotemporal dynamics of biological networks. [ABSTRACT FROM AUTHOR]

This overview summarizes findings obtained from analyzing electroencephalographic (EEG) recordings from epilepsy patients with methods from the theory of nonlinear dynamical systems. The last two decades have shown that nonlinear time series analysis techniques allow an improved characterization of epileptic brain states and help to gain deeper insights into the spatial and temporal dynamics of the epileptic process. Nonlinear EEG analyses can help to improve the evaluation of patients prior to neurosurgery, and with an unequivocal identification of precursors of seizures, they can be of great value in the development of seizure warning and prevention techniques. [ABSTRACT FROM AUTHOR]

The framework of the theory of nonlinear dynamics provides powerful concepts and algorithms to study complicated dynamics such as brain electrical activity (electroencephalogram, EEG). Although different influencing factors render the use of nonlinear measures in a strict sense problematic, converging evidence from various investigations now indicates that nonlinear EEG analysis provides a means to reliably characterize different states of physiological and pathophysiological brain function. We here focus on applications of nonlinear EEG analysis in epileptology. Epilepsy affects more than 50 million individuals worldwide – approximately 1% of the world's population. The disease is characterized by a recurrent and sudden malfunction of the brain that is termed seizure. Nonlinear EEG analysis techniques allow to reliably identify the seizure generating structure (epileptic focus) in different areas of the brain even during seizure-free intervals, to disentangle complex spatio-temporal interactions between the epileptic focus and other areas of the brain, and to define a specific state predictive of an impending seizure. Nonlinear EEG analysis provides supplementary information about the epileptogenic process in humans, contributes to an improvement of the presurgical evaluation of epilepsy patients, and offers a basis for the development of new therapy concepts for seizure prevention. [ABSTRACT FROM AUTHOR]

We examine a possible utilization of the recently proposed method of signal-induced excitation waves in nonlinear excitable media as a means for the noise-tolerant detection of zero-lag phase synchronization in very noisy time series. We show that in cases, where a relatively strong noise contamination aggravates the direct application of phase-based measures of synchronization, it is nevertheless possible to detect synchronization phenomena. [ABSTRACT FROM AUTHOR]

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from nonstationary dynamical systems with poorly understood properties. Using model systems, we first study the interdependencies of parameters involved in the calculation of both measures. Having identified appropriate parameter settings we then analyze long-lasting EEG time series recorded from an epilepsy patient. Our findings indicate that γ could be of interest for studies on the predictability of epileptic seizures. [ABSTRACT FROM AUTHOR]

Summary: The First International Collaborative Workshop on Seizure Prediction was held at the Department of Epileptology, University of Bonn, in Bonn, Germany on April 24–28, 2002. Organized by the Universities of Pennsylvania and Bonn, and funded by grants from the American Epilepsy Society, the German Section of the International League against Epilepsy, and the German Section of the International Federation of Clinical Neurophysiology, the workshop was attended by 51 researchers from 16 centers in seven countries. There were four major goals for the workshop: (1) to host a one-day didactic session on the science of seizure prediction, with lectures by leaders in the field; (2) to assess the current state of the field by applying current methods used to predict seizures to a shared set of continuous intracranial EEG data and discussing the strengths and weaknesses of each approach; (3) to establish a consensus on minimal data requirements, a common nomenclature, and objective methods for comparing system performance across platforms and laboratories for seizure prediction research; and most importantly (4) to establish a multi-laboratory, international working group dedicated to understanding seizure generation and making on-line, prospective seizure prediction a reality. Following the didactic course, each participating group presented their results, after applying their seizure prediction methods to five common data sets agreed upon in advance and distributed before the meeting. What follows is a description of the shared data set used for analysis, a summary of the major discussion points from the workshop, and points of consensus among the group. The brief discussion serves as a common introduction to the research papers that follow in this issue, and the description of the shared data is referenced in each of these papers. Participants in the workshop are listed at the end of the Conclusions section, in alphabetical order. [Copyright &y& Elsevier]

Presents a wavelet-based method for single trial analysis of transient and time variant event-related potentials (ERP). Expectation of more accurate filter settings than achieved by other techniques; Establishment of better filter performance for test signals contaminated with either white noise or isospectral noise; Application of the method to limbic P300 potentials to provide an example of real application.

Brain electrical activity of 16 patients with temporal lobe epilepsy, recorded intracranially during seizure-free intervals as well as during transitions to the seizure state, was analysed using methods derived from the theory of non-linear dynamics. Long-lasting and marked changes towards low-dimensional system states were found to occur specifically up to 25 min prior to epileptic seizures and allow to predict the occurrence of individual seizures in time. These findings reflect a continuous increase in the degree of synchronicity, and thus open a window for the study of mechanisms generating seizures in humans. This offers new possibilities for therapeutic interventions. [ABSTRACT FROM AUTHOR]

Presents information on studies conducted to detect verbal novelty within the human hippocampus, while highlighting studies conducted on animals. Reference to the importance of the human hippocampal; Methodology used to conduct study.

Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems. [ABSTRACT FROM AUTHOR]

We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter—a widely used indicator for phase ordering—to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies. [ABSTRACT FROM AUTHOR]

A lot of mileage has been made recently on the long and winding road toward seizure forecasting. Here we briefly review some selected milestones passed along the way, which were discussed at the International Conference for Technology and Analysis of Seizures—ICTALS 2022—convened at the University of Bern, Switzerland. Major impetus was gained recently from wearable and implantable devices that record not only electroencephalography, but also data on motor behavior, acoustic signals, and various signals of the autonomic nervous system. This multimodal monitoring can be performed for ultralong timescales covering months or years. Accordingly, features and metrics extracted from these data now assess seizure dynamics with a greater degree of completeness. Most prominently, this has allowed the confirmation of the long‐suspected cyclical nature of interictal epileptiform activity, seizure risk, and seizures. The timescales cover daily, multi‐day, and yearly cycles. Progress has also been fueled by approaches originating from the interdisciplinary field of network science. Considering epilepsy as a large‐scale network disorder yielded novel perspectives on the pre‐ictal dynamics of the evolving epileptic brain. In addition to discrete predictions that a seizure will take place in a specified prediction horizon, the community broadened the scope to probabilistic forecasts of a seizure risk evolving continuously in time. This shift of gears triggered the incorporation of additional metrics to quantify the performance of forecasting algorithms, which should be compared to the chance performance of constrained stochastic null models. An imminent task of utmost importance is to find optimal ways to communicate the output of seizure‐forecasting algorithms to patients, caretakers, and clinicians, so that they can have socioeconomic impact and improve patients' well‐being. [ABSTRACT FROM AUTHOR]

There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures. [ABSTRACT FROM AUTHOR]

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh–Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might not be accurate enough to properly understand the complexity of its dynamics. [ABSTRACT FROM AUTHOR]

Pharmaco-electroencephalography (pharmaco-EEG) has never gained great popularity in epilepsy research. Nevertheless, the electroencephalogram (EEG) is the most important neurological examination technique in this patient population. Development and investigation of antiepileptic drugs (AEDs) involves EEG for diagnosis and outcome evaluation. In contrast to the common use of the EEG for documenting the effect of AEDs on the presence of interictal epileptiform activities or seizures, quantitative analysis of drug responses in the EEG are not yet standard in pharmacological studies. We provide an overview of dedicated pharmaco-EEG studies with AEDs in humans. A systematic search in PubMed yielded 43 articles, which were reviewed for their relevance. After excluding studies according to our exclusion criteria, nine studies remained. These studies plus the retrieved references from the bibliographies of the identified studies yielded 37 studies to be included in the review. The most prominent method in pharmaco-EEG research for AEDs was analysis of the frequency content in response to drug intake, often with quantitative methods such as spectral analysis. Despite documenting the effect of the drug on brain activity, some studies were conducted in order to document treatment response, detect neurotoxic effects, and measure reversibility of AED-induced changes. There were some attempts to predict treatment response or side effects. We suggest that pharmaco-EEG deserves more attention in AED research, specifically because the newest drugs and techniques have not yet been subject to investigation. [ABSTRACT FROM AUTHOR]

Inferring strength and direction of interactions from electroencephalographic (EEG) recordings is of crucial importance to improve our understanding of dynamical interdependencies underlying various physiological and pathophysiological conditions in the human epileptic brain. We here use approaches from symbolic analysis to investigate--in a time-resolved manner--weighted and directed, short- to long-ranged interactions between various brain regions constituting the epileptic network. Our observations point to complex spatial-temporal interdependencies underlying the epileptic process and their role in the generation of epileptic seizures, despite the massive reduction of the complex information content of multi-day, multi-channel EEG recordings through symbolization. We discuss limitations and potential future improvements of this approach. [ABSTRACT FROM AUTHOR]

We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we demonstrate the applicability and limitations of our approach. Our findings obtained from applying our method to infer delayed directed interactions in the human epileptic brain underline the importance of our approach for improving the construction of functional network structures from data. [ABSTRACT FROM AUTHOR]

We investigate assortativity of functional brain networks before, during, and after one-hundred epileptic seizures with different anatomical onset locations. We construct binary functional networks from multi-channel electroencephalographic data recorded from 60 epilepsy patients; and from time-resolved estimates of the assortativity coefficient, we conclude that positive degree-degree correlations are inherent to seizure dynamics. While seizures evolve, an increasing assortativity indicates a segregation of the underlying functional network into groups of brain regions that are only sparsely interconnected, if at all. Interestingly, assortativity decreases already prior to seizure end. Together with previous observations of characteristic temporal evolutions of global statistical properties and synchronizability of epileptic brain networks, our findings may help to gain deeper insights into the complicated dynamics underlying generation, propagation, and termination of seizures. [ABSTRACT FROM AUTHOR]

We study scale-free networks of FitzHugh-Nagumo units whose collective dynamics exhibits rare and recurrent events of high amplitude (extreme events). We investigate which units play a crucial role in the generation of these events. Unexpectedly, we observe that extreme events originate from low-degree units, while high-degree units (hubs) appear to be crucial for the event to engulf the whole network. [ABSTRACT FROM AUTHOR]

Recent advances in neurophysiological brain network analysis have demonstrated novel potential for diagnosis and prognosis of disorders of consciousness. While most progress has been achieved on the population-sample level, time-economic and easy-to-apply personalized solutions are missing. This prospective controlled study combined EEG recordings, basal stimulation, and daily behavioral assessment as applied routinely during complex early rehabilitation treatment. We investigated global characteristics of EEG-derived evolving functional brain networks during the repeated (3–6 weeks apart) evaluation of brain dynamics at rest as well as during and after multisensory stimulation in ten patients who were diagnosed with an unresponsive wakefulness syndrome (UWS). The age-corrected average clustering coefficient C* allowed to discriminate between individual patients at first (three patients) and second assessment (all patients). Clinically, only two patients changed from UWS to minimally conscious state. Of note, most patients presented with significant changes of C* due to stimulations, along with treatment, and with an increasing temporal distance to injury. These changes tended towards the levels of nine healthy controls. Our approach allowed to monitor both, short-term effects of individual therapy sessions and possibly long-term recovery. Future studies will need to assess its full potential for disease monitoring and control of individualized treatment decisions. [ABSTRACT FROM AUTHOR]

Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive treatment option for different diseases and symptoms, such as epilepsy or depression. Its mechanism of action, however, is still not fully understood. We investigated short-term taVNS-induced changes of local and global properties of EEG-derived, evolving functional brain networks from eighteen subjects who underwent two 1 h stimulation phases (morning and afternoon) during continuous EEG-recording. In the majority of subjects, taVNS induced measurable modifications of network properties. Network alterations induced by stimulation in the afternoon were clearly more pronounced than those induced by stimulation in the morning. Alterations mostly affected the networks' topology and stability properties. On the local network scale, no clear-cut spatial stimulation-related patterns could be discerned. Our findings indicate that the possible impact of diurnal influences on taVNS-induced network modifications would need to be considered for future research and clinical studies of this non-pharmaceutical intervention approach. [ABSTRACT FROM AUTHOR]

We investigate the relative merit of phase-based methods--mean phase coherence, unweighted and weighted phase lag index--for estimating the strength of interactions between dynamical systems from empirical time series which are affected by common sources and noise. By numerically analyzing the interaction dynamics of coupled model systems, we compare these methods to each other with respect to their ability to distinguish between different levels of coupling for various simulated experimental situations. We complement our numerical studies by investigating consistency and temporal variations of the strength of interactions within and between brain regions using intracranial electroencephalographic recordings from an epilepsy patient. Our findings indicate that the unweighted and weighted phase lag index are less prone to the influence of common sources but that this advantage may lead to constrictions limiting the applicability of these methods. [ABSTRACT FROM AUTHOR]

Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately. [ABSTRACT FROM AUTHOR]

We study deterministic systems, composed of excitable units of FitzHugh-Nagumo type, that are capable of self-generating and self-terminating strong deviations from their regular dynamics without the influence of noise or parameter change. These deviations are rare, short-lasting, and recurrent and can therefore be regarded as extreme events. Employing a range of methods we analyze dynamical properties of the systems, identifying features in the systems' dynamics that may qualify as precursors to extreme events. We investigate these features and elucidate mechanisms that may be responsible for the generation of the extreme events. [ABSTRACT FROM AUTHOR]

We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures - known for their complex spatial and temporal dynamics - we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis. [ABSTRACT FROM AUTHOR]

We investigate the influence of various pathophysiologic and physiologic processes on global statistical properties of epileptic brain networks. We construct binary functional networks from long-term, multichannel electroencephalographic data recorded from 13 epilepsy patients, and the average shortest path length and the clustering coefficient serve as global statistical network characteristics. For time-resolved estimates of these characteristics we observe large fluctuations over time, however, with some periodic temporal structure. These fluctuations can-to a large extent-be attributed to daily rhythms while relevant aspects of the epileptic process contribute only marginally. Particularly, we could not observe clear cut changes in network states that can be regarded as predictive of an impending seizure. Our findings are of particular relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches. [ABSTRACT FROM AUTHOR]

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization. [ABSTRACT FROM AUTHOR]

Summary: Purpose: To assess whether EEG synchronization changes during short-term low-frequency electrical stimulation of the seizure onset zone. Methods: In 10 patients (34±11 years) with pharmaco-resistant epilepsy the seizure onset zone (9 temporal lobe, 1 frontal lobe) was electrically stimulated at 1Hz for 5min via intracranial electrodes. Bipolar stimuli were applied and four pulse widths (0.05, 0.1, 0.5, and 1.0ms) were tested. Stimulation amplitudes were held fixed at 1mA for strip electrodes and at 2mA for depth electrodes. Changes of EEG synchronization were assessed by the eigenvalue dynamics of the cross-correlation matrix computed from a 2.5s sliding window. Results: 37 stimulations were performed. We observed EEG desynchronization in 49% (18/37), an increase of EEG synchronization in 27% (10/37) and an EEG pattern with no significant change of synchronization in 24% (9/37). EEG synchronization most frequently occurred when stimulating with a pulse width of 0.5ms. In a patient with bilateral independent seizure onsets stimulation effects on EEG synchronization were different for each side. In the patient with the shortest duration of temporal lobe epilepsy, stimulation triggered periodic epileptic spikes phase-locked to stimulation. One patient experienced an aura during stimulation, which did not evolve into a seizure, and in one patient a sub-clincial seizure occurred. Discussion: Low-frequency stimulation of the seizure onset zone is associated with different changes of EEG synchronization and its effects depend on the widths of the stimulation pulses. It may be an appropriate stimulation technique for long-term studies assessing whether synchronized or desynchronized brain dynamics prevent seizure occurrence. [Copyright &y& Elsevier]

Abstract: Objective: To test whether increasing synchronization of neuronal activity might be causally related to seizure termination. Methods: Neuronal synchronization was assessed by the relative changes of the eigenvalue spectrum of the equal-time correlation matrix computed from a short window sliding along multi-channel EEGs, recorded with either intracranial or surface electrodes. Results: Synchronization dynamics of six status epilepticus EEG recordings from six patients were assessed. In all six recordings EEG synchronization fluctuated around relatively low levels during ongoing epileptiform activity. Synchronization only persistently increased before, or in one case, at the end of status epilepticus. Ongoing seizure activity stopped without pharmacological intervention in one patient. In four of the five other cases, the persistent increase of synchronization followed administration of anticonvulsant drugs. Conclusions: Our findings support the hypothesis that increasing synchronization of neuronal activity may be considered as an emergent self-regulatory mechanism for seizure termination. Significance: The traditional concept is challenged that increasing neuronal synchronization during epileptic seizures is always pathological and should be suppressed. On the contrary, our findings imply that therapeutic interventions to increase synchronization during seizures might be beneficial. [Copyright &y& Elsevier]

In clinical practice, epileptic seizures with focal onset and subsequent generalised motor involvement are referred to as secondarily generalised seizures. The purpose of this study was to investigate the degree of electrophysiological generalisation in seizures that are clinically secondarily generalised. Intracranial EEG recordings of secondarily generalised tonic-clonic seizures were visually and quantitatively analysed for the presence of epileptiform activity. In 24 (26%) of 93 seizures recorded from 17 (27%) of 64 patients, intracranial EEG channels were found that never recorded epileptiform activity during secondarily generalised tonic-clonic seizures. Our results demonstrate that seizures that are secondarily generalised clinically are not always generalised electrophysiologically. This may have therapeutic implications. [ABSTRACT FROM AUTHOR]

In humans, distinct processes within the hippocampus and rhinal cortex support declarative memory formation. But do these medial temporal lobe (MTL) substructures directly cooperate in encoding new memories? Phase synchronization of gamma-band electroencephalogram (EEG) oscillations (around 40 Hz) is a general mechanism of transiently connecting neural assemblies. We recorded depth-EEG from within the MTL of epilepsy patients performing a memorization task. Successful as opposed to unsuccessful memory formation was accompanied by an initial elevation of rhinal?hippocampal gamma synchronization followed by a later desynchronization, suggesting that effective declarative memory formation is accompanied by a direct and temporarily limited cooperation between both MTL substructures. [ABSTRACT FROM AUTHOR]

With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. We arrive at a closed-form solution expressed through conditional moments, which can be extracted directly from time-series data with a finite sampling intervals. We provide all finite-time correction terms for parametric and non-parametric estimation of the Kramers–Moyal coefficients for discontinuous processes which can be easily implemented—employing Bell polynomials—in time-series analyses of stochastic processes. With exemplary cases of insufficiently sampled diffusion and jump-diffusion processes, we demonstrate the advantages of our arbitrary-order finite-time corrections and their impact in distinguishing diffusion and jump-diffusion processes strictly from time-series data. [ABSTRACT FROM AUTHOR]