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Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks. We acknowledge funding from the Volkswagen foundation, the Spanish Ministry of Economy and Competitiveness, Grant No. FIS2014-54177-R, the CERCA Programme of the Generalitat de Catalunya (R.G.A. and G.R.), and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642563 (R.G.A. and I.M.).

International audience; In patients diagnosed with pharmaco-resistant epilepsy, cerebral areas responsible for seizure generation can be defined by performing implantation of intracranial electrodes. The identification of the epileptogenic zone (EZ) is based on visual inspection of the intracranial electroencephalogram (IEEG) performed by highly qualified neurophysiologists. New computer-based quantitative EEG analyses have been developed in collaboration with the signal analysis community to expedite EZ detection. The aim of the present report is to compare different signal analysis approaches developed in four different European laboratories working in close collaboration with four European Epilepsy Centers. Computer-based signal analysis methods were retrospectively applied to IEEG recordings performed in four patients undergoing pre-surgical exploration of pharmaco-resistant epilepsy. The four methods elaborated by the different teams to identify the EZ are based either on frequency analysis, on nonlinear signal analysis, on connectivity measures or on statistical parametric mapping of epileptogenicity indices. All methods converge on the identification of EZ in patients that present with fast activity at seizure onset. When traditional visual inspection was not successful in detecting EZ on IEEG, the different signal analysis methods produced highly discordant results. Quantitative analysis of IEEG recordings complement clinical evaluation by contributing to the study of epileptogenic networks during seizures. We demonstrate that the degree of sensitivity of different computer-based methods to detect the EZ in respect to visual EEG inspection depends on the specific seizure pattern

Time scale parametric spike train distances like the Victor and the van Rossum distances/nare often applied to study the neural code based on neural stimuli discrimination./nDifferent neural coding hypotheses, such as rate or coincidence coding,/ncan be assessed by combining a time scale parametric spike train distance with a/nclassifier in order to obtain the optimal discrimination performance. The time scale/nfor which the responses to different stimuli are distinguished best is assumed to be/nthe discriminative precision of the neural code. The relevance of temporal coding/nis evaluated by comparing the optimal discrimination performance with the one/nachieved when assuming a rate code./nWe here characterize the measures quantifying the discrimination performance,/nthe discriminative precision, and the relevance of temporal coding. Furthermore,/nwe evaluate the information these quantities provide about the neural code. We/nshow that the discriminative precision is too unspecific to be interpreted in terms/nof the time scales relevant for encoding. Accordingly, the time scale parametric/nnature of the distances is mainly an advantage because it allows maximizing the/ndiscrimination performance across a whole set of measures with different sensitivities/ndetermined by the time scale parameter, but not due to the possibility to/nexamine the temporal properties of the neural code. DC is supported by the grant 2010FI-B2 00079 of the ”Comissionat per a Universitats/ni Recerca del Departament d’Innovació, Universitats i Empresa de la Generalitat/nde Catalunya i del Fons Social Europeu” and grant 2008BE1 00166 of the ”Comissionat per a Universitats i Recerca del Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya”. RGA acknowledges grant BFU2007-61710 of the Spanish Ministry of Education and Science.

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena.A recent and not yet fully understood example is the collapse of coexisting synchronous and synchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications. The authors are grateful to Ernest Montbrió and Arkady Pikovsky for useful discussion. R.G.A. and F.M. acknowledge funding from the Volkswagen foundation. R.G.A was supported by the Spanish Ministry of Economy and Competitiveness (Grant FIS2014-54177-R). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642563 (R.G.A.). F.M. acknowledges support from the German Research Council (DFG, MO 930/4-1 and SFB 1089) and the European Commission (FP7 602102 EPITARGET). K.S. and C.R. are grateful for support by the Swiss National Science Foundation (Projects No. SNF 320030_122010, No. 33CM30-140332, No. 32003B_155950).

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals). R.G.A. acknowledges Grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science and funding from the Volkswagen Foundation. K.S. and C.R. are grateful for support by the Swiss National Science Foundation (Projects No. SNF 320030-122010 and No. 33CM30-124089).

The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure ξ , designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, ξ was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection (“focal signals”) and one set of signals recorded from brain areas that were not involved at seizure onset (“nonfocal signals”). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain. R.G.A. acknowledges grant FIS-2010-18204 of the Spanish Ministry of Education and Science. K.S. and C.R. are grateful for support by the Swiss National Science Foundation (projects nos. SNF 320030-122010 and 33CM30- 124089).

Determining how distinct neurons or brain regions are connected and communicate with each other is a crucial point in neuroscience, as it allows to investigate how the functional integration of specialized neural populations enables the emergence of coherent cognitive and behavioral states. The general concept of brain connectivity encompasses different aspects: structural connectivity is related to the description of anatomical pathways and synaptic connections; functional connectivity investigates statistical dependencies between spatially separated brain regions; effective connectivity refers to models aimed at elucidating driver-response relationships. The study of these different modes of brain connectivity is fundamental both for the investigation of the neurophysiological processes engaged in cognitive and perceptive processing and for the assessment of a variety of neurological disorders. Over the last past few decades, the continuous advancement of multichannel data acquisition technologies has made it possible to collect neuroscience data at multiple levels of description, ranging from neural spikes to local field potentials and electroencephalography (EEG)-magnetoencephalography (MEG). This increasing data availability and the contemporaneous improvement of signal processing capabilities have contributed in placing increasing demands on methods for the quantitative assessment of neural interactions. Accordingly, a variety of methodological approaches have emerged for the estimation of brain connectivity from multivariate neurophysiological time series. These approaches build on different analysis frameworks which point out specific aspects of connectivity: linear parametric models are explicitly related to the frequency domain representation of multivariate data, thus favoring the assessment of connectivity for specific brain rhythms; information theory provides tools that describe both linear and nonlinear interactions and are free from the shortcomings of model specification; phase synchronization analysis characterizes the relation between the phases of different brain units seen as coupled oscillators, allowing detection of synchronization regardless of the relation between signal amplitudes. All these frameworks provide measures able to reflect the various aspects of brain connectivity, such as undirected measures of association (e.g., coherence, mutual information, phase synchronization index) and directed measures of Granger causality (e.g., partial directed coherence, transfer entropy). To get new and deeper insights into the complex dynamics of interacting brain regions, the existing brain connectivity measures need to be refined, extended, and complemented with other tools. Common issues to be addressed are estimation problems arising in the presence of noise contamination and nonstationarity, significance assessment, distinguishing direct from indirect causal effects, and aspects related to the difficulty of performing full multivariate analyses over short data sets. An important problem of EEG/MEG recordings is that the connectivity patterns estimated at the sensor level may strongly differ from those really existing between the underlying neural sources, as a consequence of a mixing effect known as volume conduction. While a common approach to deal with this issue is to estimate connectivity after application of an inverse method for source localization, methodological advances are needed to improve the localization accuracy of ill-posed inverse problems. Moreover, once brain connectivity measures are computed, the formal representation of connectivity patterns in graph or matrix format leads to employ concepts of network analysis to interpret these patterns. Accordingly, the study of topological properties like clustering degree, modularity, and presence of network motifs is becoming increasingly popular for the investigation of the organizational principles of brain processes. The papers of this special issue reflect the variety in the approaches for the estimation of brain connectivity described above, as well as the need to improve and adapt these approaches to the more and more demanding qualitative requirements and challenges of modern neurophysiological applications. J. Sun et al. offer a review of phase synchronization analysis methods for the inference of functional brain connectivity, describing definitions, estimation, and significance assessment, presenting some extensions, and discussing the issues that affect the detection of phase synchronization from neural data. C. Alvarado-Rojas and M. Le Van Quyen exploit phase synchronization analysis and clustering techniques to identify, from intracranial EEG recordings acquired in epileptic patients during seizure-free periods, dynamic modes of brain synchrony which are characteristic for the wake-sleep cycle. L. Faes et al. introduce a common framework for the unified description of the most popular frequency domain connectivity measures based on linear parametric modeling of multiple time series, discussing their relations, theoretical interpretation, advantages and limitations, and practical estimation. A. Brovelli assesses the reliability of frequency domain Granger causality analysis performed on a single-trial basis, showing that, when combined with parametric statistical tests, Granger causality spectra successfully recover causal interactions in both synthetic and neurophysiological data. Y. Liu and S. Aviyente illustrate the advantages over linear parametric Granger causality of an information theoretic tool, the directed information, as regards the assessment of directional connectivity in both simulated time series and EEG data. D. Marinazzo et al. face the important problem of estimating causality in complex brain networks through fully multivariate approaches; working in the frame of information theory, they provide a novel approach for partial conditioning to a subset of informative variables, showing that this approach can help to overcome computational and numerical problems otherwise arising with traditional full conditioning schemes. P. Belardinelli et al. investigate in a realistic MEG environment the known localization bias due to correlation between source time series occurring for the popular beamformer inverse method, showing that this bias is relevant only for extremely high degrees of source correlation. F. Avarvand et al. combine subspace and beamformer source localization methods with estimation of the imaginary part of the coherence in simulated and real EEG data, implementing an approach that is sensitive to connectivity rather than to activity and, as such, improves localization accuracy and detection of source interactions. C. Micheli and C. Braun deal with the problem of characterizing connectivity between neural source activity and muscular activity after the localization of multiple correlated sources; when applied to MEG and electromyographic signals during a pinch grip task, their approach highlights patterns of corticomuscular coherence otherwise not obtainable with the use of standard methods. C. Schmidt et al. propose a new analytical approach to the detection of topological motifs in EEG connectivity networks estimated in patients with major depression during painful stimulation, suggesting that specific motifs may help explaining the relationship between pain and depression. A. Alvarellos-Gonzalez et al. study structural brain connectivity at the synaptic level, presenting enhanced computational models of neural networks which evidence the potentiation of synaptic connectivity that takes place in the brain when glial cells are considered in addition to artificial neurons. Luca Faes Ralph G. Andrzejak Mingzhou Ding Dimitris Kugiumtzis

Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for event-like firing patterns. Here we present a substantial improvement of this measure which eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real-time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings., Comment: 16 pages, 10 figures, 35 references; 1 supplementary figure, 1 supplementary movie (see author's webpage http://www.fi.isc.cnr.it/users/thomas.kreuz/sourcecode.html)

Comunicació presentada a ACM Multimedia, International Workshop on Machine Learning and Music (MML), celebrat del 25 al 29 d'octubre de 2010 a Florència, Itàlia. Current systems for cover song detection are based on a model-free approach: they basically search for similarities in descriptor time series reflecting the evolution of tonal information in a musical piece. In this contribution we propose the use of a model-based approach. In particular, we explore threshold autoregressive models and the concept of cross-prediction error, i.e. a measure of to which extent a model trained on one song's descriptor time series is able to predict the covers'. Results indicate that the considered approach can provide competitive accuracies while being considerably fast and with potentially less storage requirements. Furthermore, the approach is parameter-free from the user's perspective, what provides a robust and straightforward application of it. We thank Emilia G´omez for her review on a previous version of this article. J.S. has been partially funded by the A/09/96235 grant from the Deutscher Akademisch Austausch Dienst and by the Music 3.0 (TSI-070100- 2008-318) and Buscamedia (CEN-20091026) projects. R.G.A. has been funded by the BFU2007-61710 grant of the Spanish Ministry of Education and Science.

Since the introduction of a family of cost-based distancesbetween spike trains by Victor and Purpura [1,2], spiketrain distances are widely used to study the precision ofthe temporal coding of neurons (see [3] for a review).Subsequently, other distances that act on convolutedspike trains have been proposed [4,5]. All of these dis-tances involve the choice of a parameter determining thetime scale at which the spike trains are compared. In gen-eral, the extent of the stimulus-specific clustering manifestin the distances between spike trains of a neuron firing inresponse to a set of trials of different stimuli is used toquantify the mutual information between the stimuli andthe spike trains in dependence of the respective parame-ter. The time scale for which the maximum mutual infor-mation is obtained serves as an indicator about theprecision of the temporal coding.Here we discuss limitations of the use of spike train dis-tances as well as principal shortcomings of the mutualinformation maximization procedure for the study ofneural coding. The implementation of this whole proce-dure relies on some initial implicit assumptions about theactual neural code: the single neuron is assumed as thecoding unit, the stimuli are conjectured to be the onesencoded by this neuron and the existence of an optimumtemporal precision is taken for granted. However, sincethe calculation of the spike train distances and the maxi-mization of mutual information are always possible andwill always provide an optimal time scale even if theseassumptions are incompatible with the actual code, naiveapplications can lead to wrong conclusions.To demonstrate the dangers of such implicit assumptions,we simulate examples in which the relation between stim-uli and spike trains is known and study the performanceof the techniques recovering the actual coding when theassumptions above are not justifiable. In particular, weconsider the non-existence of a unique time scale simulat-ing spike trains with bimodal or non-stationary firingrates. For this case we also compare the use of the timescale parametric distances with a scale adaptive distance[6]. Furthermore we show that misinterpretations can becaused by concluding a precision for a temporal codefrom neurons which in fact participate in a populationcoding. We also show that false conclusions can be drawndue to an incorrect identification of the stimulus relevantfor the neural code.

With the increasing availability of multi-unit recordingsthe focus of attention starts to shift from bivariate meth-ods towards methods that provide the possibility to studypatterns of activity across many neurons. Measures ofmulti-neuron spike train synchrony are becoming indis-pensable tools for addressing issues such as network syn-chronization, spike timing reliability and neuronalcoding. However, many multi-neuron synchrony meas-ures are extensions of bivariate measures. Two of the mostprominent bivariate approaches are the spike train metricsby Victor-Purpura and van Rossum [1,2]. The former eval-uates the cost needed to transform one spike train into theother using only certain elementary steps [1], while thelatter measures the Euclidean distance between the twospike trains after convolution of the spikes with an expo-nential function [2]. Both methods involve one parameterthat sets the time scale. In contrast, a more recent bivariateapproach, the ISI-distance [3], is time scale independentand self-adaptive. Another essential difference is that theISI-distance relies on the relative length of interspike inter-vals (ISI) and not on the timing of spikes. Finally, thismethod also allows the visualization of the relative firingpattern in a time-resolved manner.Recently, the Victor-Purpura and the van Rossum dis-tances have been extended to quantify dissimilaritiesbetween multi-unit responses [4,5]. To calculate themulti-unit Victor-Purpura metric, simultaneous spikes arelabeled by the neuron that fired them, but this label canbe changed at an additional cost which is determined bya second parameter. By varying this population parameterthe metric is shifted from a "labeled line" (LL) code metricin which the distance is defined as the sum of the dis-tances of the single neurons, to a "summed population"(SP) code metric in which the spike trains are superim-posed before the distance is calculated [4]. In the extendedvan Rossum metric, the spike trains of each populationare located in a space of vector fields (with a different unitvector assigned to each neuron). In this case interpolationbetween the LL and the SP coding is achieved by varyingthe angle (a second parameter) between unit vectors [5].Here we present an analogous extension for the ISI-dis-tance [6] that also interpolates between the LL and the SPcodes. This multi-neuron ISI-distance inherits all the basicproperties of the bivariate ISI-distance described above; inparticular, it is also time scale independent and thus, incontrast to the other two multi-neuron metrics, dependson one population parameter only. In this study we com-pare all three multi-neuron distances using both control-led simulations and real data. We stress the advantages ofour extension with respect to visualization, computa-tional cost and applicability to larger numbers of spiketrains with higher numbers of spikes.

To detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced. These measures can, however, be biased by asymmetries in the dynamics' structure, noise color, or noise level, which are ubiquitous in experimental signals. Using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization. We furthermore diminish the remaining biases by introducing a measure based on ranks of distances. This rank-based measure outperforms existing distance-based measures concerning both sensitivity and specificity for directional couplings. Therefore, our findings are relevant for a reliable detection of directional couplings from experimental signals. DC was supported by the grant 2008FI-B 00460 of the 'Generalitat de Catalunya' and European Social Funds./nRGA acknowledges grant BFU2007-61710 of the Spanish Ministry of Education and Science.

Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages over bivariate measures. One of the most recent bivariate approaches, the ISI-distance, employs the ratio of instantaneous interspike intervals. In this study we propose two extensions of the ISI-distance, the straightforward averaged bivariate ISI-distance and the multivariate ISI-diversity based on the coefficient of variation. Like the original measure these extensions combine many properties desirable in applications to real data. In particular, they are parameter free, time scale independent, and easy to visualize in a time-resolved manner, as we illustrate with in vitro recordings from a cortical neuron. Using a simulated network of Hindemarsh-Rose neurons as a controlled configuration we compare the performance of our methods in distinguishing different levels of multi-neuron spike train synchrony to the performance of six other previously published measures. We show and explain why the averaged bivariate measures perform better than the multivariate ones and why the multivariate ISI-diversity is the best performer among the multivariate methods. Finally, in a comparison against standard methods that rely on moving window estimates, we use single-unit monkey data to demonstrate the advantages of the instantaneous nature of our methods., Comment: 15 pages, 17 figures, 30 references Changes: Abstract corrected, one Figure and one Section in Appendix added, plus some minor corrections (Final Version)

We introduce a new technique designed to quantify directional couplings between nonlinear dynamics and we evaluate its application to the study of neuronal data. Similar to existing approaches [1,2] (and references therein) this technique quantifies the degree to which similar states of the one dynamics are mapped to similar states of the other dynamics based on reconstructed state-spaces. It differs from these existing techniques in that it uses rank statistics instead of distance statistics.

Measuring the degree of synchrony between two or more neuronal spike trains is an important tool in order to address issues such as neuronal coding, information transmission and model validation. Another prominent application is to measure the reliability of the response of individual neurons upon repeated presentations of the same stimulus. A number of both multivariate and bivariate measures have been proposed to address this issue. Multivariate approaches include the reliability measures by Hunter and Milton [1] and by Tiesinga [2], while bivariate approaches comprise the Victor-Purpura [3] and the van Rossum [4] distance, as well as the similarity measure proposed by Schreiber et al. [5], and, the most recent proposal, the ISI-distance [6], a method based on relative instantaneous firing rates. These approaches can be applied to multivariate data in a pairwise fashion, e.g., reliability can be defined as the average over all pairwise similarities. ... ...

An advanced characterization of the complicated dynamical system brain is one of science's biggest challenges. Nonlinear time series analysis allows characterizing nonlinear dynamical systems in which low-dimensional nonlinearity gives rise to complex and irregular behavior. While several studies indicate that nonlinear methods can extract valuable information from neuronal dynamics, others doubt their necessity and conjecture that the same information can be obtained using classical linear techniques. To address this issue, we compared these two concepts, but included furthermore a combination of nonlinear measures with surrogates, an approach that has been designed to specifically focus on nonlinearity. As a benchmark we used the discriminative power to detect the seizure-generating hemisphere in medically intractable mesial temporal lobe epilepsy. We analyzed intracranial electroencephalographic recordings from the seizure-free interval of 29 patients. While the performance of both linear and nonlinear measures was weak, if not insignificant, a very high performance was obtained by the use of surrogate-corrected measures. Focusing on nonlinearity by using a combination of nonlinear measures with surrogates appears as the key to a successful characterization of the spatial distribution of the epileptic process.

In a growing number of publications it is claimed that epileptic seizures can be predicted by analyzing the electroencephalogram (EEG) with different characterizing measures. However, many of these studies suffer from a severe lack of statistical validation. Only rarely are results passed to a statistical test and verified against some null hypothesis H 0 in order to quantify their significance. In this paper we propose a method to statistically validate the performance of measures used to predict epileptic seizures. From measure profiles rendered by applying a moving-window technique to the electroencephalogram we first generate an ensemble of surrogates by a constrained randomization using simulated annealing. Subsequently the seizure prediction algorithm is applied to the original measure profile and to the surrogates. If detectable changes before seizure onset exist, highest performance values should be obtained for the original measure profiles and the null hypothesis. “The measure is not suited for seizure prediction” can be rejected. We demonstrate our method by applying two measures of synchronization to a quasicontinuous EEG recording and by evaluating their predictive performance using a straightforward seizure prediction statistics. We would like to stress that the proposed method is rather universal and can be applied to many other prediction and detection problems. This work was supported by the Deutsche Forschungsgemeinschaft (Grant No. SFB TR3).

We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects $X, Y,$ and $Z$ is equal to the sum of the MI between $X$ and $Y$, plus the MI between $Z$ and the combined object $(XY)$. We use this both in the Shannon (probabilistic) version of information theory and in the Kolmogorov (algorithmic) version. We apply our method to the construction of phylogenetic trees from mitochondrial DNA sequences and to the output of independent components analysis (ICA) as illustrated with the ECG of a pregnant woman., 4 pages, 4 figures

In this overview we present our work investigating the spatio-temporal dynamics of the epileptogenic process using time series analysis techniques derived from the theory of nonlinear dynamics. Apart from a localization of epileptic foci in different anatomical locations during the seizure-free interval we discuss possibilities for seizure prediction, a field that represents one of the greatest challenges in epileptology. The unequivocal definition of a pre-seizure state of a sufficient length would enable investigation of basic mechanisms leading to seizure initiation in humans and provide a basis for the development of adequate seizure prevention strategies.

Attempting to increase insight into the spatio-temporal dynamics of the epileptogenic process to address one of the greatest challenges in epileptology. In the field of EEG analysis the search for the hidden information predictive of an impending seizure has a long history. The nonlinear EEG analysis techniques we have used in principle allow one to define a pre-ictal state and to characterize different temporal and spatial aspects of this state. The results obtained so far emphasize the high value of nonlinear EEG analysis techniques for the detection of a long-lasting pre-ictal state. Once given a sufficient sensitivity and specificity of seizure prediction techniques, more extensive clinical studies on a larger population of patients, either at home or in a clinical setting, can be envisaged.

The question whether information extracted from the electroencephalogram ~EEG! of epilepsy patients can be used for the prediction of seizures has recently attracted much attention. Several studies have reported evidence for the existence of a preseizure state that can be detected using different measures derived from the theory of dynamical systems. Most of these studies, however, have neglected to sufficiently investigate the specificity of the observed effects or suffer from other methodological shortcomings. In this paper we present an automated technique for the detection of a preseizure state from EEG recordings using two different measures for synchronization between recording sites, namely, the mean phase coherence as a measure for phase synchronization and the maximum linear cross correlation as a measure for lag synchronization. Based on the observation of characteristic drops in synchronization prior to seizure onset, we used this phenomenon for the characterization of a preseizure state and its distinction from the remaining seizure-free interval. After optimizing our technique on a group of 10 patients with temporal lobe epilepsy we obtained a successful detection of a preseizure state prior to 12 out of 14 analyzed seizures for both measures at a very high specificity as tested on recordings from the seizure-free interval. After checking for in-sample overtraining via cross validation, we applied a surrogate test to validate the observed predictability. Based on our results, we discuss the differences of the two synchronization measures in terms of the dynamics underlying seizure generation in focal epilepsies. This work was supported by the Deutsche Forschungsgemeinschaft.