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Data de publicació electrònica: 18 de febrer de 2023 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. Epilepsy Foundation, Epilepsy Innovation Institute My Seizure Gauge; Medical Research Council Centre for Neurodevelopmental Disorders, Grant/ Award Number: Ref MR/N026063/1; National Health and Medical Research Council, Grant/Award Number: GNT1160815 and GNT1183119; National Institutes of Health, Grant/ Award Number: NIH NS094399 and NIH NS109062; Spanish Ministry of Science and Innovation and the State Research Agency, Grant/Award Number: PID2020-118196GBI00/ MICIN/AEI/10.13039/50110001103; Swebilius Foundation.; University of Bern, the Inselspital, University Hospital Bern, the Alliance for Epilepsy Research, the Swiss National Science Foundation, UCB, FHC, the Wyss Center for bio- and neuro-engineering, the American Epilepsy Society (AES), the CURE epilepsy Foundation, Ripple neuro, Sintetica, DIXI medical, UNEEG medical and NeuroPace.

IMPORTANCE Focal epilepsy is characterized by the cyclical recurrence of seizures, but, to our knowledge, the prevalence and patterns of seizure cycles are unknown. OBJECTIVE To establish the prevalence, strength, and temporal patterns of seizure cycles over timescales of hours to years. DESIGN, SETTING, AND PARTICIPANTS This retrospective cohort study analyzed data from continuous intracranial electroencephalography (cEEG) and seizure diaries collected between January 19, 2004, and May 18, 2018, with durations up to 10 years. A total of 222 adults with medically refractory focal epilepsy were selected from 256 total participants in a clinical trial of an implanted responsive neurostimulation device. Selection was based on availability of cEEG and/or self-reports of disabling seizures. EXPOSURES Antiseizure medications and responsive neurostimulation, based on clinical indications. MAIN OUTCOMES AND MEASURES Measures involved (1) self-reported daily seizure counts, (2) cEEG-based hourly counts of electrographic seizures, and (3) detections of interictal epileptiform activity (IEA), which fluctuates in daily (circadian) and multiday (multidien) cycles. Outcomes involved descriptive characteristics of cycles of IEA and seizures: (1) prevalence, defined as the percentage of patients with a given type of seizure cycle; (2) strength, defined as the degree of consistency with which seizures occur at certain phases of an underlying cycle, measured as the phase-locking value (PLV); and (3) seizure chronotypes, defined as patterns in seizure timing evident at the group level. RESULTS Of the 222 participants, 112 (50%) were male, and the median age was 35 years (range, 18-66 years). The prevalence of circannual (approximately 1 year) seizure cycles was 12%(24 of 194), the prevalence of multidien (approximately weekly to approximately monthly) seizure cycles was 60%(112 of 186), and the prevalence of circadian (approximately 24 hours) seizure cycles was 89%(76 of 85). Strengths of circadian (mean [SD] PLV, 0.34 [0.18]) and multidien (mean [SD] PLV, 0.34 [0.17]) seizure cycles were comparable, whereas circannual seizure cycles were weaker (mean [SD] PLV, 0.17 [0.10]). Across individuals, circadian seizure cycles showed 5 peaks: morning, mid-afternoon, evening, early night, and late night. Multidien cycles of IEA showed peak periodicities centered around 7, 15, 20, and 30 days. Independent of multidien period length, self-reported and electrographic seizures consistently occurred during the days-long rising phase of multidien cycles of IEA. CONCLUSIONS AND RELEVANCE Findings in this large cohort establish the high prevalence of plural seizure cycles and help explain the natural variability in seizure timing. The results have the potential to inform the scheduling of diagnostic studies, the delivery of time-varying therapies, and the design of clinical trials in epilepsy. Dr Leguia is supported through a grant for a postdoctoral fellowship from theWyss Center for Bio and Neuroengineering. Dr Rao is supported by the Ernest Gallo Foundation Distinguished Professorship in Neurology at the University of California, San Francisco. Dr Baud is supported by an Ambizione grant (PZ00P3_179929) from the Swiss National Science Foundation and by a grant from the Velux Stiftung (1232).

Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously, and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbors. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni- and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single-layer to multilayer networks. This project was supported by the Spanish Ministry of Economy and Competitiveness, Grant No. FIS2014- 54177-R (G.R. and R.G.A.). We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 910, Projektnummer 163436311 (I.O., G.R., J.S., E.S. and A.Z.).

The application of non-linear signal analysis techniques to biomedical data is key to improve our knowledge about complex physiological and pathological processes. In particular, the use of non-linear techniques to study electroencephalographic (EEG) recordings can provide an advanced characterization of brain dynamics. In epilepsy these dynamics are altered at different spatial scales of neuronal organization. We therefore apply non-linear signal analysis to EEG recordings from epilepsy patients derived with intracranial hybrid electrodes, which are composed of classical macro contacts and micro wires. Thereby, these electrodes record EEG at two different spatial scales. Our aim is to test the degree to which the analysis of the EEG recorded at these different scales allows us to characterize the neuronal dynamics affected by epilepsy. For this purpose, we retrospectively analyzed long-term recordings performed during five nights in three patients during which no seizures took place. As a benchmark we used the accuracy with which this analysis allows determining the hemisphere that contains the seizure onset zone, which is the brain area where clinical seizures originate. We applied the surrogate-corrected non-linear predictability score (ψ), a non-linear signal analysis technique which was shown previously to be useful for the lateralization of the seizure onset zone from classical intracranial EEG macro contact recordings. Higher values of ψ were found predominantly for signals recorded from the hemisphere containing the seizure onset zone as compared to signals recorded from the opposite hemisphere. These differences were found not only for the EEG signals recorded with macro contacts, but also for those recorded with micro wires. In conclusion, the information obtained from the analysis of classical macro EEG contacts can be complemented by the one of micro wire EEG recordings. This combined approach may therefore help to further improve the degree to which quantitative EEG analysis can contribute to the diagnostics in epilepsy patients. The authors acknowledge funding from the Spanish Ministry of Economy and Competitiveness, Grant No. FIS2014-54177-R (CM and RA) and by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme, MDM-2015-0502 (CM), from the Volkswagen foundation (FM), from the German Research Council (DFG MO 930/8-1, DFG SFB 1089 to FM).

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 29, 051103 (2019) and may be found at https://doi.org/10.1063/1.5097570., We propose a method to control chimera states in a ring-shaped network of nonlocally coupled phase oscillators. This method acts exclusively on the network’s connectivity. Using the idea of a pacemaker oscillator, we investigate which is the minimal action needed to control chimeras. We implement the pacemaker choosing one oscillator and making its links unidirectional. Our results show that a pacemaker induces chimeras for parameters and initial conditions for which they do not form spontaneously. Furthermore, the pacemaker attracts the incoherent part of the chimera state, thus controlling its position. Beyond that, we find that these control effects can be achieved with modifications of the network’s connectivity that are less invasive than a pacemaker, namely, the minimal action of just modifying the strength of one connection allows one to control chimeras.

The detection of directional couplings between dynamics based onmeasured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons.One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes.We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data. We acknowledge funding from the European Union Horizon 2020 research and innovation programme under theMarie Skłodowska-Curie Grant Agreement No. 642563 “Complex Oscillatory Systems: Modeling and Analysis” (COSMOS), (I.M., T.K., R.G.A.), and from the Volkswagen Foundation, the Spanish Ministry of Economy and Competitiveness Grant No. FIS2014-54177-R and the CERCA Programme of the Generalitat de Catalunya (R.G.A).

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

BACKGROUND/nEpilepsy surgery is a potentially curative treatment option for pharmacoresistent patients. If non-invasive methods alone do not allow to delineate the epileptogenic brain areas the surgical candidates undergo long-term monitoring with intracranial EEG. Visual EEG analysis is then used to identify the seizure onset zone for targeted resection as a standard procedure./n/nMETHODS/nDespite of its great potential to assess the epileptogenicty of brain tissue, quantitative EEG analysis has not yet found its way into routine clinical practice. To demonstrate that quantitative EEG may yield clinically highly relevant information we retrospectively investigated how post-operative seizure control is associated with four selected EEG measures evaluated in the resected brain tissue and the seizure onset zone. Importantly, the exact spatial location of the intracranial electrodes was determined by coregistration of pre-operative MRI and post-implantation CT and coregistration with post-resection MRI was used to delineate the extent of tissue resection. Using data-driven thresholding, quantitative EEG results were separated into normally contributing and salient channels./n/nRESULTS/nIn patients with favorable post-surgical seizure control a significantly larger fraction of salient channels in three of the four quantitative EEG measures was resected than in patients with unfavorable outcome in terms of seizure control (median over the whole peri-ictal recordings). The same statistics revealed no association with post-operative seizure control when EEG channels contributing to the seizure onset zone were studied./n/nCONCLUSIONS/nWe conclude that quantitative EEG measures provide clinically relevant and objective markers of target tissue, which may be used to optimize epilepsy surgery. The finding that differentiation between favorable and unfavorable outcome was better for the fraction of salient values in the resected brain tissue than in the seizure onset zone is consistent with growing evidence that spatially extended networks might be more relevant for seizure generation, evolution and termination than a single highly localized brain region (i.e. a “focus”) where seizures start. This study was supported by the Swiss National Science Foundation (SNF) via the projects 122010, 124089, 140332 and 155950. R.G. Andrzejak was supported by grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science and funding from the Volkswagen Foundation. M. Müller acknowledges the Consejo Nacionál de Ciencia y Technología, Mexico, project 156667. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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

Experimental data comprising both time-continuous flows and point processes are recorded in many scientific disciplines. The characterization of causal interactions from such signals is key to an advanced understanding of the underlying dynamics. We therefore introduce a unified approach to characterize unidirectional couplings between point processes, between flows, as well as between point processes and flows. For this purpose we show and exploit the generality of the asymmetric state similarity conditioning principle. We use Hindmarsh-Rose neuron models and Lorenz oscillators to illustrate the high sensitivity and specificity of our approach.

A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by evaluating the ratio of the instantaneous firing rates. In contrast to most previously proposed measures it is parameter free and time-scale independent. However, it is not well suited to track changes in synchrony that are based on spike coincidences. Here we propose the SPIKE-distance, a complementary measure which is sensitive to spike coincidences but still shares the fundamental advantages of the ISI-distance. In particular, it is easy to visualize in a time-resolved manner and can be extended to a method that is also applicable to larger sets of spike trains. We show the merit of the SPIKE-distance using both simulated and real data., 15 pages, 10 figures, 47 references

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.

Theta oscillations in the medial temporal lobe (MTL) of mammals are involved in various functions such as spatial navigation, sensorimotor integration, and cognitive processing. While the theta rhythm was originally assumed to originate in the medial septum, more recent studies suggest autonomous theta generation in the MTL. Although coherence between entorhinal and hippocampal theta activity has been found to infl uence memory formation, it remains unclear whether these two structures can generate theta independently. In this study we analyzed intracranial electroencephalographic (EEG) recordings from 22 patients with unilateral hippocampal sclerosis undergoing presurgical evaluation prior to resection of the epileptic focus. Using a wavelet-based, frequency-band-specifi c measure of phase synchronization, we quantifi ed synchrony between 10 different recording sites along the longitudinal axis of the hippocampal formation in the non-epileptic brain hemisphere. We compared EEG synchrony between adjacent recording sites (i) within the entorhinal cortex, (ii) within the hippocampus, and (iii) between the hippocampus and entorhinal cortex. We observed a signifi cant interregional gap in synchrony for the delta and theta band, indicating the existence of independent delta/theta rhythms in different subregions of the human MTL. The interaction of these rhythms could represent the temporal basis for the information processing required for mnemonic encoding and retrieval. This work was supported by the Intramural Research Fund BONFOR of the University of Bonn and the 6th Framework Programme of the European Commission (Marie Curie OIF 040445).

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.

We compare two conceptually different approaches to the detection of weak directional couplings between two oscillatory systems from bivariate time series. The first approach is based on the analysis of the systems’ phase dynamics, whereas the other one tests for interdependencies in the reconstructed state spaces of the systems. We analyze the sensitivity of both techniques to weak couplings in numerical experiments by considering couplings between almost identical as well as between significantly different nonlinear systems. We study different degrees of phase diffusion, test the robustness of the two techniques against observational noise, and investigate the influence of the time series length. Our results show that none of the two approaches is generally superior to the other, and we conclude that it is probably the combination of both techniques that would allow the most comprehensive and reliable characterization of coupled systems. D.A.S acknowledges financial support from the President of Russia sGrant No. MK-1067.2004.2d, Russian Science Support Foundation, program BRHE sREC006d, and RFBR sGrant No. 05-02-16305d

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 have recently introduced a measure for nonstationarity using a recurrence time statistic to assess stationarity. In this paper we propose an extension of this method based on a detailed study of the statistics for the case of stationary systems. We derive a simple scheme that allows us to estimate the effective number of degrees of freedom relevant for this statistic. This substantially improves the statistical significance of the method and can be used to improve the significance of various other nonlinear statistics. This work was supported by the Deutsche Forschungsgemeinschaft.

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

We propose a measure for nonstationarity which is based on the analysis of distributions of temporal distances of neighboring vectors in state space. As an extension of previous techniques our method does not require a partitioning of the time series. Moreover, the deviation of mean recurrence times from frequency distributions that would be expected under stationary conditions allows us to estimate the statistical significance of the method.

We were interested in how two coupled decision-making modules behave. This is for example interesting in multisensory integration, in which both auditory and visual precepts have to be integrated into one common percept. We used a biophysically realistic neural model consisting of integrate-and-fire neurons with detailed synaptic channels. We studied the influence of the strength of the cross-connection between the two decision-making modules on the performance of the model. The performance was assessed by how often the system can correctly extract the stimulus even though just weak input was applied. We found that the optimal performance of the coupled modules is achieved by a certain cross-connection strength, which is independent of the amplitude of the stimulus input. This means that once an optimal cross-connection has been learned it can be used for all types of stimulus inputs to achieve an optimal performance. We also present the mechanism, which is responsible for this improvement: Inconsistent constellations in the two modules converge to the correct response. We could also simulate the law of inverse effectiveness in our model. We related the strength of the input bias to the multisensory integration index and found an inversely correlated relationship such as observed in experimental data [1]. We also investigated a three-module architecture, in which two primary sensory areas like the auditory and the visual one are connected by a third, integrating module. The 3rd module could correspond to higher processing areas such as the STS, which mediates between the two primary sensory areas. We show that there are similar dynamics as in the two-module case, although the necessary coupling strength between the modules is increased. The coupling is more indirect than in the two-module case. We conclude that decision-making modules can be coupled to increase performance compared to single decision-making module.