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Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators’ mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups’ position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag. We acknowledge funding from the Spanish Ministry of Science and Innovation and the State Research Agency (Grant No. PID2020-118196GBI00/MICIN/AEI/10.13039/501100011033).

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.

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

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).

Complex-valued quadratic maps either converge to fixed points, enter into periodic cycles, show aperiodic behavior, or diverge to infinity. Which of these scenarios takes place depends on the map's complex-valued parameter c and the initial conditions. The Mandelbrot set is defined by the set of c values for which the map remains bounded when initiated at the origin of the complex plane. In this study, we analyze the dynamics of a coupled network of two pairs of two quadratic maps in dependence on the parameter c. Across the four maps, c is kept the same whereby the maps are identical. In analogy to the behavior of individual maps, the network iterates either diverge to infinity or remain bounded. The bounded solutions settle into different stable states, including full synchronization and desynchronization of all maps. Furthermore, symmetric partially synchronized states of within-pair synchronization and across-pair synchronization as well as a symmetry broken chimera state are found. The boundaries between bounded and divergent solutions in the domain of c are fractals showing a rich variety of intriguingly esthetic patterns. Moreover, the set of bounded solutions is divided into countless subsets throughout all length scales in the complex plane. Each individual subset contains only one state of synchronization and is enclosed within fractal boundaries by c values leading to divergence.

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.

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 30, 033125 (2020) and may be found at https://doi.org/10.1063/5.0002272., We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data- driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient. This work was funded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563 (M.G.L., I.M., Z.L., and R.G.A). R.G.A. and C.G.B.M. acknowledge funding from the Spanish Ministry of Econ- omy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. C.G.B.M. acknowledges the support by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme (MDM-2015-0502). Z.L. acknowledges funding from the Slovenian Re- search Agency via program Complex Networks P1-0383 and project J5-8236.

This scientific commentary refers to ‘Crowdsourcing reproducible seizure forecasting in human and canine epilepsy’, by Brinkmann et al. (doi:10.1093/brain/aww045). Epilepsy is characterized by recurrent spontaneous seizures that seem to occur without warning, like a bolt from the blue. Most patients with epilepsy spend over 99.9% of their time in a perfectly normal brain state. But even though epileptic seizures constitute less than 0.1% of their lifetime, it is the apparent unpredictability of these events that puts an immense psychological burden on patients and substantially compromises their quality of life. A reliable method of forecasting seizure occurrence would thus greatly diminish psychological stress for patients. Moreover, it could lead to novel therapeutic options such as on-demand treatment and ultimately even closed-loop interventional devices to prevent impending seizures from occurring (Morrell and Halpern, 2016). In this issue of Brain , Brinkmann and co-workers have used the concept of crowdsourcing to tackle the problem of seizure prediction (Brinkmann et al. , 2016). They hosted epochs of continuous multi-day recordings of intracranial EEG (iEEG) activity from both humans and canines on a website (www.kaggle.com), and started a competition open to the public in which the aim was to correctly characterize these data clips as preictal (indicative of an impending seizure) or interictal (in this study, at least 1 week away from any seizure). Participating teams were provided with a set of training data consisting of clips that were labelled as being preictal or interictal. Using these data clips, they could train and optimize their algorithms before running them on the other clips provided—the testing data. For each of these remaining clips, the candidate algorithms had to estimate the probability that the clip was preictal. Receiver operating …

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).

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.).

This study characterizes the spatial-temporal distribution of epileptic activity in mesial and neocortical temporal lobe epilepsy (TLE) assessed by subdural and depth electrodes during sleep. We determined in 13 patients the frequency, lateralization, and localization of interictal epileptic discharges (IEDs). As compared to the waking state, IEDs increased in light sleep (196%, p0.05) and in deep sleep (601%, p0.05) but did not change significantly in REM sleep (-8.33%, p = 0.94). From 11 patients with unilateral TLE, in all cases, IEDs lateralized to the seizure onset side during REM sleep and the waking state. In mesial TLE, IEDs tended to shift in an anterior-posterior axis and remained always localized in the amygdalo-hippocampal complex. By contrast, in neocortical TLE, the maximal activity moved in a mesial-lateral axis between neocortical and mesial structures. Twenty-six seizures were registered in 7 patients, 22 of which occurred in light sleep and 4 in wakefulness, but none occurred in deep or REM sleep.

Objective To show that time-irreversible EEG signals recorded with intracranial electrodes during seizures can serve as markers of the epileptogenic zone. Methods We use the recently developed method of mapping time series into directed horizontal graphs (dHVG). Each node of the dHVG represents a time point in the original intracranial EEG (iEEG) signal. Statistically significant differences between the distributions of the nodes’ number of input and output connections are used to detect time-irreversible iEEG signals. Results In 31 of 32 seizure recordings we found time-irreversible iEEG signals. The maximally time-irreversible signals always occurred during seizures, with highest probability in the middle of the first seizure half. These signals spanned a large range of frequencies and amplitudes but were all characterized by saw-tooth like shaped components. Brain regions removed from patients who became post-surgically seizure-free generated significantly larger time-irreversibilities than regions removed from patients who still had seizures after surgery. Conclusions Our results corroborate that ictal time-irreversible iEEG signals can indeed serve as markers of the epileptogenic zone and can be efficiently detected and quantified in a time-resolved manner by dHVG based methods. Significance Ictal time-irreversible EEG signals can help to improve pre-surgical evaluation in patients suffering from pharmaco-resistant epilepsies.

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.

The sudden and apparently unpredictable nature of seizures is one of the most disabling aspects of the disease epilepsy. A method capable of predicting the occurrence of seizures from the electroencephalogram (EEG) of epilepsy patients would open new therapeutic possibilities. Since the 1970s investigations on the predictability of seizures have advanced from preliminary descriptions of seizure precursors to controlled studies applying prediction algorithms to continuous multi-day EEG recordings. While most of the studies published in the 1990s and around the turn of the millennium yielded rather promising results, more recent evaluations could not reproduce these optimistic findings, thus raising a debate about the validity and reliability of previous investigations. In this review, we will critically discuss the literature on seizure prediction and address some of the problems and pitfalls involved in the designing and testing of seizure-prediction algorithms. We will give an account of the current state of this research field, point towards possible future developments and propose methodological guidelines for future studies on seizure prediction.

The investigation of synchronization phenomena on measured experimental data such as biological time series has recently become an increasing focus of interest. Different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation. For experimental data the underlying dynamics are usually not completely known, therefore it is difficult to decide a priori which synchronization measure is most suitable for an analysis. In this study we use three different coupled model systems to create a ‘controlled’ setting for a comparison of six different measures of synchronization. All measures are compared to each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. Results show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications, although certain dynamical features of a system under investigation (e.g., power spectra, dimension) may render certain measures more suitable than others. c 2006 Elsevier B.V. All rights reserved.

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).

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.

Objective: An important issue in epileptology is the question whether information extracted from the EEG of epilepsy patients can be used for the prediction of seizures. Several studies have claimed evidence for the existence of a pre-seizure state that can be detected using different characterizing measures. In this paper, we evaluate the predictability of seizures by comparing the predictive performance of a variety of univariate and bivariate measures comprising both linear and non-linear approaches. Methods: We compared 30 measures in terms of their ability to distinguish between the interictal period and the pre-seizure period. After completely analyzing continuous inctracranial multi-channel recordings from five patients lasting over days, we used ROC curves to distinguish between the amplitude distributions of interictal and preictal time profiles calculated for the respective measures. We compared different evaluation schemes including channelwise and seizurewise analysis plus constant and adaptive reference levels. Particular emphasis was placed on statistical validity and significance. Results: Univariate measures showed statistically significant performance only in a channelwise, seizurewise analysis using an adaptive baseline. Preictal changes for these measures occurred 5‐30 min before seizures. Bivariate measures exhibited high performance values reaching statistical significance for a channelwise analysis using a constant baseline. Preictal changes were found at least 240 min before seizures. Linear measures were found to perform similar or better than non-linear measures. Conclusions: Results provide statistically significant evidence for the existence of a preictal state. Based on our findings, the most promising approach for prospective seizure anticipation could be a combination of bivariate and univariate measures. Significance: Many measures reported capable of seizure prediction in earlier studies are found to be insignificant in performance, which underlines the need for statistical validation in this field. q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

The exact mechanisms leading to the occurrence of epileptic seizures in humans are still poorly understood. It is widely accepted, however, that the process of seizure generation is closely associated with an abnormal synchronization of neurons. In order to investigate this process, we here measure phase synchronization between different regions of the brain using intracranial EEG recordings. Based on our preliminary finding of a preictal drop in synchronization, we investigate whether this phenomenon can be used as a sensitive and specific criterion to characterize a preseizure state and to distinguish this state from the interictal interval. Applying an automated technique for detecting decreased synchronization to EEG recordings from a group of 18 patients with focal epilepsy comprising a total of 117 h, we observe a characteristic decrease in synchronization prior to 26 out of 32 analyzed seizures at a very high specificity as tested on interictal recordings. The duration of this preictal state is found to range from several minutes up to a few hours. Investigation of the spatial distribution of preictal desynchronization indicates that the process of seizure generation in focal epilepsy is not necessarily confined to the focus itself but may instead involve more distant, even contralateral areas of the brain. Finally, we demonstrate an intrahemispheric asymmetry in the spatial dynamics of preictal desynchronization that is found in the majority of seizures and appears to be an immanent part of the mechanisms underlying the initiation of seizures in humans.

Topologies of real-world complex networks are rarely accessible, but can often be reconstructed from experimentally obtained time series via suitable network reconstruction methods. Extending our earlier work on methods based on statistics of derivative-variable correlations, we here present a new method built on integrating an evolutionary optimization algorithm into the derivative-variable correlation method. Results obtained from our modi cation of the method in general outperform the original results, demonstrating the suitability of evolutionary optimization logic in network reconstruction problems. We show the method's usefulness in realistic scenarios where the reconstruction precision can be limited by the nature of the time series. We also discuss important limitations coming from various dynamical regimes that time series can belong to. This work was founded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563. R G A acknowledges funding from the Volkswagen foundation, the Spanish Ministry of Economy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. Z L acknowledges funding from the Slovenian Research Agency via program Complex Networks P1-0383 and project J5- 8236.

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 detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well. R.G.A. acknowledges Grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science. R.G.A. and F.M. acknowledge funding from the Volkswagen Foundation. T.K. acknowledges funding from the European Commission through the Marie Curie Initial Training Network ‘Neural Engineering Transformative Technologies (NETT)’, Project No. 289146.

In the analysis of physiological time series it is important to investigate the inter-dependence structure among the observed variables of the system. For this, a number of measures of the so-called Granger causality have been developed, and among them information measures have gained much attention. However, information measures have to deal with the estimation of probability distributions of high-dimensional vector variables, typically formed through uniform delay embedding of the time series. Here, the focus is on measures derived after nonuniform embedding. Particularly, two schemes are considered, one based on conditional mutual information and the other based on conditional entropy. We evaluate the two measures on simulated nonlinear coupled dynamical systems and apply them to signals of heart rate variability, respiration, and oxygen concentration in the blood.

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.

Summary:Several recent studies emphasize the high value of nonlinear EEG analysis particularly for improved characterization of epileptic brain states. In this review the authors report their work to increase insight into the spatial and temporal dynamics of the epileptogenic process. Specifically

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)

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

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.