Synopsis of our research lines

Development of innovative nonlinear time series analysis techniques

Nonlinear time series analysis allows characterising dynamical systems in which nonlinearity gives rise to a complex temporal evolution. Importantly, these nonlinear techniques can extract information from real-world experimental signals that cannot be resolved by classical linear techniques. Key targets of our work are the discrimination of deterministic and stochastic dynamics as well as the characterisation of directional interactions between dynamics. We introduced a coupling detection technique that substantially improves the sensitivity and specificity of previous approaches. To treat the special case of time-dependent event-related couplings, we devised the concept of time-resolved causal statistics across realisations. We furthermore introduced a unified approach to detect couplings between pairs of point processes, point processes and flows, and pairs of flows.​ We introduced the notion of coupling impact to characterize bidirectional couplings between non-identical dynamics. Recently, we introduced the nonlinear predictability score which allows to detect deterministic structure from spike trainsand time continuous signals. First applications to neuronal spiking data shows promising results. 

​Analysis of electrophysiological recordings from the brain

This analysis can contribute to the understanding of brain functions and dysfunctions and thereby advance cognitive neuroscience and neurology. Analysing electroencephalographic (EEG) recordings from epileps patients, we showed that a combination of nonlinear time series analysis techniques with surrogates allows to localise epileptic foci reliably - a finding of clear clinical relevance. We study the predictability of epileptic seizures using a variety of signal analysis techniques. In this context, we developed seizure predictor surrogates, a specialized Monte Carlo framework to assess the true predictive power of seizure prediction algorithms.​

Data-driven analysis of mathematical models of networks of coupled oscillators

Despite models of coupled oscillator networks can have a very simple form, for example a one-line nonlinear differential equation, they can show a rich and complex behavior. A recent example are networks of non-locally coupled identical phase oscillators. In so-called chimera states, these networks show a very counter-intuitive behaviour. They fall apart into two groups, a group of synchronous oscillators and a group of incoherent oscillators moving erratically. We take an innovative data-driven approach to these networks. By applying nonlinear signal analysis techniques to multivariate signals derived from these networks, one can reveal phenomena that remain elusive to analytical, numerical or experimental approaches. Importantly, this builds the bridge to complex real-world dynamics, for which data-driven approaches are sometimes the only option. This bridge can help to discover analogies such as the one between epileptic seizures and the sudden collapse of chimera states shown in a recent publication of our group. We furthermore investigated the interplay of chimera states across separate networks of coupled oscillators. We showed in that a simple coupling of oscillators across networks allows one to induce different types of synchronization between the networks. In particular, this includes so-called generalized synchronization, where the state of a driving network fully determines the state of a response network, while both networks still show chimera states with distinct spatiotemporal dynamics.

​Creation of open-access databases of electrophysiological recordings

In October 2012, our group launched the Bern-Barcelona EEG database. which provides bivariate signals of intracranial EEG recordings from epilepsy patients. This database  furthermore includes source code to analyse these signals as well as detailed results our group has derived and published on this database. These resources, as well as further free source codes can be found in the download section. First studies of these recording by other research groups were published already in 2013.

​Analysis of information retrieval signals

In this research line, which we pursue in cooperation with Dr. Joan Serrà, we use nonlinear time series analysis, data mining and machine learning approaches to study various real-world experimental signals. In the context of Music Information Retrieval, we quantified similarities and predictability of music-derived signals. In current work, we analyse signals derived from web search engines. 

Development and evaluation of spike train distances 

In cooperation with Dr. Thomas Kreuz, we contributed to the development of various spike train distances. This includes spike train distances for multivariate spike trains, distances that specifically rely on spike coincidences, and measures that can be estimated in a causal real-time way. All these approaches share the advantages to be parameter-free, time scale independent and easy to visualize in a time-resolved manner. We furthermore studied what can, and what cannot, be concluded from results of time scale parametric spike train distances.