Projects
Our research focuses on:

Dynamics of Modern Power GridsSwitching our current energy supply to renewable sources poses one of the greatest technological and social challenges of humankind. A successful transition in particular requires an intelligent upgrade of the current electric power grid.
Socalled 'smart grids' may provide part of the solution by enabling the transmission of demand and supply information across the grid online, thereby adapting energy production and distribution, and thus aiming to control the entire grid. However, stable operation as well as failures on large scales already today are consequences of the collective dynamics of the power grid and are often caused by nonlocal mechanisms.
We thus urgently need to understand the intrinsic network dynamics on the large scale to complement partial solutions of control engineering and to be able to develop efficient strategies for operating the future grid.
We thus develop and analyze appropriate coarsescale models of future power grids with an emphasis on increasingly distributed demand and supply. First results show several intriguing features. For instance, the addition of new transmission lines may *destabilize* power grid operation (via Braess paradox that we identified in oscillator networks). In addition, replacing the few large power plants by many small and distributed ones may stabilize grid operation, at least in the stationary (shorttime) regime.


Complex Disordered Systems: Statistical Physics and Symbolic ComputationMany particles interacting nonlinearly often give rise to very complex behavior. This is true even for apparently simple systems, such as those in thermal equilibrium. For instance, particles with a spin that are antiferromagnetically coupled may give rise to positive ground state entropy, an exception to the third law of thermodynamics. Investigating such complex ground states immediately leads us to hard enumeration problems in graph theory and computer science.
Here we try to understand basic features of complex macroscopic states and in parallel develop tools for analytically and computationally addressing large system with complex ground states and related graph theoretical problems.


Statistical Properties of Order BooksIn recent years there have been considerable efforts to employ methods from theoretical physics to problems in economics. Our group is interested in the dynamics of the order book, which can be seen as the ultimate microscopic level of description of financial markets.


Random focusing of tsunami wavesWe explore how tsunami waves can be focussed by even minute height variations in the ocean floor topography and study the impact of this effect on tsunami predictability.


SubsamplingIn most large networks, it is impossible to sample the activity of all nodes in parallel. For example, the human brain comprises 80 billion neurons, but current techniques allow sampling the activity from only a few hundred neurons at a time. I showed for collective states of networks that subsampling can severely impede inferences about the properties of the full system. In detail, subsampling in critical models can distort the expected power law relations, and thereby a critical system can be misinterpreted as sub or supercritical. I am currently developing an approach to overcome subsampling effects by extending methods from finite size scaling theory.


Information theoryTo understand information processing in the brain, I codeveloped an open source toolbox (TRENTOOL) that is specialized on estimating information theoretic quantities from neural recordings. Using this toolbox, I showed that transfer entropy is capable of detecting the interaction delay and the direction of information flow between brain areas, using my own turtle ex vivo recordings. Currently, the toolbox is extended to also quantify active information storage, and return the time resolved versions of both, active information storage and transfer.


The path to selftrapping of BoseEinsteinCondensatesThe Bose Einstein condensates in (leaky) optical lattices show an intriguing transition to selftrapping into intrinsic localized states, which we study theoretically.


Fluctuations in human musical rhythmsMusic generated by computers and rhythm machines sometimes sounds unnatural. One reason for this is the absence of small inaccuracies that are part of every human activity. Professional audio software therefore offers a socalled humanizing technique, by which the regularity of musical rhythms can be randomized to some extent.
But what exactly is the nature of the inaccuracy in human musical rhythms? Studying this question for the first time, we found that the temporal rhythmic fluctuations exhibit scalefree longrange correlations, i.e., a small rhythmic fluctuation at some point in time does not only influence fluctuations shortly thereafter, but even after tens of seconds. While this characterization is relevant for neurophysiological mechanisms of timing, it also leads to a novel concept for humanizing musical sequences. Comparing with conventionally humanized versions listeners showed a high preference for longrange correlated humanized music over uncorrelated humanized music.


Modeling Infectious DiseasesThe sudden appearance and rapid spread of an infectious diseases can pose a serious threat to human or animal populations that calls for immediate actions by national and international health agencies. Their response is guided by epidemiological models whose primary use is to provide means of comparing the effectiveness of different containment strategies. The focus
of our group is to quantify, how heterogeneity of the infection process affects the course of an infectious disease. In particular, we are interested in the effect of indiviudal variation in disease transmission on control strategies in the early phase of an epidemic outbreak and
the consequences of spatially varying infection rates on travel restrictions.


Subcritical Dynamics in vivoIn neuroscience, a popular hypothesis is that the collective neural dynamics should selforganize to a critical state, because at criticality simple models maximize their information processing capacities. However, criticality also comes with the risk of spontaneous runaway activity (epilepsy). I recently obtained the first evidence that neural dynamics maintains a distance to criticality, and thus can keep a safety margin to runaway activity. This distance to criticality is consistent across different species, but changes with vigilance states. Currently, I refine the methods to quantify the distance to criticality, with the aim to understand how this distance is adjusted depending on needs.


Long range correlations and musicLong range correlations dominate neural activity. Therefore music, which is considered the mirror of the soul and the brain, should also reflect these correlations. We currently investigate how long range correlations and information theoretic quantities change with genres, and whether long range correlations play a central role in making Swing swing.


Wave dynamics in correlated weakly scattering random mediaWaves propagating through a weakly disordered medium are surprisingly focused into branchlike structures. This very general phenomenon can be observed diverse systems ranging from the twodimensional electron gases in semiconductors to the focusing of tsunami waves.


Nonlinear Methods for Detecting Timing Relations in Neural DataMaking sense of huge neural data sets that contain spikes as well as temporally more coarse information constitutes a challenging task of current research. This is even more so as. for instance, the number of units possible to recorded from simulataneously, increases at a rapid pace. In this project we are developing novel methods of nonlinear time series analysis to relate dynamical quantities of neural activity on different temporal and spatial scales. We currently focus on relating the often precisely timed occurrence of spikes to the temporal evolution of local field potentials and low frequency oscillations via modern phase analysis techniques.


Structure, Dynamics and Function of Complex NetworksHow does the interaction topology of a complex network control its dynamics? Can we infer information about how a network is connected from dynamics measurements only? We address theoretical and practical aspects of such questions using mathematical modeling studies for general network dynamical systems and neural networks in particular.


Theory of Precise Timing in Spiking Neural NetworksCoordinated patterns of precisely timed activity is a key ingredient for neural information processing. This project investigates the theoretical fundamentals underlying the mechanisms for generating precisely timed spikes in complex neural networks.


Avalanches in BoseEinstein CondensatesThe dynamics of BoseEinstein condensates in leaky optical lattices is studied (in the mean field limit). For some critical values of the interatomic interaction strength, the current of atoms leaving the trap exhibits avalanches that follow a powerlaw distribution and indicate the existence of a novel phase transition.


Disorder in Quantum Systems with Antilinear SymmetriesWe study the influence of disorder on the pseudohermitian phase of (generalized) PTsymmetric systems.


Control and Selforganization for Autonomous RobotsHow can distributed or autonomous systems control themselves to function properly? We are developing a novel line of research: Advancing the theory of chaos control we strive to bring it to applications for making autonomous robots more versatile and more selforganized


Complex call sequences in social whale communicationHow do social animals communicate? Social whales may be one of the best fit animal model to study complex vocal communication patterns. We are interested in developing an automated classification system for vocalizations of killer whales and pilot whales. Very loosely speaking one can think of this as developing a "speech"recognition system for whale vocalizations. Another, more general aim of this project is to characterize whale vocalizations in terms of information theoretic measures and to compare them to human languages.


Anomalous DiffusionIf the timeevolution of the meansquared displacement of some quantity is nonlinear,
the system is said to exhibit anomalous diffusion. The underlying mechanisms leading to such anomalous diffusion can be multifold. Our group focuses on processes whose
anomalous behavior is due to heavytailed distributions of either the waiting time
distribution between the displacements or of the displacements themselves.


SelfOrganized Criticality in the Activity Dynamics of Neural NetworksNeural networks display characteristics of critical dynamics in the neural activities as theoretically predicted. The powerlaw statistics for the size of avalanches of neural activity was confirmed in real neurons, where the critical behavior is reapproached even after a substantial perturbation of the parameters of the system. These findings provide evidence for the presence of selforganized criticality (SOC). We study neural network models that exhibit powerlaw statistics with realistic synaptic mechanisms, such as synaptic depression.
