Sarah Hallerberg

Precursors of extreme increments

We investigate precursors and the predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors, on the size of the event, and on the correlation strength. We study the prediction of extreme increments analytically in an autoregressive process of order 1, and numerically in wind speed recordings and long-range correlated autoregressive moving average processes data. We evaluate the success of predictions via receiver-operator characteristics (ROC curves). Furthermore, we observe an increase of the quality of predictions with increasing event size and with decreasing correlation in all examples. Both effects can be understood by using the likelihood ratio as a summary index for smooth ROC curves.

Dynamical Interpretation of Extreme Events: Predictability and Predictions

Due to their great impact on human life, Xevents require prediction. We discuss scenarios and recent results on predictions and the predictability of Xevents, focusing on nonlinear stochastic processes since they are assumed to provide the basis for extremes. These predictions are usually of a probabilistic nature, so the benefit of this type of uncertain prediction is an additional issue. As a specific example, we report on the prediction of turbulent wind gusts in surface wind.

Reactions to extreme events: Moving threshold model

In spite of precautions to avoid the harmful effects of extreme events, we experience recurrently, phenomena that overcome the preventive barriers. These barriers usually increase drastically right after the occurrence of such extreme events, but steadily decay in their absence. In this paper, we consider a simple model that mimics the evolution of the protection barriers to study the efficiency of the systems reaction to extreme events and how it changes our perception of the sequence of extreme events itself. We obtain that the usual method of fighting extreme events introduces a periodicity in their occurrence and is generally less efficient than the use of a constant barrier. On the other hand, it shows a good adaptation to the presence of slow non-stationarities.

Predictability of critical transitions.

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However, especially in the presence of noise, it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the quadratic integrate-and-fire model and the van der Pol model under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance.

Prediction of Extreme Events

We discuss concepts for the prediction of extreme events based on time series data. We consider both probabilistic forecasts and predictions by precursors. Probabilistic forecasts employ estimates of the probability for the event to follow, whereas precursors are temporal patterns in the data typically preceeding events. Theoretical considerations lead to the construction of schemes that are optimal with respect to several scoring rules. We discuss scenarios for which, in contrast to intuition, events with larger magnitude are better predictable than events with smaller magnitude.

Network susceptibilities: Theory and applications

We introduce the concept of network susceptibilities quantifying the response of the collective dynamics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge susceptibilities, measuring the responses due to changes in the properties of units and their interactions, respectively. We derive explicit forms of network susceptibilities for oscillator networks close to steady states and offer example applications for Kuramoto-type phase-oscillator models, power grid models, and generic flow models. Focusing on the role of the network topology implies that these ideas can be easily generalized to other types of networks, in particular those characterizing flow, transport, or spreading phenomena. The concept of network susceptibilities is broadly applicable and may straightforwardly be transferred to all settings where networks responses of the collective dynamics to topological changes are essential.

Quantifying group specificity of animal vocalizations without specific sender information.

Recordings of animal vocalization can lack information about sender and context. This is often the case in studies on marine mammals or in the increasing number of automated bioacoustics monitorings. Here, we develop a framework to estimate group specificity without specific sender information. We introduce and apply a bag-of-calls-and-coefficients approach (BOCCA) to study ensembles of cepstral coefficients calculated from vocalization signals recorded from a given animal group. Comparing distributions of such ensembles of coefficients by computing relative entropies reveals group specific differences. Applying the BOCCA to ensembles of calls recorded from group of long-finned pilot whales in northern Norway, we find that differences of vocalizations within social groups of pilot whales (Globicephala melas) are significantly lower than intergroup differences.

Model-free inference of direct network interactions from nonlinear collective dynamics

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.Network dynamical systems can represent the interactions involved in the collective dynamics of gene regulatory networks or metabolic circuits. Here Casadiego et al. present a method for inferring these types of interactions directly from observed time series without relying on their model.

Critical transitions and perturbation growth directions

Critical transitions occur in a variety of dynamical systems. Here we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical transitions in several models of fast-slow systems, i.e., a network of coupled FitzHugh-Nagumo oscillators, models for Josephson junctions, and the Hindmarsh-Rose model, we find that tangencies between covariant Lyapunov vectors are a common and maybe generic feature during critical transitions. We further demonstrate that this deviation from hyperbolic dynamics is linked to the occurrence of critical transitions by using it as an indicator variable and evaluating the prediction success through receiver operating characteristic curves. In the presence of noise, we find the alignment of covariant Lyapunov vectors and changes in finite-time Lyapunov exponents to be more successful in announcing critical transitions than common indicator variables as, e.g., finite-time estimates of the variance. Additionally, we propose a new method for estimating approximations of covariant Lyapunov vectors without knowledge of the future trajectory of the system. We find that these approximated covariant Lyapunov vectors can also be applied to predict critical transitions.

Understanding and controlling regime switching in molecular diffusion.

Diffusion can be strongly affected by ballistic flights (long jumps) as well as long-lived sticking trajectories (long sticks). Using statistical inference techniques in the spirit of Granger causality, we investigate the appearance of long jumps and sticks in molecular-dynamics simulations of diffusion in a prototype system, a benzene molecule on a graphite substrate. We find that specific fluctuations in certain, but not all, internal degrees of freedom of the molecule can be linked to either long jumps or sticks. Furthermore, by changing the prevalence of these predictors with an outside influence, the diffusion of the molecule can be controlled. The approach presented in this proof of concept study is very generic and can be applied to larger and more complex molecules. Additionally, the predictor variables can be chosen in a general way so as to be accessible in experiments, making the method feasible for control of diffusion in applications. Our results also demonstrate that data-mining techniques can be used to investigate the phase-space structure of high-dimensional nonlinear dynamical systems.