Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Identifying causal gateways and mediators in complex spatio-temporal systems

J.R. received support by the German National Academic Foundation (Studienstiftung), a Humboldt University Postdoctoral Fellowship, and the German Federal Ministry of Science and Education (Young Investigators Group CoSy-CC2, grant no. 01LN1306A). J.F.D. thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. D.H. has been funded by grant ERC-CZ CORES LL-1201 of the Czech Ministry of Education. M.P. and N.J. received funding from the Czech Science Foundation project No. P303-14-02634S and from the Czech Ministry of Education, Youth and Sports, project No. DAAD-15-30. J.H. was supported by the Czech Science Foundation project GA13-23940S and Czech Health Research Council project NV15-29835A. We thank Mary Lindsey from the National Oceanic and Atmospheric Administration for her kind help with Fig. 4e. NCEP Reanalysis data provided by NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their web site at http://www.esrl.noaa.gov/psd/.Peer reviewedPublisher PD

Vulnerability of hydropower installations to climate change : preliminary study

The climate trends observed worldwide over the past few decades appear to corroborate the concerns of the scientific community about the many threats posed by global warming. Future changes of the current climate are expected to occur on different scales all around the globe, hence modifying the environmental background on the basis of which technological installations have been designed and operated. This can potentially threat the safety of the installations as well as their. The development of suitable tools aiming to predict the impact of climate change on technological installations is then essential in the wider context of climate change mitigation. Hydropower installations play often a crucial role not only as a long-term renewable resource of energy but also for flood control and water supply in the case of droughts. All these aspects highlight the increasing importance of such installations as well as their growing vulnerability to natural hazards. It is hence essential to enlarge the current understanding of the interaction mechanisms between such installations and the changing surrounding environment in order to take adequate measures for climate change adaptation and ensure the future safety and productivity of hydropower production. The current study aims to provide a novel model for the evaluation of the impact of climate change on the safety of hydropower stations. The approach adopted allows to include in the model the uncertainty inevitably associated with the input variables and to propagate such uncertainty within the analysis. The model proposed is finally applied to a realistic case-study in order to highlight its potential and limitations

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Optimal model-free prediction from multivariate time series

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostly to the univariate case. Therefore, selection strategies are needed that harness the available information as efficiently as possible. Since often the right combination of predictors matters, ideally all subsets of possible predictors should be tested for their predictive power, but the exponentially growing number of combinations makes such an approach computationally prohibitive. Here a prediction scheme that overcomes this strong limitation is introduced utilizing a causal pre-selection step which drastically reduces the number of possible predictors to the most predictive set of causal drivers making a globally optimal search scheme tractable. The information-theoretic optimality is derived and practical selection criteria are discussed. As demonstrated for multivariate nonlinear stochastic delay processes, the optimal scheme can even be less computationally expensive than commonly used sub-optimal schemes like forward selection. The method suggests a general framework to apply the optimal model-free approach to select variables and subsequently fit a model to further improve a prediction or learn statistical dependencies. The performance of this framework is illustrated on a climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure

A Survey on Causal Discovery Methods for Temporal and Non-Temporal Data

Causal Discovery (CD) is the process of identifying the cause-effect relationships among the variables from data. Over the years, several methods have been developed primarily based on the statistical properties of data to uncover the underlying causal mechanism. In this study we introduce the common terminologies in causal discovery, and provide a comprehensive discussion of the approaches designed to identify the causal edges in different settings. We further discuss some of the benchmark datasets available for evaluating the performance of the causal discovery algorithms, available tools to perform causal discovery readily, and the common metrics used to evaluate these methods. Finally, we conclude by presenting the common challenges involved in CD and also, discuss the applications of CD in multiple areas of interest