Optimal model-free prediction from multivariate time series

© 2015 American Physical Society.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 preselection 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 suboptimal 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 Niño Southern Oscillation

Phase Synchronization in Unidirectionally Coupled Ikeda Time-delay Systems

Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled systems phase synchronization (PS) does exist in a range of the coupling strength which is preceded by a transition regime (approximate PS) and a nonsynchronous regime. However, exact generalized synchronization does not seem to occur in the coupled Ikeda systems (for the range of parameters we have studied) even for large coupling strength, in contrast to our earlier studies in coupled piecewise-linear and Mackey-Glass systems \cite{dvskml2006,dvskml2008}. The above transitions are characterized in terms of recurrence based indices, namely generalized autocorrelation function $P(t)$, correlation of probability of recurrence (CPR), joint probability of recurrence (JPR) and similarity of probability of recurrence (SPR). The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets.Comment: 10 pages, 7 figure

Potentials and Limits to Basin Stability Estimation

Acknowledgments The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.Peer reviewedPublisher PD

Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods

Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26 deg S, 66 deg W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Nino/Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.Comment: 11 pages, 9 figure

Global generalized synchronization in networks of different time-delay systems

We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically coupled regular networks. We find that there exists a smooth transformation in such systems, which maps them to a common GS manifold as corroborated by their maximal transverse Lyapunov exponent. In addition, an analytical stability condition using the Krasvoskii-Lyapunov theory is deduced. This phenomenon of GS in strongly distinct systems opens a new way for an effective control of pathological synchronous activity by means of extremely small perturbations to appropriate variables in the synchronization manifold.Comment: 6 pages, 4 figures, Accepted for publication in Europhys. Let

On controllability of neuronal networks with constraints on the average of control gains

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently