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Identifying causal links (couplings) is a fundamental problem that facilitates the understanding of emerging structures in complex networks. We propose and analyze inner composition alignment-a novel, permutation-based asymmetric association measure to detect regulatory links from very short time series, currently applied to gene expression. The measure can be used to infer the direction of couplings, detect indirect (superfluous) links, and account for autoregulation. Applications to the gene regulatory network of E. coli are presented.
The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
Complex networks in climate dynamics : comparing linear and nonlinear network construction methods
(2009)
Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
In integrated medical considerations of the biological human system, both intellectual and motor performances in a similar manner are considered as a result of the function of the nervous system. Consequently, universal minimal dysfunctions of the central nervous system may lead to both intellectual and physical anomalies. Therefore, this study tests the hypothesis that there is a connection between the balance ability as a motor parameter and school success as an intellectual parameter. A postural measuring system based on the force-moment sensor technique was used to record the postural balance regulation of 773 children (circle divide 11 +/- 1 years). The school achievement of each child was determined by school grades. Data analysis was performed by linear as well as by nonlinear time series analyses. There are highly significant differences in balance regulation between good and poor pupils recognized by several linear and nonlinear parameters. Good pupils could be discriminated from pupils with bad results in learning to 80 %. The results support the hypothesis mentioned above. One possible explanation for the poor regulation of balance in bad learners could be a deficit in the neural maturity. In future, further developments will be targeted on higher discrimination levels, possibly in order to predict school success. On the other hand, the effects of special movement exercises on the neural development in childhood will be the focus in our further work
We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems
In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.
In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.
We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.