Search Results
Recurrence networks-a novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
The complexity of gene expression dynamics revealed by permutation entropy
Background: High complexity is considered a hallmark of living systems. Here we investigate the complexity of temporal gene expression patterns using the concept of Permutation Entropy (PE) first introduced in dynamical systems theory. The analysis of gene expression data has so far focused primarily on the identification of differentially expressed genes, or on the elucidation of pathway and regulatory relationships. We aim to study gene expression time series data from the viewpoint of complexity.Results: Applying the PE complexity metric to abiotic stress response time series data in Arabidopsis thaliana, genes involved in stress response and signaling were found to be associated with the highest complexity not only under stress, but surprisingly, also under reference, non-stress conditions. Genes with house-keeping functions exhibited lower PE complexity. Compared to reference conditions, the PE of temporal gene expression patterns generally increased upon stress exposure. High-complexity genes were found to have longer upstream intergenic regions and more cis-regulatory motifs in their promoter regions indicative of a more complex regulatory apparatus needed to orchestrate their expression, and to be associated with higher correlation network connectivity degree. Arabidopsis genes also present in other plant species were observed to exhibit decreased PE complexity compared to Arabidopsis specific genes.Conclusions: We show that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.
A remote-control datalogger for large-scale resistivity surveys and robust processing of its signals using a software lock-in approach
We present a new versatile datalogger that can be used for a wide range of possible applications in geosciences. It is adjustable in signal strength and sampling frequency, battery saving and can remotely be controlled over a Global System for Mobile Communication (GSM) connection so that it saves running costs, particularly in monitoring experiments. The internet connection allows for checking functionality, controlling schedules and optimizing pre-amplification. We mainly use it for large-scale electrical resistivity tomography (ERT), where it independently registers voltage time series on three channels, while a square-wave current is injected. For the analysis of this time series we present a new approach that is based on the lock-in (LI) method, mainly known from electronic circuits. The method searches the working point (phase) using three different functions based on a mask signal, and determines the amplitude using a direct current (DC) correlation function. We use synthetic data with different types of noise to compare the new method with existing approaches, i.e. selective stacking and a modified fast Fourier transformation (FFT)-based approach that assumes a 1∕f noise characteristics. All methods give comparable results, but the LI is better than the well-established stacking method. The FFT approach can be even better but only if the noise strictly follows the assumed characteristics. If overshoots are present in the data, which is typical in the field, FFT performs worse even with good data, which is why we conclude that the new LI approach is the most robust solution. This is also proved by a field data set from a long 2-D ERT profile.
Characterizing time series: When Granger causality triggers complex networks
In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIH 7 human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length.
Natural variability or anthropogenically-induced variation? Insights from 15 years of multidisciplinary observations at the arctic marine LTER site HAUSGARTEN
Time-series studies of arctic marine ecosystems are rare. This is not surprising since polar regions are largely only accessible by means of expensive modern infrastructure and instrumentation. In 1999, the Alfred Wegener Institute, Helmholtz-Centre for Polar and Marine Research (AWI) established the LTER (Long-Term Ecological Research) observatory HAUSGARTEN crossing the Fram Strait at about 79°N. Multidisciplinary investigations covering all parts of the open-ocean ecosystem are carried out at a total of 21 permanent sampling sites in water depths ranging between 250 and 5500 m. From the outset, repeated sampling in the water column and at the deep seafloor during regular expeditions in summer months was complemented by continuous year-round sampling and sensing using autonomous instruments in anchored devices (i.e., moorings and free-falling systems). The central HAUSGARTEN station at 2500 m water depth in the eastern Fram Strait serves as an experimental area for unique biological in situ experiments at the seafloor, simulating various scenarios in changing environmental settings. Long-term ecological research at the HAUSGARTEN observatory revealed a number of interesting temporal trends in numerous biological variables from the pelagic system to the deep seafloor. Contrary to common intuition, the entire ecosystem responded exceptionally fast to environmental changes in the upper water column. Major variations were associated with a Warm-Water-Anomaly evident in surface waters in eastern parts of the Fram Strait between 2005 and 2008. However, even after 15 years of intense time-series work at HAUSGARTEN, we cannot yet predict with complete certainty whether these trends indicate lasting alterations due to anthropologically-induced global environmental changes of the system, or whether they reflect natural variability on multiyear time-scales, for example, in relation to decadal oscillatory atmospheric processes.