Permutation complexity of interacting dynamical systems

The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work, we clarify the meaning of the coupling complexity by discussing in detail some cases leading to extreme values, and present examples using synthetic data to describe its properties. We also generalize the coupling complexity index to the multivariate case and derive a number of important properties by exploiting the structure of the symmetric group. The applicability of this index to the multivariate case is demonstrated with a real-world data example. Finally, we define the coupling complexity rate of random and deterministic time series. Some formal results about the multivariate coupling complexity index have been collected in an Appendix.Comment: 16 pages, 6 figure

Characterizing Synchronization in Time Series using Information Measures Extracted from Symbolic Representations

We present a methodology to characterize synchronization in time series based on symbolic representations. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after mapping all sequences into symbols. We propose a transcription scheme between symbolic representations to study the dynamics of coupled systems. This scheme allows us to use elements of group theory and to derive information measures to assess the degree of synchronization. We apply our method to a prototype non-linear system which displays a rich coupled dynamics.Comment: 9 pages, 4 figure

Information directionality in coupled time series using transcripts

In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations among information measures of the symbolic representations of time series. These theoretical results are then applied for the assessment of coupling directionality in dynamical systems, where suitable coupling directionality measures are introduced depending only on transcripts. These novel measures estimate information flow in lower space dimension and reduce to well-established coupling directionality quantifiers when some general conditions are satisfied. Furthermore, by generalizing the definition of transcript to ordinal patterns of different lengths, several of the commonly used information directionality measures can be encompassed within the same framework.Comment: 24 pages, 9 figure

Analysing Large Scale Structure: I. Weighted Scaling Indices and Constrained Randomisation

The method of constrained randomisation is applied to three-dimensional simulated galaxy distributions. With this technique we generate for a given data set surrogate data sets which have the same linear properties as the original data whereas higher order or nonlinear correlations are not preserved. The analysis of the original and surrogate data sets with measures, which are sensitive to nonlinearities, yields information about the existence of nonlinear correlations in the data. We demonstrate how to generate surrogate data sets from a given point distribution, which have the same linear properties (power spectrum) as well as the same density amplitude distribution. We propose weighted scaling indices as a nonlinear statistical measure to quantify local morphological elements in large scale structure. Using surrogates is is shown that the data sets with the same 2-point correlation functions have slightly different void probability functions and especially a different set of weighted scaling indices. Thus a refined analysis of the large scale structure becomes possible by calculating local scaling properties whereby the method of constrained randomisation yields a vital tool for testing the performance of statistical measures in terms of sensitivity to different topological features and discriminative power.Comment: 10 pages, 5 figures, accepted for publication in MNRA

Comparative Study of Different Diagnostic Routine Methods for the Identification of Acinetobacter radioresistens

Recent publications indicate that A. radioresistens can cause infections in humans, even though it is rarely reported in routine diagnostics. However, the fact that it is infrequently detected may be explained by the misidentification of the species by conventional methods. It is also likely that A. radioresistens is not considered clinically relevant and therefore not consistently included in diagnostic results. To elucidate the medical significance of this probably clinically underestimated bacterial species, we created a well-documented reference strain collection of 21 strains collected in routine diagnostics. For further analysis of A. radioresistens, it is essential to know which methods can be used to achieve a trustworthy identification. We, therefore, compared three methods widely used in routine diagnostics (MALDI-TOF MS, VITEK 2, and sequencing of housekeeping genes) in terms of secure and reliable identification of A. radioresistens. As reference methods, whole genome-based approaches were applied. VITEK 2 led to misidentification for four strains. However, MALDI-TOF MS and sequencing of housekeeping genes led to reliable and robust identifications

Analysing large-scale structure - I. Weighted scaling indices and constrained randomization

The method of constrained randomization, which was originally developed in the field of time-series analysis for testing for non-linearities, is extended to the case of three-dimensional point distributions as they are typical in the analysis of the large-scale structure of galaxy distributions in the Universe. With this technique it is possible to generate for a given data set so-called surrogate data sets that have the same linear properties as the original data whereas higher order or non- linear correlations are not preserved. The analysis of the original and surrogate data sets with measures, which are sensitive to non-linearities, yields valuable information about the existence of non-linear correlations in the data. On the other hand one can test whether given statistical measures are able to account for higher order or non-linear correlations by applying them to original and surrogate data sets. We demonstrate how to generate surrogate data sets from a given point distribution, which have the same linear properties (power spectrum) as well as the same density amplitude distribution but different morphological features. We propose weighted scaling indices, which measure the local scaling properties of a point set, as a non-linear statistical measure to quantify local morphological elements in large-scale structure. Using surrogates it is shown that the data sets with the same two-point correlation functions have slightly different void probability functions and especially a different set of weighted scaling indices. Thus a refined analysis of the large-scale structure becomes possible by calculating local scaling properties whereby the method of constrained randomization yields a vital tool for testing the performance of statistical measures in terms of sensitivity to different topological features and discriminative power