18 research outputs found
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